Section 4
cause of this inflation is not clear.68 Some scientists posit that mutual repulsion among all that was present occurred, something akin to a force of antigravity.69 The term inflation is used deliberately. It implies that the forces70 that pushed back the boundaries of space to the size of a grapefuit71 came from within. There was no without. There was and is the universe and the space it occupies. That was and is the totality of all physical existence.
Concurrent with the expansion there was a lowering of pressure and temperature. At these more moderate, expanded conditions (a mere billion billion billion degrees Kelvin), energy could now condense into the tiniest of particles, the theoretical quarks and the known electrons. This took place in accord with Einstein’s law, E = mc2, which states that energy and mass are actually different states of a single energymatter continuum, just as water, steam, and ice are all composed of a single entity, H O. Energy is matter in its 2
intangible form; matter is energy in its tangible form.
As this expansion progressed out, away from the core, pressures and temperatures fell. Conditions became less harsh. The transition of energy to the more substantive forms of tangible matter continued. The material universe as we understand it came into being. The entire process is referred to as the Big Bang. Thus far, the cosmological description of the early universe.72 (Schroeder, Genesis and the Big Bang, pp. 65–67).
68 Not clear? Why not? Because this explosion or inflation cannot be caused except by God’s creative act? Is this intrinsically caused inflation, i.e., caused by forces from within the initial core, simultaneous with the exit of this core from within God, at His creative act?
69 Is antigravity even a possibility? Is it a force in the realm of antimatter? And does this imply that matter, as we know it, is derived from antimatter; and that antimatter is therefore more fundamental than matter?
70 Are these forces in some way connected with what Lederman calls the God Particle?
71 How many seconds old was the universe when the boundaries of space had expanded from the size of a grain of mustard to that of a grapefruit? How much older than 1043
seconds?
72 Does “early universe” here mean: from zero size to grapefruit size? And how long did it take the universe to become the size of a grapefruit?
Schroeder ends his reflections on Nahmanides’ theological Big Bang account by noting that ”revelation, at least as we have it today, did not provide details” (p. 68) for our understanding of the creation and development of our physical universe. Physics and cosmology provided these details. Nonetheless, revelation did provide, for its diligent and patient and prayerful students, the truth about creation and expansion, a truth accepted not on the basis of discovery and proof, but on the basis of faith —
“faith in the accuracy of revelation even when it precedes the advances of science that eventually come to confirm it.” (p. 68).
Study the Bible, counsels Nahmanides — diligently, patiently, prayerfully. Study the sciences, he continues — perseveringly, painstakingly, deeply. Have faith, he adds — humbly, sensitively, unswervingly. The Bible will give us truth about the physical world. The sciences will confirm this truth; and, we today might hasten to note, add a wealth of mathematically expressed details. Faith confirmed, and given detail, by the sciences. St. Augustine? Fides quaerens intellectum? Faith seeking understanding — understanding from the sciences, from mathematics, from philosophy, from all that the natural powers of the human mind can discover and prove.
Like revelation, one must acknowledge with Nahmanides (and with Aquinas), the human mind, too, is from God.
10—
What Aquinas Might Have Said About Nahmanides’ Account
What, now, might Aquinas have said about the universe of Nahmanides, a universe which, in all its present immensity and diversity, expanded out of the tiniest imaginable speck of space, no larger that a grain of mustard, into which, at the beginning, all of its matter had been somehow compressed? Would Aquinas have accepted such an account?
One might begin here by making two points: 1) that the creation event described in Genesis 1, 1 is, for Aquinas as it is for Nahmanides, a creation ex Page 307
nihilo materiae, a creation out of absolutely no matter, by the infinite power of God, and that alone; and 2) that, according to Aquinas, the four elements and the heavenly bodies were brought into existence on the first of the six days, and in the first of the three works, i.e., in the work of creation, and in an instant — as to their substance, of course, and in many ways far from fully formed; and that everything else that was produced by God during the first six days was produced by Him in the second and third of the three works, i.e., in the work of distinction and adornment, and in such a way that the production of these things was by means of certain sorts of changes out of prior materials, and so was produced, not in an instant, but over a period of time.
