Ockham's Theory of Truth Conditions

Ockham's Theory of Truth Conditions by Alfred J.Freddoso 1.

In Part II of his Surmma Logicae Ockham's main task is to present a fairly comprehensive account of the truth conditions of propositions, i.e. indicative sentences. Starting with the semantically most simple kinds of propositions and gradually wending his way through more complex and troublesome cases, he hopes to put the reader in a position to determine what is necessary and sufficient for the truth of any proposition and on that basis to discern which inferences are valid and which are not.

This account of truth conditions is in part motivated by ontological concerns. Ockham has already argued in several places that there are no extramental universals or even Scotistic common natures.! He contends, rather, that terms like 'universal',

'genus', 'spécies', etc., are terms of second intention which signify certain mental qualities that are themselves individual in nature and universal or common only in signification. In chapter

' 2 of Part II he presents us, accordingly, with a theory of predication which presupposes the existence only of individual substances

'and qualities.{n this way he attempts to counter the realist's claim that we cannot account for the truth of even the simplest predication, e.g. 'Socrates is a man', without presupposing the existence of shared entities which are really (or at least formally) distinct from the individuals that possess them or are partially constituted by them. Ockham then in chapters 3 through 6 extends this account of predication to present-tense non-modal universal and particular propositions, thus insuring that none of these propositions involve a commitment to the existence of nonTheory of Truth Conditions individuals. Finally, in chapters 7 through 10 he explicates the truth conditions of past-tense, future-tense, and modal propositions in terms of the past truth, future truth, and modal status, respectively, of present-tense non-modal propositions. Hence, the tole of general terms in these semantically more complex propositions is seen to be no more problematic from an ontological point of view than their role in simpler kinds of propositions.

However, Ockham's reasons for proposing his theory of truth conditions do not all stem from ontological considerations. For he is convinced that ignorance of logic in general—and of propositions and their properties in particular—leads to errors and confusions in theology and the other disciplines. This theme is repeatedly emphasized in Part II, with "modern" theologians bearing the brunt of Ockham's criticism.

Consonant with this pragmatic motive is Ockham's interest as a logician in clarifying the sense and logical structure of semantically more complicated propositions in terms of their relations to simpler propositions. He takes present-tense non-modal cate- ! gorical propositions as his starting point and explicates their truth

| conditions directly in terms of the notion of supposition. In each case the truth of such a proposition depends on what its subject and predicate supposit for and how the suppositions of the subject and predicate are related to one another. Hence, the notion of supposition plays a role in Ockham's account which is roughly analogous to the role played by the notion of satisfaction in contemporary semantic theory. More complicated propositions are then explicated, as noted above, in terms of certain semantic properties of present-tense non-modal propositions. Ockham's project in Part II, then, is.as much an expression of a general theory of language, including tense and modality, as it is an outgrowth of his theory of universals.

In his treatment of exponible propositions (chapters 11 through 20) we find Ockham engaging in a type of analysis which, as will become clear, is similar to the type of analysis exemplified by Russell's theory of descriptions. Here Ockham deals with propositions containing connotative terms, verbs such as 'begin' and 'cease', or syncategorematic terms like 'except', 'only', and 'insofar as'. In each case he tries to show that such propositions are

Theory of Truth Conditions reducible to conjunctions or disjunctions of the sorts of propositions already treated in earlier chapters.

The next section of Part IJ (chapters 21 through 29) is devoted to a discussion of conversions, i.e. inferences involving propositions related in such a way that the subject of one is the predicate of the other and the predicate of one is the subject of the other. This tract on conversions is a necessary prelude to the treatment of syllogistic inference found in Part III-1 of the Summa Logicae. However, in what follows I will allude to this section of Part II mainly in order to shed light on certain remarks that Ockham makes about truth conditions.

The last section of Part II (chapters 30 through 37) deals with the truth conditions of hypothetical propositions, i.e. conditional, conjunctive, disjunctive, causal, temporal, and local propositions.

I will briefly try to show how this part of Ockham's account of truth conditions can best be understood as related to his earlier treatment of non-hypothetical, i.e. categorical, propositions.

In what follows, then, I will lay out and discuss the most important features of Ockham's account of truth conditions, noting along the way certain questions and problems that it engenders.

The reader is assumed to have some familiarity with the following features of Ockham's theory of terms explicated in Part I of the Summa Logicae: the relation of the mental language to spoken and written language, the distinction between categorematic and syncategorematic terms, and the distinction between absolute and connotative terms."

In order to understand Ockham's account of predication we must first understand the notions of signification and supposition as he employs them. Signification in its origin is a psychological notion. A sign signifies a thing just in case it brings that thing to mind or, in Boethius' words, "constitutes an understanding of it."" According to Ockham a mental categorematic term naturally signifies whatever it brings to mind, while its spoken or written counterpart conventionally signifies the same thing or things in virtue of being subordinated to the mental term in question. But what is signified by a categorematic term—especially a general or common term like 'man'? Since Ockham

Theory of Truth Conditions repudiates the postulation of both extramental universals and common natures, he rejects both the view that a general term signifies a universal that can be shared by many individuals and the view that a general term signifies a common nature. He claims, rather, that general terms—no less than singular terms like proper names—bring to mind only individual substances and qualities. For example, the term 'man' brings to mind all individual men in a "'confused" manner, i.e. in such a way that it brings one to mind no more and no less than it brings any other to mind. In what follows I will take this generic notion of signification as primitive.

When the concept of signification is transferred to semantic theory, a categorematic term 'T' is said to signify each entity of which it is true to say "This is possibly (a) T." (Since 'T' is used here and below as a schematic letter, my use of quotes in the principles which follow is not, strictly speaking, correct.

It is, however, more convenient and should not lead to any misunderstanding.) This, at least, is the primary sense of signification, which can be captured somewhat redundantly by the following principle:

(Pi) A term 'T' primarily signifies a thing x if and only if (i) 'T" signifies x and (ii) at least one of the following propositions is true, where 'this' indicates x: 'This is (a) T', 'This was (a) T', 'This will be (a) T', 'This is possibly (a) T'.

The term 'man', to put it somewhat indelicately, primarily signifies all present, past, future, and merely possible men. (Later I will argue that Ockham's semantic theory need not presuppose that there are merely past, merely future, or merely possible beings. If that is so, then (P1) would have to be restated more carefully.)> An'absolute! term, e.g. 'man', 'animal', 'Socrates', is such that it primarily signifies whatever it signifies. However, Connotative terms, e.g. 'white', 'chimera', 'non-man', bring to mind things of which they are not truly predicable by means of any sort of verb—present-tense, past-tense, future-tense, or modal. Just which things are brought to mind in this way is, according to Ockham, revealed by a close examination of the nominal definition of the connotative term in question. (Only connotative terms have

Theory of Truth Conditions By nominal definitions in the strict sense, i.e. definitions which are altogether synonymous with their definienda.)* For example,

'white' signifies individual whitenesses, even though it is impossible that a whiteness be white. For one who understands the term 'white' knows that a white thing is something which has whiteness, or something in which whiteness inheres. That is, one who understands the term 'white' and can use it correctly knows, at least implicitly, that its nominal definition is 'something having whiteness'. Again, even though it is impossible, according to Ockham, that a chimera exist, still the figment term 'chimera' brings to mind goats and cows, since its nominal definition is

'an animal composed of a goat and a cow', where the terms 'goat' and 'cow' occur in oblique cases rather than in the nominative case. Similar considerations apply to infinite terms (e.g. 'nonman'), privative terms (e.g. 'blind'), relational terms (e.g. 'father'), and transcendental terms other than 'being' (e.g. 'one'). Hence,

(P1) does not capture all the ways in which a categorematic term can stand in the basic semantic relation of signification to a given individual substance or quality. So Ockham recognizes a second

§ ¢ type of signification, which he sometimes calls 'secondary signification'. Unfortunately, he never gives a precise characterization of this notion, ie. one which marks off all and only those terms which. he claims at one time or another to have secondary signification. The following, somewhat inelegant, characterization is tantamount to that suggested by Paul Spade after a lengthy discussion of the difficulties surrounding this issue:5

(22) A term 'T' secondarily signifies a thing x if and only if (i) 'T' has a nominal definition in the strict sense and (ii) either (a) there is a term 'T*', distinct from 'T', such that 'T*' occurs in an oblique case in the fully expanded nominal definition of 'T', and 'T*' primarily signifies x; or (b) 'T' signifies x but does not primarily j signify x.

| Thus, while an absolute term primarily signifies whatever it signifies, a connotative term is such that it signifies something secondarily.

It is important, I think, not to take (P1) and (P2) as expressing definitions in any standard sense. For one can have all the concepts needed to understand (P1) and (P2) without accepting

Theory of Truth Conditions them. In fact, since many of Ockham's contemporaries rejected his account of primary and secondary signification, it would have been foolhardy for him to assert that principles like (P1) and (P2) are true in virtue of the meanings of their terms in the way in which, say, 'If Socrates is a man, then Socrates is rational' might be construed as true in virtue of the meanings of the terms

'man' and 'rational'. Neither are (P1) and (P2) merely stipulative definitions, since Ockham undoubtedly takes them to reflect a correct understanding of the notion of signification used by his predecessors and contemporaries. It is best, I think, to regard

(P1) and (P2) as proposals which emanate in part from Ockham's theory of universals and whose adequacy cannot be judged apart

| from that of the theory of predication that is built upon them.

Whereas signification is a characteristic which a categorematic term has independently of its use in any given proposition, supposition is a characteristic which it has only as a part of a proposition. The notion of supposition is sometimes equated with the contemporary notion of reference or, perhaps better, denotation.

However, as we shall see, this equation holds only if (a) a predicate term may be said to have reference or denotation and (b) a term may be said to have reference or denotation even when it has no referent or denotatum.

A term has supposition when by means of the proposition in which it occurs it is asserted to stand for something. The notion of supposition plays a central role in Ockham's account of the truth conditions of simple predications. The three types of proper supposition are personal, simple, and material. Of these personal supposition is the most important. For on Ockham's view, in any proposition in which a categorematic term constitutes an extreme, i.e. the whole subject or the whole predicate, that term i may have personal supposition.® That is, there is a reading of that ! proposition on which the term in question is asserted to supposit i for whatever, if anything, it primarily signifies. The following principle seems to accord with what Ockham says:

(P3) There is a reading of proposition 'P' on which term 'T' has personal supposition if and only if (i) 'T' is an extreme in 'P' and (ii) either (a) there is something which 'T' primarily signifies or Theory of Truth Conditions

(b) there is something which 'T' secondarily signifies or (c) 'T' is a demonstrative pronoun."

Hence, in 'A man is an animal' both 'man' and 'animal' have personal supposition. In this case 'man' supposits personally for all men and 'animal' supposits personally for all animals. Moreover, in 'A chimera is a man', the term 'chimera' has personal supposition, even though, if we follow Ockhan, it is impossible that there be anything for which 'chimera' supposits. However, in 'And is a conjunction', only the term 'conjunction' has personal supposition, since the term 'and' does not fulfill any of the three conditions listed under (ii) of (P3). In short, only categorematic terms and demonstrative pronouns may have personal supposition.

Further, just which things a term with personal supposition supposits for in a given proposition is a function of two factors, namely (a) which things, if any, it primarily signifies, and (b) the tense and modality of the proposition in question. We shall see more of this below.

A term, whether categorematic or syncategorematic, has mar terial supposition, generally speaking, when it is taken to supposit for just one spoken or written expression. Analogously, a term fe has simple supposition in a given proposition when it is taken to supposit for just one mental expression. Let us take 'term "T" supposits for thing x' as a primitive locution roughly synonymous with 'term "T" denotes a thing x'. Then, since a term with material or simple supposition cannot fail to have a denotatum, we can characterize these two types of supposition as follows:

(04) A term 'T' has material supposition in a proposition 'P' on reading R if and only if (i) 'T' is an extreme in 'P' and (ii) either (a) 'T' is a spoken or written term and on R 'T' supposits only for itself in 'P' or (b) 'T' is a mental term and on R "T' supposits in 'P' only for the spoken or written term which is subordinated to 'T'.®

(5) A term 'T' has simple supposition in a proposition 'P' on reading R if and only if (i) 'T' is an extreme in 'P' and (ii) either (a) 'T' is a mental term and on R 'T' supposits only for itself in 'P' or (b)

'T' is a spoken or written term and on R 'T' supposits in 'P' only for the mental term to which 'T' is subordinated.

