Section 3

et aqua, quae pro uno accipiuntur. Tertio die, qui est sextus, producuntur animalia quae habent motum in terra, ad ornatum ipsius. ( S.T. , I, q. 70, a. 1, c.).

As … was said above, three things were mentioned [in the Scriptures] in the work of creation, namely heaven and water and earth. And these same three things were given some form during the three days of the work of distinction. On the first day, heaven was given some form. On the second day, the waters were distinguished. On the third day, a distinction was made on earth, of sea from dry land. And similarly, in the work of adornment. On the first day of adornment, which is the fourth from the beginning, the lightgiving bodies which are in motion in heaven, for its adornment, were produced. On the second day, which is the fifth, birds and fishes were produced to adorn the middle element, because they move about in air and water, which are taken here as one thing. On the third day, which is the sixth, we see produced, for the adornment of the earth, the animals which move about upon it.

Three things, note the Scriptures, were brought into being as pertaining to the opus creationis, namely heaven and water and earth. Water and earth, taken together, are being contrasted with heaven, and thus quite obviously include in some way all terrestrial bodies, mixed bodies as well as elements. And so, since “it belongs to the work of creation to produce the substance of the elements,” one can conclude that all mixed bodies were in some way there in the substance of the four elements, when these elements first began to exist.

With heaven and the four elements, effects of the opus creationis, already in existence on the first day, the opus distinctionis was begun, and on that same first day — continuing on the second and third days, and followed by the opus ornatus on days four through six. — “On the first day,” writes Page 209

Aquinas (above, p. 194), ” heaven was given some form.” This turns out to mean, as Aquinas notes, that heaven was given light (lux, lumen), and this light was the sun’s light. But, adds Aquinas, this light was not then yet fully formed — sed adhuc informis. That is, the sun itself, the substance of the sun, was there; and it had some sort of general lightemitting power — virtutem illuminativam in communi, explains Aquinas, but not yet a fully formed lightemitting power, not yet of the special and determinate sort required for producing particular effects, which it acquired only later on — postmodum data est ei. 44 Aquinas writes:

… illa lux fuit solis, sed adhuc informis, quantum ad hoc quod iam erat substantia solis, et habebat virtutem illuminativam in communi; sed postmodum data est ei specialis et determinata virtus ad particulares effectus. Et secundum hoc, in productione huius lucis, distincta est lux a tenebris … ( S.T. , I, q. 67, a. 4, ad 2).

… that light [i.e., the light given to heaven on the first day] was the light of the sun,45 but not then fully formed, i.e., the substance of the sun was already there, and it had illuminating power of a common sort; but it was only afterwards that the special and determinate power to produce particular effects was given to it. And according to this, in the production of this light, light was distinguished from darkness …

44 Without stating exactly what these special and determinate powers are, and what these particular effects are, Aquinas writes: … si … lux primo die facta intelligitur lux corporalis [for some, like Augustine, suggested that this light might be a spiritual light], oportet dicere quod lux primo die fuit producta secundum communem lucis naturam;

quarto autem die attributa est luminaribus determinata virtus ad determinatos effectus; secundum quod videmus alios effectus habere radium solis, et alios radium lunae, et sic de allis … ( S.T. , I, q. 70, a. 1, ad 2). — But, Aquinas does not say exactly what the effects of the rays of the sun are (day light, warmth, sun tan?) as different from the effects of the rays of the moon (night light, coolness, a man and a woman falling in love?).

45 This light was, no doubt, in some way the light of other lightgiving bodies as well, which, like the sun, were already there. That is, the substance of these other lightgiving bodies was there, and they had some sort of lightemitting power, but not yet for producing particular effects.

“On the second day” of the six (which was also the second day of the opus distinctionis), writes Aquinas (above, p. 194), water was given some form, i.e., “the waters were distinguished;” those which are above the firmament (the firmament is some intermediate part of the whole heaven) were divided from those which are below the firmament. There is more than one way to interpret the nature of the firmament, as well as the nature of the waters both above and below the firmament, as Aquinas indicates in some detail in S.T. , I, q. 68, aa. 1–3. And it would be difficult, maybe impossible, to choose one over another. In any case, the important point is this, that the firmament itself, a not yet fully formed transparent body, divides waters from other waters, i.e., these not yet fully formed transparent bodies from those others, all of which can be designated as “waters” (including air), i.e., divides the higher ones, which could be of one nature, from the the lower ones, which could be of another nature (though both might well be of the same nature), the lower ones being obviously heavier, and the higher ones being lighter, whatever other characteristics they might have. Aquinas writes:

Sic igitur sive per firmamentum intelligamus caelum in quo sunt sidera [sc. caelum sidereum] sive spatium aeris nubilosum [sc. pars aeris in qua nubes condensantur], convenienter dicitur quod firmamentum dividit aquas ab aquis, secundum quod per aquam materia informis significatur; vel secundum quod omnia corpora diaphana sub nomine aquarum intelliguntur. Nam caelum sidereum distinguit corpora inferiora diaphana a superioribus. Aer vero nubilosus distinguit superiorem aeris partem, in qua generantur pluviae et huiusmodi impressiones, ab inferiori parte aeris, quae aquae connectitur, et sub nomine aquarum intelligitur. ( S.T. , I, q. 68, a. 3, c., in fine).

Thus, therefore, whether by the firmament we understand the heaven in which there are stars [i.e., the sidereal or starry heaven] or the cloudy part of the air [i.e., that part of the air in which the clouds come to be condensed], it is suitably said that the firmament divides the waters from the waters, according as water is taken to signify matter which is not yet fully formed; or

according as all transparent bodies are understood as included under the name of waters. For the starry heaven distinguishes the lower transparent bodies from the higher ones.

And the cloudbearing [part of the] air distinguishes the higher part of the air, in which rain, and other threatening things46 of that sort, are generated, from the lower part of the air, which touches the waters below, and so is understood as included under the name of waters.

“On the third day,” the last of the opus distinctionis, writes Aquinas (above, pp. 193–194), the earth was given some form, i.e., “a distinction was made on earth, of sea from dry land.” Of the two interpretations noted by Aquinas in S.T. , I, q. 69, a. 1, namely that of Augustine, and that of other Holy authors, that of the other Holy authors seems more likely. They suggest an interpretation in which a not fully formed matter comes first in time, and is then moved toward becoming more fully formed. Matter, of course, did not lack all form, since there already existed the three, namely heaven and water and earth (“water and earth” being taken to signify the four elements). But these three did lack certain appropriate distinctions as well as a certain complement of beauty. Heaven lacked both the beauty of light, and the distinction of day from night. Water (understood to include air as well, as Aquinas suggests; but fire, too, one ought to add)47 lacked both the beauty of an appropriate orderliness, and the distinction of the upper waters from the lower ones. Lastly, earth too lacked the beauty of an appropriate orderliness, 46 “Other threatening things of that sort” might include thunder and lightning as well, lightning being taken by Aquinas to be some form of fire.

47 Since “water and earth” signify the four elements, and since fire ought to be mentioned and included somewhere, it seems clear that it ought to be included under “water” rather than under “earth,” because of fire’s natural upward motion. That is, since water is understood to include air, which has a higher natural place than water, water ought also to be understood to include fire, which has a higher place still. It would not make sense to include fire under “earth,” since earth has the lowest place. Aquinas puts it like this: … ignis et aer, quia non distinguuntur a vulgo, inter partes; mundi non sunt expresse nominata a Moyse, sed computantur cum medio, scilicet aqua, maxime quantum ad inferiorem aeris partem.

Quantum vero ad superiorem, computantur cum caelo, ut Augustinus dicit. ( S.T. , I, q. 74, a. 1, ad 2). — To put any of the parts of air and fire together with heaven would seem to be unacceptable, if one takes heaven to be a fifth body; unless one is considering only location.

and the distinction of dry land from the sea. And so, with respect to the third day, Aquinas writes: Tertio … die formatum est ultimum corpus, scilicet terra, per hoc quod discooperta est aquis; et facta est distinctio in infimo, quae dicitur terrae et maris. Unde satis congrue, sicut informitatem terrae expresserat dicens quod terra erat invisibilis vel inanis, ita eius formationem exprimit per hoc quod dicit, Et appareat arida.48 ( S.T. , I, q. 69, a. 1, c., in fine).

On the third … day, the last body, namely earth, was given some form, by the removal of its covering of water. And a distinction was made in that lowest of bodies, i.e., the distinction of dry land and sea. Whence just as the Scriptures had expressed sufficiently suitably the incomplete formedness of the earth by saying that the earth was invisible and empty, so too the Scriptures express sufficiently suitably the earth’s being given further form by saying, And let the dry land appear.

One can suggest at this point that heaven — by means of the power of the light (and perhaps of the accompanying heat, as well) which was given to it on the first day of the opus distinctionis — brought about in some way, i.e., slowly, developmentally, progressively moving from incomplete formedness toward fuller and fuller completion, the distinction of the second day (that of the waters above the firmament from those below it) and the distinction of the third day (that of the dry land from the sea). To make this suggestion acceptable, one would have to say that the light given to heaven on the first day was not only the light of the sun, but somehow and in some not yet fully

48 It can be said, perhaps, that it was natural, in the beginning, for water to cover the earth completely, just as it was for air to surround both water and earth completely. But then, in order to have plants and animals on the earth, it became necessary for some of this covering of water to be removed; and this took place, according to some philosophers, by the heating action of the sun evaporating the waters, thereby drying some of the land: … potest dici quod naturale esset quod aqua undique esset circa terram, sicut aer undique est circa aquam et terram; sed propter necessitatem finis, ut scilicet animalia et plantae essent super terram, oportuit quod aliqua pars terrae esset discooperta aquis. Quod quidem aliqui philosophi attribuunt actioni solis, per elevationem vaporum desiccantis terram. ( S.T. , I, q. 69, a. 1, ad 4).

formed way, the light of other lightemitting bodies, like the planets and the stars, as well — as already noted above, on p. 208 in footnote 38.49

On the fourth day, which is the first day of the opus ornatus, points out Aquinas (above, p. 207), “the lightgiving bodies which are in motion in heaven for its adornment, were produced.” If the heavenly bodies are taken to be of the same nature as terrestrial bodies, as some took them to be; then they were produced by God out of the already existing four elements. If, however, they are taken to be of a nature different from that of terrestrial bodies, and so by nature incorruptible, as others took them to be; then they must have been produced by God on the first day as to their substance, but not yet fully formed, along with the sun; so that on the fourth day all of them were given further form by being given a more fully formed, a more determinate, lightemitting power for producing particular effects, the sun for these effects, the moon for those effects, and other heavenly bodies for still other effects. Aquinas writes:

… secundum . . eos qui ponunt caelestia corpora ex natura quatuor elementorum, nulla difficultas accidit, quia potest dici quod sunt formata ex praeiacenti materia … Sed secundum eos qui ponunt corpora caelestia esse alterius naturae ab elementis, et incorruptibilia per naturam, oportet dicere quod substantia luminarium a principio fuit creata; sed prius erat informis, et nunc formatur, non quidem forma substantiali, sed per collationem determinatae virtutis. — Ideo tamen non fit mentio a principio de eis, sed solum quarta die, ut Chrysostomus dicit, ut per hoc removeat populum ab idololatria, ostendens luminaria non esse deos, ex quo nec a principio fuerunt. ( S.T. , I, q. 71, a. 1, ad 1).

49 This suggestion implies that the light of the sun alone would not suffice to bring about the distinctions of the second and third days, and that these distinctions may have taken a very long period of time, so that “day” in “first day” and in “second day” and in “third day” might mean a period of time considerably longer than an ordinary day of twenty four hours.

… according to those … who hold the heavenly bodies to be of the nature of the four elements, there is no difficulty, because it can be said that they were formed out of already existing matter … But, according to those who hold the heavenly bodies to be different in kind from the elements, and incorruptible by nature, it must be said that the substance of the lightemitting bodies was created at the beginning, but that at first it was not fully formed, and now was being given further form, not indeed by means of a substantial form, but by the conferring of a determinate power. — And the reason why there was no mention of them at the beginning, but only on the fourth day, as Chrysostom says, was to remove the people from idolatry, by showing that the lightemitting bodies were not gods, not being in existence from the beginning.

On the fifth day, the second of the opus ornatus, writes Aquinas (above, p. 207), “birds and fishes were produced to adorn the middle element, because they move about in air and water, which are here taken as one thing.” In responding to an objection to the fittingness of the way in which the opus ornatus of the second day is described, Aquinas makes some interesting and instructive comments about the elements. The objection is as follows:

… videtur quod inconvenienter hoc opus [sc. opus ornatus quintae diei] describatur. Illud enim aquae producunt, ad cuius productionem sufficit virtus aquae. Sed virtus aquae non sufficit ad productionem omnium piscium et avium, cum videamus plura eorum generari ex semine. Non ergo convenienter dicitur: Producant aquae reptile animae viventis, et volatile super terram. ( S.T. , I, q. 71, a. un., obj. 1).

… it seems that this work [i.e., the work of adornment of the fifth day] was not fittingly described. For the waters produce that for the production of which the power of the waters suffices. But the power of the waters does not suffice for the production of all fishes and birds, since we see that many of them are generated from seed. Therefore, it is not fittingly said: Let the waters produce the creeping things having a living soul, and the things with wings to fly over the earth.

Aquinas’ response to this objection:

… Avicenna posuit omnia animalia [and, therefore, not only fishes and birds] posse generari ex aliquali elementorum commixtione absque semine, etiam per viam naturae.

Sed hoc videdur inconveniens, quia natura determinatis mediis procedit ad suos effectus. Unde ilia quae naturaliter generantur ex semine non possunt sine semine generari.

Et ideo dicendum est aliter, quod in naturali generatione animalium [including, therefore, fishes and birds], principium activum est virtus formativa quae est in semine, in iis quae ex semine generantur; loco cuius virtutis, in iis quae ex putrefactione generantur, est virtus caelestis corporis. Materiale autem principium in utrorumque animalium generatione, est aliquod elementum vel elementatum.

In prima autem rerum institutione [by way of contrast to in naturati generatione, as in the previous paragraph], fuit principium activum Verbum Dei, quod ex materia elementari produxit animalia vel in actu, secundum alios Sanctos, vel virtute, secundum Augustinum. Non quod aqua aut terra habeat in se virtutem producendi omnia animalia, ut Avicenna posuit, sed quia hoc ipsum quod ex materia elementari, virtute seminis vel stellarum, possunt animalia produci, est ex virtute primitus elementis data. ( S.T. , I, q. 71, a. un., ad 1).

… Avicenna held that all animals [and therefore not only fishes and birds] can be generated from some sort of mixing or other of the elements, and without seed, even by nature’s own ways.

But this seems to be unacceptable, because nature proceeds to its effects by certain determined means. Whence those things which are naturally generated from seed cannot be generated without seed.

And so, something different must be said, that in the natural generation of animals [including therefore fishes and birds], the Page 216

active principle is the formative power which is in the seed, in the case of those which are generated from seed; whereas in the case of those which are generated from putrefaction, in the place of the power in the seed is the power of a heavenly body. The material principle, however, in the generation of either of these kinds of animals is some element, or something made out of the elements [i.e., some mixed body].

But in the first production of things [by way of contrast to in their natural generation], the active principle was the Word of God, which produced animals out of elemental matter either actually, as some Holy authors would have it, or in the power [of other things], as Augustine would have it. Not that water or earth has in itself the [active] power to produce all animals, as Avicenna held; but because this, namely that animals can be produced out of elemental matter, by the [active] power of seed or by that of the stars, derives from the power [both active and material] given to the elements in the very beginning.

What is interesting and instructive about Aquinas’ response is the following. The elements play a dual role in the natural generation of corporeal things (in naturali generatione; per viam naturae) as well as in their first production by God (in prima rerum institutione). The role of the elements is in part that of a material cause and in part that of an agent cause.50 But their agent causality is of itself of insufficient power to account for the transformations of the elements into one another, and for their entering as ingredients into the composition of mixed bodies. The insufficiency of their agent causality needs to be aided by, completed by, the active formative power of seed (in the case of those living things, whether plants and animals, which are generated from seed), in conjunction with the active power of the light (and heat) of the appropriate heavenly body(ies); and at least by51 the active power of the light (and heat) of the appropriate heavenly body(ies), in the 50 See above section 3, pp. 136–142, on the sort of agent cause an element is, in addition to being a special sort of material cause.

51 See, however, footnote 43, above p. 205, on the need for an agens univocum for any kind of generation, in addition to an agens universale.

case of the generation of all other physical things, i.e., of the elements from one another, and of mixed bodies of all other sorts (i.e., other than living things generated from seed) from the elements, and from lower forms of mixed bodies, as well.

What is most particularly interesting and instructive about the response of Aquinas lies in its very last few lines, beginning with: In prima autem rerum institutione …

For these last few lines speak of the role of the power (both active and material) which was given to the elements by God in the very beginning (primitus) … hoc ipsum quod ex materia elementari … possunt animalia [et plantae, et omnia alia terrestrialia] produci est ex virtute primitus elementis data … In the first production of things (… in prima … rerum institutione …), the active principle was the Word of God, which produced animals, including the fishes and the birds of the fifth day, either actually, as some thinkers suggested, or in the power of other things antecedently brought into being, as other thinkers suggested. But this does not mean that the elements as antecedently produced had in themselves all of the active power required to produce the fishes and the birds of the fifth day (and the land animals of the sixth day). It means rather that they, i.e., the things of the fifth and sixth days, were capable of being actively produced out of the elements by the formative power of seed and/or by that of the stars, only because of the powers, both active and material, which were given to the elements themselves at the very beginning — … hoc ipsum quod ex materia elementari, virtute seminis vel stellarum, possunt animalia produci, est ex virtute [activa et materiali]

primitus elementis data … The elements, from the very beginning, were given a nature, both active and material, such that all terrestrial physical things could be derived from them as from their primary material constituents.

On the sixth day, the third of the opus ornatus, notes Aquinas (above, pp. 193–194) “we see produced, for the adornment of the earth, the animals which move about upon it.” Although some were of the opinion, notes

Aquinas, that land animals were produced in actu, i.e., as actually existing; others, like Augustine, suggested that they were not produced as actually existing, but rather potentialilter, i.e., as in the power of other things, antecedently brought into being, to produce them at some later time.

Et hic etiam [sc. in opere ornatus sextae diei,], secundum Augustinum, animalia terrestria producuntur potentialiter; secundum vero alios Sanctos, in actu. ( S.T. , I, q. 72, a. un., c.).

And here too [i.e., in the work of adornment of the sixth day], according to Augustine, the land animals were produced as in the power of other things, whereas according to other Holy authors, they were produced as actually existing.

Aquinas seems to prefer the suggestion of Augustine, a suggestion, let us be reminded, which was made as regards the work of the fifth day as well, and which comes to this. The four elements, from the very beginning, were given a nature, both active and material, such that all terrestrial things, including the land animals of the sixth day, could be derived from the elements as from their primary material constituents — given, of course, in order to bring about the actual derivation, the accompanying active formative powers of the elements themselves (admittedly insufficient), as completed by the diverse active formative powers of various sorts of heavenly bodies. These combined active formative powers were capable of explaining, as agent causes, the generation and corruption of terrestrial bodies — not only the transforming of the elements into one another, but the entering of the elements into the composition of mixed bodies, as well. Unlike heaven, or the firmament, which (on the false assumption that it is of a fifth essence, and not of the essence of the four elements) does not have within it the power to produce the lightemitting bodies which adorn it;52 the

52 … non enim habet firmamentum [sc. caelum] virtutem productivam luminarium, sicut habet terra [et aqua, et aer, et ignis, i.e., quatuor elementa] productivam plantarum [et avium et piscium et animalium terrestrium] … ( S.T. , I, q. 70, a. 1, c., in fine). And

(footnote continued on next page)

four elements do have the power, both active and material, to produce the fishes and the birds and the land animals which adorn the planet Earth, i.e., which adorn the water (the fishes) and the air (the birds) and the dry land (the animals) — in conjunction, of course, with the universal agent causality of the appropriate heavenly bodies, and the particular agent causality of the appropriate univocal causes.53

10—

The Seventh Day and Beyond, Like the First Day and Beyond:

Unfolding, Developing, Evolving Out of the Matter, and by the Agent Causality, of the Elements Having reflected on what God had made on each of the six days, Aquinas devotes a question (q. 73) to considerations pertaining specifically to the seventh day, and another one (q. 74) to questions pertaining to all seven days in common.

