Ockham on Generality
The Ontology of William of Ockham NOTES 1. Although Ockham defines the term 'syncategorematic' more narrowly than this in chapter 4, his subsequent use of the term converges with mine. See, for example, chapter 69.
2. To be accurate here we would have to employ the distinction between primary and secondary signification that I outline later. Employing that distinction we would have to say that a proposition of this sort is true just in case the subject is numbered among the primary significata of the predicate; otherwise it is false. This issue of truth conditions is pursued in the second paper,
"Ockham on Generality."
3. Of course it may be that other entities are involved, but Ockham wants to claim that if this is so the analysis of predication will never reveal it. The pressure to postulate additional entities must come from other quarters. As it turns out, additional entities (albeit individuals) are involved in the use of some predicates from the category of quality; but as the second part of this paper shows, it is the analysis of abstract terms and not predication that establishes this fact.
4. There is, of course, one sense of 'particular' in which 'particular' designates real, ie. non-linguistic entities, but in that sense it is not opposed to 'universal'. See chapters 14 and 19 for an account of this sense of the term.
5. This account is likely to remind the reader of Wilfrid Sellars' account of intentionality. Sellars himself admits his debt to medieval philosophy in general in "Being and Being Known" in Science, Perception, and Reality (New York:
Humanities Press, 1963), 41-59 and to Ockham, in particular,in ''Towards a Theory of Categories" in Experience and Theory, Lawrence Foster and J. W.
Swanson, eds. (Amherst: University of Massachusetts Press, 1970), 55-78.
6. Ockham himself introduces this dichotomy as a distinction among names, a grammatical category incorporating both nouns and adjectives. Nonetheless, this same sort of phenomenon is at work in the case of other parts of speech, e.g., verbs and their gerund-forms ('run' and 'running'). Fastening on this fact
I speak not of concrete and abstract names but of concrete and abstract terms.
7. Again, Ockham presents this dichotomy as a distinction among names; but here he clearly is tempted to extend the distinction beyond that grammatical category. Thus, he speaks of verbs, adverbs, etc. as connoting this or that about substance and quality. Following out these hints, I speak of absolute and connotative terms rather than names.
8. 'Signifyo' is neutral as between the four senses of 'signify' outlined in chapter 33. In place of this sense of 'signify', Ockham frequently employs the term 'importare'. Literally this means "'to carry into" and conveys clearly the notion of introducing into discourse.
9. 'Signify,' is roughly equivalent to the first sense of 'signify' discussed in chapter 33; and one could easily expand my account in such a way that the term could also fit the second sense of 'signify' found in that chapter. In the interests of brevity, I do not engage in the relevant expansion here.
10.'Signify,' covers both the third and fourth senses of 'signify' found in chapter 33.
11. Ockham tells us that this account of the categories originates with Averroes. Readers will find a very similar explication of Aristotle's categories in Gilbert Ryle's classic paper "Categories," reprinted in Flew, A. G. N., Logic and Language, 2nd series (Oxford: Basil Blackwell, 1953), 65-81.
The Ontology of William of Ockham 12. See in particular chapters 7 and 16.
13. In dealing with the category Ockham does not consider the case of concrete terms like 'unicorn' that have no significata,
. It seems, however, that he would want to construe them as connotative terms signifying, the truth of some proposition.
14. Ockham does not provide much commentary here. He seems to think that our natural linguistic intuitions will substantiate his claim. See, for example, chapter 8.
15. The account presented here is clearly Ockham's. The difficulty, as I suggest, is that Ockham sometimes says things that are inconsistent with this analysis. My own inclination is to emphasize the revolutionary rather than the reactionary side of Ockham's account.
16. If it is to be construed as anything more than a general way of pointing to the contents of the category of quality, this technique for dividing the category is inadequate. Thus, there are terms like 'light' that do not naturally fit any of these divisions. Actually, the only division that Ockham finds crucial is that between terms expressive of figure and form, on the one hand, and all the remaining terms in the category, on the other.
17. This premise is never stated as explicitly as I suggest here. It is rather implied as it is, for example, in chapter 44.
18. My account deviates from Ockham in order of presentation. He deals with the category of quality after he deals with the categories of quantity and relation. His analysis of figure and form, then, is far briefer than my account would suggest. He merely applies the results of his analysis of these two categories to abstract terms expressive of figure and form and concludes with little commentary that these terms are not absolute. Since I want to bring to the fore the real existents (substances and qualities) in terms of which Ockham analyzes quantity and relation, I introduce Ockham's reductionism in terms of figure and form. What I have done is expand his own treatment of this species of quality in terms of his analysis of quantity and relation.
19. This argument is found in Ockham's Commentary on the Categories which exists only in early editions.
20. This account holds only in the case of natural signs or intentions. Both Ockham and Aristotle want to claim that given the poverty of conventional languages, a term, 'T,', can be a relative even though there is no term, 'Tz,' such that'T,'is the relative of'T,'. My account requires expansion, then, to handle this case. In the interests of brevity I omit the expansion here.
21. Since this argument is found in chapter 51, it is not from Ockham's own hand; nonetheless, it is sufficiently like other arguments found in authentic sections of the text to warrant the label ""Ockhamistic."
22. My use of the term 'second intention' deviates from my analysis of that term in the first part of this paper. There I define second intentions as a subclass of intentions of the soul. Although Ockham construes this as the proper meaning of the term, he extends his use of the term as I do here, to cover conventional signs as well.
23. Of course, if we make this modification in the Ockhamistic theory of categories, the term 'substance' hardly does justice to the richness of this category. A new term would have to be introduced to capture the ontological force of the expanded category.
24. See Ockham's Commentary on Porphyry, chapter 3, Ernest Moody, ed. (St. Bonaventure, New York: Franciscan Institute Publications, 1965), 4445. Ockham refers to this passage in chapter 38 of the Summa.
Ockham on Generality Michael J. Loux Contemporary accounts of propositions like (1) Every philosopher reads Aristotle and (2) Some Greeks are sailors tend to stress the role of the expressions 'every' and 'some'. Philosophers see the apparatus of quantification beneath these expressions and attribute the generality of reference ingredient in propositions like (1) and (2) to the unique role played by the quantifier. Ockham, like other medieval logicians, takes a quite different approach. He contends that expressions like 'every' and 'some' are completely lacking in referential force. According to Ockhan,, it is only non-logical or categorematic terms that can play genuinely referring roles, so that generality of reference must ultimately be secured by the categorematic terms embedded in general propositions rather than by expressions like 'some' and 'every' which introduce them.
This theme plays a central role in Ockham's metaphysics and logic, and in this paper | would like to consider its elaboration in the Summa Logicae.
I The framework for Ockham's treatment of generality is his theory of supposition. As Ockham explains it, supposition is a semantical property that agrees with signification in involving a word-thing relation; but whereas signification is a property that is invariantly associated with a categorematic term, supposition is a property a term exhibits only within the context of a proposition.' Its role in his semantics is not unlike that played in contemporary theories by the notion of reference. To say that a term supposits for an object in a proposition is to say that the term so functions in that proposition as to stand for or denote the object in question.