Hence, on one reading of the written proposition 'Man is a threeTheory of Truth Conditions letter word', the term 'man' supposits materially, since it supposits for itself. Again, on one reading of the spoken proposition

'Man is a species', the term 'man' supposits simply, since it supposits for the mental term 'man'. These examples illustrate Ockham's rule that a term may have material or simple supposition

' in a given proposition only if the other extreme of that proposition pertains to terms. That is, the other extreme must primarily signify mental or Conventional terms.' In the above examples

'three-letter word' primarily signifies written words, and 'species', given Ockham's anti-Platonism, signifies mental terms primarily.

With these brief remarks about signification and supposition behind us, we can now turn to Ockham's account of predication.

_He begins by discussing the simplest sort of proposition, namely, 'a present-tense non-modal singular proposition which is not equivalent to a hypothetical, i.e. compound, proposition and both of whose extremes are in the nominative case. For ease of reference let us call such propositions 'S-propositions'.

Ockham 'deals explicitly with two S-propositions, namely, (1) This is an angel and (2) Socrates is a man.

A proposition like (1) or (2) is true, he tells is, just in case its subject and predicate supposit for the same thing. Since all of the extremes in these two propositions may have only personal supposition, we must first formulate the necessary and sufficient conditions for a term's suppositing personally for a thing in a given proposition. It is a general rule that @ term may supposit » personally only for a thing which it primarily signifies.1 However, if we assume for the present that a term may primarily signify

'merely past, merely future, and merely possible beings, then it is not the case that a term always supposits for every individual that it primarily signifies. In present-tense non-modal propositions, which concern us here, a Levin suppositspersonally only for those of its primary significagy | which it is truly predicable bymeans of a present-tense verb. Thus, (P6) A term 'T' supposits personally for an individual xfon (eading R ofp present-tense non-modal proposition 'P' if and only ifDR

Theory of Truth Conditions is a reading on which 'T' has personal supposition in 'P*)and Ki) 'This is (a) 7 is true, where 'this' indicates x.

(From now onI will eliminate reference to readings of propositions when it is clear that the only reading of a given propositio is one in which both extremes have personal supposition.)

Hence, 'angel' in (1) supposits for all presently existing angels (if there are any), and Fman' in (2) supposits personally for all presently existing men (if there are any)! Likewise, 'Socrates' in (2) supposits for Socrates (if he exists), and 'this' in (1) supposits personally for whatever presently existing thing (if any) it is taken to indicate by the person who formulates (1).

It is clear from what Ockham says in other places that an affirmative S-proposition is true only if both its subject and predicate supposit for something. Hence, if Socrates does not exist, then even 'Socrates is Socrates' is false. As a result, the most exact formulation of Ockham's account of the truth conditions of (2) is this:

(3) 'Socrates is a man' is true if and only if there is something for which both 'Socrates' and 'man' supposit in 'Socrates is a man'.

(In what follows I will generally omit from the right-hand side the repetition of the proposition whose truth conditions are being given. However, such a repetition should always be understood,

' since a term has supposition only in a proposition.) Accordingly, (2) is true just in case Socrates exists and is one of the things for which 'man' supposits in (2). A similar account holds for ali affirmative S-propositions. Let 'N' stand for a proper name or demonstrative pronoun and let 'P' stand for a term capable of occupying the predicate position of an S-proposition. Then,

+ (P7) An affirmative S-proposition, 'N is P', is true if and only if there is !

: something for which both 'N' and 'P' supposit.

(Although 'N is P' is, strictly speaking, a propositional schema .

~ rather than a proposition, there is no danger of confusion, I believe, if for the sake of simplicity I allude to it and other propositional schemata as propositions.)

Negative S-propositions are treated as follows:

Theory of Truth Conditions (P8) A negative S-proposition, 'N is not P', is true if and only if there is nothing for which both 'N' and 'P' supposit.

Therefore, a negative S-proposition is true just in case any one of the following conditions obtains: (a) there is nothing for which its subject supposits, (b) there is nothing for which its predicate supposits, or (c) there is something for which its subject supposits and something for which its predicate supposits, but nothing for which both its subject and predicate supposit.

Further, this account also holds for propositions—or for readings of propositions—in which one of the extremes has material or simple supposition, since such terms play a role analogous to that of proper names with personal supposition. Hence,

(4) 'Man is a species' (on the reading on which 'man' has simple supposition) is true if and only if there is something for which both

'man' and 'species' supposit.

Given that we are concerned with the reading on which 'man' has simple supposition, 'man' here supposits for the mental term

'man'. Moreover, the term 'species' has personal supposition in this proposition and has the term 'man' as one of its supposita, since it primarily signifies this term. Hence, on this reading the proposition 'Man is a species' is true.

Given Ockham's account of signification and supposition, it is not difficult to see that his theory of simple predication is consistent with his avowed anti-realism on the question of universals.

For a close inspection of (P1)-(P8), plus perhaps the treatment of abstract terms found in Part I of the Summa Logicae, reveals that'a term never supposits in an S-proposition for anything that is not an individual substance or quality. According to Ockham, then, we do not have to appeal to universals or common natures in order to explicate the truth conditions of S-propositions.

From what has been said so far it is also clear that Ockham's account of predication stands in marked contrast to at least two alternative accounts. According to the first of these alternatives a common term like 'man' in 'Socrates is a man' supposits for or denotes a universal.'° On this account an affirmative S-proposition is true just in case its subject term supposits for something which stands in the relation of exemplification (perhaps signified

} Theory of Truth Conditions by the copula) to the universal for which the predicate term supposits. By contrast, according to Ockham it is required for the truth of such a proposition that both its subject and predicate supposit for the same thing.

According to the second alternative account, the subject of such a proposition supposits for something which—if_the proposition is true~Satisfies a function of the form '.

. is F', where 'F' stands for a predicate in Ockham's sense. Hence, the proponent of this alternative account denies that the subject and predicate of an S-proposition both have the role of suppositing for or denoting something. This alternative is, of course, the standard contemporary account of predication and finds its most important formulation in Frege's writings—although certain philosophers claim that at least the rudiments of the Fregean theory can be found in the writings of one or another medieval philosopher."

Of course, contemporary philosophers differ over just what ontological consequences this function-argument metaphor has when it is employed in semantics. But whatever these ontological consequences might be, it is clear that Ockham's theory is incompatible with such an account on semantic grounds alone. For p even though Ockham does acknowledge in certain cases an asymmetry between the roles of subject and predicate, he insists that this asymmetry merely reflects a difference in the way in which subjects and predicates may be taken to supposit in certain contexts. Hence, even in such contexts both subject and predicate have the property of supposition. Moreover, such asymmetry is absent in the case of S-propositions and thus lends no support, in Ockham's eyes, to the claim that the semantic roles of subject and predicate are in general wholly disparate.

Now if we regard Ockham's account of simple predication as including his account of signification as well as (P7) and (P8), then a third alternative suggests itself. For one might accept (P7) and (P8) with equanimity and yet insist that predicates which are common terms, e.g. 'man' in (2), supposit for individuals only in virtue of the fact that those individuals exemplify or possess the universal or common nature signified by the common term in question. For example, 'man' in (2) supposits for individual men only because those individuals exemplify or possess the universal humanity or human nature. Such a proposal is

Theory of Truth Conditions obviously based on a theory of signification that differs radically from Ockham's. In fact, it employs a distinction between signification and supposition that is roughly equivalent to the distinction between sense and reference as it is used by certain contemporary Platonists. That is, a common term signifies (has as its sense) a universal (property) and supposits for (has as its reference) the individuals which exemplify that universal. It is clear from what has been said that Ockham rejects this-account of signification. On the other hand, the proponent of this third alternative agrees with Ockham that the predicates of propositions like (2) have supposition, just as their subjects do.

Ockham appears to have something like this third alternative in mind in chapter 2 of Part II, although this might not at first be evident. Consider the following passage:

. by means of propositions like 'Socrates is a man' and 'Socrates is an animal' it is not asserted that Socrates has humanity or animality.

Rather, it is asserted that Socrates is truly a man and is truly an animal.

Nor indeed is it asserted that Socrates is the predicate 'man' or the predicate 'animal'. Rather, it is asserted that he is a thing for which the predicate 'man' or the predicate 'animal' supposits.""

Ockham holds that a proposition like (1) or (2) is not exponible. That is, it is not such that it can be expounded in terms of other propositions which reveal more perspicuously its underlying logical form. One reason for this is such a proposition contains only absolute terms,/Propositions containing connotative terms, on the other hand, are exponible and thus equivalent to hypothetical propositions. For example, according to Ockham the term 'white' is a connotative term which secondarily signifies individual whitenesses. Hence, 'Socrates is white' is not an Sproposition. Rather, its underlying logical form is most clearly revealed by the following proposition: 'Socrates exists and a whiteness inheres in Socrates'.

Now except for figment terms and infinite terms, common terms belonging to the category of substance, e.g. 'man', 'animal',

'plant', etc., are, according to Ockham, absolute terms, as are proper names and demonstrative pronouns. Hence, propositions which, like (1) and (2), contain no connotative terms and no syncategorematic elements other than the copula, are not exTheory of Truth Conditions ponible. They wear their logical form on their sleeve, as it were, and cannot be rendered more perspicuous by paraphrase. This is the force of Ockham's claim in the above passage that no more is asserted by (2) than that Socrates is truly a man.

However, the alternative account under discussion in effect =! treats all common terms, including all those in the category of substance, as connotative. For on this account each common term signifies an entity, namely, a universal or common nature, of which it cannot be truly predicated. But if this is so, then even propositions like (1) and (2) are exponible. For example,

'Socrates is a man' is more perspicuously rendered by 'Socrates exists and 'Socrates has humanity', or by 'Socrates exists and "humanity is in Socrates", or by some similar realist variant. And it is precisely the claim that propositions like (2) are exponible which Ockham rejects when he denies that (2) involves the assertion that Socrates has humanity.

Strictly speaking, the proponent of this alternative account would in effect limit the designation 'S-proposition' to at most those propositions in which both the subject and the predicate are either proper names or demonstrative pronouns. Thus, he should not consider (P7) applicable to 'Socrates is a man'. Nevertheless, one who defends this account could agree with Ockham in holding that (2) is true just in case Socrates is a thing for which the predicate 'man' supposits. That is, he could accept with Ockham the following:

(5) 'Socrates is a man' is true if and only if there is some individual for which both 'Socrates' and 'man' supposit.

However, he would also accept (6) Socrates is a man if and only if Socrates exists and has humanity.

'Ockham spends the better part of chapter 2 trying to show that (6) and other realist variations on it are false. For even on the assumption that Socrates is a man, he argues, propositions like

'| 'Socrates has humanity' and 'Humanity is in Socrates' are, taken \ literally, false. The reader can judge for himself the cogency of the arguments that Ockham presents in support of this claim.

But it is clear all along that Ockham assumes that his opponent accepts (5).

Theory of Truth Conditions Perhaps, then, a theory of predication is best understood as involving, at least potentially, two sorts of analysis. The first sort, illustrated by (6), takes place at the level of the object language—or at least contains no allusion to the semantic roles of the subject and predicate of the proposition which occurs on its left-hand side. The purpose of such an analysis is to clarify the logical form, and thus the ontological presuppositions, of the simple predication in question. Ockham claims, against his realist opponent, that an S-proposition does not admit of sy h an analysis or, alternatively, that it is its own such analyaig The second sort of analysis is irreducibly metalinguistic. Its purpose is to explicate the truth conditions of a simple predication in terms of the semantic properties of its components. That 4s, it explains how those components must be linked to the ontology revealed by the first sort of analysis if the simple predication in question is to be arse. (5) serves as an illustration of this second type of analysis./So Ockham's full account of predication differs from the first and second alternatives mentioned above (at least) with respect to the results of this second type of analysis, while it differs from the third alternative with respect to the results of the first sort of analysis.

Before moving on to Ockham's treatment of other types of propositions, I wish to comment briefly on two ways of construing (P7) and (P8) which seem to me to be mistaken and to engender needless difficulties. The first is suggested by Father

Boehner, who claims that in chapter 2 of Part II Ockham is explicating the connotation of the term 'true' (as applied to propositions) in terms of the coincidence of the supposition of the _ subject and predicate terms.'? This means that Ockham's project is at least in part to formulate the correct nominal definition of 'true' and that the definition he offers is something like 'proposition whose subject and predicate supposit for the same thing'.