From q. 73, the following:

… nihil postmodum a Deo factum [sc. post septimum diem] est totaliter novum, quin aliqualiter in operibus sex dierum praecesserit. Quaedam enim praeextiterunt materialiter, sicut quod Deus de costa Adae formavit mulierem. Quaedam vero praeextiterunt in operibus sex dierum, non solum materialiter, sed etiam causaliter; sicut individua quae nunc generantur, praecesserunt in primis individuis suarum specierum. Species

(footnote continued from previous page)

that is why Augustine holds, notes Aquinas, that the lightemitting bodies were made by God as actually existing: … dicit enim [Augustinus] luminaria esse facta in actu, non in virtute tantum … ( Ibid. ). One wants to observe, here, that if one takes heaven (or, the firmament) to be of the essence of the four elements, it can very likely be seen as having within itself (given to it in the beginning by God, of course) the power to produce the lightemitting bodies which adorn it.

53 See above, p. 205, footnote 35. Any generation, it seems, whether of living things or of nonliving things, requires an agens univocum, an agens particulare, i.e., an agent of the same species as the effect, in addition to an agens universale. Otherwise, there would be no adequate explanation for the fact that the effect is of the particular sort or species that it is.

etiam novae, si quae apparent, praeextiterunt in quibusdam activis principiis, sicut et animalia ex putrefactione generata producuntur ex virtutibus stellarum et elementorum quas a principio acceperunt … ( S.T. , I, q. 73, a. 1, ad 3).

… nothing which was made by God afterwards [i.e., after the seventh day] is totally new; indeed all such things had preceded in some way in the works of the six days. Some of them had preexisted materially, as the woman had in the rib of Adam out of which God formed her. Others preexisted in the works of the six days not only materially, but also causally, as the individuals which are now being generated; they were there causally in the first individuals of their species. And new species too, if any appeared, preexisted in certain active principles, just as the animals generated from putrefaction are produced from the powers of the stars and of the elements, which (powers) they had received in the beginning …

In q. 73, Aquinas asks: Utrum completio divinorum operum debeat septimo diei adscribi. The Scriptures say explicity of the seventh day: On the seventh day God completed His work which He had made (Genesis, 2, 2). Here, as throughout his reflections on the initial production of things by God, Aquinas proceeds with Augustine’s teaching on scriptural interpretation in mind, namely this teaching, which emphasizes two points:

… sicut Augustinus docet, in huiusmodi quaestionibus duo sunt observanda. Primo quidem, ut veritas Scripturae inconcusse teneatur. Secundo, cum Scriptura divina multipliciter exponi possit, quod nulli expositioni aliquis ita praecise inhaereat quod, si certa ratione constiterit hoc esse falsum, quod aliquis sensum Scripturae esse asserere praesumat, ne Scriptura ex hoc ab infidelibus derideatur, et ne eis via credendi praecludatur … ( S.T. , I, q. 68, a. 1, c.).

… as Augustine teaches, two things are to be observed in questions of this kind. The first is this: to hold to the truth of Scripture unwaveringly. The second is this, since divine Scripture can be interpreted in many ways: not to adhere so

tenaciously to a given exposition of it as to presume to assert it as the meaning of Scripture, if it has been shown with certitude to be false; lest Scripture be ridiculed by those who do not believe, and obstacles be placed in the way of their becoming believers.

The truth to be held, here, without wavering is this, that God did complete his work of creative production on the seventh day, for this is explicitly stated in the Scriptures: Complevit Deus die septimo opus suum quod fecerat ( Genesis, 2, 2). The question now becomes: How is this to be understood? Following Augustine’s suggestion, one must not insist on taking this to mean something which is known for good reason(s), which has been shown with certitude, to be false : …

si certa ratione constiterit esse falsum. This will open God’s word to the possibility of ridicule by unbelievers, and become thereby an obstacle to their becoming believers. How then is this completion to be understood? In the body of this article, Aquinas points out that a thing can be said to be completed, or perfected, with respect to what it is, i.e., with respect to all that is required for its integrity, or wholeness, as the substance or thing that it is. This sort of completion, or perfection, is the ”forma totius, quae ex integritate partium consurgit.” But, a thing can also be said to be completed, or perfected, with respect to its end. This sort of completion, or perfection, might be 1) an end which is an operation, or activity, as the end of the citharist is to play the fourstringed musical instrument which is the cithara; or it might be an end which is 2) a thing which is attained by an operation or activity, as the end of the builder is the house which he makes by the activity of building. The first kind of completion brings about, i.e., causes, the second kind; for the form of a substance is the principle of its operation.

Now, the ultimate (i.e., second) completion, or perfection, or end of the whole universe is the perfect happiness of the Saints — which will come to be in the final consummation of time. But, the first completion or perfection of the universe, which consists in its wholeness or integrity as the thing that it is, i.e., which consists in its

“forma totius, quae ex integritate partium consurgit,” was already there in the first production, at the first founding, of Page 222

things, i.e., “in prima rerum institutione,” which took place over the six days. It is this completion which is attributed to the seventh day, and which is in its own way a cause contributing to the second completion. This is how Aquinas puts it:

… ultima [sc. secunda] … perfectio, quae est finis totius universi, est perfecta beatitudo Sanctorum, quae erit in ultima consummatione saeculi. Prima autem perfectio, quae est in integritate universi, fuit in prima rerum institutione. Et haec deputatur septimo diei … (S.T., I, q. 73, a. 1, c.).

… the ultimate [i.e., second] … perfection, which is the end of the whole universe, is the perfect happiness of the Saints, which will come to be in the final consummation of time.

The first perfection, however, which lies in the integrity of the universe, was there in the first production of things. And it is this first completion which is attributed to the seventh day …

In his response to the third objection (quoted above, p. 218), Aquinas points out that nothing made by God after the seventh day is totally new. Some of these things preexisted materially in the works of the six days; for example, observes Aquinas, the woman whom God formed out of the rib of Adam ( Genesis, 2, 21–23), whom He had made earlier out of the slime of the earth ( Genesis, 2, 7). Aquinas could have added that all things which came to be (and continue to come to be) after the seventh day, preexisted materially in the four elements, and in certain appropriate mixed bodies produced out of the elements during the work of the six days. Certain other things, continues Aquinas, preexisted in the works of the six days not only materially, but causally as well, i.e., as in the power of their agent causes. For example, all the individuals which are being generated now, were there in the first individuals of their species — there, not only as in their matter, but also as in their agent causes. And if any new (interesting and surprising) species came into existence since the seventh day, continues Aquinas, these too were there in the works of the six days, in certain active (agent) causes, as

well as in the matter of the four elements, and of certain appropriate mixed bodies. Similarly, adds Aquinas, all animals generated from putrefaction (like maggots, the legless larvae of the housefly), and even new (interesting and surprising) species of animals so generated, if any came to be, came to be from the powers of the stars (active powers) and of the four elements (active and material powers), which (powers) they (the stars and the elements) had received from God in the very beginning — in prima rerum institutione. Indeed, one can add, the same can be said about all new species, whether of animals or of plants. Moreover, every new living thing, in any sense of “new,” whether it be simply a new individual (of a species already in existence as a result of the work of the six days) or even a new species — every new living thing came to be from the powers (active) of the heavenly bodies and of the four elements (active and material). And not only living things, one can add further, but nonliving things as well. That is, even all new elements (beyond the original four, if one were to take the ancient and medieval four as truth, and if more than these four were possible; or beyond the original quarks and leptons, to take the firmer truth of what we know today), and all new mixed bodies as well, came to be out of the original elements, inasmuch as they (i.e., the original elements) had received from God — in prima rerum institutione — a nature such that they were to provide the materials, as well as the agent powers (can we today say: the agent powers of the strong nuclear force, the weak nuclear force, the electromagnetic force, and the force of gravity?), required for the orderly, developmental, unfolding, evolving production of all other physical things, out to the furthest reaches of space. In today’s firmer view, the four forces could perhaps replace (as the required agent causes) the active power of the light and heat of the heavenly bodies of the older, and considerably less firm, view; indeed, a view which has been shown with good reasons, and with a high degree of certitude, to be just false.

Also from q. 73:

… in primis sex diebus productae sunt res in suis primis causis. Sed postea ex illis primis causis res multiplicantur et conservantur … ( S.T. , I, q. 73, a.3, ad 2).

… in the first six days, things were produced in their first causes. But after that, things were multiplied by these first causes, and conserved in being by them …

In Aquinas’ response to the second objection in a. 3 (just above), one finds an excellent summary of the longer statement in his response to the third objection in a. 1

(above, p. 220). The first causes, in whose powers things were produced in the course of the first six days, are the four elements (material and agent causes) and the heavenly bodies (the aiding and completing agent causes) of the ancient and medieval view. In today’s firmer view, the first causes are the original quarks and leptons (material and agent causes) and their four forces (the aiding and completing agent causes).

From q. 74 the following:

… potest dici quod opus distinctionis et ornatus attenditur secundum aliquam mutationem creaturae, quae tempore mensuratur. Opus autem creationis consistit in sola divina actione in instanti rerum substantiam producentis. Et ideo quodlibet opus distinctionis et ornatus dicitur factum in die, creatio autem dicitur facta in principio, quod sonat aliquid indivisibile … ( S.T. , I, q.74, a.1, ad 1).

… it can be said that the work of distinction and of adornment proceeds according to certain changes in creatures, and these changes are measured by time. But the work of creation consists in a divine action, and in that alone, and this action produces the substance of things in an instant. This is why each work of distinction and of adornment is said to have been done in a day, whereas creation is said to have been done in the beginning, which indicates something indivisible …

From this response to the first objection (just above), it is clear that the four elements and the heavenly bodies were created on the first day out of absolute nothingness, and in an instant — as to their substance, of course, and in many ways not yet fully formed. And that all else which was produced by God, in the course of the first six days, was produced by Him through distinction and adornment, in such a way that its production was through certain sorts of change out of prior materials, and so was produced over a period of time.

… Deus creavit omnia simul, quantum ad rerum substantiam quodammodo informem. Sed quantum ad formationem quae facta est per distinctionem et ornatum, non simul … ( S.T. , I, q.74, a.2, ad 2).

… God created all things all together [i.e., at the same time], as regards their substance, but their substance in a way not yet fully formed. As regards their being more fully formed, however, which came about by distinction and adornment, this did not take place all together [i.e., not at the same time] …

Here, in his response to the second objection (just above), Aquinas explicitly states that the substance of all things (and not only of the heavenly bodies and the four elements) was created all together, though in some way — quodammodo — not yet fully formed. The substances of the heavenly bodies and of the four elements, of course, were there and in actual existence, but not yet with all their powers; whereas the substances of all other things were there only potentialiter, i.e., only in the power of the heavenly bodies and of the elements to produce them over time.

… in die septimo cessavit Deus a novis operibus condendis, non autem a propagandis quibusdam ex aliis, ad quam propagationem pertinet quod post primum diem alii succedunt … ( S.T. , I, q.74, a.2, ad 3).

… on the seventh day, God ceased from doing new works, but not from propagating certain things from other things [already made], to which propagation it belongs that after the first day there followed other days …

This propagation from certain other things, things which had already been made, began with the opus distinctionis (days one through three), moved through the opus ornatus (days four through six), and continues into the present day.

… habet … aqua praecipue vitalem virtutem, quia plurima animalia generantur in aqua, et omnium animalium semina sunt humida … ( S.T. , I, q.74, a.3, ad 4).

… water has a special lifegiving power, because many animals are generated in water, and the seed of all animals is moist …

Aquinas’ response to the fourth objection (just above) raises the question: Do the other elements have special lifegiving powers? Isn’t it clear that living things need to be of a certain temperature (from the inclusion of fire?), but not too hot, nor too cold (from the inclusion of an appropriate measure of air and water and earth?)? Isn’t it also clear that living things must be of a certain weight (from the inclusion of an appropriate measure of earth) in order to be kept close to the surface of our planet, and thus in an environment in which they can be provided with all that they need for nourishment, growth, and reproduction? And isn’t it also clear that the food which they need must be heavy enough (earth) and wet enough (water) and porous enough (air) and warm enough (fire) to make possible the performance of the operations of life?

… [sunt aliqui qui posuerunt quod] in prima rerum productione materia erat sub formis substantialibus [quatuor] elementorum, … [et] non fuerunt animalia et plantae in actu …

[et quod] post primam productionem creaturae, fuit aliquod tempus in quo non erat lux, item in quo non erat firmamentum formatum, item in quo non erat terra discooperta aquis, et in quo non erant formata caeli luminaria … ( S.T. , I, q.74, a.2, c.).

… [there are some who held that] in the first production of things matter existed under the substantial forms of the [four] elements, … [and] that animals and plants did not actually exist … ; [and] that after the first production of created things, there was a period of time in which there was no light, in which the firmament had not been fully formed, in which the earth had not had its covering of water removed, and in which the lightemitting bodies of heaven had not been fully formed [either] …

Just after the instant of creation, the four elements were there, and the heavens with their lightemitting bodies were there, but far from fully formed, far from in possession of all their distinctive powers for producing particular effects. They were in process of being banged out of their previous nondimensional existence in God. And then, in the very next instant, they were caught up in the process of expanding out of the initially unimaginably miniscule quasipoint of the first instant after creation, toward an unimaginably vast threedimensional existence, and toward being more and more fully formed through the three days of distinction and the three of adornment, and beyond that into the present time. The heavenly bodies were caught up in the process of acquiring particular lightemitting powers, of moving away from one another, and of acquiring certain locations in relation to one another. The planet Earth was caught up in the process of developing its oceans, and its continents, and the primitive life forms out of which all the life forms which are now in existence emerged and evolved.

11—

The Elements and the Eduction of Substantial Forms from the Potency of Matter

It is the view of Aquinas that substantial forms come to be neither by being generated, nor by being created; they come to be by being educed. This is so, he points out, because they neither exist as subsistent things, nor do they have matter as part of their natures. They come to be when the subsistent matterform composites of which they are a component come to be, and they come to be as that by which these composites exist. They preexisted in the matter of the thing(s) out of which the subsistent matterform composite of which they are now a component is generated. Not actually yet hiddenly, notes Aquinas, as some maintained. Nor potentially in the sense that matter survives in them as part of what they are; but potentially in another sense, in the sense that matter, being disposed in a certain way by the substantial form which is now in it, can receive a certain sort of new substantial form, and only that sort, given of course the required attendant agent cause(s). Thus, to come to be at the generation of a matterform composite, by the agent causality of another matterform composite(s), not as a subsistent thing, nor as having matter as part of its nature, but as that by which the composite comes to be and continues to be, is to be educed from the potency of matter. The role of the elements in eduction is this. By its nature, matter first acquires the substantial forms of the elements, and is so disposed by these forms and the activities of their qualities, i.e., hot, dry, wet, and cold, that, given the sort of agent causes which exist in the natural world, and which act from without, in conjunction with the accompanying agent causality of the elements themselves, which act from within, matter can receive only suchandsuch substantial forms, and only in suchandsuch an order, from lower to higher.

To make the immediately preceding clear, it will be helpful to begin with the question: What exactly is a substantial form? For there are some, perhaps many, who would welcome a clear answer to this question. A substantial form is a differentiating factor of a certain sort. It is required to understand Page 229

changes which can be called radical changes, i.e., changes in which something goes out of existence with the result that something else comes into existence. That is, a thing of one sort (or kind) goes out of existence, and its going out of existence is identically the coming into existence of a thing of another sort (or kind). For example, sperm and ovum go out of existence with the result that a human being comes into existence. That in the resulting human being by which the human being differs from the sperm and ovum is the human substantial form. According to Aquinas, the human substantial form is the human soul. A substantial form not only differentiates the result (the end term, or e.t.) of a radical change from that from which it came to be (the beginning term, or b.t.), but by its appearance accounts for the beginning of the existence of the thing which is the e.t.; and by its presence, for the continued existence of that thing. The substantial form of the e.t. is not the e.t. itself, but only one component of the e.t., the differentiating component. There is another component in the e.t., the surviving component, i.e., something which survives in the e.t. from the b.t. This surviving component is matter — prime matter at least, when the e.t. is an element; prime matter plus the powers of certain required elements, when the e.t. is a mixed body.

The substantial form of a thing differs from the essence of a thing, though both are differentiating factors. Whereas the substantial form differentiates the e.t. of a radical change from the b.t. , the essence differentiates that e.t. from nothingness. Whereas the e.t. of a radical change differs from the b.t. by reason of the substantial form alone, since the matter of the b.t. has survived in the e.t.; the e.t. differs from nothingness by reason of its essence, i.e., by reason of the substantial form in conjunction with the matter which has survived in it from the b.t. The essence of a thing is all that within it by which it exists. The substantial form of a thing is but one component of that by which the thing exists, i.e., just one component of the thing’s essence.

The substantial form of a thing is not something senseperceivable. But it is real. It is as real as radical change. Clearly, what is real does not have to be senseperceivable. Minds are real, but not senseperceivable. Ideas are real, but not senseperceivable. To be sure, a substantial form is neither a mind, nor an idea. We do, of course, form an idea of what a substantial form is, and we do this with our minds. But the substantial form is neither our idea of what it is, nor is it the mind with which we form that idea. The substantial form is real, and is found in the real e.t. of a real radical change as that by which the real e.t. differs from the previously real b.t. The substantial form is something perceivable by the mind, something intelligible — like an idea or a mind, without itself being either an idea or a mind. The substantial form is an intelligible component of a senseperceivable thing, the matterform composite.

Though the substantial form itself is not senseperceivable, because it is of itself without dimensions; it gives rise nonetheless to many features or characteristics or properties which are senseperceivable. The most basic feature to which the substantial form gives rise is three dimensional quantity, which, though like substantial form also not senseperceivable, is that in which senseperceivable features (some of which are productively emitted by the substantial form) reside. The substantial form itself, as noted above (p. 166), is of itself both like and unlike a mathematical point; like, inasmuch as it is of itself without dimensions; unlike, inasmuch as it is capable of physical causality of various sorts, including an agent causality with respect to quantity, by which (agent causality) it causes the ” small” Big Bang that gives size (dimensions) to the elements, and to all mixed bodies as well. Once dimensioned, the physical thing can take on senseperceivable qualities of various sorts, like hot, cold; wet, dry; soft, hard; rough, smooth; heavy, light; short, long; some of which are caused from within by the substantial form itself, others from without by physical causes of various sorts in the surrounding environment.

The substantial form of a thing differs not only from the essence of that thing, but from the thing’s accidental forms as well. A thing can have but one substantial form, but simultaneously many accidental forms. Moreover, whereas a substantial form is not itself a complete essence, since it is not a subsisting thing; it is nonetheless part of a complete essence, i.e., of the essence of the subsisting matterform composite; the other part being either prime matter alone, in the case of something which is an element (the substantial form of an element needs prime matter as its appropriate subject); or prime matter plus certain elements (as virtual, dispositional, retrievable ingredients, which function as conjoined instrumental agent causes), in the case of something which is a mixed body (the substantial form of a mixed body needs both prime matter and a certain mix of elements as its appropriate subject). An accidental form, on the other hand, is neither a complete essence, since it itself is not a subsisting thing, but needs a subsisting thing as the subject in which it exists; nor is it part of a complete essence, for though it is in the subsisting thing, it is nonetheless not of the essence of, not an ingredient of, the essence of the subsisting thing, The three dimensions of a subsisting matterform composite are among its accidental forms, as are features like its color, its weight, its being hot or cold, wet or dry, rough or smooth, soft or hard, and the like; each of which is properly said to be of a being (entis), rather than simply a being (ens); i.e., not itself a subsisting thing, though real; but of a subsisting thing.