The implications of the first point, together with what Aquinas says explicitly about the second point (already described in some detail, above in sections 8–10, on pp. 192–227) make it quite clear that Aquinas would have accepted Nahmanides’ “expanding grain of mustard” account. Or, if that is too strong, that what Aquinas says, both implicitly and explicitly, about the creation, distinction, and adornment of the first six days is compatible with Nahmanides’ account, or at least not incompatible with it.
The first point: Creation as described in Genesis 1, 1 is creation out of absolutely no matter What does this sort of creation imply? It implies that in the beginning instant of the existence of the physical universe, just after the first now of time, just after it had been created by God — everything which came into existence must have been in some way all together, all together in the minutest possible particle of matter. The universe, in that first instant of time, must have been so small that it could not possibly have been any smaller. Indeed, it must have been even smaller than Nahmanides’
grain of mustard; unless, as Schroeder suggests, the expression “grain of mustard” be
taken to mean the tiniest imaginable speck, 73 and even so, not the tiniest imaginable to us, but the tiniest imaginable in itself, i.e., such in itself that it could not possibly have been any tinier.
To clarify the immediately preceding. — Within their cause, “before” they were brought into being (i.e., within God, and only God, since there was no preexisting matter), the things that came into existence in that first instant of time, i.e., the four elements and the heavenly bodies, must have been gathered together as though within a mathematical point, since God is a pure spirit, a thing without dimensions. There within God, these things took up no space at all; there was no space for them to take up. They were there, within God’s infinite power to call them into existence, but not as within some preexisting matter, nor therefore as with dimensions, nor therefore as taking up any space. There was then only God, nothing but God; no matter, no dimensions, no space, nothing at all outside of God as distinct from God, for God had not yet created. Nor was there within God any matter, or dimensions, or space, as part of His nature, for God is a pure spirit. As soon as God uttered His creating word, Fiant (Let them come to be), the infinite power of these words hurled these things, i.e., the four elements and the heavenly bodies, out from within Himself, hurled them out into their own existence, and in all directions, with an emerging motion which began to accelerate into a space which came to be with them, and which (space) began to expand in all directions with an accelerating speed which equalled the accelerating speed of their motion. But “before” this, these things had been within God, from forever, without motion and without dimensions. And so, when they emerged into their own existence, the motion with which they emerged was a motion which had to begin, and the dimensions which they took on had to begin to be taken on. Now, the acceleration of motion takes time; and taking on dimensions takes time, too. In the beginning instant of its existence, therefore, the material universe — a universe just emerging out of its prior dimensionless existence in God — must have been as small as it could
73 Schroeder, Genesis and the Big Bang, p. 65.
possibly have been, the tiniest possible in itself, as noted just above; and the motion by which it began to exit its prior motionless existence within God must have been as slow as it could possibly have been. In that beginning instant, these things must have been in some way all together in a particle of matter so small (and this particle in a space just as small) that it could not in principle have been any smaller (or any bigger); and the emerging motion of each of these things must have been so slow that, though it was on its way to acceleration, it could not in principle have been, in that first moment of time, any slower (or any faster). This was the moment of Nahmanides’ grain of mustard. But then, i.e., in the very next moment, and continuing in all succeeding moments right up to the present time, the ethereal matter in that tiny place “expanded,” as Nahmanides put it, “expanding the universe as it did so, … [and from it] everything that has existed, or will ever exist, was, is and will be formed.” (above, p. 298). Quite clearly, Aquinas and Nahmanides are quite in accord. This brings us to the second point.
The second point: The four elements and the heavenly bodies were created on the first day, out of absolutely no prior matter, and in an instant; all other physical things which came to be during the first six days, and after those days to the present, were produced, not in an instant, but over a period of time, and out of prior matter A brief recap of what Aquinas says explicitly about this second point (already seen above at some length, on pp. 192–227) will be a convenient and helpful way to proceed.