_ The most obvious objection to Boehner's claim is that the definition of 'true' which he takes Ockham to be proposing is inadequate even as applied to S-propositions, since it does not define the truth of negative S-propositions."* And even though

Ockham-—clearly through an oversight—does not deal explicitly with negative S-propositions in chapter 2, (P8) above is a necessary addendum to his account of simple predication and one

Theory of Truth Conditions which is consistent with remarks he makes about negative propositions both in Part I and in later sections of Part II.

However, a more serious objection to Boehner's claim is this:

| there is simply no good reason to believe that in Part II Ockham is trying to define the term 'true' at all. It seems more likely that he accepts something like the Aristotelian definition, e.g. 'proposition signifying of what is that it is or of what is not that it is not'. In Part II he is trying to formulate the conditions under which various types of propositions fulfill that definition. But the definition of truth remains the same throughout.

This way of viewing Ockham's project obviates one serious problem that Boehner poses for him and other medieval logicians.

For if we assume that Ockham is defining truth in terms of the supposition of subject and predicate, then it is not clear how this definition can apply to hypothetical propositions (or even, as we shall see, to certain types of categorical propositions). However, no such problem arises if Ockham accepts throughout something like the Aristotelian definition of 'true' and is simply trying to formulate the conditions under which propositions of various kinds are true. For it is no more surprising that the truth conditions of, say, a disjunctive proposition differ from those of an Sproposition than it is that the truth conditions of an affirmative

S-proposition differ from those of a negative S-proposition.

, The second issue that I wish to comment on is raised by Mari- ' !? lyn McCord Adams.' In the present context the problem can be stated as follows. (P7) and (P8) are circulat, at least in cases where both the subject and the predicate have personal supposition. For in (P7) and (P8) truth is defined in terms of supposition and in (P6) a term's suppositing personally for a thing is defined in terms of the truth of propositions of the form 'This is (a) T', which are themselves S-propositions when 'T' stands for an absolute term.

The proper response to this problem is simply to point out that (P6), (P7), and (P8) arenot properly construed as definitions. I have already argued this in the case of (P7) and (P8).

Likewise, (P6) merely explicates the conditions which must obtain in order for a term to supposit personally for a thing in a present-tense non-modal proposition. However, it does not define the term 'supposit' or even the expression 'supposit personally for something'. Supposition must, I believe, be regarded either

Theory of Truth Conditions as a primitive notion or as defined in terms of the primitive notion of a term's taking the place of (or being asserted to take the place of) something within a propositional context."

However, perhaps the problem of circularity can be stated more forcefully as follows. (P7) and (P8) are meant to provide us with criteria for determining whether a given S-proposition is true. But according to (P7) and (P8) we must first know what, if anything, the subject and predicate terms of the S-proposition in question supposit for. However, according to (P6) we can know what these terms supposit for only if we first know the truth value of certain

S-propositions of the form 'This is T'. Thus, (P7) and (P8) can serve as criteria for determining the truth value of S-propositions only if we already can determine whether certain S-propositions are true or false. Thus, Ockham's account of simple predication suffers from a circularity which renders it useless as a general cri_terion for determining the truth or falsity of S-propositions.

It is clear, however, that Ockham isnot attempting to provide us here with epistemic criteria for determining the truth value of S-propositions. In fact, he would surely agree that we can ascertain the truth value of many S-propositions without recourse at all to the notion of supposition. Rather, he is trying to determine the semantic relations which obtain between the terms of a given

S-proposition and the individuals which compose the world if and only if the S-proposition in question is true. Such an account is independent of our knowing or being able to determine whether those conditions actually obtain. This latter is a concern for the theory of knowledge, which Ockham deals with in other places.

Of course, in certain instances the theory of truth conditions might help us to determine the truth value of a given proposition. But that is not its primary purpose. For in Part If Ockham is not asking how one determines whether propositions are true.

Rather, he is asking what semantic conditions are necessary and sufficient for the truth of given types of propositions—whether or not anyone is actually in a position to determine their truth values, 3.

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ƼɃ Ƀ Ļ4Ƨȡ 8$bɃ Ƀ ļ ǈ| óɃ Theory of Truth Conditions (P9) A present-tense non-modal A-proposition, 'Every A is B', is true if and only if (i) there is something for which 'A' supposits and (ii) there is nothing for which 'A' supposits and for which 'B' does not supposit.

(P10)A present-tense non-modal I-proposition, 'Some A is B', is true if and only if there is something for which both 'A' and 'B' supposit.

(P11)A present-tense non-modal E-proposition, 'No A is B', is true if and only if there is nothing for which both 'A' and 'B' supposit.

(P12) A present-tense non-modal O-proposition, 'Some A is not B', is true if and only if either (i) there is nothing for which 'A' supposits or (ii) there is something for which 'A' supposits and for which 'B' does not supposit.

As with affirmative S-propositions, an affirmative universal or particular proposition is true only if there is something for which its subject term supposits and something for which its predicate term supposits. Hence, if there are no men, then 'Every man is an animal' is false, while its contradictory, 'Some man is not an animal', and its contrary, 'No man is an animal', are both true.

('Some man is not an animal', however, must be carefully distinguished from 'Some man is a non-animal'. The latter is an Iproposition and thus false if there are no men. The use of infinite terms like 'non-animal' will be discussed below.) Thus, for Ockham the inference from an A-proposition to the corresponding I-proposition is valid whether or not anything exists. The same holds for the inference from an E-proposition to the corresponding O-proposition.

Corresponding to the four traditional forms of universal and particular propositions are four other forms, which I will call

A'-propositions, I'-propositions, E'-propositions, and O'-propositions. In all such propositions the predicate is a common term determined by a universal sign. Ockham discusses only the first two of these forms. However, the other two are their contradictories and so it is not difficult to formulate their truth conditions on the basis of what he says explicitly:*

(P13)A present-tense non-modal A'-proposition, 'Every A is every B', is true if and only if (i) 'A' supposits for exactly one thing and (ii) 'B' supposits for exactly one thing and (iii) there is something for which both 'A' and 'B' supposit.

Theory of Truth Conditions (P14)A present-tense non-modal I'-proposition, 'Some A is every B', is true if and only if (i) there is something for which 'A' and 'B' both

-supposit and (ii) 'B' supposits for exactly one thing.

(P15) A present-tense non-modal E'-proposition, 'No A is every B', is true if and only if either (i) there is nothing for which both 'A' and 'B' supposit or (ii) it is not the case that 'B' supposits for exactly one thing.

(P16)A present-tense non-modal O'-proposition, 'Some A is not every B', is true if and only if either (i) it is not the case that 'A' supposits for exactly one thing, or (ii) it is not the case that 'B' supposits for exactly one thing, or (iii) there is nothing for which both 'A' and 'B' supposit.

The inferential relations which hold among these propositions mirror exactly those which hold among their traditional counterparts. Furthermore, the inferential relations which hold between these propositions and their traditional counterparts can easily be formulated by examining (P9)-(P16).

Ockham thus extends to present-tense non-modal particular and universal propositions the same sort of account which he gives of the truth conditions of S-propositions. And, once again, his theo of predication—construed here to include his theory of signification—guarantees that the truth of particular and universal proposi tions does not presuppose the existence of non-individual things.

One reason whyI have given a prominent place to (P13)-(P16) is that they help to shed some light on a problem which is currently being debated by students of Ockham's logic. The problem is this: how can one relate the above theory of truth conditions for propositions containing quantifiers to the putative rudimentary theory of quantification found in Ockham's discussion of th

"modes of common personal supposition (MCPS) in chapters 69 through 75 of Part I of the Summa Logicae?

Some writers suggest that in Part I Ockham is trying to formulate necessary and sufficient conditions for the truth of propositions containing quantifiers by analyzing such propositions, via the MCPS, into conjunctions and disjunctions of propositions in which only singular terms occur—namely, singular terms composed of a demonstrative adjective and the common terms which served as the subject and predicate of the original proposition.' An exTheory of Truth Conditions ample might help here. In the I-proposition 'Some man is an animal' both the subject and the predicate, Ockham tells us, have determinate personal supposition. For 'Some man is an animal' implies the disjunctive proposition 'This man is an animal or that man is an animal .

. ." and so on for each man. That is, one can validly 'descend' under the term 'man' to a disjunctive proposition, in which singular terms composed of a demonstrative adjective and the term 'man' are the subjects of the various disjuncts.

Likewise, 'Some man is an animal' implies the disjunctive proposition 'Some man is this animal or some man is that animal

'and so on for each animal. That is, a similar descent can be performed under the term 'animal'. And in both cases any one of the disjuncts implies the original I-proposition. Hence, if we perform both of these descents we can, at least in principle, formulate a proposition which is strictly equivalent to the original Iproposition and in which all the terms are singular terms having discrete supposition. This can be shown somewhat more formally as follows. Let { AD/'A'} , following Michael Loux's convention, designate the set of all those things, if any, for which the term

'A' supposits in a present-tense non-modal proposition.?° Further, replace Ockham's demonstratives with numerical subscripts, so that 'A, ', 'A,', etc., are singular terms corresponding to 'this A',

'that A', etc. Then we can formulate the truth conditions for an I-proposition, schematized by 'SomeA is B', in the following way:

(7) 'Some A is B' is true if and only if (i) {AD/'A') is not empty; and (ii) {[(A, is B,) or (A, isB,) or... or (A, isB »)| or [(A,is B,) or (A, is B,) or... or (A, is BY] or [(A, is B,) or (A, is B,) or... or (A, is BL], where A, -A,, exhaust {AD/'A'} and B, -B, exhaust {AD/'B'}).

(7) seems to work fairly well—as well, it seems, as (P10). Moreover, Ockham gives rules for assigning modes of common personal supposition to the subjects and predicates of other types of propositions containing quantifiers. To complete the picture, a term with confused and distributive supposition is such that one (a)

Theory of Truth Conditions can validly descend from it to a conjunctive proposition of the type in question and (b) cannot validly ascend to it from any of the singular propositions which serve as the conjuncts. A term with merely confused supposition is such that one (a) can validly descend from it only to a proposition with a disjunctive extreme

(and not to a disjunctive proposition) and (b) can validly 'ascend to it from any of the singulars. It appears, then, that in Part I Ockham is giving an account of the truth conditions for propositions containing quantifiers, even though he never explicitly claims that this is the project he has in mind.

Unfortunately, one can attribute such a project to Ockham in Part I only if he is also willing to attribute to Ockham a mistake which a logician of his stature would hardly be expected to make.

For, as Gareth Matthews has pointed out, Ockham tells us that the predicate of an O-proposition has confused and distributive supposition.2! Thus, one can descend under the predicate of 'Some man is not an animal' to the conjunctive proposition 'Some man is not this animal and some man is not that animal..

.' and so on for each animal. However, although such an inference is valid, its converse is clearly not valid. Hence, if Ockham is here attempting to provide us with a theory of quantification, i.e. with an account of the sufficient as well as necessary conditions of the truth of propositions containing quantifiers, then he has blundered by assigning confused and distributive supposition to the predicate of an O-proposition. But surely Ockham would not have made such an elementary mistake. Moreover, a close reading of the text reveals that he neve? asserts that in every instance a descent of the appropriate type will yield a proposition that is equivalent to the original proposition.

Nevertheless, some who hold that the account of the MCPS constitutes Ockham's theory of quantification have pointed out, correctly, that the defect just alluded to can easily be rectified by assigning merely confused supposition to the predicate of an O-proposition.?? For the following biconditional is true: 'Some man is not an animal if and only if some man is not this animal or that animal .

." and so on for each animal. Since this is the only case in which Ockham's own assignment of a mode of common personal supposition does not yield equivalence, it is perhaps

Theory of Truth Conditions not unreasonable to conjecture that he simply made a careless mistake in this one isolated instance. Even Matthews does not seem to regard the objection in question as conclusive. Rather, he is more concerned with problems that arise when the common term under which a descent is to be made either is empty or has exactly one suppositum.

However, we are now in a position to see that the case in question is not an isolated one. For a theory of quantification based on the account of the MCPS is also clearly inadequate when applied to E'-, A'-, and I'- propositions. Moreover, given Ockham's interest in propositions of these three forms, it is surely the case that he would have noticed this deficiency and taken steps to correct it—if, that is, he had been proposing a theory of quantification in Part I.

Take the E'-proposition 'No man is every animal'. If one attempts to descend first under the predicate 'animal', he finds that it is impossible to assign any of the three modes of common personal supposition to that predicate. For each of the following inferences is invalid:

(8) No man is every animal, therefore no man is this animal and no man is that animal, etc.