Having considered the question: What exactly is a substantial form?, it will be helpful to consider next why Aquinas maintains that substantial forms come to be by being educed; and neither by being created, nor by being generated, nor by being brought somehow out of a hidden actuality.

… sicut probat Aristoteles in VII Metaph. ,54 id quod proprie fit, est compositum. Formae autem corruptibilium rerum habent ut aliquando sint, aliquando non sint, absque hoc quod ipsae generentur aut corrumpantur, sed compositis generatis aut corruptis, quia etiam formae non habent esse, sed composita habent esse per eas. Sic enim alicui competit fieri, sicut et esse. ( S.T. , I, q. 65, a. 4, c.).

… as Aristotle proves in Bk. VII of the Metaphysics, that which properly comes to be is the composite. The forms of corruptible things exist at times, and at times do not exist, without themselves being generated or corrupted, but rather at the generation and corruption of composites. For it is not these forms themselves which have existence; it is rather the composites which have existence through these forms. And coming into existence belongs to a thing in the same way in which existence belongs to it.

Aquinas notes just above, agreeing with Aristotle, that in the physical world, it is the composite of matter and form which subsists, and not its form. And so, it is the composite which is generated, and not its form. Its form comes to be when the composite comes to be, but only the composite subsists. The form is rather that by which the composite subsists. As Aquinas puts it just above, ”… it is not these forms themselves which have existence; it is rather the composites which have existence through these forms.”

… omnes qui non consideraverunt hoc quod philosophus supra ostendit, quod formae non fiunt, passi sunt difficultates circa factionem formarum. Propter hoc namque quidam coacti sunt dicere omnes formas esse ex creatione. Nam ponebant formas fieri, et non poterant ponere quod fierent ex materia, cum materia non sit pars formae. Unde sequebatur quod fierent ex nihilo, et per consequens quod crearentur. E contrario autem quidam posuerunt, propter hanc difficultatem, formas 54 Aristotle, Metaphysics, Bk. VII, ch. 8, 1033 a 24–b 8; ch. 9, 1034 b 7–16. In Aquinas, see In VII Metaph. , lect. 4, nn. 1417–1423; lect. 8, n. 1458.

praeexistere in materia actu, quod est ponere latitationem formarum, sicut posuit Anaxagoras.

Sententia autem Aristotelis, qui ponit formas non fieri, sed compositum, utrumque excludit. Neque enim oportet dicere quod formae sint causatae ab aliquo extrinseco agente, neque quod fuerint semper actu in materia, sed in potentia tantum. Et quod in generatione compositi sint eductae de potentia in actum. ( In VII Metaph. , lect. 7, n. 1430).

… all who did not take into account what the Philosopher showed above, that it is not forms which come to be [but rather composites], were beset with difficulties concerning the making of forms. For it was because of this that some were driven to say that all forms derive from creation. They held that forms come to be, but could not hold that they came to be out of matter, since matter is not a part of what a form is. Whence it followed that they came to be out of nothing, and consequently that they were created. There were others who, because of this difficulty, held on the contrary that forms preexisted in matter in a state of actuality, which is to hold the hiddenness of forms, as Anaxagoras did.

Now the opinion of Aristotle, who holds that it is not forms which come to be, but rather the composite, excludes both creation and hiddenness. For it is not necessary to say that forms are caused by an extrinsic [creative] agent, nor that they have always existed in matter in a state of actuality, but rather only in a state of potentiality; and that they are educed from potency into actuality in the generation of the composite.

Just above, Aquinas is pointing out that it was puzzling to some to hold both that forms come to be, and that matter is not a part of their nature. For this seemed to mean that these forms did not come to be out of matter, and that hence they came to be out of nothing, and that therefore they must have been created. To others this seemed to mean, rather, that since these forms could not come to be out of a matter which would survive in them as a part of their nature, they must have preexisted in their matter in a state of hidden

actuality. So that they were generated, rather than created; but that generation was simply some sort of removal, or undoing, or unscrambling, of the hiddenness of their actuality. Now, if one attends to the fact, notes Aquinas, that it is not the form which comes to be, but rather that of which the form is a component (along with the appropriate matter), as Aristotle maintained, one can easily exclude both the need for creation and the need for hiddenness. For forms, as Arisotle sees it, preexist in matter, not in a state of actuality (though hidden), but rather in a state of potentiality, from which they are educed (not generated) when the composite is generated.

… formae … proprie non fiunt, sed educuntur de potentia materiae, in quantum materia quae est in potentia ad formam fit actu sub forma, quod est facere compositum. ( In VII Metaph. , lect. 7, n. 23).

… forms … do not properly come to be, but are educed from the potency of matter, inasmuch as matter which is potency to a form comes to be actually under that form; and this is to make the composite.

Just above, Aquinas confirms the point made in the preceding passage, i.e., that it is not the form which properly comes to be, but the composite. And the coming to be of the composite is, one might add, identically the eduction of the form of the composite from the potency of the matter which survives in the composite as part of what the composite is.

… multis error accidit circa formas ex hoc quod de eis iudicant sicut de substantiis iudicatur. Quod quidem ex hoc contingere videtur quod formae per modum substantiarum signantur in abstracto, ut albedo, vel virtus, aut aliquid huiusmodi. Unde aliqui modum loquendi sequentes, sic de eis iudicant ac si essent substantiae. Et ex hinc processit error tam eorum qui posuerunt latitationem formarum, quam eorum qui posuerunt formas esse a creatione. Aestimaverunt enim quod formis competeret fieri Page 235

sicut competit substantiis. Et ideo non invenientes ex quo formae generentur, posuerunt eas vel creari, vel praeexistere in materia, non attendentes quod sicut esse non est formae, sed subiecti per formam, ita nec fieri quod terminatur ad esse, est formae, sed subiecti. Sicut enim forma ens dicitur, non quia ipsa sit, si proprie loquamur, sed quia aliquid ea est;

ita et forma fieri dicitur, non quia ipsa fiat, sed quia ea aliquid fit, dum scilicet subiectum reducitur de potentia in actum. ( Q.D., De Virt. in Comm. , q. un., a. 11, c., in princ.).

… an error with respect to forms has befallen many, because they think about forms as they think about substances. And it appears that this happens because forms are designated in the abstract in the manner of substances, as whiteness, or virtue, or other things of this sort. Whence some, following a way of speaking, thought about forms as if they were substances. And from this comes the error both of those who held the hiddenness of forms, and of those who held that forms derive from creation. For they thought that coming to be belongs to forms as it belongs to substances. And so, not finding anything from which forms might be generated, they held either that forms are created, or that they preexisted in matter, not paying attention that just as existence does not belong to form, but to the subject through the form, so too neither does coming to be which terminates in existence belong to form, but to the subject. For just as the form is said to be a being, not because it itself exists, if we speak properly, but because something [else]

exists by reason of it; so too the form is said to come to be, not because it itself comes to be, but because something [else] comes to be by reason of it; and this, precisely when the subject is reduced from potency to actuality.

Just above, Aquinas gives an extraordinarily clear account of what happened to some when they allowed themselves to be mislead by a way of speaking. We speak of forms in the abstract, Aquinas notes, as if they were substances, e.g., whiteness, softness, hardness, virtue. And so, it seemed to them that coming to be belongs to forms as it belongs to substances. But, since matter is not a part of what a form is, there seemed to be nothing out of which forms could come to be. And so it seemed either that these forms were

created (i.e., came to be out of nothing), or that they preexisted in their matter in a state of (hidden) actuality. — But again, forms do not come to be, in the proper sense of coming to be, since forms are not subsisting things. Rather, the subsisting composite comes to be; and the form is that by which the composite comes to be.

Or, if the form can be said to come to be, this can be said only in an improper sense, meaning that it comes to be not as a subsisting thing, but only as that by which the subsisting thing subsists.

… ex mixtione elementorum nedum intellectus, sed nec anima vegetabilis producitur … ( De Unitate Intellectus contra Averroistas, c. 1, n. 47).

… nulla anima [nec vegetabilium, nec animalium, nec hominum] ex commixtione elementorum causetur … (Ibid.).

… it is not only the intellect which is not produced out of a mixing of elements, but neither is the vegetable soul …

… no soul [neither of vegetables, nor of animals, nor of man] is caused out of a mixing of elements …

Just above, Aquinas observes that it is not only man’s soul, the intellectual soul, which is not produced out of a mixing of elements, but neither is the vegetable soul, nor indeed any soul at all. What he means is that a mixing of elements — with no living thing, no thing which has a soul, in attendance as an actively engaged extrinsic agent cause — cannot produce a new living thing. A new living thing with a vegetable soul can indeed be produced out of a certain mixing of elements, but only if, along with the intrinsic instrumental agent causality of those elements and the extrinsic universal agent causality of some appropriate heavenly body(ies), there is also the extrinsic particular and univocal agent causality of a living thing with that same sort of vegetable soul.55 Similarly with respect to the production of a new living thing with an animal soul. But the human soul, the intellectual soul, can be produced only by God, by a direct act of creation.

55 See above pp. 206–207, with special attention to footnote 43.

To be sure, even the human soul needs a certain sort of matter in which to be created by God, i.e., a matter in which is found the appropriate mix of elements; and this mix is brought about, prior to God’s creation of the human soul, by an appropriate conjunction of agent causes: not only certain required elements as intrinsic instrumental causes, but also certain heavenly bodies as extrinsic universal and analogical causes, and an already existing pair of human beings as extrinsic particular and univocal causes.

… sicut totum esse earum [sc. formarum quae differunt ab anima intellectiva] est in concretione ad materiam, ita totaliter educi dicuntur de potentia materiae. Anima autem intellectiva, cum habeat operationem sine corpore, non est esse suum solum in concretione ad materiam; unde non potest dici quod educatur de materia, sed magis quod est a principio extrinseco. ( De Unitate Intellectus contra Averroistas, c. 1, n. 46).

… just as the whole being [of forms which are different from the intellectual soul] lies in their being bound to matter, so they are said to be totally educed from the potency of matter. But the intellectual soul, since it has an operation without the body, is not such that its existence consists only in being bound to matter. Whence it cannot be said that it is educed from matter, but rather that it is from an extrinsic [and creating] principle.

Just above, Aquinas is pointing out a significant difference between the human soul, the intellectual soul, on the one hand, and all other types of soul, on the other hand.

Man’s soul has an operation without the body — habet operationem sine corpore — i.e., an activity which the soul performs independently of the body and all bodily organs, including the brain. All the activities of lower types of soul are with the body, i.e., completely dependent on the body for their performance —

dependent on the various elements, atoms, molecules, tissues, organs, etc., which are components of the body. From this it follows, as Aquinas sees it, that lower types of soul can be educed from the potency of matter, i.e., that they can be brought into existence by a Page 238

conjunction of the following, without need of a direct and special creating act of God: prime matter, properly disposed by an appropriate substantial form and by an appropriate mix of elements, along with the agent causality of certain heavenly bodies and certain particular matterform composites. And so, the receptive and agent capacities which reside in the physical world can produce of themselves, i.e., without a special creating act of God, various lower types of soul. That is, these lower types of soul are totally educed from the potency of matter, since they are totally bound to matter in their existence and in their activities. But, the human soul is not bound to matter in its existence and activities, and so cannot be educed from the potency of matter, i.e., its production is wholly outside the receptive and agent capacities which reside in the physical world. The human soul, therefore, is derived from an extrinsic principle, i.e., extrinsic to the physical world, by which Aquinas means God. As Aquinas puts it in the passage just above: Anima … intellectiva, cum habeat operationem sine corpore, … non potest dici quod educatur de materia, sed magis quod est a principio extrinseco.

… creari est quoddam fieri … Fieri autem ordinatur ad esse rei. Unde illis proprie convenit fieri et creari, quibus convenit esse. Quod quidem convenit proprie subsistentibus, sive sint simplicia, sicut substantiae separatae, sive sint composita, sicut substantiae materiales. Illi enim proprie convenit esse, quod habet esse; et hoc est subsistens in suo esse.

Formae autem et accidentia, et alia huiusmodi, non dicuntur entia quasi ipsa sint, sed quia eis aliquid est; ut albedo ea ratione dicitur ens, quia ea subiectum est album. Unde, secundum Philosophum, accidens magis proprie dicitur entis quam ens. Sicut igitur accidentia et formae, et huiusmodi, quae non subsistunt, magis sunt coexistentia quam entia; ita magis debent dici concreata quam creata. Proprie vero creata sunt subsistentia. ( S.T. , I, q. 45, a. 4, c.)

… being created is a kind of coming to be … Now coming to be is ordered to the being of a thing. Whence coming to be and being created belong properly to those things to which being belongs. Now, being belongs properly to subsisting things,

whether they are simple, like the separated substances, or composite, like material substances. For being belongs properly to that which has being; and this is something which subsists in its own being. Now forms and accidents, and other things of this sort, are not said to be beings as if they themselves exist, but rather because something [else] exists by reason of them. For example, whiteness is said to be a being, because its subject is white by reason of it. Whence, according to the Philosopher, an accident is more properly said to be of a being than a being. Therefore, just as accidents and forms, and the like, which do not subsist, coexist rather than exist; so too, they ought to be said to be cocreated rather than created. Things which are properly created are subsisting things.

Just above, Aquinas is noting that creation, like generation, is a kind of coming to be. So that creation, like generation, belongs properly only to that to which existence belongs. And that is the subsisting thing, whether it is simple, like a separated substance, or composite, like a material substance. Now, substantial forms and accidental forms are said to exist not because they are themselves subsisting things, but rather because they are either that by which a subsisting thing subsists (these are substantial forms) or that by which a subsisting thing is white, or tall, or virtuous, or something else of this sort (these are accidental forms). And so, since substantial forms and accidental forms do not subsist, they are coexistents (coexistentia), rather then existents (existentia). And this is why they ought to be said to be cocreated (concreata) rather than created (creata). And, one can add, this is also why they ought to be said to be cogenerated (cogenerata) rather than generated (generata). And for a substantial form to be cogenerated is for it to be educed from the potency of matter.

… quod creatur est ex nihilo. Composita autem non sunt ex nihilo, sed ex suis componentibus. Ergo compositis non convenit creari. ( S.T. ,b I, q. 45, a. 4, obj. 2).

… creatio non dicit constitutionem rei compositae ex principiis praeexistentibus; sed compositum sic dicitur creari, quod simul cum omnibus suis principiis in esse producitur.

( Ibid. , ad 2).

… what is created comes to be out of nothing. Now composites do not come to be out of nothing, but out of their components. Therefore it does not belong to composites to be created.

… creation does not mean the putting together of a composite thing out of preexisting principles. Rather the composite is said to be created in such a way that it is brought into being together with (at the same time as) all its principles.

Just above, Aquinas clarifies what it means for a composed thing to be created, in order to make clear that a composed thing, whether an element or a mixed body, can be created. The objection has it that composed things cannot be created, because they come to be out of their components, rather than out of nothing. Aquinas responds by emphasizing that the creation of a composed thing does not mean that it was constituted or put together out of component principles which preexisted — i.e., prior to its creation. It means rather that all of its component principles were brought into existence when it itself was brought into existence. In terms of the passage considered just prior to this one, the component principles of a composed thing are cocreated when the composed thing itself is created. And these cocreated component principles, one should point out, are prime matter and substantial form along with an appropriate mix of elements, in the case of a mixed body;

prime matter and substantial form alone, in the case of an element. It should be clear that a cocreated substantial form, precisely as cocreated, was not educed from the potency of matter, for there was no preexisting matter from which it could be educed.

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And so, some sort of answer has been given to the following questions. 1) What exactly is a substantial form? A substantial form, briefly, is a certain sort of real differentiator, intelligible not senseperceivable; it differentiates

the real end term (e.t.) of a real radical change from the real beginning term (b.t.) of that real change. 2) Why does Aquinas maintain that when substantial forms come to be (after God’s initial creative production of things) they come to be by being educed, rather than by being created, or by being generated, or by being brought somehow out of some sort of hidden actuality? Briefly, this is so because it is within the causal capacities, both receptive (forms preexist in matter not actually, but potentially) and agent, of things in the material world to bring these substantial forms into existence (as that by which subsisting things exist), without need of a direct and special creative act of God. 3) Why is it that the human soul, among substantial forms, cannot be educed from the potency of matter, but needs rather a direct and special creating act of God to bring it into existence? Briefly, this is so because the human soul has an operation which is performed independently of the body and all of its components, from the lowliest of quarks to the most sophisticated of bodily organs, like heart and brain. 4) What is the role of the elements in the eduction of lower souls and lower forms? Briefly, their role is that of a set of virtual, dispositional, retrievable, and instrumentally agent material ingredients. 5) What role, if any, do the elements have in relation to the creation of human souls? Briefly, an appropriate mix of elements is required to provide the sort of matter which even God needs as the matter in which He can create a human soul.

PART FOUR—

THE ELEMENTS IN AQUINASAND THE ELEMENTS TODAY

This part, PART FOUR, looks at an assortment of things from different sources, in an attempt to make clearer, as far as this can be done, both what Aquinas thought about the elements and what we today think about them. These two views, i.e., that of Aquinas and that of people today, might well, by appropriate comparisons and contrasts, illuminate one another in helpful and welcome ways.

It seems appropriate to begin this part with some thoughts on how quarks (which, along with leptons, are said today to be the elements of physical things) remain in the protons of which they are the constituents, thoughts patterned after the way in which, in the view of Aquinas, the four elements of his physical theory remain in the mixed bodies of which they are the constituents. These opening thoughts might be given the title De Mixtione Quarcorum, turning the English word ”quark” into a second declension neuter Latin noun, “quarcum, i,” and inserting it into the title, De Mixtione Elementorum, in the place of the word “Elementorum.”

1—

How Quarks Remain in Protons

An element of things in the physical world, as Aquinas understands it, and as we indicated above (pp. 103–104), has the following characteristics: 1. It is a simple body, out of which a mixed body is made, as out of a primary constituent, i.e., a constituent which itself has no prior bodily constituents.

2. It remains in some way in the mixed body, i.e., not by reason of its substantial form, but by reason of its powers, i.e., its qualitites: hot, cold, wet, dry. As remaining, it is not completely corrupted; neither is it completely

preserved. What is preserved are its powers, which, precisely because preserved, are retrievable. Its substantial form, too, is retrievable, and precisely via its powers, functioning as the appropriate dispositions (above, pp. 125–126).

3. It is indivisible in kind, i.e., it cannot be broken down so as to yield parts which are different in kind from its own kind.

4. It can exist separately, i.e., not as a constituent of a mixed body, both before and after having been such a constituent.

5. Elements can act upon, and be acted upon by, one another.

6. Elements become constituents of a mixed body only after they have been altered by one another, though not beyond retrievability.

The substantial forms of the quarks which enter the constitution of a proton are not actually present in the proton. Each proton has its own, and one, substantial form.

And it is this substantial form which manifests its proper activities through its proper qualities, which had been the distinctive qualities, i.e., the extreme or excelling, qualities (now brought, or tempered, to a mean) of the formerly separately existing quarks. The mixed body which is the proton, like any bodily substance, can have actually but one substantial form, its own. Potentially, however, i.e., both virtually (in their power) and retrievably, it has as many substantial forms, in number and in kind, as the quarks which are required as its ingredients — required by the nature of the proton, from which (nature), as employing the preserved powers of the constituting quarks, arise the powers for the performance of its (the proton’s) proper activities.

If the substantial forms of the three quarks which make up a proton remained — remained actually — in the proton, the proton would be a proton throughout, yet simultaneously a uquark in two of its parts, and a dquark in the third of its parts; inasmuch as a proton is said to be made up out of two uquarks and one dquark.