… it belongs to the work of creation to produce the substance of the elements, whereas it belongs to the work of distinction and of adornment to form certain things out of the already existing elements … (above, p. 207)
… three things were mentioned [in the Scriptures] in the work of creation, namely heaven and water and earth. And these Page 310
same three things were given some form during the three days of the work of distinction… … And similarly [these same three things were adorned] in [the three days of] the work of adornment … (above, p. 208)
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, notes Aquinas, 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 (i.e., as in their preexisting matter, and in their partial agent cause) 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, followed by the opus ornatus on days four through six.
… 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 … (above, p. 224) The four elements and the heavenly bodies, products of the opus creationis, were created by God on the first day out of absolute nothingness, and in an instant. But the things made by God as products of the opus distinctionis and the opus ornatus, were made by Him by means of certain sorts of changes out of already existing materials (basically the four elements), and so were produced over a period of time, namely that of the six days.
… 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] … (above, p. 225) 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 were there as actually existing, 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.
… 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 … (above, p. 220)
None of the things made by God after the seventh day is totally new, points out Aquinas. 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, whom He had made earlier out of the slime of the earth. 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
four elements during the work of the six days. Certain other things, continues Aquinas, preexisted in the works of the six days causally, i.e., in the power of their agent causes to produce them, as well as materially. For example, all the individuals which are being generated at the present time, were there in the first individuals of their species — there, not only as in their matter, but also as in the productive power of their agent causes. And if any new species came into existence since the seventh day, continues Aquinas (this reference to new species is quite interesting, and in a way surprising), 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, 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, if any came to be, and all new mixed bodies as well, came to be out of the original elements, inasmuch as they (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, which are required (in conjunction with the agent powers of the heavenly bodies) for the orderly, developmental, unfolding, evolving production of all other physical things, in the whole of the physical universe, out to the furthest reaches of space.
<><><><><><><><><><><><>
Thus — from what Aquinas says, both implicitly and explicitly, about the creation, distinction, and adornment of the first six days — it is quite clear that in the beginning instant of the existence of the physical universe, all bodily things were there in some way, and all together, in a particle of matter so small that it could not possibly have been any smaller. The first three, i.e., heaven and water and earth,74 were there in one way — i.e., they were there as actually existing substances, but far from fully formed; and the light of the sun was there, and of other heavenly bodies as well,75 coming to be later on during the work of the first day, but still to acquire, on a later day (i.e., on the fourth day), their special powers for producing particular effects. The firmament, too, was there, and the waters which came to be both above it and below it (coming to be as the work of the second day), but in another way — i.e., as in their agent and material causes. And in that same way, the sea too was there, and the dry land (emerging as the work of the third day); in that same way, the lightgiving bodies (or at least their special powers) which were to adorn heaven, were there76 (emerging as the work of the fourth day); in that same way, the birds and the fishes, which were to adorn the air and water, were there (emerging as the work of the fifth day); in that same way, the animals, and man’s body as well, which were to adorn the earth, were there (coming to be as the work of the sixth day). All these things were there — in the material and the agent causality of the four elements, in part; and in other part, in the agent causality of the heavenly bodies. But the human soul was not there in any way at all. Man’s soul came to be in man’s body on the sixth day, indeed, but by a direct and special creative act of God.