Ockham on Generality Now, Ockham holds that one and the same term can, in different propositional settings, refer to or supposit for categorically different objects.
This view is developed in his claim that there are three different kinds of supposition He calls these material, simple, and personal supposition.
Material supposition is the kind of reference a term has when it is used to refer to itself. 'Man', for example, has material supposition in ' "Man" is a three-letter word'. Although it is a general term, it is functioning there as a singular term taking itself as referent or suppositum. In simple supposition, on the other hand, a term supposits for a concept or intention of the soul. Thus, 'man' supposits simply in 'Man is a species'. In characterizing simple supposition we can mobilize Ockham's theory of thinking as a kind of inner speech and say that when a term supposits simply, it functions as a singular term suppositing for that conceptual word which in the inner language of the soul plays the same role that it plays in overt speech."
Ockham construes both material and simple supposition as deviant forms of supposition; together they stand opposed to the normal referential use of terms in personal supposition. He explicates the notion of personal supposition in terms of the concept of signification. As we defined the notion earlier a term signifies, all and only those objects of which it can be truly predicated. Ockham tells us that a term supposits personally when it supposits for the object or objects it signifies,.? Thus, 'Socrates' has personal supposition in 'Socrates is wise' since it supposits in that proposition for the individual that is its bearer—Socrates, and 'man' supposits personally in 'Every man is an animal'; for according to Ockham it so functions in that proposition as to refer to the various objects of which it can be truly predicated.
These two examples exhibit the two kinds of personal supposition— discrete supposition, where the suppositing expression is a singular term referring to its sole significatum,, and general supposition, where a general term supposits for all its significata,. Ockham says little about the former.
It is the case of general supposition that receives his detailed attention, and the focus of his attention is the fact that with general supposition, generality of the sort we want to consider enters language. if When he first considers the notion of general supposition Ockham provides an account that is meant to handle a narrow range of cases, and his consideration of even these cases is subject to an idealizing restriction that is only later lifted.' He limits himself to the supposition of general terms in propositions which involve exclusively the use of present tense verbs and which are through-and-through assertoric; the idealizing restriction is the contrafactual assumption that all general terms have non-empty extensions.
In the interests of clarifying the scope of Ockham's initial account of supposition it will prove useful to consider an imaginary language, E*.
Although it is a much weaker language, E* has much in common with English. Indeed, we can think of E* as that fragment of English which remains when we eliminate (a) propositions which involve verbs in any of the past or future tenses, (b) propositions which incorporate, even if only implicitly, terms expressing the modalities, and (c) propositions consisting of one or more categorematic terms with empty extensions. Ockham's initial presentation of the concept of general supposition can be construed as the attempt to explicate the way in which general terms in E* supposit.
As we have described E*, all of its general terms have non-empty extensions. Employing the concept of signification;, we can say that every general term in E* has at least one significatum,. Since E* has no resources for incorporating these general terms into propositions that involve, even implicitly, the modal notions of necessity or possibility, we can think of these non-empty extentions as consisting exclusively of actualized objects; and since the propositions of E* are all in the present tense the extensions of the general terms of E* can be construed as incorporating only presently existing objects.
Let us think of these extensions as domains for the terms in question.
Associated with each general term in E*, then, there is a non-empty domain consisting of all and only those actual, presently existing objects that are significata, of the term in question. Philosophers before Ockham frequently called the objects of each such domain the appellata of the term whose domain they constitute.> Employing this piece of jargon, I shall call these non-empty domains appellative domains, and | shall employ the symbol }AD/'T'} to mark the class of objects that constitute the appellative domain for a term, '7'.
Now, Ockham holds that when a term in E* supposits generally, it supposits for all the elements in its appellative domain; nonetheless, he wants to maintain that general terms can supposit for these objects in a variety of styles. His claim is that by specifying these different styles of supposition, we can generate a set of semantical relationships rich enough to provide an account of the logical structure of all the general propositions of E*.
The first style of general supposition which Ockham considers he calls determinate supposition. He describes it as follows:
Ockham on Generality .
.. whenever it is possible to descend to the particulars under a general term by way of a disjunctive proposition and whenever it is possible to infer such a proposition froma particular, the term in question has personal determinate supposition.
Ockham explicates determinate supposition in terms of the inference patterns which the use of an expression exhibiting this form of supposition licenses for the proposition in which it is embedded. The claim here is that where a term supposits determinately in E*, we can "descend" from the proposition embedding the term to a certain disjunction of singular propositions and we can "ascend" from any one of the singular propositions in the disjunction to the embedding proposition.* Talk of warranted "descent" and "ascent" is clearly talk about entailment, and the examples Ockham employs indicate that the singular propositions in question are propositions differing from the embedding proposition only in replacing the term suppositing determinately (along with any syncategorematic terms welded to it) by singular terms suppositing discretely for the various elements in the appellative domain of the suppositing term. I shall call these propositions singular instantiations of the embedding proposition and shall say that they instantiate it with respect to the suppositing term. The view, then, is that where a term supposits determinately in E*, it so functions that the proposition in which it is embedded entails the disjunction of all those propositions that instantiate it with respect to the suppositing term and is entailed by any one of these propositions. Since, however, to be entailed by any one singular instantiation is to be entailed by the disjunction of all of them, we can say that A term, 'T', in E* supposits determinately in a context (.....T.....) just incase (.....7.....) entails and is entailed by [(.....T1.....) V(....-T2..
2. DV wee Vw...) (where 'T,' - 'T,' are singular terms whose significata, exhaust Ockham's example is the term 'man' as it functions in the E* proposition 'A man is an animal'. The referential force of 'man' in this proposition is such that 'A man is an animal' entails and is entailed by 'This man is an animal, or that man is an animal, or .
. ." Thus, while 'man' is suppositing for all the elements in {AD/'man'} it is suppositing for them in a special style. We can call it a propositionally inclusive style of supposition: in the E* proposition 'A man is an animal', 'man' so supposits for the elements in its appellative domain that the use of the term has the effect of reiterating the context '.
. is an animal' over each of the elements in that domain. But while it is a propositionally inclusive style of supposition,
'man' supposits only disjunctively in 'A man is an animal'; for the use of 'man in this proposition has the effect of reiterating the embedding context only disjunctively across {4D/'man'} .
Terms which exhibit determinate supposition in E*, then, supposit in a propositionally inclusive, yet merely disjunctive way. Opposed to determinate supposition, we have what Ockham calls confused supposition.
Actually, this is not a single style of general supposition, but two quite different styles which agree only in lacking one of the two properties which are constitutive of determinate supposition One, confused and distributive supposition, is a propositionally inclusive style of reference that is not merely disjunctive; whereas, the other, merely confused supposition, is disjunctive, but not propositionally inclusive.
Let us consider confused and distributive supposition first. Ockham says, Confused and distributive supposition occurs when.