Which is quite clearly impossible, i.e.,

for a thing to be of one sort throughout, and at the same time of another sort(s) in different parts of itself. It must be the case then that, when two uquarks and one dquark become constituents of a proton, they cease being the uquarks and the dquark respectively. For a proton is a proton, and just a proton. Nonetheless, the uquarks and the dquark must remain in some way in the proton. For, all three are retrievable (which I shall assume, if they are really elements; since elements are retrievable). But, how exactly do they remain? Not actually; this is clear. For then, a proton would not be a proton, but just three juxtaposed quarks — in addition to being of one sort throughout, and at the same time of other sorts in different parts of itself, as noted just above. Potentially, then? This seems the right thing to say;

for what other alternative is there? But, what exactly does this mean? Shall we say, as Aquinas would, that what this means is that they (the quarks) remain by reason of their active and passive qualities (whatever these may be), but as altered somehow into a set of mean qualities of some sort, which are the qualities distinctive of, appropriate to, a proton (whatever these may be) —altered by means of their (the quarks’) protonconstituting interaction? And shall we take this to mean, as Aquinas would, that the substantial form of a proton is both brought into existence and (having been brought into existence) acts through these mean qualities, until such time as some external agent (or agents) “realters” the proton’s mean qualities, i.e., nullifies the prior protonconstituting interaction between the uquarks and the dquark, releasing thereby the distinctive elemental qualities which belong to them as quarks, and thereby in turn bringing about their regeneration as actual, and separately existing and acting, physical entities?

Assuming that the generation of a proton is a true mixing, in the sense in which Aquinas understands a true mixing, the quarks do not survive with their respective substantial forms. What survives is their active and passive qualities, appropriately changed (constricted, contracted, restrained; imprisoned, so to say) by the required alteration into a set of mean qualities. These mean qualities serve as 1) the dispositions by which the proton (like any other mixed body) is brought into existence, 2) as that by which the

proton acts, and 3) as that by the removal of which the quarks are released (as though from prison) to exist again as actual and separate and free physical realities. The required alteration affects the two uquarks and the one dquark which remain in the makeup of the proton. But, how are these quarks affected? And by what? Shall we say, as Aquinas might well have said, had he lived in the twentieth century, that they are affected by their respective electrical charges? And by the gluons which carry the strong nuclear force which binds them together within their proton prison?

To make this clearer, one should keep in mind what is meant, as Aquinas sees it, by the virtual, retrievable, dispositional and instrumental presence of the lower in the higher, and apply it to what we know today about the makeup of physical things. Certain elements (the simplest and lowliest of bodily components, like quarks and electrons), and certain other bodily components as well (complex and higher ones, like the chemical elements of the periodic table, and the molecules made out of these) are required as ingredients in the makeup of progressively more and more complex bodily things, all the way up to, and including the most complex bodily thing which we know, i.e., man. That is, one should keep in mind Aquinas’ view 1) that prime matter is in potency to forms in a certain order, and relate this to his view 2) that whereas a mixed body can have actually only one substantial form, its own; potentially, nonetheless, it can have — indeed must have — at least as many substantial forms, in number and in kind, as the elements (as well as the lower kinds of mixed bodies) which are required as its ingredients, i.e., without which it could not be or act.

What, one may ask, is to be said about characteristic 4? It has been pointed out that “quarks are never free,“1 that “there can be no such thing as 1 Lederman, Leon (with Dick Teresi), The God Particle: If the Universe is the Answer, What Is the Question? New York: Houghton Mifflin Company, 1993; p. 305. — The subtitle of this book might make more sense, it seems, if it read the other way around, i.e.: If the Universe is the Question, What is the Answer? Don’t we confront the universe, and ask: What is the universe? And, why does the universe exist? And don’t we propose the following as possible answers? What the universe is, is precisely this: something (footnote continued on next page)

a free quark.“2 If quarks cannot exist separately (i.e., by themselves all alone, as opposed to as constituents of a proton, both before and after having been such constituents), doesn’t this make it difficult (at least difficult, maybe even impossible) to accept them as true elements? Unless, of course, it is just too cold now, not hot enough now, to sustain a free quark.

And what about characteristics 5 and 6? If quarks cannot exist alone, in separation from the protons of which they are said to be the constituents, how can we come to understand how they can act upon, and be acted upon by, one another, so as to enter into the composition of a proton? That is, how can we come to know what their active and passive qualities (powers, or properties) are — before they become constituents of a proton? If quarks cannot be free, how can their “before”

properties be determined? Are quarks retrievable from their imprisonment within the confines of a proton? Can our particle accelerators produce the heat, the energy, required to retrieve them? Is it possible to construct such an accelerator? An accelerator which is capable of producing heat, energy, of an intensity to match the heat

“just after” the Big Bang, i.e., infinitesimally minisculely beyond it,3 when the world is said by (footnote continued from previous page)

made up out of quarks and leptons, arranged in certain specific ways. And, the reason why (or at least, one reason why) the universe exists, is precisely this (the very same reason): because it is something made up out of quarks and leptons, arranged in certain specific ways. Moreover, strictly speaking, things, i.e., real things like the universe, are not, cannot be, answers to questions, any more than they can be the questions themselves. Answers, like questions, are not real things. They are things of a grammatical or logical or mental sort. They are sentences, or propositions, or ideas. Both questions and answers are about things. They are not those things themselves.

2 Lederman, op. cit. , p. 318.

3 Prior to 1043 seconds after the Big Bang? Gerald L. Schroeder, physicist and theologian, points out: “While the conditions that existed prior to the appearance of energy and matter

[i.e., prior to the Big Bang] are not known, we can attempt to describe them at the briefest instant following the beginning, at about 1043 seconds after the start.” ( Genesis and the Big Bang, New York: Bantam Books, 1992; p. 65). Is it possible, in principle, to construct a particle accelerator which can recreate the conditions of the newly beginning universe prior to 1043 seconds after the start?, even though “physics and mathematics, as we know them today, cannot deal with times earlier than 1043 seconds after the beginning,” because “prior to that time, the temperatures and densities of matter exceeded those that can be described by the laws of nature as we now understand them.” (Schroeder, ibid. , p. 66).

some to have been a sea of free quarks (and perhaps of free leptons as well), i.e., a sea of separately existing and acting quarks (and leptons)?

2—

A Quark, Like Any Element, Is an Agent Cause of a Special Sort, Besides Being a Material Cause of a Special Sort It is the view of Aquinas that all types of nonliving things, reaching down to and including the elements, are related to the substantial forms of all higher types of things, living as well as nonliving, as that which can be their matter (subject) and their instrument, i.e., as that in which these substantial forms can exist (their matter, or subject) and that through the surviving powers of which (their instrument) they can perform their proper or distinctive activities.

To make this clearer, one should keep in mind, as noted above (pp. 140–141) that an instrument can be either a separated instrument, i.e., one whose form is a form different from that of the principal agent, like the pen (instrument) with which I (the principal agent) write; or a conjoined instrument, i.e., one whose form is the form of the principal agent, like a hand, or a vital organ (e.g., the liver), or a molecule of carbon dioxide, or an atom of oxygen, or a proton, or a quark, or a lepton; all of which are in various ways parts or components of mixed bodies, however lowly (the lowly proton is composed of quarks), or however exalted (man is composed of quarks, and protons, and atoms, and molecules, and vital organs, and hands, etc.).

Now quarks, Aquinas would say, are related to the form of a proton as matter (elemental matter, not prime matter) and as conjoined instrument. That is, not only do quarks enter into the proton as ingredients (matter) of what the proton is, but they do (agent) what quarks, as put together into a Page 251

proton, have the power to do; and thereby enable (as instrument) the proton to do what a proton, as proton, does. That is, the quarks are a conjoined instrument;

their form is the form of the proton. Protons, in turn (along with the quarks which are their ingredients), are similarly related to the form of an atom, i.e., as matter (quasielemental4 matter, not prime matter) and as conjoined instrument. That is, not only do the protons (and their ingredient quarks) which compose the atom (along with some electrons and neutrons) enter into the atom as ingredients (matter) of what the atom is, but they do (agent) what protons and quarks and electrons and neutrons, as put together into an atom, have the power to do; and thereby enable (as instrument) the atom to do what an atom, as atom, does. Protons (along with their brother atomic components) are a conjoined instrument; their form is the form of the atom. Molecules, in their turn (through the conjoined instrumentality of their ingredient quarks and electrons and protons and neutrons) are related to the forms of progressively higher bodily things, up to and including man, as their quasielemental matter and conjoined instrument. So that in man we have a highly complex entity which can do, has the power to do, what man does, precisely because of a serial ordering of quasielemental matters which are also conjoined instruments: his component bodily organs, like heart and liver, use their component molecules, like carbon dioxide, which use their component atoms, like oxygen, which use their component electrons and protons and neutrons, the last two of which (i.e., protons and neutrons) use their component quarks, to do what they, as put together into man can do, thereby enabling man to do what man, as man, does. Thus, quarks (along with protons, atoms, molecules, etc., on up to vital bodily organs) are all of them, each in its own way, not only material causes of a special sort (i.e, capable of agent causality, because of certain remaining powers, as distinct

4 The term “quasielemental” is being used to mean: like, or resembling (quasi), an element, without being an element. That is, just as an element, e.g., a quark, remains (as ingredient) in the proton with its powers, though without its substantial form (it is by those remaining powers that the quark functions as a conjoined instrument of the proton); so too the proton remains (as ingredient) in the atom with its powers, though without its substantial form (it is by those remaining powers that the proton, in its turn, functions as a conjoined instrument of the atom).

from prime matter which is a purely passive or receptive potentiality), but also agent causes of a special sort, i.e., conjoined instrumental agent causes. — And this is why it can be said that quarks, along with these other components, from the lowest to the highest, have, all of them, a virtual, retrievable, dispositional, and instrumental presence, the lower in the higher; and why the higher cannot exist and act without the lower, though the lower can, and does, exist and act without the higher.5

3—

Ingredients in the Definitions of Quarks and Leptons

Atoms today are defined in terms of the protons, neutrons, and electrons which compose them; protons and neutrons, in terms of the quarks which compose them.

But what about the quarks themselves? And their sister elements, the leptons, e.g., electrons? How are they to be defined? What are their intrinsic components (if that is the right question)? What are the ingredients of their essences? That is, what is that within them which accounts for the fact 1) that they have come into existence (their becoming), and 2) that they are now in existence (their being), and 3) that they do what they do (their activities)?

It will be helpful to begin here with a reminder of what is meant by an element. This will be to begin as we did earlier (pp. 180–181) with respect to the four elements in the physical theory of Aquinas; an eminently appropriate way to begin, since that meaning of “element” is as applicable to the quarks and leptons of today (because, as far as we know, but only as far as we know,6 they are ultimate particles) as it was to the the four elements of days gone by. And with that firmly in mind, one would be in a position to

5 For Aquinas on the material and agent causality of the four elements, see above, pp. 137–143, section 3, Is an element in any way an agent cause, in addition to being a special sort of material cause?

6 See below, pp. 286–287, on the rishon.

proceed more profitably in pursuing the questions: What is a quark? What is a uquark? A dquark? And all other types of quarks? What is a lepton? What is an electron? An electron neutrino? And all other types of leptons? We shall not pursue all these questions, just those which will suffice for our purposes.7

What then, as a reminder, is an element? An element is a simple body, i.e., something composed out of prime matter and a substantial form (but not out of any prior bodies, since there are no prior bodies), which (substantial form), as efficient cause, not only extends the element threedimensionally (and keeps it so extended),8 but also causes it to have certain proper accidents by which it can both affect, and be affected by, the other elements, so as to undergo the substantial changes in which it is transformed into other elements (can a quark of one type be transformed into a quark of another type,9 or into a lepton; can a lepton of one type be transformed into a lepton of another type, or into a quark?), and the alterations by which it becomes an ingredient in the makeup of mixed bodies (like protons, neutrons, atoms, molecules, and the like, ascending to ever more complex entities, up to and terminating in man, the most complex).

Fire, suggests Aquinas as we saw above (pp. 168–169), can be defined as a simple body, hot and dry. Now bodies are either simple (the elements themselves) or mixed (made out of elements). A mixed body is doubly composed: not only 1) out of prime matter and substantial form, but also 2) out of simple bodies, i.e., out of elements. These elements are put together not by simple aggregation, in the way in which a heap is made out of, say, bricks and stones; nor by a composition which not only puts them together in

7 See below, p. 256, the paragraph beginning with the words: “Quarks and electrons … ”

8 This is a kind of “small” Big Bang, as we noted earlier (p. 166) — small since it occurs within, and is limited to, the confines of the element. Any substantial form does this for the body of which it is the substantial form.

9 See Lederman, The God Particle, pp. 325–326, where he points out that a quark of one type can be transformed into a quark of another type, e.g., a uquark becomes a dquark, and vice versa.

some given order, in the way in which a house is made out of an orderly arrangement of wood and bricks and stones, but also holds them together by certain joining or binding materials, like nails and glue and mortar; but by a mixing (per mixtionem) in which the elements affect and alter one another so as to remain in the mixed body in a special way, i.e., virtually, or with their powers (as well as retrievably, dispositionally, and instrumentally), though not actually (i.e., not with their substantial forms). — A simple body, on the other hand, is composed out of prime matter and substantial form indeed, but not also out of simple bodies. A simple body is not doubly composed. It has no composing bodily ingredients, in addition to its composing prime matter and substantial form. There are no prior bodily things out of which simple bodies could be composed. Simple bodies, i.e., elements, are the ultimate bodily constituents of all other bodily things. The expression “simple body,” it is quite clear, functions as a genus in this definition of fire. That is, all elements have this in common that they are simple bodies. The expression “hot and dry,” by way of contrast, functions as a specific difference. Hot and dry are proper accidents of fire, caused by, and manifesting, the substantial form of fire.

A quark (and a lepton), like any element (assuming that each is, indeed, an element), is a simple body, i.e., composed out of prime matter and substantial form, but not also out of prior bodily components. Assigning this genus is an easy matter. For anything which comes to be in change is composed of prime matter and substantial form; quarks and leptons come into being in change. And any element is such that it cannot be composed out of prior bodily things; there are no prior bodily things.

But, what is to function as the specific difference? Hot and dry, as Aquinas sees it, are proper accidents of fire, caused by, and manifesting, the substantial form of fire; this is why the expression “hot and dry” functions as expressing the specific difference. What, now, are the proper accidents, i.e., the substantialformmanifesting characteristics or properties or attributes, of quarks and leptons? To identify these is, clearly, to identify Page 255

what will be expressed in their specific differences. And physicists have already identified them.

In his The God Particle, which he sees as a kind of play or drama, Leon Lederman, experimental physicist and Nobel laureate, begins with a page entitled DRAMATIS PERSONAE. Some of the actors in his play are matter particles (e.g., quarks, electrons), others are reaction particles (e.g., neutrinos), still others are force carrying particles (e.g., gluons, photons). From his list of performers in this atomiccosmic drama: Atomos or atom: Theoretical particle invented by Democritus. The atom, invisible and indivisible, is the smallest unit of matter. Not to be confused with the socalled chemical atom, which is merely the smallest unit of each of the elements [in the periodic table] (hydrogen, carbon, oxygen, and so on).

Quark [a matter particle]: Another atom [but a contemporary one, as opposed to an atom of Democritus]. There are six quarks — five discovered, one still sought after (in 1993).

Each of the six quarks comes in three colors. Only two of the six, the up and the down quark, exist naturally in today’s universe.

Electron [a matter particle]: The first atom discovered, in 1898. Like all modern atoms, the electron is believed to have the curious property of “zero radius.” It is a member of the lepton family of atoms.

Neutrino [a reaction particle]: Another atom in the lepton family. There are three different kinds. Neutrinos are not used to build matter, but they are essential to certain reactions.

They win the minimalist contest: zero charge, zero radius, and very possibly zero mass.

Photon, graviton, the W+, W, and Z0 family, and gluons [force carrying particles]: These are particles, but not matter particles like quarks and leptons. They transmit the electromagnetic [transmitted by photons,] gravitational [by gravitons], weak [by

the W+, W, and Z0 family], and strong [by gluons] forces, respectively. Only the graviton has not yet been detected. (Lederman, The God Particle, p. ix).

Quarks and electrons (electrons are one of the leptons) are matter particles, as different from reaction particles and force transmitting particles. The attempt at this point is to describe, with help from Lederman and others, some of the intrinsic properties (i.e., the proper accidents, or substantialformmanifesting properties, as Aquinas would put it) which physicists have identified as belonging to the three fundamental matter particles, i.e., 1) the up quark (uquark), 2) the down quark (dquark), and 3) the electron — since a) this will more than suffice for our purposes (i.e., to try to understand how uquarks and dquarks combine to form protons and neutrons, how protons and neutrons combine to form the nucleus of an atom, and how electrons combine with the nucleus to form an atom), and b) since, as Lederman explains to Democritus, “almost everything in the universe today is composed of only two quarks — the up and the down —and the electron. The neutrino

[another of the leptons, but a reaction particle] zings around the universe freely and pops out10 of our radioactive nuclei, but most of the other quarks and leptons must be manufactured in our laboratories.“11

Before describing the proper accidents, i.e., the substantialformmanifesting properties, of the uquark, the dquark, and the electron, one should perhaps consider whether an elementary particle — any elementary particle — can be something without dimensions. For Lederman, as well as others, points out many times that quarks are thought to be without dimensions. And this seems difficult to accept, since dimensions (three 10 Does “pops out” imply that the neutrino was an ingredient or component, in some sense of “ingredient” or “component,” of those nuclei? But, isn’t a neutrino a lepton? Can leptons be ingredients of the nucleus of an atom?? Mustn’t leptons be extranuclear ingredients of atoms? Are leptons ever subject to the strong nuclear force?

11 Lederman, op. cit. , p. 51. Lederman is speaking to Democritus, in one of many very clever, entertaining, and most instructive dialogues, scattered throughout the book.

dimensions) belong to anything which has a substantial form.

Quarks, physicists say, have no size at all; they are like geometrical points; they are there, i.e., have a location or a place, but take up no space. This may sound “real crazy,” Lederman apologizes. But it makes sense, some philosophers might want to note, at least in a way. That is, an explanatory principle (or cause) must be in some significant way unlike what it explains. For, if the explanans and the explanandum are alike in every way, no explanation has been given. To say that what has dimensions is made up out of components each of which has dimensions, and to stop there, is not to have explained why what has dimensions has the dimensions that it has. And so, it seems, the dimensions of what has dimensions must be explained by components which do not themselves have dimensions. The dimensioned, as such, is quite appropriately explained by the dimensionless. But this dimensionless component, the quark, must be unlike a geometrical point, as well as like one.

A quark is after all a physical reality, a physical point, not a mathematical point. As physical, a quark has something dimensionless within it which enables it to account for the dimensions of the whole, the proton or the neutron, of which it is an ingredient. As Aquinas would insist, it has a substantial form, which, as efficient cause, does exactly that, i.e., accounts for the dimensions of the whole. But, this must be properly understood. Since a quark is said to be an element, it itself must have dimensions,12 however small they may be; it itself must be something bodily, for elements are ultimate bodies. That is, elements are the bodily 12 It itself must have dimensions, or one or other of its properties. Is it its mass that has these dimensions? Is it its charge? Is it some other of its properties? To what exactly does the word “it” refer, in the expression “it itself;” or the word “its,” in expressions like “its mass”? — And an additional and related question: Are mass and charge and spin, and the other properties which are attributed to particles — are these properties such that only things with dimensions can have them? Or is Lederman right when he notes that if you ask questions like, ”What is it that’s spinning?,” when scientists tell you that particles have spin (which question seems to imply that what has spin is something which has dimensions); then “you expose yourself as one who has not yet been cleansed of impure prequantum thinking … ” (Lederman, The God Particle, p. 344).

constituents of all other bodies, they themselves having no bodily constituents.13 Nonetheless, since a quark comes to be in change, it must have prime matter and a substantial form as its basic constituents; and both of these are, in themselves, dimensionless. And so, it is not the quark itself which is without dimensions, even though it is said to be pointlike — a pointlike atom.14 It is prime matter (and the substantial form as well which actualizes it) which is without dimensions. And this is why, it appears, Lederman says at times that quarks have no dimensions15 (recognizing dimensionless prime matter in some implicit and unwitting way, though wrongly attributing its dimensionlessness to quarks themselves) and at times that they, i.e., quarks, do have dimensions, but dimensions which are so incredibly small that quarks are “as good an approximation to points as you can get.“16 It is not the quark itself which is pointlike; it is rather the prime matter within it which is pointlike.17 Quarks themselves have the dimensions which they have because of the ongoing efficient causality of their dimensionless substantial forms and the ongoing receptive causality of their dimensionless prime matter; but the proton, of which the quarks are constituents, has the dimensions which it has, because of the dimensions of its constituent quarks, which (dimensions), though they survive in the

13 See above, p. 159, for a brief discussion of the question: How is it that an element is a bodily thing, i.e., something threedimensional, since an element is composed only out of prime matter and substantial form, and neither of these components is a body? See also above, pp. 165–167, on the description of the birth of an element, for more details with respect to this question.