(9) No man is every animal, therefore no man is this animal or no man is that animal, etc.

(10) No man is every animal, therefore no man is this animal or that animal, etc.

Suppose that there are many men, that every man is an animal and that the only animals are men. Then in each of (8), (9), and (10) the antecedent is true and the consequent false. Moreover, in Part I Ockham—wisely, as we can now see—does not assign any of the MCPS to the predicate of an E'-proposition, even though in Part II he is clearly anxious to give an account of the truth conditions of propositions of this type.

If Ockham were proposing a theory of quantification in Part I, he would surely adopt one of two fairly obvious solutions to the problem posed by E'-propositions. The first solution is to recog-. nize a fourth mode of common personal supposition, in which a descent is made to a proposition with a'conjunctive extreme."?

For the following biconditional is true: 'No man is every animal Theory of Truth Conditions if and only if no man is this animal and that animal .

.' and so on for each animal. Ockham discusses propositions with conjunctive predicates in chapter 37 of Summa Logicae II and thus could easily yesort to the notion of a conjunctive extreme in this situation fAn alternative solution is to adopt a 'priority of analysis' tule/ according to which the descent under the predicate term of an E'-proposition must be preceded by the descent under the subject term."* In the above example the first descent would yield a conjunctive proposition, each of whose conjuncts is of the form

'This man is not every animal'. And Ockham explicitly, and correctly, assigns determinate supposition to the predicate of such a proposition.?5 This solution, like the first one, yields both necessary and sufficient conditions for the truth of an E'-proposition.

But Ockham would surely realize this if he were proposing a theory of quantification in Part I. Yet he nowhere even mentions either a fourth type of supposition or a priority of analysis rule.

Moreover, neither of these solutions will help in the case of A'and I'-propositions. Ockham assigns confused and distributive supposition to the predicates of propositions of this type.? However since a proposition of this sort is true only if its predicate supposits for exactly one thing, the only descent possible under the predicate will take the following form: 'Every (some) A is every

B, therefore every (some) A is this B'.27 But it:is clear that the converse of such an inference is not valid, no matter which type of common personal supposition—including the fourth type alluded to above—is attributed to the predicate of the original proposition.

Further, a priority of analysis rule does no good here, since precisely the same problem arises with singular propositions of the form 'This A is every B'. Here, then, is another indication that Ockham did not intend his account of the MCPS to be part of his theory of truth conditions. i However, none of this should be surprising. For(Ockham never

{ Claims that his account of the MCPS is part of his'theory of truth | conditi6ns, whereas he does explicitly claim that the account of -, quantified propositions found in Part II and partially summarized

|| by (P9)-(P16) above is part of his theory of truth conditions.

What is surprising is that so many recent commentators have not taken Ockham at his word. The reasons for this phenomenon need not concern us here. What is important is that Ockham's

Theory of Truth Conditions avowed theory of quantification, found in Part II, is much ' stronger than any theory of quantification that can be con- ' structed from his account of the MCPS—even when that account is amended along the lines suggested above. First, the theory found in Part II handles without emendation all the problem cases cited above. Second, the theory offered in Part II is simpler than any theory based on the MCPS, since both types of theory require the notion of supposition, while only the latter requires in addition the MCPS. Third, as Paul Spade has noted, the theory offered in Part II enables us to formulate in a finite sentence the truth conditions for any universal or particular proposition—even one in which the subject or predicate supposits for infinitely many things."® However, a theory of quantification based on the account of the MCPS requires that a complete explication of the truth conditions of a universal or particular proposition contain an infinitely long proposition if either the subject or the predicate of the original proposition supposits for infinitely many things.

The ability to deal successfully with infinite domains is, of course, a necessary condition for the adequacy of any purported theory of quantification. In the. present context this is sufficient to corroborate my contention that the theory of quantification found in Part II is preferable to any theory based on the account of the MCPS. Moreover, it is interesting to note in passing that Ockham himself could appreciate the importance of this advan_ tage of the theory proposed in Part IJ. For although he denies that there can be an actual infinity of substances or qualities, he clearly holds that a material substance has an actual infinity of parts. For instance, in his commentary on Aristotle's Categories he says:

Although there are infinitely many parts in a continuous thing, it is not possible, according to the Philosopher's principles, that there be infinitely many things, none of which is a part of another."

In fact, in chapter 50 of Summa Logicae I, Ockham employs the assumption that a piece of wood has an actual infinity of proper parts in order to show that if there are any relations at all, then there are infinitely many of them." But since the conTheory of Truth Conditions sequent of this conditional is false, so is the antecedent. Further, he explicitly denies that the parts of such a substance exist only potentially and, hence, that they constitute only a potential infinity. For in that case, he argues, it would be true that an actual~ substance is composed of non-beings—an obvious absurdity. Hence,

Ockham must have realized that his theory of truth conditions had to accommodate the truth, accepted on metaphysical grounds, of certain propositions in which the quantified term supposits for infinitely many things. Indeed, he devotes a whole chapter of Part II to a discussion of the term 'totus', which in its syncategorematic use means 'each part of... '.7!

In light of all this, it is puzzling to find Loux remarking that the mathematics of Ockham's day [does not] 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.°?

(By 'supposition theory' here Loux means the account of the MCPS.) Even if it is the case, as Loux goes on to suggest, that Ockham would have had grave doubts about Cantor's ascending order of infinities, it seems fairly clear that he had no reservations about the existence of actual denumerable (in Cantor's sense) infinities of parts of material things.

Others have argued that Ockham admits into his ontology an actual infinity of possibilia, ie. unactualized possible things, and hence that his theory of truth conditions must be able to handle infinite domains in order to provide a satisfactory treatment of modal propositions containing quantifiers.*>

I will argue later that there is good reason to believe that Ockham neither accepts \ ' nor is commited to the existence (or subsistence) of possibilia.™* However, if I am mistaken in this claim, then we have another indication that Ockham did not intend the account of the MCPS to be a theory of quantification. For such a theory would not be sufficiently powerful to deal with his antecedent ontological commitments—and he himself would surely have noticed this.

It seems plausible, then, both that the account of quantificaTheory of Truth Conditions tion found in Part II is philosophically preferable to any such account based on the MCPS and that Ockham himself would have recognized this fact.

Now perhaps someone will agree that the theory found in Part II is indeed better, but insist that Ockham himself regarded the account of the MCPS as a theory of quantification and that he,

"albeit mistakenly, took the two theories to be equivalent. For in Part II, after giving the truth conditions for particular propositions, he adds that it is sufficient for the truth of a particular proposition that one of its singulars be true.*> Likewise, after giving the truth conditions for universal propositions, he adds that it is commonly said that for the truth of such a proposition it is sufficient that each of its singulars be true.** But such talk of singulars is reminiscent of the account of the MCPS.

Thus, perhaps Ockham proposed two distinct theories of quantification and thought of them as equivalent.

This suggestion, however, is misguided. Ockham's talk of singulars in this section of Part II has to do with singular propositions which are formed by replacing the particular or universal sign determining the subject with a demonstrative term. Thus,

'This man is an animal' is a singular of both 'Every man is an animal' and 'Some man is an animal'. Likewise, 'This man is every animal' is a singular of both 'Every man is every animal' and 'Some man is every animal'. But the predicate of such a singular proposition remains the same as the predicate of the corresponding universal or particular proposition. In terms of the account of the MCPS, then, Ockham's talk of singulars in : Part II involves only the supposition of the subject term of a universal or particular proposition—and not the supposition of the predicate term. But if that is so, then his reference to inferences from singular propositions to their particular and universal counterparts does not constitute an allusion to a fullblown theory of quantification based on the account of the MCPS. For, as noted above, such a theory involves descents to and ascents from propositions which are not only singular propositions but also propositions in which both the subject and predicate are singular terms.

Furthermore, Ockham explicitly claims only that the truth of one (or all) of its singulars is a sufficient condition for the Theory of Truth Conditions truth of the particular (or universal) proposition in question. And later in the Summa Logicae he emphatically asserts that the truth of one (or all) of its singulars is not a necessary condition for the truth of a particular (or universal) proposition, since some true particular and some true universal propositions have no singulars.

Consider the following passage from Summa Logicae III-3, chapter 32:

It should be noted that sometimes a universal proposition has singulars and sometimes it does not have singulars. For when the subject is truly predicated of something, then it has singulars, but when it is not truly predicated of anything, then it does not have singulars.°"

Two points should be made here. First, it is clear from the context of this passage and from the examples that Ockham uses in this chapter that the singulars to which he is alluding need not have singular terms as their predicates. This is consonant with what I said above.

Second, it is true, as Loux has shown in some detail, that the point made by Ockham in the above passage can be accommodated by a theory of quantification based on the account of the MCPS. This is accomplished by adding the appropriate affirmative or negative existential proposition, as either a 'conjunct or a disjunct, to the account of the truth conditions for a universal or particular proposition of a given type. Nevertheless, it seems more reasonable to take the account of the MCPS and Ockham's remarks about singulars as belonging to his theory of inference— which presupposes the theory of truth conditions for categorical propositions—rather than as belonging to his theory of truth conditions.*® There are several considerations in favor of this claim, but I will present only one of them here. Take a universal affirmative proposition like

(11) Each part of this table is a created thing, in which the subject term supposits for infinitely many beings.

As noted above, according to a theory of quantification based on the account of the MCPS the explication of the truth conditions of (11) contains an infinitely long proposition. Since human beings cannot entertain infinitely long propositions, the proposed explication does not render the truth conditions of (11) intelligible

Theory of Truth Conditions to us. Hence, the theory of truth conditions that yields this explication is not one which we can justifiably accept.

Nevertheless, if we grant that there are or can be infinitely long propositions (in Ockham's sense of 'proposition'), then what Ockham says about singulars does commit him to the claim that (11) may be validly inferred froma certain infinitely long conjunctive proposition—call it C. But this claim is not philosophically troublesome if it belongs to Ockham's theory of inference. First, both (11) and C can be handled satisfactorily by the theory of truth conditions found in Part II. The truth conditions of (11) are explicated in accord with (P9) above, and—according to chapter 32 of Part [II—C is true just in case each of its conjuncts is true. Second, even if we cannot entertain infinitely long propositions, we can comprehend the following rule of inference:

(12) A universal proposition of the form 'Every A is B' in which the subject 'A' supposits for infinitely many beings may be validly inferred from an infinitely long conjunctive proposition, each of whose conjuncts is of the form 'This A is B'.

Hence, if we take the account of the MCPS along with the remarks about singulars to be part of Ockham's theory of truth conditions, then the resulting theory of truth conditions is seriously defective. On the other hand, if we take them as part of his theory of inference and take the theory of quantification partially summarized by (P9)-(P16) as part of his theory of truth conditions, then infinitely long conjunctive (or disjunctive) propositions present no serious problems.

The account of past-tense and future-tense propositions that Ockham gives in chapter 7 of Part II, even when it is supplemented by his treatment of the conversion of such propositions in chapter 22, is rather sketchy. Nevertheless, these chapters do provide at least a basis for determining the truth conditions which Ockham would assign to various types of past-tense and future-tense propositions, even though certain ambiguities remain unresolved. For the sake of simplicity I will limit my discussion here to past-tense propositions, since on Ockham's view the semantic account of past-tense propositions corresponds,

Theory of Truth Conditions mutatis mutandis, to that of their future-tense counterparts. This reflects his insistence that every future-tense proposition is either true now or false now.*° Thus, the principles given below can be made to apply to future-tense propositions simply by changing each occurrence of the term 'past' to the term 'future' and each occurrence of the verb 'was' to the verb 'will be'.

Ockham's general strategy is to formulate the truth conditions for a past-tense proposition in terms of the past truth of some present-tense proposition. We can represent this strategy schematically as follows, where the verbs embedded in the propositional contexts '..." and '_ _ _' are the principal verbs of the propositions in question, and where the blank '___' is filled by an appropriate temporal determination:

(13) '...was...'is true if and only if' _ _ _ is __ _' was true at In order to provide an account of the truth conditions of a pasttense proposition P, then, one must determine both (a) which present-tense proposition P is correctly mapped onto and (b) which temporal determination is appropriate in the instance of the above schema that pertains to P.

From (13) it is clear that Ockham formulates the truth conditions of past-tense propositions only indirectly in terms of the notion of supposition. That is, his treatment of past-tense propositions is parasitic on his previous treatment of present-tense propositions and is not formulated—appearances sometimes to the contrary—in terms of the supposition of the subject and predicate in a past-tense proposition. I will discuss this general point in more detail below.