. it is possible. . . to descend by a conjunctive proposition and impossible to infer the original proposition from any of the elements in the conjunction.
Again, this style of supposition is defined with reference to the inferential moves which terms exhibiting it license; and once again, these moves bear, on the one hand, on the proposition in which the suppositing term is embedded and, on the other, on the propositions which instantiate it with respect to the suppositing term. Where a term in E* has confused and distributive supposition, it is possible to "descend" from its embedding proposition to the conjunction of all the relevant singular instantiations.
Ockham tells us that no one of those instantiations warrants an "ascent" to the embedding proposition, but it is clear that the conjunction of all of them does, so that A term, '7', in E* has confused and distributive supposition in a context
(.....7.....) just in case (.....7.....) entails and is entailed by (where T,-T, exhaust {AD/'T'} ).7
An example is the subject in the E* proposition 'Every man is an animal'; here, 'man' so supposits that 'Every man is an animal' entails and is entailed by the conjunctive reiteration of '..
. is an animal' across {AD/'man'} . Confused and distributive supposition, then, is a style of supposition that is like determinate supposition in being propositionally inclusive, but unlike it in being conjunctive rather than merely disjunctive.
Merely confused supposition, on the other hand, is neither propositionally inclusive nor conjunctive. Defining it, Ockham says,
Ockham on Generality Merely confused supposition occurs when a common term supposits personally and it is impossible .
. to descend to particulars by way of a disjunctive proposition, but it is possible to descend by way of a proposition with a disjunctive predicate and it is possible to infer the original proposition from any particular.
The claim is that where a term in E* has merely confused supposition, its embedding proposition is entailed by any proposition which instantiates it with respect to the suppositing term; but while granting this, Ockham denies that the use of a term to supposit in this way licenses even the disjunctive reiteration of the embedding context across its appellative domain.
Where a term has merely confused supposition, however, we can make a "descent" to a kind of disjunction—what we might call a terminal disjunction. An expression with this form of supposition so functions that singular terms suppositing discretely for each of the elements in its domain can be disjunctively reiterated within the embedding context. Ockham's definition suggests that only the predicate-terms of E* propositions can exhibit merely confused supposition, but in other contexts he explicitly tells us that the notion has a more general application. Consequently, if we employ a new symbol (v as opposed to V) to signal terminal disjunction, we can say that A term, '7' in E* has merely confused supposition in a context
(.....7.....) just in case (.....7.....) entails and is entailedby (....-Tiv Trv.....v Ty...) (where T,-T, exhaust 'Animal' has merely confused supposition in the E* proposition 'Every man is an animal'. The use of this term does not license the reiteration of 'Every man is...' across the domain of animals either conjunctively or disjunctively; for if we assume that the number of men is greater than one, then there is no one animal that they all are. Nevertheless,
'animal' so functions in 'Every man is an animal' that it warrants the inference from its embedding E* proposition to the E* proposition 'Every man is this animal or that animal or.
According to Ockham, determinate, confused and distributive, and merely confused supposition exhaust the styles of general supposition.® His contention is that with these three styles of general supposition in hand, it is possible to exhibit the logical structure of all the general propositions in E*; and after distinguishing these styles, Ockham provides us with a set of rules which enable us to move from the syntactical characterization of a term in such a proposition to the conclusion that it exhibits one and only one of these three styles. These rules tell us, for example, that if a term in Ockham on Generality
E* immediately follows the expressions 'every' or 'no', it has confused and distributive supposition; but while helpful, Ockham's rules tend to be something of a hodge-podge. Consequently, I shall not attempt to systematize or even summarize them. I shall, on the contrary, display the semantical structure which these rules dictate for the familiar A, E, J, and O forms of the traditional square of opposition as these forms appear in E*.
In Ockham's analysis, all A-propositions in E* are composed of a subject exhibiting confused and distributive supposition and a predicate with merely confused supposition, so that an E* proposition of the form
'Every A is B' comes out as (A, is Biv Bev .....v Ba) A (AoisBiv Bev ....vBa)A.....
A (A, is Biv Bry .....
Bu) (where A,-A, and B,-B, exhaust {AD/'A'} and {AD/'B'} respectively).
In the E-propositions of E*, both subject and predicate have confused and distributive supposition. Thus, E* propositions of the form 'No A is B' receive the following treatment:
((A; is not B,) A (A, isnot B.) A ..... A (Aris not B,)] A ((A, is not B,) A (A; isnot B:) A..... A (Azis not B,)] A..... A[(Anis not B,) A (A,isnot Bs)A.....
A (A, is not B,)] (where A,-A, and B,-B, exhaust {AD/'A'} and {AD/'B'| respectively).
I-propositions have both subject and predicate suppositing determinately, with the result that an E* proposition of the form 'Some 4 is B' is exhibited as .
[(A, is B:) V (A; is Bz) V..... V (A; is Ba)] V [(A:2 is Bi) V (A, is Bs) V ..... V (Avis Bs)] V.....
V [(Anis Bi) V (An is Bo) V..... V (Anis B,)] (where A.-A, and B,-B, exhaust {AD/'A'} and {AD/'B'} respectively).
Finally, while the subject of an O-proposition in E* has determinate supposition, the predicate has confused and distributive supposition. Consequently, E* propositions exhibiting the form 'Some 4 is not B' can be displayed as follows:
[(A; is not B,) A (A; is not B.) A ..... A (A; is not B,)] V [(A; is not B:) A (A; is not B.) A.....A(AzisnotB,)]V.....
V[(A, is not B:) A (A, is not B.) A..... A (Anis not B,)] (where A,-A, and B,-B, exhaust }AD/'A'} and {AD/'B'! respectively).
Ockham on Generality Now, Ockham maintains that these expansions provide us with an analysis of the meaning of E* propositions of the relevant forms, but he also contends that they provide the machinery for specifying the truth conditions for general propositions of E*. Given a general proposition exhibiting one of the four forms, we can say that it is true just in case the relevant expansion is true. But, then, the truth value of a general proposition in E* turns out to be truth functionally dependent upon the truth values of the singular instantiations which comprise the different expansions. This should be immediately obvious in the case of the J, E, and O forms, for in these cases the expansions involve only truth functional connectives. It is less clear in the case of A-propositions in E*, for there our expansion incorporates the terminal connective, v, and we have not provided any general directions for reducing that connective to propositional connectives. Now, it may be that no such general directions are possible; but within the context of our expansions, such a reduction is clearly legitimate, for 'A, is B, v B,v .....v B,' is equivalent to (A, is B,) V (Ar is Bz) V..... V (Aris Ba) where v gives way to the truth functional V. But, then, even in this case, the truth value of a general proposition turns on the truth value of a truth functional compound of singular propositions.