14 This is said to be the case as regards leptons, too: “… [there are] two classes of pointlike atoms — the quarks and the leptons. ” (Lederman, op. cit. , p. 309).

15 Lederman writes: “And here’s Boscovich [Roger Joseph Boscovich, eighteenth century scientist] putting forth the proposition that matter is composed of particles that have no dimensions!] We found a particle just a couple of decades ago [Lederman is writing in 1993] that fits such a description. It’s called a quark.” (Lederman, op. cit. , p. 103). See also Lederman, ibid. , p. 55: “The quarks — they’re all pointlike, dimensionless; they have no real size.”

16 This is said about leptons as well: “The radius of a quark is less than an incredibly small 1021 centimeters. As far as we can tell, quarks and leptons are as good an approximation to points as you can get.” Lederman, op. cit. , p. 405.

17 See above p. 253, the paragraph beginning with the words: “What then, as a reminder, is an element?” See also p. 166.

proton which is generated out of their conjunction (though not as dimensions of the quarks, since the quarks do not survive with their substantial forms), are maintained in existence by the substantial form of the proton. That is, the dimensions (which were the dimensions of the just corrupted quarks) survive in the newly generated proton (though the quarks themselves do not), and are kept in existence by the conjoined ongoing efficient causality of the dimensionless substantial form of that proton and the ongoing receptive causality of its dimensionless prime matter (thereby becoming the dimensions of the proton itself), which (prime matter) has survived in it (i.e., in the newly generated proton) from the just corrupted quarks.

It seems clear, from the immediately preceding, that any and every elementary particle, i.e., anything at all which is said to be an element, must have dimensions, i.e., three dimensions. For elements are ultimate bodies. It may be difficult, perhaps even impossible (in some sense of “impossible”) to determine whether its dimensions are the dimensions of its mass, or of its charge, or of its spin, or of some other of its properties. It may even be that it (i.e., the elementary particle) has several sets of dimensions, one set for its mass, another for its charge, another for its … , etc. But it must have dimensions. These are conferred on it, as they are on anything which is composed of prime matter and substantial form, by its substantial form. In addition, one wants to ask whether particle properties like mass, charge, spin, etc., are such that something without dimensions can have them; and whether, if something without dimensions can have these properties — whether these properties themselves can exist without having dimensions of their own. This is like asking whether something without dimensions can be soft or hard, rough or smooth, red or blue. And if it can, whether softness, hardness, etc. themselves can exist without having dimensions of their own. — Consider, moreover, a world in which there is matter, but this matter is without dimensions. Could there be, in such a world, a numerical plurality of things composed out of matter and form, things which come into existence in change? If matter were not quantified, if it did not have dimensions; there

would be no possibility of dividing this matter, and so no possibility of a numerical plurality of things made of matter. If matter were not quantified, it would be like a mathematical point. If matter were not quantified, there could not be a plurality of elementary particles, whether quarks, or leptons, or particles of any other sort. Nor could there be a plurality of things made up out of elementary particles. If matter were not quantified, the physical universe — as a whole — would be like a mathematical point.

Having seen that any elementary particle must have three dimensions, we turn now to define the three fundamental matter particles, i.e., the uquark, the dquark, and the electron — in terms of a listing of the intrinsic properties (i.e., the proper accidents, or substantialformmanifesting attributes) which physicists have identified as belonging to them. This will be followed by a brief description or definition of each of these intrinsic properties. And this, in turn, will be followed by a definition of the force transmitting (or messenger) particles, i.e., gluons (for the strong force), photons (for the electromagnetic force), W+ and W and Z0 particles (for the weak force), and gravitons (for the force of gravity) — these definitions, too, in terms of a listing of the intrinsic properties which physicists have identified as belonging to them.

Matter Particles:

A uquark is a simple body (genus), with a radius of less than 1021 centimeters, a mass of 10 (in terms of the mass of the electron, taken as unity), a rest energy of 5

MeV, an electric charge of +2/3, a color charge (chromodynamic charge) of either red, or yellow, or blue (some physicists call the yellow one green, still others call it white), a spin of 1/2, and a baryon number of +1/3 (these intrinsic properties taken together constitute the specific difference).

A dquark is a simple body (genus), with a radius of less than 1021 centimeters, a mass of 20 (in terms of the mass of the electron, taken as unity), a rest energy of 10 MeV, an electric charge of 1/3. a color charge of either red, or yellow, or blue (some physicists call the yellow one green, still others call it white), a spin of 1/2, and a baryon number of +1/3 (these intrinsic properties taken together constitute the specific difference).18

An electron is a simple body (genus), with a radius of less than 1018 centimeters, a mass of 1030 kilograms (i.e., of about 9.107 x 1028 gram; or 1/1837 that of a proton), a rest energy of .511 MeV, an electric charge of 1 (i.e., a negative electric charge of about 1.602 x 1019 coulomb), a spin of 1/2, and a baryon number of 0, i.e., no baryon number (these intrinsic properties taken together constitute the specific difference).19

It is to be noted, and emphasized, that the above definitions of the uquark, the dquark, and the electron are being patterned after Aquinas’ definition of the element fire as a simple body (genus), hot and dry (specific difference).

18 It is to be noted that no one alone of the intrinsic properties of the uquark and of the dquark functions as the cause which initiates, and sustains, the exchange of gluons which binds the quarks together to form a proton and a neutron — but rather, all of them taken together. That is, all of these properties, taken together, enable quarks to combine with other quarks (and with antiquarks) to form baryons and mesons. And this is so, because all of them taken together constitute the specific difference.

19 Similarly, all of the intrinsic properties of an electron, taken together, initiate and sustain the exchange of photons which binds the electron to the nucleus. And all of the intrinsic properties of the nucleus, too — taken together — contribute to initiating and sustaining this binding exchange of photons. Similarly, again, all of the intrinsic properties of particles subject to the weak nuclear force initiate and sustain the exchange of W+ and W and Z0 particles, which (exchange) causes certain processes, like the conversion of a neutron into a proton, or vice versa. Lastly, mass is the only intrinsic property of physical bodies which initiates, and sustains, the exchange of gravitons causing bodies to attract one another.

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To make the preceding definitions at least minimally understandable to those of us who are not physicists, it will be helpful to give some sort of definition of radius, mass, rest energy, electric charge, color charge, spin, and baryon number (and of certain related things like diameter, chord, weight, density, and others).

Radius: the distance in a straight line from the center of a spherical or circular physical object to its outer edge.

If the dimensions of particles are given in terms of the diameter, then:

Diameter: a chord through the center of a spherical or circular physical object; the radius times two.

Chord: the distance in a straight line between two points on a curve.

Mass: the amount of “stuff” in a physical object. Mass is neither the size, nor the weight, nor the density of the physical object. Mass is that characteristic of a body which relates that body to other bodies by pulling on them, and to imposed forces by resisting them. Mass is a scalar quantity, as opposed to a vector quantity, i.e., it has magnitude but no direction. When physicists say, “mass,” without specifying whether they mean inertial mass or gravitational mass, (see below, p. 263, for the difference), they mean inertial mass.

Weight: the force that pulls a physical body directly toward a nearby celestial body, e.g., the planet Earth. This force is due to the gravitational attraction between the two bodies. Weight is not mass. A body of a given (i.e., same) mass weighs more on Earth than it does on the Moon. Weight is a vector quantity, i.e., it has magnitude and direction.

Density: the mass of a physical body in a given volume, or per unit of volume. Density is a scalar quantity.

Gravitational mass: the amount of stuff in a physical object which pulls on another physical object. Gravitational mass is a scalar quantity.

Inertial mass: the amount of stuff in a physical object which resists a force, and determines the resulting motion. It is that property of matter which is measured by the response of a physical object to a force. Inertial mass and gravitational mass are two quite different attributes of matter. But, the gravitational stuff of a physical object is precisely equal to its inertial stuff, i.e., to the stuff (inertial mass) which appears in Newton’s second law, i.e., F=ma: force is equal to the mass multiplied by the acceleration. Acceleration is the rate at which the speed of a motion changes (increases). Mass (inertial) is equal to the force divided by the acceleration.

Inertial mass is a scalar quantity.

Rest mass: the amount of stuff in a physical object prior to any increase of mass which a body takes on, according to the theory of relativity, because of an acquired motion, or acceleration thereof. Rest mass is a scalar quantity.

Relativistic mass: rest mass plus any increase of mass which a body takes on, according to the theory of relativity, because of an acquired motion, or acceleration thereof. Relativistic mass is a scalar quantity.

Energy: the capacity for doing work, e.g., for bringing to rest a body which was in motion, or for putting into motion a body which was at rest, or for changing the direction of the motion of a body, or for accelerating the motion of a body. Energy is a scalar quantity.

Rest energy: the rest mass of a physical object, converted into energy, and expressed in terms of the electron volt (eV). Rest energy is a scalar quantity.

It is to be noted that “rest energy,” “rest mass,” and “inertial mass” have the same referent, but they are conceptually different. Their conceptual differences are clearly expressed in their definitions, above.

Electric charge: a nongravitational force which arises when two different bodies such as glass and a silk cloth are rubbed against each other, and which is either positive (+) by arbitrary convention, like that on the glass, or negative () by arbitrary convention, like that on the silk. Positive charges repel one another; negative charges repel one another. A positive charge and a negative charge attract one another, e.g., the negatively charged electrons of atoms and their positively charged nuclei attract one another, thereby binding them into the physical unit which is the atom. Electric charge is the source of the electromagnetic force, which is infinite in range and is transmitted by photons. Electric charge is a scalar quantity.

Color charge (or, color force): a nongravitational force which arises out of the color of a quark. Just as electric charge is the source of the electromagnetic force, so too color charge, which arises out of quark color, is the source of the strong nuclear force which binds quarks into hadrons, and quarks and antiquarks into mesons.

The strong nuclear force has been named the chromodynamic force, from the Greek word “chroma,” meaning color. The chromodynamic force is transmitted by particles called gluons (from the word “glue” ). Whereas the electromagnetic force is infinite in range, the strong nuclear force is limited to the confines of the nucleus of the atom. Color charge is a scalar quantity.

Spin: the rotation of a physical object on its axis, in addition to other motions it might have; e.g., the rotation of the Earth on its axis, causing night and day, in addition to its orbital motion around the Sun. With respect to particles, spin was first found in the electron, later on in other elementary particles. Spin is a fundamental intrinsic property of a particle, along with its electric charge and its mass. In relation to elementary particles, it is more accurate to say that the particle has an intrinsic angular momentum (of a given quantity), called spin, as if it were rotating about its axis, rather than really rotating about that axis. Spin is a vector quantity, with an axis of rotation, and a direction of rotation as well (i.e., either righthanded or lefthanded).

Baryon number (or baryonic charge): an intrinsic property of certain particles (i.e., of baryons and antibaryons), along with other intrinsic properties like mass, charge, and spin. It explains the stability of the proton (i.e., prevents its decay), among other things, e.g., it prevents mesons from being the sole products of a collision between two protons, and permits mesons to be the sole products of an interaction between a proton and an antiproton. All threequark particles, i.e., baryons, e.g., the proton, the neutron, the lambda, have a baryon number of +1. All antibaryons, e.g., the antiproton, the antineutron, the antilambda, have a baryon number of 1. All particles of other types have a baryon number of 0. Baryon number is a scalar quantity Force transmitting (messenger) particles:

A gluon is a simple body (genus), which transmits the strong nuclear force, has zero mass, zero charge, and a spin of 1 (specific difference).

A photon is a simple body (genus), which transmits the electromagnetic

force, has zero mass, zero charge, and a spin of 1 (specific difference).

A W+ particle is a simple body (genus), which transmits the weak nuclear force, has a rest mass (expressed as rest energy) of 80 GeV, a charge of +1, and a spin of 1 (specific difference).

A W particle is a simple body (genus), which transmits the weak nuclear force, has a rest mass (expressed as rest energy) of 80 GeV, a charge of 1, and a spin of 1

(specific difference).

A Z0 particle is a simple body (genus), which transmits the weak nuclear force, has a rest mass (expressed as rest energy) of 91 GeV, zero charge, and a spin of 1

(specific difference).

“But why,” one wants to ask, as Leon Lederman himself does, ” three [weak force] carriers? Why three messenger particles [for the weak force] … ?” ( The God Particle, p. 325). Experimental data, Lederman answers, gathered by the 1970s “insisted that the weak force had to be carried by three massive messenger particles … — one positively charged [the W+], one negatively charged [the W], and one neutral [the Z0] — … to propagate the field that induces the changes” ( op.

cit. , p. 325) which result in the decay of unstable hadrons. These changes are “really manifestations of the constituent quarks undergoing [multiple and complex]

reactions [with a number of intermediate stages] — for example, an up quark changing to a down quark or vice versa.” ( op. cit. , p. 325). It is the multiplicity and complexity of these reactions, with their many intermediate stages, which require three different force carriers.

A graviton is a simple body (genus), which transmits gravitational force, i.e., the force of gravity, has zero mass, zero charge, and a spin of 2 (specific difference).

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The following definitions will be helpful at this point.

Force: in classical physics, force is defined as something capable of affecting the motion of a body (stopping its motion, starting it up, speeding it up, slowing it down, changing its direction, and so on), or of distorting the shape of a body. In particle physics, force is the cause of every change, reaction, creation and disintegration.

For example, when two particles collide, resulting in the creation of new particles, a certain force is responsible. When particles decay into other particles, there is a force which is responsible, and it may be seen as acting between the original particle (even though it no longer exists) and the decay products, after they have begun to exist. Forces are vector quantities.

Gravitational force (the force of gravity): the first force to be identified by physicists. It is the force by which every piece of matter, however large or small, in the universe attracts (never repels) every other piece of matter. Under certain circumstances, gravity can cause black holes. Gravitational force acts on all particles;

indeed, on all pieces of matter, however large or small.

The electromagnetic force: identified by physicists after the force of gravity. It is a combination of the electrostatic force and the magnetic force. Unlike gravity which is always an attracting force, the electromagnetic force can either attract (when one charge is positive and the other is negative) or repel (when both are either positive or negative). Electromagnetic force acts on all charged particles.

The electrostatic force: the force acting between two stationary charges. One of the aspects of the electromagnetic force.

The magnetic force: the force which arises between moving charges. Another of the aspects of the electromagnetic force. Since the magnetic force between moving charges has been shown to be a direct consequence of the electrostatic force, it has become customary to speak of a unified electromagnetic force.

The strong nuclear force: the short range attracting force between nucleons (i.e, protons and neutrons), which binds together protons and neutrons to form nuclei.

It has come to be seen as a kind of residual overflow of another and more fundamental strong force, i.e., the strong force (color charge, or color force; see above p.

264) which binds quarks together within nucleons. The strong nuclear force acts only on some particles, i.e., only on hadrons, e.g., protons, neutrons, and pions; and on the quarks (and antiquarks) which compose them. The strong force does not act on leptons.

The weak nuclear force: the force, arising from within particles, which causes certain conversions, e.g., the conversion of a neutron into a proton (beta decay), or vice versa, of a pion into a muon, of a muon into an electron. The weak nuclear force and the electromagnetic force combine to become the electroweak force, in a way which is much like the way in which the electrostatic force combines with the magnetic force to become the electromagnetic force. The weak nuclear force acts on all particles.

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From the preceding definitions (pp. 260–268), one may be able to understand (if he has been a diligent and attentive reader) how uquarks and dquarks combine to form protons and neutrons, how protons and neutrons combine to form the nucleus of an atom, and how electrons combine with the nucleus to form an atom.

Nonetheless, these things will become clearer (and more understandable, it is hoped) below, at a more suitable and helpful point, on pp. 281–284, beginning with:

“Physicists say that the strong nuclear force is generated by an exchange of gluons … ”

4—

Is There Such a Thing As a Mixing? Are Protons Mixings of Quarks?

C. J. F. Williams’ book on Aristotle’s De Generatione et Corruptione 20 offers a translation which is very clear, appropriately ascetic yet easy and pleasurable to read, and followed by a copious, hardthinking and challenging commentary, which he most modestly calls Notes. His comments on what Aristotle says about mixis (mixtio, in Aquinas), the topic of Bk. I, ch.10, begin with a reference to Harold H. Joachim’s translation:21

The word translated here [i.e., by Williams] as ‘mixing’ is rendered by Joachim ‘combination’. He [i.e., Joachim] thus assimilates the distinction between mixing (mixis) and composition (synthesis) — cf. 328 a 6 — to the modern distinction between chemical combination and mechanical mixture. The analogy is good in so far as chemical combination is a more intimate union of substances than is mechanical mixture, as mixing is than composition; but the word ‘combination’ by itself does not have this sense, and the complete phrase ‘chemical combination’ imports too much modern theory. Moreover, the modern theory is alien to Aristotle’s thinking on the subject; for in chemical combination the atoms of the combining substances remain intact and change only in respect of their relation to each other. For Aristotle this would be a case of mere ‘composition’. Modern chemistry is, after all, atomistic.22

Joachim, notes Williams, is in effect likening what Aristotle calls mixis to what we nowadays call chemical combination, and what Aristotle calls synthesis to what some nowadays call mechanical mixture. This likening is both good and bad, continues Williams. It is good inasmuch as a chemical 20 Williams, C. J. F., Aristotle’s De Generatione et Corruptione, Translated with notes (in the Clarendon Aristotle Series), New York: Oxford University Press, 1982.

21 Joachim, Harold H., translation of De Generatione et Corruptione in The Basic Works of Aristotle, edited and with an introduction by Richard McKeon, New York: Random House, 1942; pp. 470–531.

22 Williams, op. cit. , p. 142.

combination is a more intimate union of things than a mere mechanical mixture, just as a mixis is a more intimate union than a mere composition (synthesis). In the result of a mere mechanical mixture, the ingredients do not interact with one another so as to cause changes which affect them intrinsically; they are simply moved about so as to be intermingled in the way in which grains of wheat, for example, might be intermingled with, mixed together with, grains of oats or grains of barley, each of the grains surviving as, each continuing to be just, the grain that it was; or in the way in which stones and bricks might be thrown together into a heap, each continuing to be just the stone and just the brick that it was. It is bad inasmuch as the word “combination,” used by itself, does not convey the meaning which Aristotle intends by mixis, and the whole phrase “chemical combination” carries with it too much modern scientific theory. Besides, continues Williams, modern scientific theory is alien to Aristotle’s way of thinking about mixis. For Aristotle, the combining ingredients in a mixis do not remain intact, though they do remain in some way, since they are retrievable. In chemical combination, urges Williams, the combining ingredients remain intact, which seems to mean that they undergo no changes which affect them intrinsically; they ”change only in respect of their relation to each other.” But Williams does not specify what he has in mind when he notes that they “change only in respect of their relation to each other.”