The simplest case here is that of a singular past-tense nonmodal proposition whose subject is either a proper name or a demonstrative pronoun standing alone, e.g. 'Socrates was white',

'This was running', 'That was hot', etc. Let us call such propositions P-propositions. Then (P17) An affirmative P-proposition, 'N was P', is true if and only if 'N is P' was true at some past time.

In this case the relevant present-tense proposition is simply the exact present-tense counterpart of the past-tense proposition in Theory of Truth Conditions question. Further, the temporal determination is suitably indefinite with respect to the past.

Negative P-propositions are somewhat more troublesome. At first glance it seems that a proposition of the form 'N was not P' should be true just in case 'N is not P' was true at some past time. In that case an affirmative P-proposition would not be the contradictory of its negative counterpart, since the relevant present-tense propositions might have been true at different times in the past. For instance, 'Socrates was white' and 'Socrates was not white' would not be contradictories, since 'Socrates is white' might have been true at one time in the past and 'Socrates is not white' might have been true at some other time in the past. However, Ockham claims in chapter 22 that 'Socrates was not white' implies and is implied by 'Nothing which was white was Socrates'.

And this latter proposition appears to entail that nothing was ever both white and Socrates. But if this is so, then Ockham would treat a negative P-proposition as follows:

(P18)A negative P-proposition, 'N was not P', is true if and only if 'N is not P' was true at every past time.

Given (P18), an affirmative P-proposition and its negative counterpart are indeed contradictories. Note, however, that on this account an affirmative proposition of the form 'N was non-P' is compatible with the corresponding proposition of the form 'N was P' and thus does not imply the corresponding proposition of the form 'N was not P'. For instance, 'Socrates was nonwhite' does not imply 'Socrates was not white', even though

'Socrates is non-white' does imply 'Socrates is not white'. So either account of negative P-propositions has the consequence that the inferential relations among P-propositions do not exactly mirror those that obtain among their present-tense counterparts.

If the predicate of a P-proposition contains a more specific temporal determination, as in 'Socrates was white yesterday', then that determination is included in the truth conditions as a modifier of the phrase 'was true'. Hence, 'Socrates was white yesterday' is true just in case 'Socrates is white' was true at some time yesterday. In the same way, 'Socrates was not white yesterday' is true just in case 'Socrates is not white' was true at every time yesterday. The limiting case is one in which a precise moTheory of Truth Conditions ment is specified, as in 'Socrates was white yesterday at 2 P.M.'.

This proposition is true just in case 'Socrates is white' was true yesterday at 2 P.M.

In a P-proposition, Ockham tells us, there is no ambiguity with respect to how the terms supposit. For instance, in 'Socrates was white yesterday' the term 'Socrates' is said to supposit for what was Socrates yesterday and the term 'white' is said to supposit for what was white yesterday. (Later I will argue that this manner of speaking is dispensable and thus does not commit Ockham either to the present existence of merely past individuals or to the possibility that a merely past individual stands in relations:to a presently existing term.) However, whena past-tense proposition has a subject which is or includes a common term, further complications arise. Ockham claims that such a proposition is equivocal and '"'must be distinguished."' For its subject term may be taken to supposit either for just those things of which it is truly predicable by means of a present-tense verb or for just those things of which it is truly predicable by means of a past-tense verb. For example, 'Some white thing was black' may be taken as equivalent either to 'Something which is white was black' or to 'Something which was white was black'. Hence, for each past-tense proposition whose subject is or includes a common term we need two accounts of truth conditions, corresponding to the two distinct ways in which its subject may be understood.

The predicates of such propositions, however, do not share in this ambiguity. For the predicate, Ockham emphasizes, "names its form,"' while the subject does not. This means that the predicate is fixed by the past-tense verb and the further temporal determinations, if any, of that verb. That is, the predicate of a pasttense proposition P must occur unchanged as the predicate of the present-tense proposition in terms of which the truth conditions of P are explicated. Further, the past-tense verb and other temporal determinations, if any, specify the temporal parameters of the truth of that present-tense proposition. Ockham himself says:

In order for a [past-tense] proposition to be true . .

. it is required that the very same predicate be truly predicated of that for which the subject supposits in the manner asserted by means of such a proposition.*!

Theory of Truth Conditions Hence, 'Socrates was white' is true only if some instance of the schema ' is white' was true, and 'Some white thing was black yesterday' is true only if some instance of the schema '____ is black' was true yesterday.

However, as noted above, when the subject of a past-tense proposition is or includes a common term, it is not fixed in this way. If such a subject is taken to supposit only for those things of which it is truly predicable by means of a present-tense verb, then the same subject will not appear in the relevant present-tense proposition. Rather, a coreferential demonstrative pronoun or proper name will appear in its place. Hence, if its subject supposits only for what is now white, then 'Some white thing was black' is true just in case 'This is black' was once true, where

'this' indicated something for which 'white' now supposits in a present-tense proposition. Accordingly, 'Some white thing was black', so understood, may be true, even though 'Some white thing is black' was never true.

In general, when the subject of a past-tense proposition is taken to supposit for what is now such-and-such, we must guarantee that the subject of the relevant present-tense proposition picked out what the subject of the past-tense proposition is intended to pick out—no matter what changes have taken place.

What we need, in short, is a term which picks out one and the same thing at every moment at which it exists. Such a term serves, in contemporary parlance, as a rigid designator across all the times at which its referent exists.

With this in mind, we can now proceed to formulate the truth conditions of past-tense propositions in which the subject is or includes a common term. First we will deal with cases in which the subject is taken to supposit for what is now such-and-such.

Let a Q-proposition be a past-tense non-modal proposition in which the subject is a singular term composed of a demonstrative adjective and a common term. Then

(P19) An affirmative Q-proposition, 'That A was B', where 'that A' is taken to supposit only for something which is now A, is true if and only if (i) there is something for which 'that A' supposits and (ii) 'This is B' was true at some past time, where 'this' indicated the thing for which 'that A' supposits.

Theory of Truth Conditions (P20)A negative Q-proposition, 'That A was not B', where 'that A' is taken to supposit only for something which is now A, is true if and only if either (i) there is nothing for which 'that A' supposits or (ii) 'This is not B' was true at every past time, where 'this' indicated (or was asserted to indicate) the thing for which 'that A' supposits.

Note that 'This is not B' is true whenever the thing for which 'this' is taken to supposit does not exist. Ockham seems to treat demonstrative pronouns on a par with proper names. Since on his view a proper name can fail to supposit for anything in a meaningful and genuinely singular proposition, the same holds for a demonstrative pronoun.

Universal and particular propositions of the sort in question may be treated in the following way:

(P21) A past-tense non-modal A-proposition, 'Every A was B', where 'A' is taken to supposit only for what is now A, is true if and only if (i) there is something for which 'A' supposits and (ii) 'This is B' was true at some past time, no matter which of the supposita of 'A' was indicated by 'this'.

(P22)A past-tense non-modal I-proposition, 'Some A was B', where 'A' is taken to supposit only for what is now A, is true if and only if (i) there is something for which 'A' supposits and (ii) in at least one instance in which 'this' indicated something for which 'A' supposits, 'This is B' was true at some past time.

(P23) A past-tense non-modal E-proposition, 'No A was B', where 'A' is taken to supposit only for what is now A, is true if and only if either (i) there is nothing for which 'A' supposits or (ii) 'This is not B' was true at every past time, no matter which of the supposita of 'A' was indicated (or asserted to be indicated) by 'this'.

(P24)A past-tense non-modal O-proposition, 'Some A was not B', where 'A' is taken to supposit for what is now A, is true if and only if either (i) there is nothing for which 'A' supposits or (ii) in at least one instance in which 'this' indicated (or was asserted to indicate) something for which 'A' supposits, 'This is not B' was true at every past time.

This account can easily be extended to propositions which contain more specific temporal determinations and also to propositions in which the predicate is modified by a universal sign.

Theory of Truth Conditions When the subject term of such a past-tense proposition is taken to supposit for what was such-and-such, a problem of interpretation arises. Take, for instance, the past-tense I-proposition 'Some white thing was black'. Ockham tells us that when the subject of this proposition is taken to supposit for what was white, then this proposition is equivalent to 'Something which was white was black'.

However, this latter proposition is ambiguous, One way to read it is as follows: 'Something which was white at some past time was black at some past time'. On this reading the proposition in question is possibly true, since it does not imply that something was both white and black at the same time. A second way to read it is this: 'Something was both black and white at the same time in the past'. On this construal the proposition in question is necessarily false.

It is difficult to know which reading Ockham took to be the correct one, since his examples are inconclusive on this point.

Loux appears to adopt the first of these readings in his brief discussion of past-tense propositions.*? However, it seems to me that the second reading is more natural, and so I will interpret such propositions accordingly. Although this move will simplify my discussion, nothing essential depends on it. For the principles pertaining to past-tense propositions in Ockham's semantic theory provide us with the resources to handle the propositions in question, no matter how they are interpreted.

One further problem is this. Ockham's talk of a term being taken to supposit for what was such-and-such seems at first glance to commit him to the possibility that things which no longer exist stand in relations to presently existing terms. For, it appears, even if Socrates no longer exists, the subjects of the following propositions supposit for him: 'Socrates was a man' and 'Some man was white', where 'man' is taken to supposit only for what was a man. Nevertheless, Ockham seems to have accepted—and correctly, I believe—the metaphysical principle that only actually existing things can have properties or stand in relations. For, as we shall see below, he insists that a proposition can have a truth value—or, presumably, properties in general—only if it exists. And he often talks in a way which indicates that he would extend this principle to all substances and qualities. But if this is so, then if Socrates no longer exists, no presently existing term can now

Theory of Truth Conditions supposit for him. What, then, does 'Socrates' now supposit for in 'Socrates was a man'?

One solution to this dilemma is to claim that merely past (and merely future) entities do in fact exist in the present, even though they are not 'present in the present'. It is not immediately obvious how to understand this suggestion. Perhaps it entails that all moments of time exist eternally and become present successively. Likewise, each being exists eternally, although some, like

Socrates, are at first merely future beings, become present beings for a short while, and then become merely past beings. Hence, strictly speaking, we should not say that Socrates no longer exists but rather that he is no longer present. Further, it is not the fact that God exists eternally which distinguishes him from mortals like ourselves. Rather, God, unlike a creature, is such that he is always present and never merely past or merely future.

Whether this proposal can be made entirely coherent is a moot: point. It is clear, however, that Ockham would not accept it. For in his commentary on Aristotle's Categories he explicitly denies that the past and future exist:

Furthermore, no part of time exists, since neither the past nor the future exists, Therefore, time itself is not some existent thing totally distinct from other things.** Moreover, the picture painted above has theological consequences that Ockham clearly could not accept. For it entails that no being can either come into existence or pass out of existence. To say, in ordinary parlance, that a thing comes into existence is merely, on the proposed view, to say that it becomes present after having been merely future. Likewise, to say that a thing passes out of existence is merely, on the proposed view, to say that it becomes merely past after having been present. Hence, God cannot now either create a new being from nothing or completely annihilate any existing being. But Ockham would surely reject such a limitation on God's power. Hence, he could not accept the proposal in question.

At this point someone familiar with the entire Summa Logicae might object that the problem that I have constructed is not really a problem for Ockham at all. For he himself alludes

Theory of Truth Conditions to cases in which a term may supposit for a non-being. Specifically, in Part JIJ-4, chapter 13, he says:

[In the inference] 'The Antichrist is not, therefore the Antichrist is not thought of by you'... there is a fallacy of relative and absolute. For one argues from the verb 'to be' taken by itself to the same verb followed by a predicate. And the predicate in question is able to agree with a term which supposits for a non-being as well as with a term which supposits for a being.* Hence, Ockham does not accept the general principle attributed to him above, namely, that a thing cannot stand in relations to existing terms unless it itself exists. But if this is so, then there is no reason why a term cannot supposit for a non-being in a past-tense proposition like 'Socrates was white'.

Before responding to this point I will list a few other examples of invalid inferences that Ockham cites in the context of the passage quoted above. They are: 'The Antichrist does not exist, therefore the Antichrist is not possible'; 'A is producible by God, therefore A exists'; 'A does not exist, therefore A is not producible by God'; 'The Antichrist does not exist, therefore the Antichrist is not foreknown by God'; 'The Antichrist is foreknown by God, therefore the Antichrist exists'. It should be clear that each of these cases involves modality, either alethic or epistemic.