The significance of this point should be clear. Given any general proposition in E*, the expansions enable us to reduce questions about the truth of that proposition to more manageable questions about the truth of singular propositions in E*.!° The questions are all the more manageable since the relevant singular propositions are uniformly identity-statements or the negations of such, and Ockham thinks that the truth-conditions for propositions of that sort can be specified in a straightforward way. He tells us that an affirmative proposition of the form 'A, = B,' is true in E* just in case the object for which 'A,' supposits is numerically identical with the object for which 'B,' supposits; whereas, an E* proposition of the form 'A, # By' is true just in case 'A, =B,' is false. But, then, having applied this schema to all the singular instantiations comprising our expansions, we need only consult the logic of truth functions to determine the conditions under which a general proposition in E* comes out true.!1
The reader is likely to see an analogy here between Ockham's account and the account which the contemporary logician provides for quantificational formulae as they bear on finite domains. Where finite domains are involved, the logician tells us that (x) Fx and (Ex) Fx can be construed as mere abbreviations for truth functional compounds of singular propositions of the form 'Fa'. There are, of course, important differences in Ockham on Generality the two accounts. For one thing, the contemporary logician employs the function-argument schema and, consequently, his analysis makes no attempt to eliminate all vestiges of general terms. But even when we point to such differences the analogy remains strong.'? It is an important analogy, inasmuch as it shows that Ockham's account of generality is meant to handle the use of general terms only where their appellative domains are finite. Ockham's account hinges on the various expansions we have presented. Now, those expansions presuppose the possibility of providing a list incorporating each of the various objects falling within the appellative domain assigned to a term, and where the objects constituting those domains are infinite in number, no such list is possible. Nor is the demand that the domains be finite an idiosyncrasy of Ockham's treatment of E*; for even when we extend the account beyond the limited resources of E* to handle the case of general terms without supposita, the case of modal propositions, and the case of propositions involving the past and future tenses, Ockham's account presupposes that the domains over which general terms range are finite.
It is tempting to convert the analogy into an objection; for whereas the apparatus of quantification can be extended to handle domains that are not finite, Ockham's account cannot be extended in the same way. But, of course, if the system was not meant to be extended in that way, it hardly constitutes an objection to point this out. The objection would have to be reformulated to show that there are contexts (such as those provided by the work of the mathematician) which require the assumption of nonfinite domains. My suspicion is that Ockham would repudiate this claim, but how he would frame his defense to handle the contexts in question is not altogether clear.* A related, yet different objection, would focus on the fact that all of the expansions provided by Ockham's analysis require supplementation by means of clauses of the form (where A,-A, and B,-B, exhaust {4D/'A'} and {AD/'B'} respectively).
What such clauses amount to is the claim that A,-A, and B,-B, are all the A's and all the B's that there are, but this is to say that implicit in the supplementary clauses is the syncategorematic expression 'all'. The objection, then, would be that although Ockham's analysis is meant to eliminate the syncategorematic signs of generality, the expansions employed to eliminate these expressions implicitly contain them.
Now, it may be that Ockham's analysis is meant to show the dispensability of the various signs of generality. If it is, this is a very powerful
Ockham on Generality objection. But in defense of Ockham, it might be urged that nothing in the text forces us to impute this sort of aim to him. Indeed, if the expansions he points to require the quantifiers, it would seem to be sound interpretation to conclude that he wasn't trying to show their dispensability. What is clear from the text is that Ockham means to provide an account of generality according to which the referring devices in general propositions are general terms and not the syncategorematic expressions welded to them. It seems to me that Ockham could have held that it is general terms which play the referring role in propositions like our original (1) and (2) while granting the non-eliminability of the quantifiers, and if this is what
Ockham is maintaining, the objection loses its force.
Il However interesting it may be as a model, the account of generality in E* represents only the rudiments of an adequate theory of supposition.
What we want, in the end, is a theory which can handle the case of propositions incorporating the various modalities, the full range of tenses, and general terms with empty appellative domains. To display the relevant extensions in Ockham's theory, let us imagine successive enrichments in the resources of E*. Let us suppose, first of all, that the vocabulary of our imaginary language is increased to include categorematic terms with empty appellative domains. To simplify matters, let us think of this enriched
; version of E* as that fragment of English containing, in addition to the propositions of E*, all of the present tensed, assertoric propositions of English which incorporate categorematic terms with empty appellative domains; and let us call the result of so enriching E*, E**.
Our problem, then, is one of extending the theory of supposition for E* to handle the supposition of terms in those propositions wherein E* and E** differ. We want, that is, a generalized account of supposition, one that covers indifferently the use of general terms in E* and E**.
Initially, such an account might seem unattainable. Indeed, it might even seem that when we confront the new propositions of E**, the term
'supposition' ceases to be applicable. As we have presented (and as Ockham himself presents) the notion of supposition, suppositing terms always supposit for something. Where there is no suppositum, one wants to say, there can be no supposition. Ockham is aware of this difficulty; his response is simply to extend the notion of supposition, so that even terms with empty appellative domains can be said to supposit.
Now, we might be willing to accept this extension of the notion of supposition; but when we find Ockham telling us that the problematic terms of E** can supposit in the various styles outlined, we are bound to become anxious. It is simply not clear how our original definitions of the various styles of general supposition can have any application where terms have empty appellative domains. Those definitions stipulate that where a term exhibits one of the three styles of general supposition, its use warrants an expansion for the embedding proposition, an expansion involving the various objects which comprise the appellative domain of the suppositing term. But if there are no such objects, then the relevant expansions would appear to be impossible and the definitions inapplicable.
Actually, there is not just one difficulty here, but several. The first concerns the possibility of a proposition's having instantiations with respect to a term lacking significata,. But is this a genuine difficulty? I think not; for suppose (.....7.....) is a proposition in E** incorporating a general term, '7', with an empty appellative domain. Just because there are no T's it does not follow that we cannot construct E** propositions of the form (.....7T;.....) and (.....72.....). Given our description of E**, there seems to be no difficulty in this at all; we could simply invent singular terms to form the required instantiations.
But allowing such deviant forms, new questions arise. How are the propositions we have constructed to be treated? Are they to be construed as true? False? Should we assign thema truth value at all? Although it is difficult to be certain how Ockham would answer these questions, it is tempting to construe him as a Russellian; for he frequently talks as though non-modal, present tensed propositions with singular terms lacking a suppositum are false, But if we are willing to see beneath such remarks a developed position, it seems less clear that our definitions are inapplicable. As we stated them the definitions stipulate that a term supposits determinately, for example, just in case the proposition embedding the suppositing term entails and is entailed by a disjunctive proposition, one whose disjuncts instantiate the embedding proposition with respect to the suppositing term. But if Ockham is the Russellian it is tempting to think he is, all these disjuncts come out false; so also, then, does their disjunction. Now, presumably the entailment at work in our definition is the standard form of entailment. Presumably we were using the term 'entails' in such a way that one proposition entails another just in case it is impossible for the first to be true and the second false. But, then, so long as we stipulate that all the propositions of E** which incorporate terms with determinate supposition but no supposita are false, our definition remains intact; and clearly the same point will hold for our definitions of the Ockham on Generality other forms of general supposition. Thus, if Ockham is willing to grant that all general propositions incorporating general terms with empty domains come out false, his original definitions turn out to be general definitions holding not only for the propositions of E*, but for the propositions of E** as well.