One must note that when hydrogen and oxygen combine chemically, i.e., interact, to form water, the resulting water is neither hydrogen nor oxygen; each molecule of water is just water, and throughout. To be sure, the hydrogen and the oxygen are retrievable, and so they survive in the newly formed water in some way. But it is clear that they do not survive intact, i.e., that they undergo some sort of change which affects them intrinsically; that something of them does survive, but that they, as they, intact and intrinsically unchanged, do not.

Similarly, when two uquarks and one dquark combine to form a proton, the resulting proton is neither a uquark nor a dquark; the proton is a proton throughout.

The quarks are retrievable, and so they survive in the newly formed proton in some way. But it is also clear that they do not survive intact, i.e., that they undergo some sort of change which affects them intrinsically; that something of them does survive, but that they, as they, intact and intrinsically unchanged, do not.

For Aristotle, states Williams in the end, the case in which the combining ingredients “remain intact and change only in respect of their relation to each other” (by which William seems to mean that the only thing which has changed is where each ingredient is) would be a case of mere composition, a case in which the ingredients have been simply juxtaposed, put next to or alongside one another, and only that. Modern chemistry is, after all, atomistic, adds Williams, by way of explanation.

Atomistic changes are changes in which each of the combined ingredients undergoes no intrinsic change of any sort, whatever other sorts of changes, locational or other, and however many, each might be said to have undergone. But mixis, for Aristotle, continues Williams, is what gives rise to homoeomers, and the nature of a homoeomer, as the word itself indicates, is to be such that every smallest part of it is of the same character as every other and as the whole.23

But this means, one must be reminded, that a mixis is a change in which the ingredients about to be combined act upon, and are acted upon by, one another (and by certain required extrinsic agents, as well) in such a way that the result is a thing which is different in kind from any of its ingredients. Water is different in kind from the oxygen and the hydrogen which have interacted to generate it. Similarly, the proton is different in kind from the uquarks and the dquark which have interacted to generate it. It may just be,

23 Williams, Aristotle’s De Generatione et Corruptione, p. 142.

one wants to say, that the chemical combination of the mutually interacting hydrogen and oxygen, as they become water, is not atomistic, after all; that the generation of a proton out of mutually interacting quarks is not atomistic either; and that modern scientific theory is just wrong when it “denies that anything occurs which can properly be so described [i.e., as a mixis. ]”.24

A mixing (mixis, mixtio), as we indicated above (p. 250), results neither in something which is like a heap, e.g., of bricks and stones, in which its constituents are simply thrown together; nor does it result in something which is like a house, i.e., something which is not simply thrown together, but carefully put together out of constituents, e.g., wood and bricks and stones, arranged in an orderly way, and held together by certain joining materials, e.g., nails and mortar and glue. It results rather in something, i.e., a mixed body (like a molecule of water, or a proton), which differs in kind from any and all of its constituents, and in which the constituents, having undergone a mutual interactive alteration, remain in a special way, i.e., virtually, though not actually — virtually, meaning: with their powers, but these powers appropriately altered by means of their preceding interactive alteration (as well as retrievably, dispositionally, and instrumentally); though not actually, meaning: not with their substantial forms, because a substance (e.g., a molecule of water, or a proton) can have actually but one substantial form, its own.

The point to be stressed here is this, that a mixed body differs in kind from all of its constituents, and so must have a substantial form of its own to account for this difference in kind. And this is why the constituents of a mixed body do not survive therein with their substantial forms. If they did, then a molecule of water would be water (actually water) throughout, and at the same time hydrogen (actually hydrogen) in these two parts, and oxygen (actually oxygen) in that third part. Similarly, a proton would be a proton (actually a proton) throughout, and at the same time a uquark (actually a 24 Williams, ibid.

uquark) in these two parts, and a dquark (actually a dquark) in that third part.

To make it clearer that modern scientific theory may be just wrong when it “denies that anything occurs which can properly be so described [i.e., as a mixis],” it will be helpful to consider the following summary of what Aristotle has to say about mixis (mixtio, in Aquinas) in Bk. I, ch. 10 of his De Generatione et Corruptione: Deinde … recapitulat [Philosophus] quae dicta sunt de mixtione … , dicens manifestum esse … et quod est mixtio, et quid est, et quare est: quia propter passionem et actionem contrariorum.

Et dictum est etiam quae sunt miscibilia: quando ista [sunt] passiva ad invicem, et bene terminabilia; et talia sunt bene divisibilia.

Dictum est etiam, quod ad hoc quod sit mixtio, necessarium est quod miscibilia non sint simpliciter corrupta, nec sunt simpliciter eadem ut prius. Sunt enim corrupta quantum ad formas, et remanent quantum ad virtutem, …

Adhuc etiam ostensum est quod mixtio non est compositio minimorum secundum naturam, sicut dicebat una opinio, nec minimorum secundum sensum, ut dicebat alia. Talia enim minima non sunt miscibilia. Sed illud est miscibile, quod cum sit bene determinabile, est activum et passivum; et illud quod admiscetur cum tali miscibili, est miscibile ad homiomerum, idest facit cum alio mixtum quod est ejusdem rationis in toto et in partibus.

Patet etiam quod mixtio est miscibilium alteratorum unio. Quae quidem alteratio solum est intelligenda in virtutibus sive qualitatibus eorum. Sed, si etiam alteratio sumatur improprie, mixtio est miscibilium alteratorum et corruptorum secundum formas unio.25

25 In I De Gen. et Corrupt. , lect. 25, in fine. This summary is not the work of St. Thomas Aquinas, whose commentary on Aristotle’s De Gen. et Corrupt. is unfinished, terminating with Bk. I, lect. 17. The rest was written by Thomas Sutton and others (see above, p. 172, footnote 11).

Then … he [Aristotle, the Philosopher] recapitulates what he had said about mixing, noting that it is clear … that there is such a thing as mixing, and what mixing is, and why mixing takes place, namely because of the passivity and activity of contraries.

He had also pointed out what sorts of things are mixables, namely things that can be acted upon by one another, and can be easily bounded, and such things are things which can be easily divided.

He had also said that for mixing to take place, it is necessary that the mixables be neither simply corrupted, nor remain simply the same as before. For they are corrupted with respect to forms, and remain with respect to power, …

He had also pointed out … that mixing is not [just] a composition of particles of the smallest sort according to nature, as one opinion had it; nor of particles of the smallest sort according to sense, as the other had it. For it is not the smallness of the particles that makes them mixables. Rather, only that is a mixable which can be easily bounded, is both active and passive, and when reacting with another mixable produces something homoeomerous, i.e., a mixed body which is of the same nature in its totality as it is in each of its parts.

Lastly, it is clear that a mixing is a uniting of altered mixables; this alteration being understood as an alteration in their powers or qualities only. But, if alteration be taken in an improper sense, a mixing is a uniting of mixables, altered and corrupted with respect to forms.

Is there such a thing as a mixing? This question raises a prior one, namely, what exactly does the word “mixing” mean? As indicated just above, the word “mixing”

means: a uniting of altered mixables. Now, mixables, notes Aristotle and the author of the justabove quoted summary as well, are things which can be easily bounded, such things being things which

can be easily divided, or parted. Liquidlike things (a not uncommon example of the ancients and medievals), say, water at room temperature, and airlike things, say, water in the form of steam, can be easily divided, or parted. But easy divisibility, partibility, is not enough. Mixable things must also be capable of acting upon, and being acted upon by, one another, and in such a way that they alter one another without totally corrupting one another: ” … it is necessary that the mixables be neither simply corrupted, nor remain simply the same as before … ” That is, the mixed body which is generated from their interaction must be such that the interagent mixables survive in it (i.e., in the mixed body) in some way. The mixables are there, i.e., in the mixed body, in a way, and not there, in a way: there with their powers (“… [they] remain with respect to power … “), appropriately altered of course, and these powers function as instruments of the form of the mixed body, and thus also as ingredients without which the mixed body could not exist; not there with their substantial forms (“… they are corrupted with respect to forms … ”), since the mixed body exists as a thing different in kind from any of its ingredient mixables. The mixed body is through and through of a given kind, and this kind is not the kind of any of its ingredients.

Now a proton, being a mixed body, could not exist and perform as a proton does, without its constituent elements, i.e., its three constituent quarks, two uquarks and one dquark. But a proton is not a quark, neither as a totality nor in any of its parts; not a uquark in these two parts of itself, nor a dquark in that third part of itself. A proton is a proton through and through. This means that the quarks which have interacted, and, having interacted, have survived in the newly generated proton, have not survived with their substantial forms, though they have survived, though they are there in some way. They have been corrupted with respect to what they actually are, as determined by their substantial forms. But they have not been corrupted with respect to what they can actually do, i.e., with respect to their powers. Their powers, appropriately altered by the preceding proton

generating interaction26 among the required quarks, have been preserved, by the substantial form of the newly generated proton, in order to function as instruments through which the newly generated proton does what protons do. The quarks are there, in the sense that the proton has certain quarkenabled powers. But the quarks themselves, as things with their own substantial forms, are not there. What is there now is a proton, different in kind from any of the quarks which are said to have survived as its constituents.

Aristotle, and the author of the above summary as well, speak of easy divisibility. How is this to be understood? An element, unlike a mixed body, cannot be divided, or resolved, by a required alteration of an appropriate sort (as opposed to being divided by a simple act of cutting, as with a saw)27 into bodies which are more simple than the element itself. There are no such more simple bodies. Only prime matter and substantial form are more simple than an element, and neither one nor the other is a body. When the ancients and the medievals spoke of the easy divisibility of an element, say of water, they were speaking of what one might describe today as a

“sea of free particles of water,” i.e., a quantity of water in its liquid state (not a single molecule of H O), as opposed to water in its frozen state, patterning this 2

description after the way in which people today often speak of the “sea of free quarks” which (quarks), they say, whizzed about just after the Big Bang. One can think of these free quarks as slipping by and around, over and under, to the left of and to the right of, one another, much as molecules of water do in a churning river. And just as a sea of particles of water, the ancients and the medievals would say, could be mixed, and with ease, with a sea of particles of 26 Can this preceding protongenerating interaction be said to be, or at least include in some way, the exchange of gluons which generates the strong nuclear force? And is this exchange of gluons a continuing interaction within the proton, required to account for the continued existence of the proton? Is this what Lederman has in mind when he talks about “how quarks whirl about each other in their proton prison”? (Lederman, The God Particle, p. 209). That is, is this “whirling about each other” connected in some way with the quark to quark exchange of gluons?

27 See above, pp. 53–54, on how an element’s indivisibility according to species is to be understood.

air, or a sea of air with a sea of fire, because each of these seas is very easily partible or divisible, thus enabling these particles, in contact with one another, to interact by means of their distinctive powers or qualities, i.e., hot, cold, wet, dry, in order to produce mixed bodies of various sorts; so too a sea of free uquarks, we today might say, can be mixed, and with ease, with a sea of free dquarks, or squarks, or free quarks of any other flavor, because each of these seas is very easily partible or divisible, if they are in heat as intense as it was just after the Big Bang — but now in the relative cold of 15 billion years later, only with the greatest difficulty — thus enabling them (the quarks), in contact with appropriate others, to interact with one another by means of their distinctive powers or qualities, e.g., mass, charge, spin, baryon number, strangeness, both in order to be transformed into one another, and in order to produce mixed bodies of various kinds, e.g., protons and neutrons.28 Easy divisibility yields easy mixability, as a kind of contactual prelude to the mixing which comes about by way of appropriate alteration, and which results in the generation of a mixed body. “Mixable,” thus, has two senses in this context: 1) mixable, because easily partible or divisible, in the sense in which a sea of free quarks of one flavor is mixable with a sea of free quarks of another flavor, and 2) mixable, as in the definition of mixing, i.e., a uniting of altered mixables.

The first sense applies to a sea of particles, and prior to the alteration which results in a mixed body(ies). The second sense applies to single particles, e.g., to single uquarks or dquarks, and posterior to this alteration

Moreover, it is not the smallness of mixable particles (in both senses of “mixable”) that makes them mixable things, though the ultimate mixables are of the smallest possible sort, and of this sort in themselves (i.e., “… according to nature … ” ), as opposed to being particles of the smallest possible sort in relation to our sensory perception of them (i.e., “…

28 There is a quark to quark exchange of gluons in the production of protons and neutrons, inasmuch as it is this exchange of gluons which generates the strong nuclear force, which binds the quarks to one another. What, if anything (if this is an appropriate question), is exchanged in the transformation of one sort of quark into another sort?

according to sense … “). Indeed, it is often said today that quarks and leptons have no dimensions at all, that they are absolutely pointlike. Which is very difficult, very difficult indeed, to understand and accept; and perhaps even untrue. Rather, what makes mixable particles mixable things is 1) their easy partibility or divisibility as ingredients of a sea, and 2) their having mutually interactive powers or qualities by which they can generate (by way of exchanging the appropriate forcecarrying particles, whether gluons, or photons, or the weakforcecarrying particles of the W+ and W and Z0 family, or gravitons?) something homoeomerous, i.e., a mixed body, like a proton, which is of the same nature in its totality as it is in each of its parts.

As a last point in commenting on the summary, the recapitulation, which appears above (pp. 273–274), it should be noted that alteration belongs properly to qualities or powers, corruption to things (substances). When a mixing occurs, i.e., when a mixed body comes into existence out of the required preexisting mixables, the powers or qualities of the mixables are altered, being brought thereby to an appropriate mean or middle (or, if to speak of “an appropriate mean or middle” turns out to be unacceptable, for some convincing reason, one could perhaps speak of “an appropriate state“) — appropriate to the mixed body about to come to be; but the mixables themselves, as things or substances with their own substantial forms, are corrupted. They, as they, do not survive. What survives is their altered, and thereby brought to an appropriate mean or state, powers or qualities.

Returning now to the question asked above, at the top of p. 269: Is there such a thing as a mixing?, one must note that the answer is: Yes. But accepting this answer depends on the prior acceptance of substantial change as a fact, and in particular on the prior acceptance that there are things (substances) which differ in kind from the previously existing elements which survive in them as their constituents. And so, if there are such substances, there must be mixings.

Now, will the physicist deny that protons differ in kind from the quarks which survive in them as their constituents? A substance can have actually only one substantial form, its own. And so, if protons differ in kind from the surviving quarks which are their components, the quarks cannot survive with their own substantial forms. They do, nonetheless, survive with their powers, altered (by means of an exchange of gluons?), of course, to a protonappropriate mean or state; otherwise a proton could neither be, nor behave as, a proton. The generation of a proton comes about, therefore, by way of a mixing. The conclusion follows, therefore, that since there are protons which come to be out of quarks, there must be mixings.

Someone might say that a proton is certainly not like a heap of things, e.g., of bricks and stones, in which the bricks and stones which are its constituents are simply thrown together; but that it is just as certainly like a house, i.e., not just thrown together, but carefully put together out of constituents, e.g., wood and bricks and stones, which are arranged in an orderly way, and which are held together by certain joining materials, e.g., nails and mortar and carpenter’s glue. For, isn’t a proton carefully put together out of two uquarks (one green, the other blue), and one dquark (red) — green, blue and red being needed to get something white or colorless29 — arranged in an orderly way, and held together by the strong

29 Lederman, The God Particle, p. 335. “[The color of a quark] has nothing to do with color as you and I recognize it. Color explains certain experimental results and predicts others. For example, it explained how a proton could have two up quarks and a down quark, when the Pauli principle specifically excluded two identical objects in the same state. If one of the up quarks is blue and the other is green, we satisfy Pauli’s rule. Color gives the strong force the equivalent of electric charge.

“Color must come in three types, said GellMann and others who had worked in this garden. Remember that Faraday and Ben Franklin had determined that electric charge came in two styles, designated plus and minus. Quarks need three. So now all quarks come in three colors. Perhaps the color idea was stolen from the palette because there are three primary colors.

A better analogy might be that electric charge is onedimensional, with plus and minus directions, and color is threedimensional (three axes: red, blue, and green).

(footnote continued on next page)

nuclear force, i.e., the quarkquark force carried by the appropriate gluons?30

How, one might ask, is the joining or binding function of the gluons within a proton different, if it is, from that of the nails and the mortar and the carpenter’s glue in a house? Is the whole or totality which is a proton different, in some significant way, from the whole or totality which is a house? Do quarks exist as quarks before they enter the constitution of the proton which is generated out of their conjunction, in the way in which wood and bricks and stones exist as wood and bricks and stones before they enter the makeup of the house which comes to be out of their conjunction? And if they do, what accounts for this prior existence? And what about gluons? Do they have a preproton existence? Or do they come into existence with the proton itself, emerging somehow out of the combining interaction of the quarks (and of other necessary agents, if there are any others) which ushers the proton into existence?

(footnote continued from previous page)

Color explained why quark combinations are, uniquely, either quark plus antiquark, (mesons) or three quarks (baryons). These combinations show no color; the quarkness vanishes when we stare at a meson or a baryon. A red quark combines with an antired antiquark to produce a colorless meson. The red and antired cancel. Likewise, the red, blue, and green quarks in a proton mix to make white (try this by spinning a color wheel). Again colorless.

“Even though these are nice reasons for using the word ‘color,’ it has no literal meaning. We are describing another abstract property that the theorists gave to quarks to account for the increasing amount of data.” (Lederman, ibid. , pp. 334–335).

“And what about the messenger particles? How do we describe the colorforcecarrying particles? What emerged was that gluons carry two colors — a color and another anticolor —

and, in their emission or absorption by quarks, they exchange the quark color. For example, a redantiblue gluon changes a red quark to an antiblue quark. This exchange is the origin of the strong force, and Murray [i.e., Murray GellMann] the Great Namer dubbed the theory quantum chromodynamnics (QCD) in resonance with quantum electrodynamics (QED).

The colorchanging task means that we need enough gluons to make all possible changes. It turns out that eight gluons will do it. If you ask a theorist, ‘Why eight ?’ he’ll wisely say,

‘Why, eight is nine minus one.’ ” (Lederman, ibid. , pp. 335–336).

30 “… we define it [i.e., the strong nuclear force] as the quarkquark force carried by gluons. But what about the ‘old’ strong force between neutrons and protons? We now understand this as the residual effects of the gluons, sort of leaking out of the neutrons and protons that bind together in the nucleus. The old strong force that is well described by exchange of pions is now seen as a consequence of the complexities of quarkgluon processes.” (Lederman, ibid. , p. 338).

Physicists say that the strong nuclear force is generated by an exchange of gluons among quarks. This seems to imply that the gluons derive somehow from the quarks themselves; that the quarks are interacting with one another, and in some way altering one another, by transmitting these gluons to one another, or in some way drawing them out of one another (or both) — in order to absorb them, and then to reexchange them, in a continuing and repetitive process. Can this be taken as a sophisticated 20th century scientific account of what Aristotle and the medievals called a mixtio — i.e., a miscibilum alteratorum unio? — Moreover, when it is said that the electromagnetic force is generated by an exchange of photons between the electrons of an atom, on the one hand, and the nucleus of the atom, on the other, is it being said that the photons derive somehow from within the electrons and the nucleus themselves? That the electrons and the nucleus are interacting with one another, and in some way altering one another, by transmitting these photons to one another, or in some way drawing them out of one another (or both) — in order to absorb them, and then to reexchange them, in a continuing and repetitive process? And can this be, again, a sophisticated and detailed 20th century account of the inner workings of a mixtio? — When it is said that the weak force is generated by an exchange of the W+ and W and Z0 particles, is it being said that these bosons derive somehow from the particles between (among) which they are being exchanged, that these latter particles are interacting with one another, and in some way altering one another, by transmitting these bosons to one another, or in some way extracting them out of one another (or both) — in order to absorb them, and then to reexchange them, in a continuing and repetitive process? And can this be, again, a detailed 20th century account of the viscera of a mixtio? — When it is said that the force of gravity is generated by an exchange of gravitons, is it being said that these gravitons derive somehow from within the bodies themselves between (among) which they are being exchanged, that these bodies are interacting with one another, and in some way altering one another, by transmitting these gravitons to one another, or in some way extracting them out of one another (or both) — in

order to absorb them, and then to reexchange them, in a continuing and repetitive process? To be sure, the exchange among gravitons cannot be seen as a 20th century account of the inner workings of a mixtio. Unlike what happens in the exchange of gluons, and of photons, and of the weakforcecarrying bosons, i.e., the generation of a mixed body(ies); there is no mixed body which results from an exchange of gravitons. The result here is, rather, simply bringing the bodies spatially closer together. And this is significant, for it can be seen as a result which is necessary to enable the other three forces to do their work.