74 See above, pp. 208–209.
75 See above, p. 209, especially footnote 45; also p. 213, with special attention to footnote 49.
76 See above, pp. 211–212, for two views on the production of heavenly bodies other than the sun.
And so, as a final comment for this recap (begun above on p. 309). — Just after the instant of creation, according to Aquinas, the four elements (the aqua et terra of the first three)77 were there; and the heavens, too, with their lightemitting bodies (the caelum of the first three) were there — as actually existing substances, but far from being fully formed, far from being in full possession of all their distinctive powers for producing particular effects. They were beginning to emerge, beginning to be hurled out of, banged out of, their former motionless and dimensionless existence within God. And then in the very next instant, they (the first three) were taken up into a process of expanding out of that unimaginably small quasipoint of the first instant after creation into a threedimensional existence which was becoming unimaginably ever more vast; they were moving toward becoming more and more fully formed, and toward becoming more and more fully empowered to produce particular effects — throughout the three days of distinction and the three days of adornment, and beyond that into the present time. The heavenly bodies were taken up into a process of acquiring particular lightemitting powers, of moving away from one another, and of acquiring their various locations in relation to one another. And the planet Earth was taken up into a process of developing its oceans, and its continents, and the few primitive life forms out of which the multiple and complex life forms which are now in existence emerged and evolved.78 — Thus Aquinas. Penning
77 See above, pp. 208–209.
78 It ought to be noted that Darwin, at least in word if not in truth, takes pleasure, at the end of his Origin of Species, in the “grandeur,” as he puts it, of the way in which the Creator breathed the several powers of life into a few forms or into one, and how from so simple a beginning endless most beautiful and wonderful forms of life have been, and continue to be, evolved. — “It is interesting to contemplate a tangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent upon each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction, Inheritance … , Variability … , a Ratio of Increase … , a Struggle for Life … , Natural Selection … , Divergence of Character … , Extinction of lessimproved forms. Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, (footnote continued on next page)
details remarkably in accord with Nahmanides. Details which provide a striking complement to, a striking filling out of, Nahmanides’ simple and undetailed account.
Considerably more than just not incompatible with that account. Considerably more than simply compatible with it. Indeed, details which fill out Nahmanides’
account as though Nahmanides himself had written them.
(footnote continued from previous page)
with its several powers, having been originally breathed by the Creator into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being evolved.” (Darwin, Charles, The Origin of Species (Abridged and Introduced by Philip Appleman), New York: W.W. Norton and Company, 1975; p. 123).
INDEX OF NAMES
A
Anaxagoras, 233
Aquinas,
Compendium Theologiae, 183, 184, 188
De Ente et Essentia, 287, 288
De Natura Materiae et Dimensionibus Interminatis, 160, 161
De Unitate Intellectus contra Averroistas, 236, 237
In Aristotelis De Anima, 142, 144, 145
In Aristotelis De Caelo et Mundo, 156, 158, 200, 203
In Aristotelis De Generatione et Corruptione (but see 172, footnote 11), 122, 137, 138, 172, 173, 175177, 181, 186188, 191, 273, 274
In Aristotelis De Sensu et Sensato, 169, 170
In Aristotelis Metaphysicorum, 12, 43, 67, 71, 116, 118, 232234, 285
In Aristotelis Physicorum, 108, 117
In Boetii De Trinitate, 133, 134, 154
In Sententias Petri Lombardi, 69, 168, 202
Quaestiones Disputatae De Anima, 163
Quaestiones Disputatae De Spiritualibus Creaturis, 164
Quaestiones Disputatae De Virtutibus in Communi, 234, 235
Summa Contra Gentiles, 131, 144, 157, 198