Unfortunately, Ockham's view does not prove to be so accommodating; for while, in the case of Aand Jpropositions, he agrees that the use of general terms with empty domains results in the falsity of the embedding proposition, he wants to deny that this is so in the case of Eand O-propositions. Thus, although Ockham holds that the E** proposition 'Every man is an animal' is true only if there are both men and animals, he contends that the E** propositions "No rhinoceros is a dinosaur' and 'Some rhinoceros is not a dinosaur' come out true even in the case where there are no rhinoceri.
We need new definitions, then, for the styles of supposition as they appear in the negative propositions of E**. Ockham never states these new definitions explicitly, but from a number of his remarks it is clear how they are to go. Determinate supposition in negative propositions, for example, is to be defined as follows:
A term '7' in E** has determinate supposition in the negative context (-.....7.....-) justin case (-.....7.....-) entails and is entailed by [(There are no T's) or <(-.....T).....-)
V(-.... Ta...) Vii... V(-.....Tn...+-) >] (where T,-T, exhaust {AD/'T'} ).
The original definitions for merely confused and confused and distributive supposition require parallel reformulations. In each case the definition stipulates that the negative proposition in E** which embeds the suppositing term entails and is entailed by a disjunctive proposition, whose disjuncts are (a) the proposition that there are no supposita for the suppositing term and (b) the proposition expressing the expansion specified by the original definition.
Our original definitions of the three styles of supposition could remain unaltered for the case of affirmative propositions, but to make explicit the existence requirement underlying this form of supposition we could so revise the original definitions that a term, '7' in E** is said to supposit in one of those ways just in case its embedding proposition (.....T.....) entails and is entailed by the conjunctive proposition whose conjuncts are
(a) the proposition that there are T's and (b) the proposition expressing the relevant expansions.
When we apply these new definitions to the case of E**'s A, E, /, and O forms, we get results that depart radically from the treatment these forms receive at the hands of the contemporary logician. There is, however, a rationale behind Ockham's interpretation of the different forms. To bring this out I shall begin with the case of E** propositions of the J-form, for here Ockham's account does not deviate from the contemporary analysis. Then, moving from the case of J-propositions to the case of A,
O, and E propositions, I shall try to exhibit the reasoning that led him to interpret the remaining forms in the way that he did.
Ockham stipulates that no /-proposition in E** can be true unless both its subject and predicate have non-empty domains; but since the relevant expansions can hold only if the predicate term has a non-empty appellative domain, we can say that an E** proposition of the form
Some A is B is true just in case (1) {AD/'A'| is non-empty; and (2) [<(A, is B,) V (A, is B.) V ....... V (Aris Bs)> V <(A; is B:) V (A. is B2) V..... V (Ao is Bi) > Ve...
V <(A, is B:) V (A, is Bs) V ..... V (An is Bn) >] is true (where A,-A, and B,-B, exhaust {AD/'A'| and }AD/'B'} respectively) ; and this is just not that different from the contemporary claim that (Ex)
(Ax A Bx) is true just in case there is some object that satisfies both 'A' and 'B'.
Ockham, like most medievals, wanted to preserve an inferential link between 'every' and 'some'. He wanted, that is, to guarantee all entailments of 'Some .....' by 'Every .....'; but if this inferential link is to be preserved, the existence requirement must be written into the truthconditions for A-propositions. Thus, Ockham maintains that E** propositions of the form
Every A is B are true just in case (1) {AD/'A'| is non-empty; and (2) ((A: is Biv Bev .....v Br) A (Ar is Biv Bev .....
Vv Bn) A ..... A (A, is B, v B2 v ..... v B,)] is true (where A,-A, and B,-B, exhaust {AD/'A'} and {AD/'B'} respectively) ; and here we have an obvious departure from the contemporary treatment
Ockham on Generality of A-propositions according to which 'Every 'A is B' comes out true even in the case where there are neither A's nor B's.
The second major departure is in Ockham's interpretation of Opropositions in E**. Here Ockham allows a proposition to come out true even in the case where its subject term has an empty appellative domain.
But why? Well, the medievals construed O-propositions as the contradictories of A-propositions. As Ockham interprets it 'Some A is not B' is simply 'It is not the case that every A is B', but, then, the truth conditions for the O-propositions of E** can be obtained merely by negating the truth conditions for A-propositions in E**. In (2) of the truth conditions for A-propositions, we have a formula incorporating terminal disjunction; but as we have seen the terminal disjunction operating there can be eliminated in favor of propositional disjunction, so that the expansion specified in (2) above can be read as [(A, is B:) V (A: is Bh) V ..... V (A, is BLT A [(A2 is B:) V (A, is Be)V..... V (Ar is Ba)]A ..... A [A, is Bi) V (A, is Be) V..... V (Anis Ba).
Once we make this transformation we can see how Ockham's account of O-propositions follows directly from his account of the truth conditions for A-propositions, for he tells us that E** propositions of the form
Some A is not B are true if and only if it is not the case that either {4D/'A'} is nonempty or the expansion just mentioned holds; but employing truth functional equivalences, this is simply to say that E** propositions of the form
SomeA is not B are true just in case (1) {AD/'A'} is empty; or (2) [<(A: is not B,) A(A; isnot Bs) A..... A (A, is not B,)> V <(A, is not B,) A (A; is not B.)
A..... A (A,is not B,)> V.....
V <(Anis not Bi) A (A, is not B.) A ..... A (An is not B,)>] is true (where A,-A, and B,-B, exhaust {AD/'A'} and {AD/'B'! respectively).
Ockham's interpretation of E-propositions in E** does not differ from that provided by the contemporary logician, nor should this surprise us.
On both accounts E-propositions are taken to be the contradictories of I-propositions; and since /-propositions receive the same treatment on both accounts, their contradictories will as well. To construct the truth conditions for E-propositions in E** we need merely negate the truth conditions for J-propositions, so that E** propositions of the form
No A is B come out true just in case either (1) jAD/'A'} is empty; or (2) [<(A, is not B:) A (A, is not Be) A..... A (A, is not B,)> A <(A:2 is not Bi) A (A, is not Bs) A ..... A (Azisnot Bs)> A..... A <(A, is not B,) A (Anis not B,) A...... A (A, is not B,)>] is true (where A,-A, and B,-B, exhaust }AD/'A'| and {AD/'B'} respectively).
And by interpreting E-propositions in this way the tie between 'no' and 'some ..... not' is preserved in the bargain.
We have so far interpreted these accounts as statements of truth conditions, but when we eliminate their meta-linguistic overtones, we get what Ockham construes as analyses of the meaning of the A, E, J and O propositions of E**. Thus, he takes it to be part of the meaning of the E** proposition 'Every A is B' that there be A's; and he thinks that 'No A is B', as it appears in E**, is to be analyzed as the disjunctive proposition that either there are no A's or that every A is such that it is not B.