A thought experiment may be of some help to make this last comment understandable. Imagine a universe in which there are only the following elementary particles: two uquarks, one dquark, and one electron — and nothing else. Imagine further that these particles are motionless. That they are very far apart from one another, at the outer edge of a universe as large as a grapefruit (if a grapefruit is too large, let it be as large as a mustard seed), on the circumference of that mustard seed, and in a same plane (to make this consideration more simple). That they are located at points on that circumference which (points) divide that circumference into four more or less equal parts. Can it be said that there will be first of all an exchange of gravitons to bring these particles closer and closer together? And then, when appropriately close together, that there will be an exchange of gluons among the quarks to generate a proton, followed by an exchange of photons between the proton and the electron to form a hydrogen atom? And then, when the right time comes, that there will be an exchange of whatever weak bosons are there to be exchanged, so as to cause the proton to decay (if this be possible)? And that this decay will somehow send the original four particles back out to the outer edge of our mustardseed universe, where gravitons will again begin their exchanging work, which will enable the gluons to do their exchanging work, which will in turn enable the photons to do their exchanging work, thereby generating again a hydrogen atom, which will

again decay, and so on ad infinitum cyclicum. — Gravity, thus, would bring the elementary particles close enough together to enable the strong force, the electromagnetic force, and the weak force to do their respective jobs. And the weak force would initiate the decay (could this, too, be some sort of “small” Big Bang? — see above, p. 166, and p. 253, footnote 8) which would send the particles out to the outer edges, where gravity would again take over. If this could be the case, then it seems that all forcecarrying particles derive somehow out of the mass of physical things, and that mass therefore would be the originating source of all physical forces.

From the preceding, it is quite clear that the binding function of the gluons within a proton is radically different from that of nails and mortar and carpenter’s glue in a house. For the gluons emerge out of the nature of the quarks themselves which compose the proton, whereas nails and mortar and carpenter’s glue do not emerge out of the nature of the composing wood and bricks and stones. Quarks are such by their nature that they emit gluons to, and extract them from, other quarks, thereby generating protons (and neutrons; as well as mesons of various sorts in conjunction with the appropriate antiquarks). Protons and neutrons, in turn, along with electrons, are such by their nature that they emit photons to, and extract them from, one another so as to form atoms, which in turn are such by their nature that they emit the appropriate force carrying particles to, and extract them from, other atoms to form molecules; and so on, to higher and more complex types of physical bodies, up to and including man, the most complex. What is important here is that these particles are such by their nature. And this is exactly what Aquinas has in mind when he points out that the elements (in his day, earth and water and air and fire) were given (by God) at the very beginning, i.e., when they were first brought into being at creation, a nature, both active and material, such that all terrestrial physical things could be derived from them as from their primary material constituents. 31 The

31 See above, p. 217, the paragraph beginning with the words: “What is most particularly interesting and instructive about the response of Aquinas … ”

quarks and the leptons of today’s physics were given at the very beginning, i.e., when they first came into being out of the fires of the Big Bang, a nature, both active and material, such that all physical things, celestial as well as terrestrial, could be derived from them as from their primary material constituents.

5—

Particle Physics and Prime Matter

The Neutrino

A neutrino is, in a way, like prime matter. Whereas prime matter has no properties (no forms) at all, a neutrino has very few of them. The neutrino is just a convenient example; many of the particles of today’s physics are almost propertyless.

Reflecting on the agonies of the status of the Standard Model in 1993, one of which (agonies) is not knowing whether neutrinos have any rest mass, Lederman looks at one of the neutrinos, i.e., the electron neutrino, “the gardenvariety, first generation neutrino — since it has the lowest mass. (Unless, of course, all neutrino masses are zero).“32 The electron neutrino, Lederman points out, has no electric charge, no strong force, no electromagnetic force, no size (no spatial extent, zero radius), and it may not have a mass. “Nothing has so few properties … as the neutrino. Its presence is less than a whisper.“33 But the neutrino, continues Lederman, does have

“a sort of location — a trajectory, always heading in one direction with a velocity close (or equal) to that of light [depending on whether or not 32 Lederman, The God Particle, p. 343.

33 Lederman, op. cit. , p. 344.

it has a rest mass].”34 It has spin, too; and this spin is always lefthanded.35 “This handedness [i.e., chirality] is one of the few properties the poor little fellow has.“36

The word “chirality,” or handedness, derives from the Greek word, chiros, which means hand. “The neutrino is said to have left handedness or [left] chirality, while the antineutrino has a right handedness [or right chirality].“37 The neutrino, lastly, has the weak force.38

A neutrino, some philosophers might want to say, is as close to prime matter as one can get; and if not that, very close indeed. That “whisper” of a particle, as Lederman fondly calls it, with almost no properties to its name, quite naturally brings to mind Aquinas’ comment (following Aristotle) that prime matter of itself, considered as such, is neither a substance, nor a quantity, nor a quality, nor anything else which is found in any of the ten categories:

[Dicit Aristoteles] materiam esse “quae secundum se,” idest secundum sui essentiam considerata, nullatenus est “neque quid,” idest substantia, “neque qualitas, neque aliquid aliorum generum, quibus ens dividitur, vel deteminatur.” (In VII Metaph., lect. 2, n. 1285).

[Aristotle says that] matter is that “which according to itself,” i.e., considered in its essence, is in no way a “thing with a what [or essence],” i.e., a substance, “nor is it a quality, or anything else of the other genera by which being is divided, or determined.”

Prime matter, the ultimate matter, the ultimate subject, the matter prior to which there is no matter — this matter is such in itself that it is not only absolutely matterless, but absolutely formless as well; such in itself that

34 Lederman, ibid.

35 Lederman, op. cit. , p. 345.

36 Lederman, ibid.

37 Ne’eman, Yuval and Kirsh, Yoram, The Particle Hunters (second edition), Cambridge, England: Cambridge University Press, 1996; p. 175.

38 Lederman, The God Particle, p. 345.

no forms at all are intrinsic ingredients of its nature, neither substantial forms nor accidental forms. It is such by its nature that it can acquire all these forms (in a certain order, of course, beginning with substantial forms, moving on to accidental forms); it is pure potentiality for all these forms. Of itself, it is absolutely without any properties at all.

The Rishon

The rishon model proposed by Haim Harari (which is a model attempting to go beyond the Standard Model, in which quarks and leptons are taken to be really elementary) has it that “both quarks and leptons [have an inner structure, i.e., that they] are constructed of … two types of ‘ultimate’ particles which Harari called rishons. ( Rishon in Hebrew means first or primary.) The two rishons are designated T and V for Tohu and Vohu. (These mean ‘formless’ and ‘void’ [like prime matter, one wants to note] in Hebrew. This is the description of the universe in its initial state, according to the first chapter of Genesis.)“39 The only property which the rishons seem to have is electric charge; at any rate, this is the only property which Ne’eman and Kirsh mention in their brief account of the rishon model.40 The T rishon has an electric charge of +1/3, and the V rishon is neutral. But there are also antirishons, the antiT rishon with a charge of 1/3, and the antiV rishon with a charge of 0.

Quarks and leptons come to be out of certain combinations of T and V and antiT and antiV.41

39 Ne’eman and Kirsh, The Particle Hunters, pp. 276–277.

40 Ne’eman and Kirsh, ibid.

41 “In Harari’s model any three rishons and any three antirishons may be combined together, but rishons and antirishons do not intermingle. This rule allows 8 combinations which correspond to the 8 quarks and leptons of the first generation and their antiparticles.” (Ne’eman and Kirsh, op. cit., p. 277). Three T rishons combine to generate a positron, and three antiT rishons combine to form an electron. Three V rishons constitute the neutrino, and three antiV rishons the antineutrino. Other allowed combinations yield fractionally charged quarks, e.g., two T’s and one V make up the uquark, one antiT and two antiV’s make up the dquark. (Ne’eman and Kirsh, ibid. ) Page 287

So far, however, although Harari’s model accounts nicely for certain properties of quarks and leptons, it has failed to account for all of their properties; and a good model, of course, ought to account for all of them. Nonetheless, it is interesting to notice that as particle physics makes its way toward particles which are hoped to be the truly elementary particles, i.e., such that there are no prior particles out of which they themselves are structured, the particles have fewer and fewer properties, they are seen to be more and more like prime matter — i.e., like matter which is both matterless and formless, “formless” meaning without properties. And this brings to mind what Aquinas points out in a context in which he is grading forms from the highest to the lowest. Just as there are forms, he notes, above the human soul, so too there are forms below it. And just as forms above it have more actuality than the human soul, and are thus further removed from the potentiality of matter, so too the forms below it have more potentiality than the human soul, and thus come closer and closer to the potentiality of matter. The grading here is from the sensitive, through the vegetative and the nonliving mixed bodies, down to the forms of the elements, whose operations or activities are simply those which are required for preparing matter for its tranformations from element to other element, and for the eduction of the forms of mixed bodies, i.e., of things composd out of the elements.

Aquinas writes:

… post istam formam, quae est anima [humana], inveniuntur aliae formae plus de potentia habentes et magis propinquae materiae, intantum quod esse earum sine materia non est.

In quibus etiam invenitur ordo et gradus usque ad primas formas elementorum, quae sunt propinquissimae materiae; unde nec aliquam operationem habent, nisi secundum exigentiam qualitatum activarum et passivarum, et aliorum quibus materia ad formam disponitur. ( De Ente et Essentia, cap. 5, n. 87).

… posterior to this form which is the [human] soul are found other forms which have more potency, and which are still closer to matter, so close that they do not exist without matter. Among these forms, too, is found an order and a grading, down to the first forms, the forms of the elements, which are the closest to Page 288

matter, so close indeed that they have no activities other than those which arise out of their active and passive qualities, and others, by which matter is made ready, or disposed, for form.

6—

Eddington’s Two Tables

I have settled down to the task of writing these lectures and have drawn up my chairs to my two tables. Two tables! Yes; there are duplicates of every object about me — two tables, two chairs, two pens …

One of them [i.e., of my two tables] has been familiar to me from earliest years. It is a commonplace object of that environment which I call the world. How shall I describe it? It has extension; it is comparatively permanent; it is colored; above all it is substantial. By substantial I do not merely mean that it does not collapse when I lean up on it; I mean that it is constituted of “substance,” and by that word I am trying to convey to you some conception of its intrinsic nature. It is a thing; not like space, which is a mere negation;42 nor like time, which is — Heaven knows what! But that will not help you to my meaning because it is the distinctive characteristic of a “thing” to have this substantiality, and I do not think substantiality can be described better than by saying that it is the kind of nature exemplified43 by an ordinary table …

Table no. 2 is my scientific table. It is a more recent acquaintance and I do not feel so familiar with it. It does not belong to the world previously mentioned — that world which spontaneously appears around me when I open my eyes, though how much of it is objective and how much subjective I do not 42 Space is not a mere negation. Democritus’ understanding of space (the void) as a real, threedimensional, empty, penetrable receptacle, in which things or substances (the atoms) can move about, is more plausible. On Democritus’ view, to call space a negation would be to point only to its intrinsic emptiness.

43 When a description, or definition, of what a thing is is not forthcoming (for whatever reason), it is always helpful, in a way even necessary, to turn to examples.

here consider. It is part of a world which in more devious ways has forced itself on my attention. My scientific table is mostly emptiness. Sparsely scattered in that emptiness are numerous electric charges rushing about with great speed; but their combined bulk amounts to less than a billionth of the bulk of the table itself. Notwithstanding its strange construction it turns out to be an entirely efficient table. It supports my writing paper as satisfactorily as table no. 1; for when I lay the paper on it the little electric particles with their headlong speed keep on hitting the underside, so that the paper is maintained in shuttlecock fashion at a nearly steady level. If I lean upon this table I shall not go through;

or, to be strictly accurate, the chance of my scientific elbow going through my scientific table is so excessively small that it can be neglected in practical life …

There is nothing substantial about my second table. It is nearly all empty space — space pervaded, it is true, by fields of force, but these are assigned to the category of

“influences,” not of “things.” Even in the minute part which is not empty we must not transfer the old notion of substance … … our scientific information is summed up in measures … [of] an external world; but the attributes of this world, except insofar as they are reflected in the measures, are outside scientific scrutiny …44

The commonplace table can be described, notes Eddington, as having extension, as being comparatively permanent, as being colored, etc., but above all, as being substantial. But he experiences some difficulty in explaining what he means by the word “substantial.” He means, he says, not only that the table does not collapse when he leans on it, but that it is a thing, as opposed to space which, he observes, is a kind of nothing, or nothing, i.e., a “mere negation,” as he puts it. Nor is the table like time, which is — and here he falters, not knowing what to say about time. He means, perhaps, that time is not something permanent (he had said that the table is comparatively permanent), i.e., time is moving from the past, into the present, then into the future; or the other way around, the future of time slips somehow into the

44 Eddington, Sir Arthur S., The Nature of the Physical World (The Gifford Lectures, 1927), Cambridge, England: Cambridge University Press, 1929; Introduction, pp. ix–xi.

present, which in turn slips somehow into the past. Perhaps, also, that the table is there altogether, with all its parts, all at once; whereas time is not.

The scientific table, by way of contrast, observes Eddington, is mostly emptiness. And throughout this emptiness there are numerous, but sparsely scattered, electric charges, rushing about with incredibly great speed. This table supports his writing paper as satisfactorily as the commonplace table, for the little electric charges with their great speed keep hitting the bottom side of the paper, and by their shuttlecock action keep the paper at a relatively steady level. When he leans his scientific elbow on his scientific table, there is hardly a chance that it will go through. For ordinary purposes, both tables seem to be on a par. But there is nothing substantial about the scientific table. It is not a thing. It is mostly a nothing, mostly a negation, mostly empty space; but an “empty” space which is also “full” — full of force fields. It is empty in one way, full in another. These fields, like the scientific table, however, are not things either; they are influences. Better still, he notes, they are just numbers resulting from measurements. Whereas the commonplace table is substantial, i.e., solid or full, and impenetrable, “… it being the intrinsic nature of substance to occupy space to the exclusion of other substances … ;” the scientific table is not, except perhaps, but only questionably, in the thinly scattered tiny specks which are its intrinsic electric particles. Whereas the commonplace table is a substance throughout, the scientific table is a substance only here and there, if at all.

How, now, are these two tables connected? Or, more generally, how are the commonplace and the scientific worlds connected? They may well be “one and the same world,” observes Eddington, though differently described, differently interpreted.45 “It is true,” writes Eddington, “that the whole scientific inquiry starts from the familiar world and in the end it must return to the familiar world; but the part of the journey over which the physicist has 45 Eddington, ibid., p. xii.

charge is in foreign territory.“46 Foreign territory? What does Eddington mean by “foreign territory”? As though to answer this question, Eddington adds that “there is a familiar table parallel to the scientific table, but there is no familiar electron … parallel to the scientific electron … ” And there is no desire or attempt to find a familiar counterpart to the scientific electron, which could be used to explain47 that scientific electron. For it is the scientific which explains the commonplace, and not the other way around. The electron — along with force fields, and other scientific measures — is the unfamiliar foreigner in the land of the scientific table which is used to explain substantiality — and other familiar properties — in the land of the commonplace table. Scientific inquiry “starts from the familiar world,” moves into a foreign world in quest of an explanation, then returns ”to the familiar world” to explain that world.

But what sort of explanation is this? It is an explanation of a most interesting sort, indeed. Explanations, one must note, identify causes. But these causes — electrons, force fields, quanta, and the like — are only a different way of describing “one and the same world,” one and same table. The commonplace world, with its tables and chairs and papers and pens, is the “world which spontaneously appears around me when I open my eyes.” 48 It is the world given to me in my ordinary sensory perceptions. The scientific world is that same world, but at a different level. It is not given to me in my ordinary sense perceptions; it does not appear around me spontaneously “when I open my eyes.” It is, in a way, invented by me; but also, in a way, discovered by me. Today’s physics assures me that “my scientific table is the only one which is really there …;“49 and that it explains my commonplace table. Its electrons, force fields, etc., explain why it is that my commonplace table is said by me, on the basis of my open eyes and ears and

46 Eddington, ibid. , p. xiii.

47 “We do not even desire to manufacture a familiar counterpart to these things [i.e., electrons, quanta, potentials, Hamiltonian functions, etc.] or, as we should commonly say, to

“explain” the electron.” (Eddington, ibid. , p. xiii).

48 Eddington, ibid. , p. x.

49 Eddington, ibid. , p. xii.

the touch of my fingers, to be a thing (a substance), to have extension, to be impenetrable, to be comparatively permanent, to be colored, etc. The unfamiliar (the uncommon, the unperceived by ordinary means) is that deep within the familiar (the common, the perceived by ordinary means) which explains why the familiar is the sort of thing that it is. Although it is the unfamiliar which causes the familiar, the unfamiliar is at the same time the same as the familiar, though only in a way, i.e., at a different level. This table is at once commonplace and scientific; has at once scientific features and commonplace features; and the scientifc features cause, and thereby explain, the commonplace ones. The table is at once, and most interestingly, this collection of effects (commonplace) produced by that collection of causes (scientific), and that collection of causes (scientific) producing this collection of effects (commonplace).

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Can one say, now — moving beyond Eddington (1928) to the present day (1997) — that this commonplace table is this extended, somewhat permanent, colored, etc., thing (or substance) — as caused by that scientific collection of uquarks, dquarks, neutrons and electrons which reside deep within itself? And that it (i.e., this commonplace table) is also that scientific collection of uquarks, dquarks, neutrons and electrons — but as causing, from deep within itself, the extended, somewhat permanent, colored, etc., thing (or substance) which it is? Or, perhaps better, that this commonplace table is nothing but, i.e., identical with, these scientific uquarks, dquarks, neutrons and electrons arranged and interacting in a given way — though differently described, i.e., either as a cause (the scientific) producing an effect or as an effect (the commonplace) being produced by a cause.

Can one say, further — moving back into the past of the medievals, in particular to that of Aquinas — that the commonplace table (as a mixed body) Page 293

is just what it is because of the special sort of material and agent causality being exercised by its ingredient mixables?, i.e., by its component quarks, protons, neutrons, electrons, atoms, molecules; which are not only material causes of a special sort, i.e., capable of agent causality (because of certain surviving active potentialities or powers, as different from prime matter which is a purely passive or receptive potentiality), but also agent causes of a special sort, i.e., conjoined intrumental agent causes (see above, section 2, A quark, like any element, is an agent cause of a special sort, besides being a material cause of a special sort, pp. 250–252).

Can one say, further still — again moving back to Aquinas — that to speak of the commonplace characteristics of things as caused by the scientific components within them is to speak in some way — though without intending it and without being very clear or explicit or complete — about why substantial forms other than the human soul are educed from the potentiality of matter, rather than being created, or generated, or brought out of some sort of hidden actuality? These substantial forms (i.e., all forms with the exception of the human soul) can be so educed, i.e., brought into existence without need of a direct and special creative act of God (since this eduction is within the causal capacities, both receptive and agent, of things in the physical world) by a conjunction of the following: prime matter, properly disposed by an appropriate substantial form and by an appropriate mix of scientific components, like quarks, protons, neutrons, electrons, atoms, molecules, along with physical agent causes of certain appropriate sorts. The same scientific components which actively cause, and passively retain (within the mixed bodies which arise out of their conjunction), the commonplace features of our ordinary senseperceivable world, provide the complex of disposing receptive ingredients required for the eduction of their educible physical forms. Their role, thus, in such eductions, is that of a set of virtual, dispositional, retrievable, and instrumentally agent material ingredients (see above, section 11, The elements and the eduction of substantial forms from the potency of matter, pp. 228–241).