Summa Theologiae, 141, 146, 147, 149, 157, 162, 163, 167, 186, 188, 192201, 203216, 218222, 224227, 238240, 309311
Aristotle, 200, 204206, 233, 238, 239, 273, 274, 276, 281, 285
Categoriae, 114, 115
De Anima, 147, 148
De Caelo et Mundo, 156, 203
De Generatione Animalium, 63
De Generatione et Corruptione, 47, 48, 122, 137, 168, 269
De Historiis Animalium, 63
De Partibus Animalium, 63
Metaphysica, 12, 36, 37, 39, 43, 44, 47, 48, 53, 56, 92, 116, 118120, 137, 232
Physica, 39, 41, 43, 44, 108, 109, 117, 119, 156, 158, 205
Augustine, 193195, 200, 209, 211, 215, 216, 218220, 306
Averroes, 56
Avicenna, 37, 38, 215, 216
Liber Secundus Physicorum Avicennae, ”Sufficientia,” 36, 84
B
Boscovich, Roger Joseph, 258
C
Christiani, Pablo, 299
Chrysostom, John, 213, 214
D
Darwin, Charles,
Origin of Species, 314, 315
E
Eddington, Sir Arthur S.,
The Nature of the Physical World, 288291
Einstein, Albert, 301, 305
G
GellMann, Murray, 280
Genesis, Book of, 192, 221, 222, 300, 306
J
James of Aragon, 299
L
Lederman, Leon,
The God Particle: If the Universe is the Answer, What is the Question?, 248, 249, 253, 255258, 266, 276, 280, 284, 285, 305
M
Maimonides (Moses ben Maimon), 298
Mattingly, Basil M., O.S.B.,
De Principiis Naturae of St. Thomas Aquinas, 36, 43, 56, 84
Melissus, 108
Moses, 211
N
Nahmanides [Moses ben Nahman],
Commentary on the Torah, 297315
Ne’eman, Yuval and Kirsh, Yoram,
The Particle Hunters, 285, 286
P
Parmenides, 108
Plato, 200, 204, 205
S
Schroeder, Gerald L.,
Genesis and the Big Bang, 249, 298306, 308
Searle, John R.,
Minds, Brains and Science, 294297
T
Telushkin, Rabbi Joseph,
Jewish Literacy, 299
W
Williams, C.J.F.,
Aristotle’s De Generatione et Corruptione, 269272
INDEX OF SUBJECTS
A
Accident,
necessary and not necessary accidents, 1516
per se accidents, 162
predicamental accident, 18, 19, 133
Accidental change. See Change
Accidental existence, 15
Accidental form. See Form
Active quality. See Quality
Actuality,
actual existence, 13, 7, 3133
priority and posteriority of, 65
Air,
account of the essence of, 171, 173183
B
Baryon number,
definition of, 265
Baryonic charge. See Baryon number
Becoming. See Change
Big Bang,
conditions immediately after, 249
description of, 304305
distinguished from creation, 300
Nahmanides’ thirteenthcentury theological Big Bang, 297315
related to Aquinas, 195, 207, 227
related to Medieval theory of the four elements, 192
“small” Big Bang, 153, 166, 183
Body, 61
mixed body, 6971, 103115, 121126, 130136, 144, 145, 151, 152, 272
mixed body as opposed to a simple body, 168, 254
mixed body, as brought about by the work of distinction and the work of adornment, 199
mixed body,
corruption of, 123
generation of, 123
proton as a mixed body, 247, 275, 276
natural body, 52, 54
natural organed body, 144, 145, 148, 151, 152
simple body, 104107, 110, 121, 122, 125, 168
C
Cause, 56
agent cause, 3941, 55, 5864, 99
agent cause, elements as agent causes, 137143, 216220, 223
agent cause, necessity for in generation, 3436
agent cause, voluntary distinguished from natural, 3639
coinciding of form, end and agent, 7173
composite cause, 8385
convertibility of, with effect, 5961, 64
distinguished from principle, 3941, 4346
extrinsic and intrinsic causes distinguished, 3941, 4346
final cause, 3941, 5864, 99
as cause of causes, 5960, 62
as end of generation, 7174
as end of the generated thing, 7174
as first cause needed in explanation, 78, 79
as uncaused cause, 62
necessity for, in generation, 3639
priority and posteriority of, 65, 66
formal cause, 3941, 5864, 99
the four causes, in the generation of one element from another, 166, 167
in act, 8587
in potency, 8587
material cause, 5864, 99
elements as material causes, 4749, 137143
of an element, 55
as first material components, 81
more universal concept as matter for less universal concept, 80
multiplicity of causes, 57, 58
per accidens, 8183
per se, 8183
priority and posteriority of causes, 63 67, 7579
proximate, 7679
remote, 7679
simple, 8385
singular, 88
universality of causes, 7679, 88, 99
universality of, in definition, 88
universality of, in explanation, 88
universality of predicable universals, 79, 80
Change,
accidental change, 131
alteration, 55, 109, 110
decomposing alteration, 53
becoming, 64