IV But, of course, E** is not our language. To arrive at a theory of supposition that can handle the complete range of propositions we employ, we must extend the account to handle the supposition of terms in past and future propositions and in modal contexts. In closingI want to consider the resources in Ockham's analysis for dealing with these cases.
Once again let us begin by enriching our imaginary language. Let us increase the propositional resources of E** by the addition of all the non-modal propositions of English which incorporate the past and future tenses, and let us call this new language E***, Now, it might seem that the new cases which E*** brings to the scene could be handled in a straightforward way. We could begin by assigning new domains to our general terms (i.e., domains of past objects and domains of future objects); then, retaining the definitions of the various modes of supposition as they
Ockham on Generality function in E**, we could make explicit in our applications of these definitions to the deviant cases that the domains in question are the new domains. Thus, to handle E*** propositions of the form 'Some A was B', we could assign to 'A and 'B' domains consisting of all and only those objects that were A and were B at any moment prior to the present— preterite domains for 'A' and 'B' ( {PD/'A'} and {PD/'B'} ). These new domains would incorporate some, but perhaps not all of the objects comprising {A4D/'A'} and }AD/'B'} and, presumably many other objects as well. Having identified these new domains we could say that E*** propositions of the form Some A was B are true just in case (1) {PD/'A'} is non-empty; and (2) [<(A, was B,) V (A, was B.) V.....V (A, was B,)> V <(A, was B,) V (A, was B.)
V..... V (A: was BL) > V «ww...
V <(An was Bi) V (A, was B.) V..... V (An was B,)>] is true (where A,-A, and B,-B, exhaust {PD/'A'} and {PD/*B'} respectively).
Although this sort of account appears plausible, Ockham finds it unsatisfactory. In informal terms the account construes the E*** form
'Some A was B' as the claim that at some time in the past something was simultaneously both A and B, and while this analysis does justice to many
E*** propositions there are others that resist it. The E*** proposition 'Some good man was evil', for example, is quite likely true, but in the account just presented it can be true only if at some time in the past the inconsistent proposition 'This good man is evil' was true. In fact all that is required for the truth of 'Some good man was evil' is the existence of at least one man who, while now good, was formerly evil. Ockham takes this as his clue for dealing with the past tense propositions of E***. He contends that 'Some A was B' is implicitly the disjunctive proposition 'Either some object that now is A was formerly B, or some object that was formerly A was formerly B'; and he insists on writing the disjunctive character of the proposition into the statement of its truth conditions, so that E*** propositions of the form Some A was B are true just in case Ockham on Generality either (1) {AD/'A'} is non-empty; and (2) [<(A, was B,) V (A, was B,) V.....V (A, was B,)> V <(A: was B,) V (A: was B,)
V (A: was By) > V.....
<(A, was B,) V (A, was B:) V..... V (A, was B,) >] is true (where A,-A, and B,-B, exhaust }AD/'A'} and {PD/'B'} respectively) ; or (1) {PD/'A'| is non-empty; and (2) [<(A, was B,) V (A, was B,) V..... V (A; was Bu) >V <(Az was B,) V (A; was B,) V..... V (Az was B,)>
V.....V <(A, was B,) V (An was B.) V..... V (A, was B,) >] is true (where A,-A, and B,-B, exhaust {PD/'A'} and \PD/'B'| respectively).
Past tense propositions of the A, E, and O forms can be treated in precisely the same way, anda parallel form of analysis will accommodate the various general propositions of E*** whose main verb is in the future tense, According to Ockham such propositions are implicitly disjunctive; but if we are to exhibit the character of the disjunction, we must assign to each general term a domain consisting of all and only those objects which at any time later than the present will be its significata,. Employing these future domains ( {FD/'T't ) we can say, for example, that E*** propositions of the form
No A will be B are true just in case either (1) }{AD/'A'| is empty; or [<(A, will not be B,) A (A, will not be B,) A..... A (A; will not be B,)> A <(A: will not be B,) A (A, will not be B.) A..... A (A, will not be B,)> A ..... A <(A, will not be B,) A (A, will not be B.) A..... A (A, will not be B,) >] is true (where A,-A, and B,-B, exhaust {AD/'A'} and }FD/'B'! respectively). or (2) jFD/'A'| is empty; or [<(A, will not be B,) A (A, will not be B2)
A..... A (A, will not be B,)> A <(A; will not be B,) A (A; will not be Be) A ..... A (A, will not be B,)> A Ockham on Generality ..... A <(A, will not be B,) A (A, will not be B.) A ..... A (A, will not be B,) >] is true (where A.-A, and B,-B, exhaust {FD/'A'} and {FD/'B'} respectively).
Now, it is tempting to think that the truth conditions for the singular propositions incorporated in this schema (as well as that provided in the case of 'Some A was B') are self-explanatory; for it seems only plausible to think that 'A, was B,' is true just incase
'A, is B,' was true at some time in the past and that 'A, will not be B,' is true just in case 'A, is not By' will be true at some point in the future. But appealing as it is, Ockham rejects this sort of account. We can get at his reasons for rejecting it if we reflect on the fact that expressions of the form 'A,' and 'B,' can be supplanted by a variety of kinds of singular terms. They deputize not only for proper names, but also for demonstratives, and demonstratives-cumgeneral terms (i.e., by expressions like 'this A' and 'this B' where 'A' and 'B' are the general terms which 'A,' and 'B,' limit).14 When we stated the truth conditions for the identity statements in E* and E**, it was unnecessary to take account of this fact; but in the case of E*** propositions, we must be more discriminating.
The claim that a past or future tensed identity statement is true just in case the corresponding present tensed identity statement was or will be true works well enough where the singular terms embedded in the past or future tensed identity statement are proper names or demonstratives; but our experience with "Some good man was evil' suggests that the account will yield unsatisfactory results when we confront past and future tensed identity statements whose singular terms are demonstratives-cum-general terms. To stick with our example, 'This good man was that evil individual' is of the form 'A, was B,'; but while it may well be true, the corresponding present tensed proposition ('This good man is that evil individual') was never true. This is not to say that the present truth of 'This good man was that evil individual' does not presuppose the past truth of any present tensed identity statement; the point is rather that the present tensed identity statement in question cannot be one in which the demonstrativecum-general term 'this good man' plays any role. Ockham exploits this insight and tells us that 'A, was B,' is true just in case 'a is B,' (where
'a is a demonstrative or proper name whose suppositum is identical with the suppositum of 'A,') was true at some time in the past and that 'A, will be B,' is true just in case 'a is B,' (where parallel restrictions are placed on 'a') will be true at some time in the future.'*
To conclude our succession of imaginary languages, let us add to E*** the various propositions of English which incorporate the modal notions of possibility and necessity. Now, if it is clear how we are to extend Ockham's analysis to cover general propositions incorporating past and future tenses, it is less easy to be certain how his account handles the propositions proper to our new language, E***. The difficulty is that Ockham's remarks on this topic are sparse; and where he does consider examples, they tend to be propositions the contemporary philosopher would be reluctant to construe as modal. The examples are generally propositions of the form 'Some A can be B' or 'Every A is capable of being B'. Ockham's strategy with propositions of these forms is to invoke the kind of analysis to which he subjects supposition in past and future propositions. We are told to assign domains of possibilia to 'A' and 'B'
({OD/'A} and {D/'B'} ). Ockham never tells us precisely which entities we are to admit into these domains; but presumably he wants
{OD/'A'} , for example, to include not only all of the objects constituting {PD/'A'}, {AD/'A'}, and {FD/*A'}, but other "objects" as well— "objects" that will never be actualized but are such that (a) their being actualized entails no impossibility and (b) were they to be actualized, they would be A. Employing domains of this sort we are told to treat 'Every A can be B' in the way we treated 'Some A was B' and 'No A will be B'— as an implicitly disjunctive proposition, so that 'Every A can be B' is parsed as 'Either every object in {AD/*A'} can be an object in {OD/'B'
, or every object in {<>D/'A'} can be an object in {>D/'B'.