What Ockham says in the passage quoted above is, if taken literally, clearly inconsistent with the account in Summa Logicae

II of the truth conditions of propositions containing infinite terms. For, as we will see below, he makes it clear that he takes every singular proposition of the form '___ is a non-being' to be necessarily false. Yet the passage just cited commits him to the thesis that there are non-beings, i.e. things which do not actually exist. So the account of truth conditions found in Part II is incompatible with his claim here that a term may supposit for a non-being.

Moreover, as noted above, the inferences which Ockham is concerned with here all involve modal notions. In the next section I will argue that his treatment of modality in Part II does not commit him to the thesis that there are things which do not actually exist. My own inclination, then, is to take the theory of truth conditions found in Part II as canonical and then to Theory of Truth Conditions argue that that theory can, without making the assumption that there are non-beings, yield the result that each of the inferences listed above is indeed invalid. Summa Logicae IlI-4 constitutes

Ockham's tract on fallacies. His main purpose in the above passage, then, is simply to point out that the inferences he cites are invalid. On my view, however, the reason for their invalidity is stated rather carelessly. And although I will not return to this problem in the present essay, I believe that. the invalidity of such inferences can be adequately explicated within the framework of the modal semantics outlined below, supplemented by Ockham's account of intentionality in those cases which involve epistemic modality.** It should also be noted in the present context that none of the examples cited by Ockham involves a past-tense or future-tense proposition. Hence, it is not clear that he intends the point he is making to apply to such propositions in general.

In view of all this, I will concentrate in this essay on the following question: does Ockham's theory of truth conditions as presented in Part II of the Summa Logicae involve an irrevocable commitment to the thesis that there are merely past, merely future, or merely possible entities?*® And I will assume for now that the theory presented in Part II can adequately explain the reason for the invalidity of the inferences alluded to above.

With this in mind, we can return to our original problem: if Socrates no longer exists, then what does the term 'Socrates' supposit for in 'Socrates was a man'? The solution to this problem is, I believe, suggested by the fact that Ockham explicates the truth conditions of past-tense propositions in terms of the past truth of present-tense propositions rather than directly in terms of the supposition of subjects and predicates in past-tense propositions. A close examination of (P17) and (P18) reveals that at no point is there mention of a term suppositing at present for a past individual. Rather, the occurrence of terms which are taken to supposit for what was such-and-such points back, as it were, to previous occurrences of those same terms in present-tense propositions.*" For example, Ockham does not say that 'Socrates was white' is true now just in case 'Socrates' supposits for a past individual which 'white' also supposits for. Rather, this proposition is true, he tells us, just in case 'Socrates is white' was once true,

Theory of Truth Conditions i.e. just in case the terms 'Socrates' and 'white' once supposited for the same individual in the present-tense proposition 'Socrates is white'. The same treatment is accorded the predicate terms in propositions of the forms explicated in (P19)-(P24).

Hence, talk about merely past individuals—in fact, talk about a past individual in general, whether or not it has ceased to exist— can be dispensed with in favor of talk about the semantic relations which terms once entered into in the context of presenttense propositions. Thus, in order to give truth conditions for past-tense propositions, Ockham has to talk only of what terms once supposited for in present-tense propositions—and not of what terms now supposit for in past-tense propositions. And this interpretation is suggested straightforwardly by the essential role that Ockham assigns to present-tense propositions in his account of the truth conditions of past-tense (and future-tense) propositions.

With this in mind we can proceed to an explication of those past-tense propositions in which the subject is or includes a common term and is taken to supposit for what was such-and-such:

(P25) An affirmative Q-proposition, 'That A was B', where 'that A' is taken to supposit for something which was A, is true if and only if 'That A is B' was true at some past time.

(P26) A negative Q-proposition, 'That A was not B', where 'that A' is taken to supposit for something which was A, is true if and only if 'That A is not B' was true at every past time.

(P27) A past-tense non-modal A-proposition, 'Every A was B', where 'A' is taken to supposit only for what was A, is true if and only if (i) 'Every

A is B' was true at some past time and (ii) 'Every A is B' was true at every past time at which there was something for which 'A' supposited.

(P28) A past-tense non-modal I-proposition, 'Some A was B', where 'A' is taken to supposit only for what was A, is true if and only if 'Some A is B' was true at some past time.

(P29) A past-tense non-modal E-proposition, 'No A was B', where 'A' is taken to supposit only for what was A, is true if and only if 'No A is B' was true at every past time.

(P30) A past-tense non-modal O-proposition, 'Some A was not B', where 'A' is taken to supposit only for what was A, is true if and only if either (i) 'Some A is not B' was true at every past time or (ii)

'Some A is not B' was true at some past time at which there was something for which 'A' supposited.

Theory of Truth Conditions Someone might object that the left-hand side of each. of (P25)- (P30) still contains the problematic phrase '"'where 'A' is taken to supposit only for what was A." However, locutions of this sort are meant merely to disambiguate past-tense propositions in which the subject is or includes a common term. But the ambiguity of such propositions can be adequately characterized in syntactic terms alone, without any reference to the notion of supposition, for this ambiguity is in essence a scope ambiguity. In an ambiguous past-tense proposition the past-tense verb (including its more specific temporal determinations, if any) may have as its scope either the whole proposition or just the predicate alone.*® And the scope of the verb, as we have seen, determines just which present-tense proposition it is that the past-tense proposition in question is to be mapped onto. When the scope of the verb is the whole proposition, then both the subject and the predicate will appear unchanged in the relevant present-tense proposition.

On the other hand, when the scope of the verb is the predicate alone, only the predicate will appear unchanged in the relevant present-tense proposition. The ambiguity in question is, in fact, like that between the sense of composition and the sense of division in the case of modal propositions with a dictum. This latter ambiguity will be discussed below.

Hence, we could rewrite (P22) and (P28), for example, as follows:

(P22*) 'Some A was B', taken in the sense of division, is true if and only if (i) 'Some A is a being' is true and (ii) in at least one instance in which 'this' indicated something for which 'A' supposits in 'Some A is a being', 'This is B' was true at some past time.

(P28*) 'Some A was B', taken in the sense of composition, is true if and only if 'Some A is B' was true at some past time.

An Ockhamistic semantics, then, is not irrevocably committed to the existence of either merely past or merely future individuals.

And there is at least some evidence to suggest that Ockham himself understood this.

There is much more that could be said about Ockham's account of past-tense and future-tense propositions. However, I will limit the present discussion to one problem that might occur to Theory of Truth Conditions the reader of Part IJ. Ockham, as we have seen, attempts to explicate the present truth of past-tense propositions in terms of the past truth of present-tense propositions. However, as noted above, in several places he explicitly denies that propositions are eternal entities. In order to have a truth value a proposition must exist, and in order to exist it must be formulated by some person.*" Now according to the principles laid out above, the present truth of a given past-tense proposition entails that some specific present-tense proposition was true in the past, and hence that it existed in the past, i.e. was formulated by someone. But it is surely implausible to believe that every true past-tense proposition is such that the present-tense proposition that appears in the account of its truth conditions was once uttered or thought or otherwise expressed by someone. Even the simplest case serves to illustrate this fact. Suppose that Socrates was white yesterday.

It surely does not follow that anyone, including Socrates, formulated the proposition 'Socrates is white' at some time yesterday. And suppose that no one did formulate it. Then it was not true at any time yesterday—and thus, on Ockham's account

'Socrates was white yesterday' is false, even though we assumed that Socrates was white yesterday. The problem obviously becomes more acute when we are dealing with past-tense propositions—of the sort to be found in geological and cosmological writings—which make ostensibly true claims about times at which no intelligent creature existed. It seems, then, that Ockham's strategy in dealing with past-tense and future-tense propositions is, though clever, doomed to failure.

One interesting response to this problem would be an attempt to recast (P17)}(P30) above directly in terms of the supposition of the subjects and predicates of past-tense propositions. For instance, the truth conditions of an affirmative P-proposition might be reformulated as follows:

(14) An affirmative P-proposition, 'N was P', is true if and only if 'N' supposits for what was N and 'P' supposits for what was P and there was something for which both 'N' and 'P' supposit.

In this way we could avoid any reference to a proposition other than the past-tense proposition which is being explicated.

Theory of Truth Conditions First of all, however, it is not clear to me whether this wholesale revision of Ockham's theory could be carried out successfully. Second, even if it could be, the proposal itself raises anew the question of whether it is generally true that the terms of pasttense propositions may supposit for merely past beings. In light of our previous discussion of this issue, it seems best to regard the suggestion in question as one which should be adopted only if there is no workable alternative.

A more attractive response to the problem in question is to resort to subjunctive conditionals of the form (15) If proposition 'P' were to exist in the future at such-and-such a time, then it would be true and (16) If proposition 'P' had existed at such-and-such a time in the past, then it would have been true.

Ockham himself, in fact, makes use of such conditionals at one point in chapter 7. Adopting this suggestion, we could change the general form of the explication of the truth conditions of a pasttense proposition to (17) Past-tense proposition 'P' is true if and only if either (i) presenttense proposition 'Q' was true at such-and-such a past time or (ii) if 'Q' had existed at every past time, it would have been true at such-and-such a past time.

We could then reformulate (P17)-(P30) accordingly.

However, there is a further problem here. Suppose that 'Socrates is white' was formulated yesterday and was true. Then, given

(17), it follows that a certain past-tense proposition, namely, 'Socrates was white', is true today. Hence, it follows that that past-tense proposition is formulated today. But even if 'Socrates is white' was true yesterday, it is clearly possible that no one will formulate the proposition 'Socrates was white' today. In that case, one who endorses (17) is forced to admit that it is possible for a proposition to be true even when it does not exist.

The only escape from this difficulty is to employ subjunctive conditionals on both sides of a principle like (17), as in oY

Theory of Truth Conditions (18) Past-tense proposition 'P' is true, or would be true if it now existed, if and only if either (i) present-tense proposition 'Q' was true at such-and-such a past time or (ii) if 'Q' had existed at every past time, it would have been true at such-and-such a time.

(18) at least tries to accommodate the commonsense intuition that there are unexpressed truths about the past. But a moment's teflection reveals that we must make an analogous move in the treatment of present-tense propositions in order to accommodate the intuition that there are unexpressed truths about the present.

This may not be an insuperable objection to the suggestion in question, but it is obvious that the resulting theory of truth conditions would be enormously complicated. Unfortunately, this might be the price that Ockham has to pay in order to remain consistent.

In any case, it is certainly true that Ockham's theory would be greatly simplified by the assumption that every proposition exists at every moment of time. In fact, he often proceeds as if this were the case. Apparently, his main reason for denying that every proposition always exists is his reluctance to posit entities that are both eternal and independent of God. But it is not immediately clear why he cannot hold that certain propositions— namely, those formed by God—are eternal but dependent entities. Further, such propositions would be individuals, just as are the propositions formed by angels and men.*°

However, Ockham's understanding of the notion of divine simplicity seems to rule out this alternative. For such propositions would have to be individual qualities of God's intellect, and there would be an infinite number of them. But God can have no such qualities—and, moreover, he knows everything by means of one act of knowing which is identical with his essence.

Nevertheless, Ockham often speaks of God's knowing propositions.5! That is, in order to explicate the notion of God's omniscience, Ockham speaks as if God has a divine language, analogous to human language, in which he formulates propositions. God is omniscient in that he knows with respect to every proposition whether it is true or false. If we take such talk literally, then

Theory of Truth Conditions God's being necessarily omniscient appears to entail that he forms propositions. In that case, the assumption that he formulates every proposition at every moment, and hence that every proposition exists at every moment, is unexceptionable.

The relevant question, of course, is this: should we take literally the notion of a divine language? Is the above picture of God's mental life compatible with Ockham's construal of the notion of divine simplicity? If so, then the above solution is available to him. If not, then some version of the proposal to introduce subjunctive conditionals into the explication of truth conditions appears to be his most promising escape from the problem we have been discussing. In that case, however, Ockham's failure to treat explicitly the truth conditions of subjunctive conditionals takes on added significance.

Ockham's complete account of modal propositions—scattered as it is through the various parts of the Summa Logicae—is much too extensive to be treated fully here. Nevertheless, I will try to sketch its basic features and discuss certain questions to which it gives rise.