becoming, composite of matter and form as that which properly comes to be, 232
corruption, 69, 70, 105110, 120, 121
accidental corruption, 9, 10
nonapplicability to the heavens and the heavenly bodies, 185, 200205
nonapplicability to prime matter and substantial form, 29, 30
of a mixed body, 123
of one element from another, 165167
of the elements, 165167, 186188
substantial corruption, 9, 10
generation, 2, 10, 11, 1521, 55, 63, 64, 66, 7072, 109, 110
accidental generation, 7, 8
need for agent cause in, 3436
need for final cause in, 3639
nonapplicability to the heavens and the heavenly bodies, 185
nonapplicability to prime matter and substantial form, 29, 30
of a mixed body, 123
of one element from another, 165167, 189192
of the elements, 165167,186188
role of matter and privation in, 8
substantial generation, 7, 8
radical change (i.e., substantial change), coming into existence and going out of existence, 229
substantial change, 54, 55, 130, 131
role of matter in, 229
terminus a quo, 11, 1618, 20, 22, 25, 28, 58
terminus ad quem, 11, 16, 17, 20, 22, 25, 3436, 54, 55, 58
Chord,
definition of, 262
Composite,
of matter and form, as that which properly comes to be, 232
Composition,
out of contraries, 71
three sorts distinguished: simple aggregation, composition in a given order, mixing, 168
Constituent, 108, 111
primary constituents, 103, 104
Contraries, 6971, 109
Convertibility,
of cause and effect, 5961, 64
Corruption. See Change
Creation,
and the elements, 183199
distinguished from the Big Bang, 300
Nahmanides’ thirteenthcentury theological Big Bang, as creation, 297315
with regard to time, 198, 224, 225
D
Definition,
according to Aquinas, 152
role of the elements in, 154
Density,
definition of, 263
Diameter,
definition of, 262
Difference,
analogical, 90, 91, 94
in genus, 90, 91
in number, 90, 91
in species, 90, 91
Disposition,
of matter, 109, 110
Divisibility,
in quantity, 30, 31, 47, 48, 5254
E
Earth,
account of the essence of, 172183
Eduction,
of substantial forms from matter, 228, 231241
Effect,
convertibility of, with cause, 5961, 64
multiplicity of, 58
Element,
definition of, 47
Elements, 45, 47, 56, 103126, 129136
account of the essence of air, 171, 173183
account of the essence of earth, 172183
account of the essence of fire, 167171, 173183
account of the essence of water, 171183
as agent causes, 137143, 216220, 223
as material causes, 4749, 137143
as opposed contraries, 69, 70
characteristics of, 245, 246
corruption of, 165167, 186188
creation of, 183199
definition of, 253
dispositional presence of, 140
divisibility of, 4752, 54
generability of, one from another, 165167, 189192
general account of the essence of the four elements, 157167
generation of, 165167, 186188
how defined, 155, 156
indivisibility of, 4754
instrumental presence of, 140, 141
quarks and leptons related to fire, air, water and earth, 283, 284
role of, in definition, 154
role of, in the eduction of substantial forms from matter, 228, 231241
Energy,
definition of, 263
rest energy, definition of, 264
Essence, 99
how essence differs from substantial form, 229
Evolution,
related to Aquinas, 195, 207, 227
related to Medieval theory of the four elements, 192
F
Fire,
account of the essence of, 167171, 173183
First Way,
Aquinas’ proof of God’s Existence, 87
Force,
chromodynamic force. See strong nuclear force
color charge,
definition of, 264
electric charge,
definition of, 264
electromagnetic force, 264, 265
definition of, 267
electrostatic force,
definition of, 267
gluon,
as transmitter of the strong nuclear force, 264, 265
gravitational force, 266
definition of, 267
magnetic force,
definition of, 268
origin of forces in subatomic particles, 281283
photon, as transmitter of electromagnetic force, 264265
strong nuclear force, 264, 265
definition of, 268
weak nuclear force, 266
definition of, 268
Form, 10, 17, 18
actuality of matter, 7
as one of the three principles of nature, 2, 3436, 3941
as per se principle, 1519, 2123
accidental form, 68, 1011, 114, 115
how accidental form differs from substantial form, 231
artificial forms as accidental forms, 1011
distinguished from matter and privation, 2325
priority and posteriority of, 65
sameness and difference of, 90, 91