Apart from the new domains, then, the machinery required to handle 'Every A can be B' is simply the machinery at work in Ockham's treatment of the propositions peculiar to E***. When we turn to propositions that are more explicitly modal, Ockham seems to think that the same type of analysis applies. Thus, £**** propositions of the form 'Every A is possibly B' are to receive precisely the same treatment accorded 'Every
A can be B', Indeed, the text suggests that Ockham construes 'EveryA is possibly B' as synonymous with 'Every A can be B'; and although the textual evidence is weaker, Ockham seems to think that a parallel analysis holds in the case of E**** propositions of the form 'Every A is necessarily
B'. There are no reliable clues as to the domains 'A' and 'B' are to be assigned in this case; but perhaps Ockham again wants these to be
{AD/'A'}, {OD/'A'}, and {D/'B'} respectively, so that E**** propositions which exhibit the form 'Every A is necessarily B' are to be analyzed as 'Either every object in {AD/'A'} is necessarily an object in {OD/'B'} , or every object in {<>D/'A'} is necessarily an object in {oD/'B}'.
Ockham on Generality The various disjunctions which explicate the general propositions peculiar to E**** give way to singular propositions like 'A, can be B,',
'A, is possibly B,', and 'A, is necessarily B,';and Ockham's account of the truth conditions for these propositions parallels that provided in the case of propositions like 'A, was B,'. There, the move was to interpret the present truth of past and future tensed identity statements in terms of the past or future truth of present tensed identity statements. In the same way, in dealing with identity statements incorporating the modalities, Ockham wants to claim that a proposition like 'A, is possibly B,' is true just in case some assertoric identity statement is possible. Our difficulties with 'A, was B,' and 'A, will be B,', however, should alert us to the fact that where 'A, is possibly B,' is the proposition whose truth conditions are to be stated, the relevant assertoric proposition cannot, in general, be
'A, is B,'. 'This white man is possibly black', for example, may well be true; but the proposition 'The white man is black' is impossible. Once again, it is demonstratives-cum-general terms that cause problems, and Ockham handles these problems in just the way he handled them within the context of E***, He tells us that 'A, is possibly B,' is true just in case 'a is By'
(where 'a' is a demonstrative or proper name whose suppositum is identical with the suppositum of *A,') is possible; and he holds that a parallel account works in the case of identity statements embedding the adverb
But this technique of moving the modality from the inside to the outside of a proposition suggests that even if my account is faithful to Ockham's treatment of the propositions peculiar to E****, it handles only half the difficulties associated with supposition in this language. The technique reminds us that the modalities can enter discourse either in their de re form (where they intervene adverbially between subject and predicate) or in their de dicto form (where they are predicated of propositions taken as wholes), and my account covers only the supposition of terms in E**** propositions which engage modalities de re.
Unfortunately, Ockham's discussion of supposition is of no help in filling in this gap; for in that section of the Summa, he completely ignores the supposition of terms in contexts which involve modality de dicto.
In a later section of the Summa, where Ockham actually treats the distinction between modality de re and modality de dicto, he once again fails to relate the distinction to his theory of supposition.!® What I would like to suggest is that his failure to do this may not be a mere oversight on Ockham's part.
In discussing the case where a modality is predicated of a general proposition, Ockham asks whether the resulting proposition is properly classified as general. He never provides any determinate answer to the question; but he expresses doubt about the view that propositions of the form ' "Every A is B" is necessary' are to be construed as universal affirmative propositions. The grounds of his doubt here are perhaps revealed in an earlier passage, where Ockham argues that truly predicating a modal expression of a general proposition does not guarantee that the same modal expression can be truly applied to any instantiation of that proposition. His example is the E**** proposition ' "Every true contingent proposition is true" is necessary'; and he contends that while this proposition is true, its instantiations (e.g., ' " 'Nixon is president' is true" is necessary') are obviously false. The force of this example should be clear: when a modality is predicated of a general proposition, the patterns of "descent" and "ascent" which dominate Ockham's theory of supposition do not apply. But since Ockham construes those patterns as definitive of the concept of a general proposition, it is plausible to think that he sees in their inapplicability to the case of modality de dicto grounds for doubting that the propositions in question are properly construed as general.
But if they are not general, it is reasonable to ask just how they are to be construed. Ockham is reluctant to commit himself on this point, but occasionally he implies that they are to be treated as singular propositions.
Although he never deals with the point in any detail, it is easy enough to see why Ockham finds such an account appealing. The double quotes suggest that 'Every true contingent proposition is true' has not personal, but material supposition in ' "Every true contingent proposition is true" is necessary'. Now, if we take this suggestion seriously, we will be inclined to say that in the relevant context 'Every true contingent proposition is true' is functioning as a singular term taking itself as suppositum; and, consequently, we will be tempted to think of the proposition whose subject it is as a singular proposition. But if this line of reasoning represents an accurate reconstruction of Ockham's position, then the fact that he never confronts this sort of case with his theory of general supposition has a ready explanation: the theory simply does not apply there. General terms which (like 'true contingent proposition' and 'true' in our example) come under the scope of a modality de dicto are not suppositing personally and so, a fortiori, are not suppositing in any of the three styles which are exhaustive of Ockham's notion of general supposition.1*
Now, while E**** is either English or something quite close to English, my account of Ockham's treatment of E**** hardly handles all of the difficulties which arise with regard to that language. I have, for example, considered only generality in propositions that can be plausibly
Ockham on Generality interpreted on the subject-predicate model. I have not considered the supposition of general terms within the context of propositions where one or more quantifiers come under the scope of some other quantifier. Neither have I considered the difficulties associated with supposition in epistemic contexts. That I have not dealt with these and other problems about supposition is traceable, in part, to the aim of the paper — to provide a brief reconstruction of Ockham's theory; it is also traceable to Ockham's failure to treat these problems in any detailed way. But despite its shortcomings, my account has, I hope, shown the rigor and sophistication of Ockham's theory of generality. Perhaps, too, it has done something to dispel the myth that logic was born at the hands of Russell and Whitehead.