It should first be noted that on Ockham's view any term which can be truly predicated of a whole proposition is a mode and is capable of rendering a proposition modal. Hence, all of the following are modes: 'necessary', 'possible', 'impossible', 'contingent',

'true', 'false', 'written', 'spoken', 'thought', 'known', 'believed', 'opined', etc. In the present context I will concentrate on the first four of the modes just mentioned. Moreover, since Ockham takes 'contingent' to mean 'neither necessary nor impossible' (or:

'possible but not necessary') and 'impossible' to mean 'not possible', we can simplify matters by limiting our discussion to the modes 'necessary' and 'possible'.

Ockham's strategy in dealing with modal propositions is analogous to his strategy in dealing with past-tense and future-tense propositions, In each case he explicates the truth conditions of the modal proposition in question in terms of the modal status of some non-modal proposition.*? This strategy is captured by the following schema, where '.. ." and '_ _ _' are propositional contexts:

Theory of Truth Conditions (19) 'It is necessary (possible) that .

. ." is true if and only if this is necessary (possible): '__ _.

Roughly speaking, just as the past and future tenses were relegated to the metalanguage in the explication of the truth conditions of past-tense and future-tense propositions, so too modal terms are now relegated to the metalanguage in the semantic account of the truth conditions of modal propositions. They become, in fact, metalinguistic predicates.*? So in order to determine the truth conditions for a given modal proposition we must map that proposition onto the appropriate non-modal proposition and predicate the appropriate modal term of the latter.

Let us assume for now that the standard form of a de necessario proposition is (20) It is necessary that P, and that the standard form of a de possibili proposition is

(21) It is possible that P, where 'P' takes indicative sentences as substitutes. A proposition of the form of (20) or (21) is said to be a modal proposition

'with a dictum', where 'that P' in English corresponds to the Latin accusative-with-infinitive construction, which medieval logicians called the dictum of such a proposition. According to Ockham and others, a proposition of the form of (20) or (21) is ambiguous, since it may be understood in either the sense of composition or the sense of division. When such a proposition is taken in the sense of composition (or composed sense), it is asserted that the modal term is truly predicable of the proposition which corresponds to the dictum. Hence, we can formulate the following principles, which hold no matter which proposition is substituted for 'P':

(P31) 'It is necessary that P', taken in the sense of composition, is true if and only if this is necessary: 'P'.

(P32) 'It is possible that P', taken in the sense of composition, is true if and only if this is possible: 'P'.

Ockham later asserts that a proposition is necessary just in case, if it exists, it is true and cannot be false. On the other

Theory of Truth Conditions hand, a proposition is impossible just in case its existence entails its being false."* From this we can infer that a proposition is possible just in case its existence is compatible with its being true.

Unfortunately, Ockham's insistence that propositions are neither eternal nor necessary existents leads to difficulties here, just as it did in the case of past-tense and future-tense propositions. In fact, the problem is somewhat more intractable with respect to modal 'propositions.°*> Take the proposition 'No proposition is negative'. Its contradictory, namely, 'Some proposition is negative', is not necessary, since it could exist and be false if God were to destroy all negative propositions. But if its contradictory is not necessarily true, then we should expect that 'No proposition is negative' is possible. However, the latter is impossible according to the above characterization of a proposition's being impossible, since it cannot exist without being false. For it constitutes its own counterexample. Moreover, many other such puzzles are generated by the above characterization of necessity and impossibility.

The obvious—and ultimately, perhaps, the best—solution to this problem is simply to admit that propositions exist necessarily and eternally.*° However, we have already seen that Ockham is reluctant—on theological grounds—to make such a move.

Excluding this radical solution, the most ingenious alternative is suggested by Buridan, who distinguishes a proposition's being possible from its being possibly true and a proposition's being necessary from its being necessarily true.*' A full discussion of this proposal would take us too far afield. However, there are some interesting treatments of Buridan's distinctions in recent philosophical literature, and the interested reader may wish to consult them.*® I will simply sidestep this issue for the present by assuming that propositions are necessary beings. This will at least provide us with the chance to look at other aspects of Ockham's treatment of necessity and possibility. One final point on this matter is, however, in order. Ockham here and in other places emphasizes that it is not sufficient for a proposition's being necessary that it always be true (or even that it be true whenever it exists).

Rather, it must also be such that it cannot be false. Moreover, Theory of Truth Conditions even though Ockham acknowledges a type of necessity which is had by every true (genuinely) past-tense proposition, once again the key is not that such a proposition will always be true in the future, but rather that it cannot be made false in the future— even by the power of God.* (I will not be discussing this latter type of necessity, sometimes called "necessity per accidens," in this introduction, since Ockham does not talk about it specifically in Part II—even though a few of his examples presuppose it. Rather, he is mainly concerned with logical necessity and logical possibility. Hence, in what follows 'necessary' and 'possible' should be read as 'logically necessary' and 'logically possible'.)

With all this in mind, take a simple S-proposition, e.g. 'Socrates is a man'. This proposition is necessary just in case it cannot be false. Since it entails that Socrates exists, it is necessary only if 'Socrates exists' is necessary. But, according to Ockham, 'Socrates exists' can indeed be false, since Socrates can cease to exist.

Hence, 'Socrates is a man' is not necessary. (The same holds, interestingly enough, for 'Socrates is Socrates'.) On the other hand,

'God exists' is necessary, since God is not a contingent being.

However, 'God is a creator' is not necessary, since God could have chosen not to create anything, in which case 'God is a creator' would have been false.

When propositions of the form of (20) or (21) are taken in the sense of division (or divided sense), the explication of their truth conditions becomes more complicated. In such cases the modal term does not have as its scope the whole embedded proposition. Rather, it determines only the predicate. Hence, a modal proposition with a dictum, taken in the sense of division, is equivalent to a modal proposition without a dictum. A proposition of this latter type takes the following form:

(22) Sis P, where 'S' and 'P' stand for the subject and predicate of the proposition embedded in the corresponding proposition with a dictum, and the blank is to be filled by the adverbial form of the mode in question. Some examples are 'Some man is necessarily an animal' and 'This white thing is possibly black'. Hence, a modal proposition of the form of (20) or (21) is ambiguous in Theory of Truth Conditions a way analogous to that in which a past-tense or future-tense proposition is ambiguous when its subject is or includes a common term. Ockham notes this analogy at several places in the Summa Logicae. And he deals with the ambiguity of modal propositions with a dictum in the same way. That is, he maps propositions taken in the sense of composition onto their exact non-modal counterparts; and he maps propositions taken in the sense of division onto non-modal propositions in which the subject term is a demonstrative pronoun or a proper name.

In Summa Logicae Il1-3, chapter 14, Ockham divides de necessario and de possibili propositions without a dictum into those which are primary and those which are derived.®® In each instance a primary proposition has a derived counterpart to which it is equivalent in virtue of the interrelations between the modes of necessity and possibility. Although this division will strike the contemporary reader as somewhat arbitrary, it proves to be a convenient ordering principle. According to Ockham, a modal proposition is primary just in case its modal term is not preceded by a negation. Ockham himself divides only particular and universal propositions in this way, but we can easily extend the distinction in question to singular propositions—both those whose subject is a proper name or demonstrative pronoun and those whose subject includes a common term.

Let an R-proposition be a singular present-tense de possibili or de necessario proposition without a dictum, whose subject is a proper name or demonstrative pronoun. R-propositions can be of one of four primary forms listed below (with their respective derived forms in parentheses):

(23) N is necessarily P (N is not possibly not P) (24) N is necessarily not P (N is not possibly P) (25) N is possibly P (N is not necessarily not P) (26) N is possibly not P (N is not necessarily P) From what Ockham says about such propositions we can conclude that (23) and (26) are contradictory forms, as are (24) and (25).

The following captures Ockham's account of the truth conditions of R-propositions:

Theory of Truth Conditions (P33) An affirmative de necessario R-proposition, 'N is necessarily P', is true if and onlyif this is necessary: 'N is P'.

(P34) A negative de necessario R-proposition, 'N is necessarily not P', is true if and only if this is necessary: 'N is not P'.

(P35) An affirmative de possibili R-proposition, 'N is possibly P', is ; true if and only if this is possible: 'N is P'.

(P36) A negative de possibili R-proposition, 'N is possibly not P', is true if and only if this is possible: 'N is not P'.

Hence, in giving the truth conditions for an R-proposition, Ockham maps the R-proposition in question onto its exact nonmodal counterpart. One interesting consequence of this treatment is.that 'Socrates is necessarily a man' turns out to be equivalent to 'It is necessary that Socrates is a man', taken in the sense of composition. As we have already seen, the latter is false. Thus, the former is also false.

This result appears to place in doubt Ockham's commitment to an essentialist account of substance, i.e. to the thesis that a substance is characterized necessarily (or essentially) in certain ways and only contingently (or accidentally) in other ways. For the truth of propositions like 'Socrates is necessarily a.man' is often thought to be crucial to such an account. According to Ockham, however, an affirmative de necessario R-proposition is true only if its subject term supposits for a necessary being. And the only necessary being is God.*!

Nevertheless, there is really no problem here. For Ockham can and does accept propositions such as (27) Socrates is a man and Socrates is necessarily not a non-man and (28) Socrates is a man and it is necessary that if Socrates is a being,

But it is precisely propositions like (27) and (28) which the essentialist typically takes to be equivalent to 'Socrates is necessarily a man' and which are themselves the comerstone of an essentialist account of substance. The only disagreement between Ockham and these other essentialists, then, centers on the claim that (27) or (28) is equivalent to 'Socrates is necessarily a man'.

Theory of Truth Conditions Ockham can deny such an equivalence and yet remain an essentialist by accepting propositions like (27) and (28) themselves.

It is also interesting to note that Ockham apparently does not believe that an R-proposition of the form 'N is possibly P' entails the corresponding proposition of the form 'N exists' or 'N is a being'. The reason for this is that, given (P35), the proposition

'Socrates is possibly a carpenter', for instance, is equivalent to 'It is possible that Socrates is a carpenter', taken in the sense of composition. But the latter itself does not, on Ockham's view, entail that Socrates exists. For it is reasonably clear that Ockham believes that a proper namie, once imposed ona given individual, continues (or, at least, may continue) to function as a proper name even after that individual has ceased to exist. Hence, even though Socrates no longer exists, the term 'Socrates' is a proper

'name in our language, and the proposition 'Socrates is a carpenter' is a meaningful, albeit false, singular proposition in our language. But 'Socrates is a carpenter' is not impossible. Therefore,

'Socrates is possibly a carpenter' is true, even though Socrates does not exist.

This result is somewhat counterintuitive, since one might be tempted to think that the proposition in question is equivalent to the claim that Socrates has the characteristic of being possibly such that he is a carpenter. But given that Socrates has no characteristics at all unless he exists, this claim entails that he does indeed exist. Ockham, on the other hand, is apparently not tempted to think of 'Socrates is possibly a carpenter' in this way.

We are now ready to treat singular propositions of the type in question in which the subject includes a common term. Let a Tproposition be a singular present-tense de necessario or de possibili proposition without a dictum, in which the subject term is composed of a demonstrative adjective and a common term. Tpropositions may be divided into primary and derived forms as follows:

(29) That A is necessarily B (That A is not possibly not B) (30) That A is necessarily not B (That A is not possibly B) (31) That A is possibly B (That A is not necessarily not B) (32) That A is possibly not B (That A is not necessarily B)

Theory of Truth Conditions (29) and (32) are contradictory forms, as are (30) and (31). The account of the truth conditions of (29) and (30) are relatively straightforward. In de possibili propositions of this type, however, the subject term may be taken to supposit only for what is actually such-and-such or for that which is possibly such-and such as well. This distinction raises some rather interesting semantic and philosophical problems. However, I will postpone a discussion of them until later. For the present I will concentrate on the less problematic cases, i.e. those in which the subject term is taken to supposit for what is actually such-and-such. As far as I can tell, Ockham takes this reading of (31) and (32) to be the one on which they are the contradictories of (30) and (29), respectively. With this in mind, we can formulate the truth conditions for T-propositions as follows:

(P37) An affirmative de necessario T-proposition, 'That A is necessarily B', is true if and only if (i) there is something for which 'that A' supposits and (ii) 'This is B' is necessary, where 'this' indicates the thing for which 'that A' supposits.

(P38) A negative de necessario T-proposition, 'That A is necessarily not _B', is true if and only if either (i) there is nothing for which 'that A' supposits or (ii) 'This is not B' is necessary, where 'this' indicates the thing for which 'that A' supposits.