sensible form, 149151
substantial form, 68, 54, 55, 105126, 129133, 136, 163, 166, 167
as source of actual existence and knowability, 28
account of what a substantial form is, 228231
its eduction from matter, 228, 231241
grades of, 164, 165
how it differs from accidental form, 231
how it differs from essence, 229
incorruptibility and ingenerability of, 29, 30
in relation to three dimensionality and the “small” Big Bang, 166, 224, 253, 283
G
Generation. See Change
H
The heavens and the heavenly bodies,
causality of, 205219, 223
circular motion of, 203
classification of the heavens, 199
incorruptibility and ingenerability of, 185, 200205
matter of, 200
nature of, 199205
three basic characteristics of, 202, 203
I
Incorruptibility and ingenerability,
of the heavens and the heavenly bodies, 185, 200205
of prime matter and substantial form, 29, 30
Indivisibility,
in form, 47, 48, 50
in kind, 103, 104106
in quantity, 30, 31, 47, 48, 52
in species, 47, 48, 51, 53
into parts, 53
of elements, 53, 54
Ingredient,
actual ingredient of the essence, 133
matter and form as ingredients, 17
of the essence, 42, 99, 131, 132
virtual ingredient of the essence, 133
Instrument,
conjoined instrument, 142, 143
separated instrument, 142
M
Macroproperties, 294297
Man,
definition of, 153
Mass,
definition of, 262
gravitational mass,
definition of, 263
inertial mass,
definition of, 263
relativistic mass,
definition of, 263
rest mass,
definition of, 263
Matter, 10, 17, 19, 108110,
as concomitant to privation, 18
as one of the three principles of nature, 2, 3436, 3941
as per se principle, 1519, 2123
designated matter, 91
disposition of matter, 109, 110
distinguished from form and privation, 2325
eduction of substantial forms from, 228, 231241
its role in substantial change, 229
matter in which, 35
matter out of which, 35
of the heavens and heavenly bodies, 200
potentiality for form, 7
prime matter, 36, 54, 129133, 136, 166, 167
as not having existence per se, 31 33
as unknowable per se, 27
incorruptibility and
ingenerability of, 293
numerical oneness of, 30, 31
receptivity of, 160
related to the neutrino, 284286
related to the rishon, 286288
simply prime matter distinguished from relatively prime matter, 2529
priority and posteriority of, 65
role of, in generation, 8
sameness and difference of, 90, 91
M
Mean quality. See Quality
Microproperties, 294297
Mixing, 168
as opposed to simple aggregation and composition in a given order, 168
distinction between “mixis” and “synthesis” in Aristotle, 269, 270
mixability, 273278
mixing according to sense, 108115, 120
related to microproperties and macro properties, 297
true mixing, 108115, 120, 121
proton as a true mixing of quarks, 247
what is a “mixis”?, 26927
Moved movers, 87
N
“Nature,”
meaning of, in the title, De Principiis Naturae, 1214
Necessity,
necessity of death, 66, 6971
absolute, 6669, 71
conditional, 6668
from the agent, 67, 68
from the end, 6668
from the form, 68
from matter, 6668
O
Organed ( “organicum” ), 144, 145
P
Part,
accidental part, 134136
essential part, 134136
quantitative part, 52, 53, 111
Particle,
atomos, atom (Democritean atom), 255
electron,
definition of, 261
general description of, 255
force transmitting particle, 255, 256
gluon,
definition of, 265
general description of, 255
graviton,
definition of, 266
general description of, 255
lepton,
genus of, 254
specific difference of, 254
matter particle, 255, 256
neutrino,
general description of, 255
related to prime matter, 284286
photon,
definition of, 265
general description of, 255
proton,
as a mixed body, 247, 275, 276
quark,
as agent and material cause, 250252
as element, 250252
dimensions of, 256269
dispositional presence of, 250252
general description of, 255
genus of, 254
instrumental presence of, 250252
retrievable presence of, 250252
specific difference of, 254
virtual presence of, in a proton, 246, 247, 250252, 275, 276
dquark,
definition of, 260
uquark,
definition of, 260
reaction particle, 255, 256
rishon, related to prime matter, 286288
W+ particle,
definition of, 266
general description of, 255
W particle,
definition of, 266
general description of, 255
Z0 particle,
definition of, 266
general description of, 255
Passive quality.