NOTES 1As Ockham employs the term, a proposition is an indicative sentence possessing a truth value. I shall use the term in the same way.
2Ockham would be unhappy with my account of both material and simple supposition. He holds that a term can exhibit material supposition when it is suppositing for an expression other than itself. Thus, Ockham claims that in the Latin sentence 'Hominem currere est propositio vera', 'hominem currere' is suppositing materially; nonetheless, it is suppositing here not for itself, but for 'Homo currit'. Likewise, he thinks that a term can supposit simply when it supposits for an intention of the soul whose semantical role in the language of the soul is different from the semantical role which the suppositing term plays in overt speech. Thus, 'hominem currere' supposits simply in 'Hominem currere est propositio mentalis', but it supposits in that proposition not for the intention (hominem currere) whose semantical role it shares, but for the intention Homo currit. My own view is that Ockham is confused here. Were he to have attended to the distinction between direct and indirect quotation, he would not have assimilated what are clearly quite different uses of language.
%Actually, the issue is more complicated than my definition suggests; for the subject of 'Intention is an intention' is suppositing simply, even though it is suppositing for one of its significata,. Likewise, although the word 'noun' is suppositing for one of its significata, in ' "Noun" begins with an "n"', it is suppositing materially in that context. Ockham handles the complexities such examples introduce by saying that where a term supposits personally, it supposits for the object or objects it signifies, and is functioning significatively.
We catch the force of this qualification if we note that all the exceptions to the tule that a term suppositing personally supposits for its significata, are general terms. Some general terms (those signifying, certain intentions or linguistic expressions) can supposit materially or simply and yet be suppositing for onc of their significata,, but when they do they cease to play their standard significative role and function as singular rather than general terms.
4Ockham never explicitly tells us that his initial account of supposition is subject to these limitations, but in subsequent chapters of the section on supposition, he points to deficiencies in the original account and revises it accordingly. I shall attempt to organize Ockham's presentation of his theory by construing his original account and the revisions he points to as a series of different theories of supposition, each more powerful than its predecessor. The final theory in the series will present itself as a general theory capable of handling the supposition of terms in all linguistic contexts.
5By the time Ockham wrote the Summa, logicians employed the term 'appellatio' more narrowly to refer to a property possessed exclusively by expressions functioning as predicates. Ockham himself almost never uses the expression.
SAlthough Ockham does not use the term 'ascensus' in this context, his contemporaries frequently use it in the sense in which it is employed here.
7Actually, Ockham's scheme is more complicated than my account suggests. He divides confused and distributive supposition into two kinds—mobile and immobile supposition. It is only in the case of confused and distributive supposition which is mobile that my definition applies. Where a term supposits immobily (e.g., as 'man' supposits in 'Every man except Socrates runs'), the "descent" which the use of the term licenses does not extend across the appellative domain of the suppositing term; one or more elements are excluded from the "descent." Immobile supposition does not play a very significant role in Ockham's theory, so that, in the interests of simplifying the theory, I ignore it, but it should be clear that my framework for explicating the forms of general supposition could be employed in its case.
8Ockham interprets 'Every man is this animal or that animal or.
. ." as a proposition in which it is affirmed of each man in turn, that he/she is this animal or that animal or...
In the interest of keeping the complications to a minimum,I do not consider the first part of Ockhams' definition here. The claim is that where a term has merely confused supposition, its embedding proposition is entailed by any proposition which instantiates it with respect to the term with merely confused supposition. Thus, 'Every man is this animal' entails 'Every man is an animal', inasmuch as if the first proposition is true, the second is true as well; but, of course, 'Every man is this animal' can be true only when {AD/'man'} consists of just one element, so that while the entailment holds, the conditions under which it can apply are almost never satisfied.
®My account suggests the possibility of a fourth style of general supposition, a style that is conjunctive but not propositionally inclusive. One might argue that this style of supposition is required to handle the kind of referential force exhibited by 'apostles' in 'All the apostles are twelve'. An even more likely candidate would be 'dog' in 'Some man loves every dog.'
1Actually, my account of Ockhams' theory deals only with the supposition of terms in propositions that involve a single quantifier. Ockham himself attempted to apply his theory to the case where one or more quantifiers come under the scope of some other quantifier; but although he makes a number of interesting remarks in this context, it would be wrong to think that he has provided anything like a gencralized theory to handle propositions exhibiting nested quantifiers.
Ockham on Generality Although Ockham is not dealing with the formulae of quantification theory, my account of his view suggests certain affinities with the so-called substitutional theory of quantification. Now, there are fairly clear signs of an incipient substitutionalism in Ockham's account, but he sometimes uses language witha referentialist ring to it. We need not, on this account, accuse
Ockham of confusion; for since the domains his theory is geared to handle are all finite, the two views would come to much the same thing.
!But while the analogy exists, it would be a mistake to represent the analyses Ockham provides by means of the formulae of quantification theory; for in the language of quantification, it is the quantifier, together with the variables it binds, that plays the referring role. But the apparatus of quantification is the logician's way of reconstructing the role of syncategorematic expressions like 'some' and 'every'. To express Ockham's theory in this way, then, would completely misrepresent what he was trying to do, viz., to provide a theory of generality according to which it is categorematic rather than syncategorematic terms that play the referential role in general propositions.
13]t is tempting to argue that Ockham would have held that the domains in question are infinite, for he surely would have accepted the Aristotelian slogan that the members of a species are infinite in number. My suspicion, however, is that the concept of infinity at work in this slogan bears no affinity to that found in post-Cantorian mathematics. The slogan was generally employed in explaining the view that it is the universal rather than the individual which is the concern of the sciences. The force of the slogan, then, is simply that the individuals falling under the various infimae species are too numerous to constitute, each of them, subjects for scientific research. Neither does the mathematics of Ockham's day employ a notion of infinity that is recognizably like that found in contemporary mathematics. It is only plausible to assume, then, that it never occurred to Ockham that there was any need for a stronger theory of generality than that provided by supposition theory; and in any case,
Ockhams account of number-words bears sufficient affinities to constructivist theories of numbers to suggest that he would have grave doubts about the Cantorian infinities.
"Since Latin lacks the definite article, Ockham does not consider the case of definite descriptions. The remarks that hold true of demonstratives-cumgeneral terms will, however, apply in the case of definite descriptions as well.
15Where 'A,' is a demonstrative or a proper name, 'a' may, of course, be just 'A,'. Ockham himself limits the characterization to demonstratives, but it seems to me that his intentions are better served by my more general characterization.
\6The passage in question is found in Part II of the Summa.
'Jt is easy enough to see why Ockham might have been reluctant to commit himself to this view. Since it effectively denies that the proposition 'Every
A is B' has any internal structure in "Every A is B" is necessary', it makes it difficult to explain just how the proposition figures in inferential contexts.
From ' "Every A is B" is necessary' and ' "Every B is C" is necessary', we can infer ' "Every A is C" is necessary'; and clearly it is the internal structures of 'Every A is B' and 'EveryB is C' that guarantee the inference.