7—

Searle On MicroProperties and MacroProperties

What Sir Arthur Eddington said (in 1928) in terms of his two tables has been said more recently (1984), and perhaps more clearly and instructively, by John R.

Searle, in terms of microproperties and macroproperties:

A common distinction in physics [today] is between micro and macroproperties of systems — the small and large scales. Consider, for example, the desk at which I am now sitting, or the glass of water in front of me. Each object is composed of microparticles. The microparticles have features at the level of molecules and atoms as well as the deeper level of subatomic particles. But each object also has certain properties such as the solidity of the table, the liquidity of the water, and the transparency of the glass, which are surface or global features of the physical systems. Many such features or global properties can be causally explained by the behaviour of elements at the microlevel. For example, the solidity of the table in front of me is explained by the lattice structure occupied by the molecules of which the table is composed. Similarly, the liquidity of the water is explained by the nature of the interactions between the H O molecules. Those macrofeatures are causally explained by the behaviour50 of elements at the microlevel.

… we have no difficulty at all in supposing that the surface features [like solidity, liquidity, and transparency] are caused by 50 Searle speaks of properties, features, structures, interactions, and behaviours, as though they were the same. But, they seem to be different, and Searle does not point out the differences. “Feature” and “property” seem to be words with a sort of general meaning, so that a feature (or property) can be either a structure, or an interaction, or a behavior.

Does it make sense to call a lattice structure a behavior?

the behaviour of elements at the microlevel, and at the same time we accept that the surface phenomena just are features of the very systems in question. I think the clearest way of stating this point is to say that the surface feature is both caused by the behaviour of microelements, and at the same time is realised in the system that is made up of the microelements. There is a cause and effect relationship, but at the same time the surface features are just higher level features of the very system whose behaviour at the microlevel causes those features.

… someone might say that liquidity, solidity, and so on are identical with features of the microstructure. So, for example, we might just define solidity as the lattice structure of the molecular arrangement, just as heat is often identified with the mean kinetic energy of molecule movements. This point seems to me correct … It is a characteristic of the progress of science that an expression that is originally defined in terms of surface features, features accessible to the senses, is subsequently defined in terms of the microstructure that causes the surface features. Thus, to take the example of solidity, the table in front of me is solid in the ordinary sense that it is rigid, it resists pressure, it supports books, it is not easily penetrable by most other objects such as other tables, and so on. Such is the commonsense notion of solidity. And in a scientific vein one can define solidity as whatever microstructure causes these gross observable features. So one can then say either that solidity just is the lattice structure of the system of molecules and that solidity so defined causes, for example, resistance to touch and pressure. Or one can say that solidity consists of such high level features as rigidity and resistance to touch and pressure and that it is caused by the behaviour of elements at the microlevel.51

The desk at which I am now sitting, points out Searle, the drinking glass in front of me, and the water within it, all three, are objects composed of microparticles. And these microparticles have features or properties at various levels, e.g., at the level of the molecule, at the level of the atom, at 51 Searle, John R., Minds, Brains and Science, Cambridge, Mass.: Harvard University Press, 1984; pp. 20–22.

the level of the subatomic. But physical objects, such as my desk, also have certain other properties or features, like solidity (the desk) or liquidity (the water) or transparency (the drinking glass, and the water). These features are surface features, global features, i.e, “features accessible to the senses,” “gross observable features.” Now many of these surface features, continues Searle, can be causally explained by certain molecular, or atomic, or subatomic features, in brief, by certain microfeatures, of the particles which make up the very objects which have these surface features. The commonplace (Eddington) or macro (Searle) can be causally explained by the scientifc (Eddington) or micro (Searle). The solidity of the table, exemplifies Searle — that is, the fact “that it is rigid, it resists pressure, it supports books, it is not easily penetrable by most other objects such as other tables, and so on” — can be ”explained by the lattice structure occupied by the molecules” of which the table is composed. The liquidity of the water can be explained by the sort of interaction which takes place among H O molecules, i.e., they move freely 2

among themselves without any tendency to separate. The transparency of the drinking glass (and of the water) can be explained (my guess) by the fact that the quarks and leptons which compose it are so arranged that they permit light to pass between them (and so, through the glass), thereby making the glass seethroughable by our eyes.

Having noted that the macro can be explained by the micro, Searle points out the interesting aspect of this sort of explanation. The macro is both caused by the micro and realized in the object that is made up of the micro. “I think,” emphasizes Searle, “the clearest way of stating this point is to say that the surface feature is both caused by the behaviour of the microelements, and at the same time is realised in the system that is made up of the microelements. There is a cause and effect relationship, but at the same time the surface features are just higher level features of the very system whose behaviour at the microlevel causes those features.”

Indeed, continues Searle, one can even say that solidity, liquidity, transparency, etc., are identical with features of the microstructure. Thus, for example, solidity is nothing but, is identical with, the lattice structure of the arrangement of the

molecules; liquidity is nothing but, is identical with, the free movement of molecules among themselves without any tendency to separate. It can be said, thus, either that solidity is nothing but the lattice structure of a collection of molecules (micro), and that, so defined, it is the cause of rigidity, resistance to pressure, impenetrability, etc. (macro); or that solidity consists of rigidity, resistance, impenetrability, etc. (macro), and that, so defined, it is the effect of the lattice structure (micro). Macrofeatures are both caused by, and retained in (realized in) one and the same object — caused by certain features of microparticles, and at the same time retained in the object that is composed of these microparticles. In the language of Aquinas, the object (desk, drinking glass, water) is just what it is because of the special twofold causality being exercised by the mixables which enter into its makeup, i.e., by its component microparticles (quarks, protons, neutrons, electrons, atoms, molecules), which are not only 1) material causes of a special sort, i.e., capable of agent causality, but also 2) agent causes of as special sort, i.e., conjoined instrumental agent causes. As conjoined instrumental agents, the microparticles cause the macrofeatures, and as material causes, they retain these macrofeatures. Macrofeatures are both caused by, and realized in, this physical object, just because this physical object is the sort of mixed body which it is — just because it is the intimately conjoined (by mixing, i.e., mixtio) collection of microparticles which it is.

8—

Nahmanides’ Thirteenth Century Theological Big Bang

Nahmanides’ account of the first seconds of the universe reads like this: At the briefest instant following creation all the matter of the universe was concentrated in a very small place, no larger than a grain of mustard.52 The matter at this time was

52 From the words “a very small place,” and “no larger than,” it is clear that matter, at this briefest instant following creation, was already corporeal, i.e., already had dimensions.

so thin, so intangible, that it did not have real substance.53 It did have, however, a potential to gain substance and form and to become tangible matter. From the initial concentration of this intangible substance in its minute location, the substance expanded, expanding the universe as it did so. As the expansion progressed, a change in the substance occurred. This initially thin noncorporeal54 substance took on the tangible aspects of matter as we know it. From this initial act of creation, from this ethereally thin pseudosubstance, everything that has existed, or will ever exist, was, is, and will be formed. [Nahmanides, Commentary on the Torah, Genesis, 1, 1].

Nahmanides’ reference to a grain of mustard is the traditional way of saying, “in the language of man,“55 the tiniest imaginable speck of space. Nahmanides taught that at the beginning, all that is on and within the Earth and all the heavens, in fact all the universe, was somehow packed, compressed, squeezed into this speck of space, the size of a mustard grain. (Schroeder, Gerald L., Genesis and the Big Bang, New York: Bantam Books, 1990; pp. 64–65).

Nahmanides, or Moses ben Nahman (1194–1270), was a contemporary of St. Thomas Aquinas (1225–1274); but neither, it seems, knew of the work of the other;56

quite unlike Maimonides, or Moses ben Maimon (1135–1204),

53 “To have real substance” seems to mean, here, to be tangible, i.e., to be something one can get a hold of — solid, rigid, resisting pressure, impenetrable by other bodies, capable of supporting other bodies.

54 “Noncorporeal” here cannot mean without dimensions. It means ethereally thin, as Nahmanides himself explicitly indicates just two lines below. For ethereally thin, can we say: firelike, or airlike, mistlike, foglike, smokelike, vaporlike, steamlike, in that it is easily partible, easily penetrable?

55 “In the language of man,” i.e., ordinary, everyday language, but as given a certain precision for theological purposes — as opposed to “in scientific terms.” See Schroeder, Gerald L., Genesis and the Big Bang, New York: Bantam Books, 1990, p. 57, where he writes: “Old Testament theology talks in the language of man, while current cosmology makes its statements in scientific terms. ”

56 Is there any explanation for this? Is it just that there was not enough time for their works to be copied, and then to be brought to one another — by foot or by donkey or by horse, or by whatever other, clearly slow, means of transport available at that time? Nahmanides was in Spain prior to 1263, when he engaged in Barcelona (his opponent was (footnote continued on next page)

whose work Aquinas knew very well, and admired very much.

What is to be made of Nahmanides’ account of the state of the universe just the briefest instant after its creation by God? In the beginning, the matter of the physical world was called into being out of nothingness by God’s creative act. And at the briefest instant after creation, points out Nahmanides, all this matter was somehow concentrated, packed, squeezed, compressed into a “very small place, no larger than a grain of mustard.” At this time, matter was a very thin, intangible, ethereal (again we ask, can one say, firelike, airlike, mistlike, foglike, vaporlike, smokelike, steamlike?) pseudosubstance. It had no real substance (tangibility); but it did have a potential to take on substance and form (differentiation), to become a tangible and differentiated matter. And then, just after the briefest instant after creation, continues Nahmanides, this matter began to expand (under God’s creative direction, no doubt), causing that initial very small place to begin to expand as well, so as to become the space of the universe as we know it, in all its immensity, a universe in which, “as the expansion progressed,” that “initially thin noncorporeal substance took on the tangible aspects of matter.”

In pursuing the question, What is to be made of Nahmanides’ account?, it will be helpful to consider what Schroeder has to say about it (if only because it is from Schroeder that I first heard of Nahmanides); then to consider what Aquinas would have (might have) said about it, if he had had the good fortune of having heard of Nahmanides, and of having known his work, The Commentary on the Torah.

(footnote continued from previous page)

the apostate Jew, Pablo Christiani) in perhaps the most famous of all the medieval JewishChristian debates. This debate was held in the presence of the Spanish king, James of Aragon, and Nahmanides was assured by the king that he could speak without fear of censorship or retribution. Nonetheless, in spite of all of King James’ assurances and good intentions, Nahmanides decided that it would be prudent for him to leave Spain. When the debates were over, Nahmanides emigrated to Palestine. (SeeTelushkin, Rabbi Joseph, Jewish Literacy, New York: William Morrow and Company, Inc., 1991; pp. 187–188). From Spain to France or Germany or Italy, and the other way around, before 1263; and from Palestine after that — too far away, and too little time, during the lifetime of each of them?

But first, a point to clear up about the meaning of the word “creation.” It is used both scientifically, notes Schroeder, and theologically: scientifically, to designate the event known today as the Big Bang, and theologically, to designate the event described in Genesis 1, 1: In the beginning, God created heaven and earth. But these two events, one must point out, are not one and the same event; and Schroeder does not make this clear. Indeed, what he writes on pp. 56–57 — while considering the question he had just raised, namely, What was happening before the beginning, i.e., before creation?, — seems to take these two creation events to be one and the same thing. He talks about events “that preceded the beginning, that is the creation” of Genesis 1, 1; and then refers to these same events as “events prior to the Big Bang,” seeming thereby to identify the creation of Genesis with creation by the Big Bang. Schroeder is concerned here to point out that events before the creation event, if there are any,57 are not accessible to human investigation; unlike events which occur after the creation event, which are.

Before creation in the theological sense, one must hasten to point out, there was nothing in existence but God; thus no physical matter. And thus no possibility of any sort of physical event at all. But before creation in the scientific sense, i.e., before the Big Bang, something did exist, i.e., the preBig Bang particle, which contained the original materials out of which the whole physical universe was to expand. Or, is that a misunderstanding of what science says? Is it, rather, the view of science that the original particle and the Big Bang came on the scene together, so that the original particle did not exist before the explosive instant of the Big Bang? In any case, whereas creation in the theological sense is creatio ex nihilo materiae, 58 and by the 57 Schroeder wonders about this explicitly, i.e., about whether there were any precreation events, as he asks, “But what was happening before the beginning? Can we study, either theologically or scientifically, what there was before the beginning, if anything?” (Schroeder, Gerald L., Genesis and the Big Bang, p. 56). Notice the last two words. i.e., if anything.

58 Although Schroeder does not, on pp. 56–57, make it clear that the creation event described in Genesis 1,1, is not the same thing as the creation event we designate today as (footnote continued on next page)

infinite power of God; creation in the scientific sense is creatio ex particula materiae, and the power of God is irrelevant. What then, one wants to ask, accounts for the existence of that particle of matter? Is one to say that it always existed, since something must always have existed because something exists right now (and it might as well be that particle which always existed, as anything else, e.g., God, some might want to say)?

9—

Schroeder On Nahmanides’ Account of the Beginning and Expansion of the Universe

Having pointed out that both science and theology have come to the same conclusion (though from different directions, i.e., for different reasons)59 about events before the creation event, i.e., about prebeginning

(footnote continued from previous page)

the Big Bang, he does recognize that the former is a creation out of absolute nothingness. He writes: “The creation of the heavens and the Earth from absolute nothing is at the root of biblical faith … The Hebrew word used for creation, barah, is the only word in the Hebrew language that means the creation of something from nothing. Biblically it is applicable only to the actions of God. It is the second word of the Bible.” (Schroeder, op. cit. , p. 62).

59 As regards the reason of theological tradition, Schroeder writes: “Because the Bible begins with a letter [the Hebrew letter beth] that is bounded on all sides except the forward, so the events that occur after ‘the beginning’ are those that are accessible to human investigation. Similarly, those that preceded the beginning, that is the creation, are not open to investigation.” Schroeder, op. cit. , p. 57) — As regards the reason of science, Schroeder writes: “This melee of random highenergy collisions [among particles of matter, i.e., quarks and electrons, and the packets of energy we call photons, behaving according to Einstein’s E=mc2, at the earliest instant after the Big Bang about which scientists can theorize, i.e., about 1043 seconds after the start] precluded any possibility of order in the energy of particles present, order that would have contained information related to what preceded that instant. Without order, information cannot be transferred across a sequence of time, a temporal interface, separating the ‘before’ from the ‘after’.” (Schroeder, ibid. , pp. 57–58). “The matter and space of this moment [i.e., of the earliest instant about which we can theorize] were so tightly packed, so dense, that the violent collisions among the particles of matter and those packets of energy we refer to as photons were continually shattering each other into and out of existence. Energy and matter were in a fluid interchange, just as Einstein’s most basic statement of relativity implies: E = mc2 and, equally true, mc2 = E. At this early time, the E, that is the energy, of the photons was converting into the m, the mass, of mc2, and equally rapidly, this very m of the mc2 was reconverting to E.” (Schroeder, ibid. , p. 57).

(precreation, preBig Bang) events — namely, the conclusion that these events are not accessible, not open, to human invesitigation; Schroeder moves on to point out what science and theology have to say about events after the creation event; in particular to point out that the “parallel between the opinion of presentday cosmological theory and the biblical tradition that predates it by over a thousand years is striking, almost unnerving … ,“60 — the tradition that began with Nahmanides in the thirteenth century.

According to Nahmanides, the creation of the matter of the physical universe, points out Schroeder, brought with it both time and space. Prior to the creation of the physical universe, there was neither time nor space. And this makes sense, one wants to note, for time is the measure of the various motions or changes of material things; and space is the real, penetrable, threedimensional emptiness in which material things exist, and in which their various motions or changes take place. No matter, therefore no motion or change, therefore no time. No matter, therefore no space, i.e., no real penetrable emptiness which, though different from matter, is that precisely in which matter exists and changes. Both science and the theology of the biblical tradition agree on this.

But, according to science, the matter present at the very beginning “is pressed into a space of zero size61 and infinite density,” whereas according to biblical tradition, matter at the beginning was contained “in a tiny but finite speck of space, about the size of a grain of mustard.“62 No size (science), as opposed to some size, though very small (biblical tradition).

60 Schroeder, ibid. , p. 67.

61 Zero size is very difficult to accept, unless it is taken to refer to the existence which matter, and the space which is its receptacle, had in God before God’s creative act; for a dimensionless matter and a dimensionless space in the physical world seems an impossibility. More likely, talk of zero size at the very beginning is required by the mathematics which physicists use in their attempt to describe the condition of our universe at that very early time.

62 Schroeder, ibid. , p. 63.

According to Nahmanides — whose insight depends on three things, as Schroeder sees it, namely 1) on what has been revealed in the Bible, 2) on a study of the natural sciences, and 3) on having received what Nahmanides calls a “hidden wisdom,” which appears to be some sort of “grace” or free gift from God as one studies the Scriptures63 — this beginning matter was very tiny, as well as very thin (i.e., intangible, without substance, ethereal). It had nonetheless, a potential to expand, and at the same time to take on, somehow, substance (tangibility) and form (differentiation), and to give rise to everything which was, is, and ever will be.64 God created (barah) this tiny speck of thin matter, this tiny speck of superrarefied matter, out of nothing (creatio ex nihilo materiae); and gave it this explosive, expanding, condensing or substanceacquiring, and differentiating potential (or nature).

What today’s cosmologists say about the physical universe, emphasizes Schroeder, is very much like what Nahmanides had said — there is a beginning matter which is very small and very rarefied and undifferentiated, followed by an expansion which condenses this matter into multiple and differentiated forms. But unlike Nahmanides, today’s cosmologists add many details, mathematically expressed and with incredible precision, which Nahmanides, in the thirteenth century (no telescopes and no particle accelerators), quite understandably could not have done. Schroeder presents some of these details in what he calls cosmology’s

“description … for that same early time in our evolution,” i.e., the time of Nahmanides’ grain of mustard at the briefest instant following creation: 63 Schroeder, ibid. , p. 64. This free gift from God might be a special sort of crowning supernatural power of insight, added to the natural power of insight which theologians develop because of a long familiarity with their field. Long familiarity with a given field — whether theology or philosophy or science, or whatever — produces in the faithful and diligent investigator, as is well known, a natural power of insight of a very special and extraordinary sort.

64 Schroeder, ibid. , p. 65.

The present universe, according to current cosmological understanding, is the result of a Big Bang, a massive expansion from a single point … … at the briefest instant following the beginning, at about 1043 seconds after the start, … the universe was … the size of a speck of dust …

At this early time, all matter was concentrated into one miniscule core location. The temperature was 10320 K (100 million million million million million degrees Kelvin) …

… Physics and mathematics, as we know them today, cannot deal with times earlier than 1043 seconds after the beginning. Prior to that time, the temperatures and densities of matter exceeded those that can be described by the laws of nature as we now understand them …

As the study of events following the Big Bang is extended mathematically to earlier times, the size of the universe shrinks toward zero and, inversely, the temperature and density increase toward infinity. The actual instant of the beginning envisions, for physicists, a moment when an infinitely small65 point of space was packed with matter squeezed to an infinitely high density.66 This conditon of infinities is referred to as a singularity, and singularities cannot be treated by conventional mathematics …

In very early times, matter was not matter as we know it. The high pressure and temperature in this core had reduced all matter to its form as pure energy.67 The concept of matter, even of the tiny theoretical fundamental particles called quarks, has no meaning for the temperature, pressure, and spacial dimensions that are speculated to have existed at this very early time. There was exquisitely hot energy and very little else. Within the initial core location, an explosion or inflation occurred that forced the energymatter out in all directions. The

65 Does “infinitely small” mean zero size?

66 Does “infinitely high density” imply zero size?

67 Does “pure energy” imply zero size? Did the high pressure and high temperature in this core have the effect of squeezing all the dimensionality out of matter — out of all the fundamental particles, like quarks and leptons?

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