See Quality
Per accidens reduced to per se, 3943
Per se existence, 3133
Potentiality, 17, 20, 63, 64
potential existence, 15, 7, 3133
priority and posteriority of, 65
pure potency, 55
Power, 122
active power, 55
Predication,
analogical, 9194
equivocal, 92, 93
of universals, 79, 80
univocal, 92, 93
Presence,
dispositional presence, 140, 250252
instrumental presence, 140, 141, 250252
retrievable presence, 250252
virtual presence, 133, 246, 247, 250252, 275 , 276
Prime matter. See Matter
Principle, 56, 99
distinguished from cause, 3941, 4346
principles of nature: matter, form and privation, 2, 3436, 3941
Priority and posteriority,
in completeness, 6365
in existence, 64
in generation, 6365
in perfection, 6365
in substance, 6365
in time, 6365
of actuality, 65
of cause and effect, 6367, 7579
Privation,
as concomitant to matter, 18
as one of the three principles of nature, 2, 10, 3436, 3941, 99
as per accidens principle, 1519, 2123
as principle of generation, 8, 1523
distinguished from form and matter, 2325
Property,
macroproperties, 294297
microproperties, 294297
Proton,
as a mixed body, 247, 275, 276
Q
Quality,
active quality, 105, 106, 108, 112, 121, 123
of a mixed body, 122
of a simple body, 122
of an element, 123125
passive quality, 105, 106, 108, 112, 121, 123
mean quality, 105, 107, 108, 112, 121, 123, 125, 126
of quarks in a proton, 247
Quantity, 108, 109
quantitative divisibility and indivisibility, 30, 31, 47, 48, 5254
quantitative part, 52, 53, 111
R
Radius,
definition of, 262
Rishon, 286288
S
Sameness,
analogical, 90, 91, 93, 9499
in genus, 90, 91, 9799
in number, 90, 91, 9799
in species, 90, 91, 9799
“Small” Big Bang,
in relation to substantial form and threedimensionality, 166, 224, 253, 283
Soul, 61, 144, 164
as selfmoving, 147
definition of, 145
intellectual soul distinguished from sensitive and vegetable souls, as requiring more than the receptive and agent causes of the physical world for its production, 236238
production of, 236, 237
rational soul, 146, 147
sensitive soul, 146151
vegetable soul, 147, 148,151
Space,
origin of, 308
Spin,
definition of, 265
Subject, 35
Substantial existence, 15
Substantial form. See Form
T
Terminus a quo (of a change), 11, 1618, 20, 22, 25, 28, 58
Terminus ad quem (of a change), 11, 16, 17, 20, 22, 25, 3436, 54, 55, 58
Time, 86, 87, 310
in the creation of things, 224, 225
origin of, 308
part of the work of creation, 198
Tree of Porphyry, 81
U
Unmoved Mover, 87
W
Water,
account of the essence of, 171183
Weight,
definition of, 262
Work of adornment ( opus ornatus), 192195, 197, 207, 208, 213219, 226, 309, 310
as productive of mixed bodies, 199
Work of creation ( opus creationis), 192195, 197, 207209, 309, 310
the elements, the empyrean heaven, the angels, and time, as parts of, 199
Work of distinction ( opus distinctionis), 192195, 197, 207212, 226, 309, 310
as productive of mixed bodies, 199