(P39) An affirmative de possibili T-proposition, 'That A is possibly B', where 'that A' is taken to supposit for something which is actually

A, is true if and only if (i) there is something for which 'that A' supposits and (ii) 'This is B' is possible, where 'this' indicates the thing for which 'that A' supposits.

(P40) A negative de possibili T-proposition, 'That A is possibly not B', where 'that A' is taken to supposit for something which is actually

A, is true if and only if either (i) there is nothing for which 'that A' supposits or (ii) 'This is not B' is possible, where 'this' indicates the thing for which 'that A' supposits.

Since the subject term of a T-proposition includes a common term, the non-modal proposition onto which it is mapped has as its subject a demonstrative pronoun (or proper name) that supposits for the same thing that the subject of the T-proposition supposits for. Hence, 'This white table is possibly black' is true just in case 'This is black' is possible, where 'this' and 'this white

Theory of Truth Conditions table' supposit for the same thing. On the reasonable assumption that this latter proposition is indeed possible, 'This white table is possibly black' is true, even though 'This white table is black' is impossible.

The situation is similar with respect to universal and particular modal propositions without a dictum. Such propositions are divided into primary and derived forms as follows:

(33) Every A is necessarily B (No A is possibly not B) (34) Every A is necessarily not B (No A is possibly B) (35) Some A is necessarily B (Some A is not possibly not B) (36) Some A is necessarily not B (Some A is not possibly B) (37) Every A is possibly B (No A is necessarily not B) (38) Every A is possibly not B (No A is necessarily B) (39) Some A is possibly B (Some A is not necessarily not B) (40) SomeA is possibly not B (SomeA is not necessarily B) I will again take the de possibili propositions to be such that their subject terms are understood to supposit for what is actually such-and-such. Hence, the following pairs are contradictory: (33) and (40), (34) and (39), (35) and (38), and (36) and (37). And, Ockham tells us, the following pairs are related as logical contraries: (33) and (34), (33) and (36), and (34) and (35). These relationships are captured by the following:®

(P41) A present-tense de necessario A-proposition, 'Every A is necessarily B', is true if and only if (i) there is something for which 'A' supposits and (ii) 'This is B' is necessary, no matter which of the supposita of 'A' is indicated by 'this'.

(P42) A present-tense de necessario E-proposition, 'Every A is necessarily not B', is true if and only if (i) there is nothing for which 'A' supposits or (ii) 'This is not B' is necessary, no matter which of the supposita of 'A' is indicated by 'this'.

(P43) A. present-tense de necessario I-proposition, 'SomeA is necessarily B', is true if and only if (i) there is something for which 'A' supposits and (ii) in at least one instance in which 'this' indicates something for which 'A' supposits, 'This is B' is necessary.

(P44) A present-tense de necessario O-proposition, 'Some A is necessarily not B', is true if and only if either (i) there is nothing for which Theory of Truth Conditions 'A' supposits or (ii) in at least one instance in which 'this' indicates something for which 'A' supposits, 'This is not B' is necessary.

(45) A present-tense de possibili A-proposition, 'Every A is possibly B', where 'A' is taken to supposit only for what is actually A, is true if and only if (i) there is something for which 'A' supposits and (ii) 'This is B' is possible, no matter which of the supposita of 'A' is indicated by 'this'.

(P46) A present-tense de possibili E-proposition, 'Every A is possibly not B', where 'A' is taken to supposit only for what is actually A, is true if and only if either (i) there is nothing for which 'A' supposits or (ii) 'This is not B' is possible, no matter which of the supposita of 'A' is indicated by 'this'.

(P47) A present-tense de possibili 1-proposition, 'Some A is possibly B', where 'A' is taken to supposit only for what is actually A, is true if and only if (i) there is something for which 'A' supposits and (ii) in at least one instance in which 'this' indicates something for which 'A' supposits, 'This is B' is possible.

(P48) A present-tense de possibili O-proposition, 'Some A is possibly not B', where 'A' is taken to supposit only for what is actually A, is true if and only if either (i) there is nothing for which 'A' supposits or (ii) in at least one instance in which 'this' indicates something for which 'A' supposits, 'This is not B' is possible.

(P41)-(P48) constitute, I believe, a faithful rendering of what Ockham has in mind.

But how are we to deal with a proposition like 'Some A is possibly B' when 'A' is taken to supposit for what can be or is possibly A? Does Ockham believe that the subject of such a proposition may have among its supposita merely possible beings? And, given that he believes some such propositions to be true, is he thereby committed to the thesis that there are merely possible beings, i.e. unactualized possible beings?

These questions are rather difficult to settle on textual grounds alone. However, I believe that a strong case can be made for each of the following claims: (a) that Ockham explicitly rejects in the Summa Logicae the thesis that there are merely possible things; and (b) that his treatment of modal propositions in the Summa

Logicae does not commit him, as it were unwillingly, to that thesis.

One way to understand the claim that there are merely possible Theory of Truth Conditions things is as follows: among the things which populate our world some are actual beings and others are merely possible beings. The latter might have actually existed if things had turned out differently, e.g. if God had decided to create things other than those which he has created and will create. The term 'being' signifies both actual and merely possible beings, then, in the affirmative present-tense proposition (41) Some beings are merely possible.

This proposition is taken to be a non-modal proposition whose subject is 'being' and whose predicate is 'merely possible (being)'.

This predicate signifies beings which are, so to speak, real but not actual.

Now it is clear beyond doubt that Ockham rejects the claim that there are merely possible beings when it is interpreted in this way. The clearest indication of this comes in chapter 38 of Summa Logicae I, where he says the following:

Similarly, being is divided into being in potency and being in act. This should not be understood to mean that something which does not actually exist but possibly exists is truly a being, and that something else which does actually exist is also a being. Rather, in dividing being into potency and act in Metaphysics V, Aristotle meant that the term 'being' is predicated of some (terms) by means of the word 'is' in a proposition that is simply non-modal and not equivalent to a de possibili proposition, e.g. 'Socrates is a being' and 'A whiteness is a being'; but of other (terms) it is not predicated except in a de possibili proposition, e.g. 'The Antichrist is possibly a being' or 'The Antichrist is a being in potency'. Hence, in the passage in question he wants to say that 'being', like 'knowing' and 'sleeping', is predicable both potentially and actually—and yet nothing knows or sleeps unless it 'actually knows or sleeps.

Again, in chapter 31 of Summa Logicae III-1 Ockham explicitly asserts that 'Every being is actual' is a necessary proposition.**

Hence, (41) and the equivalent (42) Some merely possible beings are beings are false if taken to be non-modal propositions, since the term

'being' in such a proposition supposits only for things which actually exist. Ockham, then, pretty clearly rejects the claim that there are merely possible beings.

Theory of Truth Conditions Perhaps, however, there is another way to understand the claim in question. As we saw in section 3, Ockham rejects the suggestion that the parts of material objects are only potential beings, since in such a case a being would be composed of non-beings. It may be that he uses the term 'being' in such a way that it is equivalent to 'actual thing'. Hence, it is not surprising that he rejects (41) and (42). Nevertheless, he might consistently admit there are merely possible things and that these things are nonbeings, where 'thing' is a term which signifies both beings and non-beings.

This proposal is tantamount to the suggestion that Ockham might consistently take the following proposition to be true:

(43) Some things are non-beings and some non-beings are (merely) possible things.

However, if there are non-beings, then it might be thought that their number includes impossible as well as merely possible things.

Yet Ockham explicitly denies that (44) A chimera is a non-being is true.*5 But even if we prescind from impossibilia, it is clear from what Ockham says about infinite terms that he takes every instance of the schema ' is 'a non-being' to be necessarily false. Hence, it is also clear that he does not accept (43). Moreover, it seems doubtful to me that there is any other coherent interpretation of the claim that there are merely possible things which does not entail either (40) or (43).

But even though Ockham does not accept the thesis that there are merely possible things, it may still be the case that his treatment of modal propositions presupposes that there are such entities. Just how, then, does he explicate the truth conditions of 'Some A is possibly B' when 'A' is taken to supposit for what is possibly A?

There is no easy answer to this question, since the few hints which he does give us are open to divergent interpretations. In chapter 25 of Part II Ockham claims that the proposition 'Someone living on earth is possibly damned', where 'living on earth' is taken to supposit for what possibly lives on earth, is equivalent to 'Someone who is possibly damned is possibly living on earth'.®

Theory of Truth Conditions This suggests that, in general, a proposition of the form 'Some A is possibly B', where 'A' is taken to supposit for what is possibly

A, entails that something actually exists and that some actually existent being is both possibly A and possibly B. Likewise, 'Every

A is possibly B', where 'A' is taken to supposit for what is possibly A, is true just in case some actual existent is possibly: A and every actual existent which is possibly A is also possibly B. Oand E-propositions of this sort could be treated along the same lines, with the stipulation that they are true if no actual existent is possibly such that the subject of the Oor E-proposition in question is truly predicated of it.

On this interpretation, then, the correct account of the truth conditions of such propositions does not presuppose that there are merely possible things. Rather, such propositions, like their counterparts explicated above in (P45)-(P48), make assertions only about possibilities which pertain to actually existing things.

Unfortunately, this interpretation conflicts with what Ockham says in later sections of the Summa Logicae, For example, in expounding his theory of demonstration he asserts that (45) Every man is possibly something which laughs is necessarily true, as long as 'man' is taken to supposit for what is possibly a man. That is, (45) would be true if there were no men—in fact, it would be true even if there were no creatures at all. But if that is so, then 'man' in (45) must, it seems, have merely possible men among its supposita.

One might object at this point that God exists necessarily and, given the doctrine of the Incarnation, is both possibly a man and possibly something which laughs. Hence, (45) would still be necessarily true even on the interpretation suggested above. For even if there are no creatures, there is an actual being, namely, God, who is the sole thing which is possibly a man, and who is also possibly something which laughs. Furthermore, perhaps Ockham believes that God may assume any nature at all, e.g. that of a stone or of a donkey. In that case, each proposition like (45) that Ockham takes to be necessarily true can be handled in a similar fashion.

However, it is clear that Ockham cannot accept this rather quaint suggestion. First of all, he would surely accept.as necessarily true

Theory of Truth Conditions (46) Every whiteness is possibly a color where 'whiteness' is taken to supposit for what is possibly a whiteness. But he explicitly claims that (47) God is a whiteness is necessarily false.*7 Hence, the above proposal would not afford him with a perfectly general account of propositions like (45).

Moreover, he claims that the proposition (48) Some donkey is possibly a man, where 'donkey' is taken to supposit for what is possibly a donkey, is necessarily false."* But the proposal under discussion has as a consequence the claim that (48) is true, indeed necessarily true.

For if God can assume any nature at all, then there is a necessary existent, namely, God, who is both possibly a donkey and possibly a man. Hence, Ockham cannot accept the account given above of the truth conditions for de possibili propositions in which the subject term supposits for what is possibly such-and-such. But in that case, if he takes (45) to be necessarily true, he must, it seems, be presupposing that there are merely possible men.

Nevertheless, although Ockham never gives a complete account of the truth conditions for propositions like (45), such propositions can be adequately treated within the framework of his semantic theory in a manner consistent with his avowed denial that there are merely possible beings. The first step is to show that such proposi.:ns are equivalent to propositions which are not of the type unc:.> discussion. The second step is to show that the latter propos: 'ions themselves do not entail the thesis that there are merely possible beings.

Ockham dces give us one clue which proves helpful in the explication of the truth conditions for the de possibili propositions in question. In chapter 23 of Summa Logicae III-1 he admits that with respect to affirmative de possibili propositions that are ambiguous, it is more correct to say that the subject term is asserted to be able to supposit for what is possibly such-andsuch than to say that the subject term is able to supposit for what is possibly such-and-such.®? Analogously, he notes in other places that with respect to an affirmative S-proposition like

Theory of Truth Conditions 'Socrates is a man', it is more correct to say that its subject is asserted to supposit for Socrates rather than to say that its subject does supposit for Socrates. For if Socrates does not exist, then 'Socrates is a man' is both meaningful and false. Similarly, in the present case Ockham seems to be claiming that a proposition of the form 'SomeA is possibly B' or of the form 'Every Ais possibly B', where 'A' is taken to supposit for what is possibly

A, implies that it is possible that there be A's. It is not clear whether he wishes to extend this condition to Oand E-propositions of this type as well. I will simply assume that he does not, i.e. that such propositions are true if it is impossible that their subject terms supposit for anything in a present-tense non-modal affirmative proposition. However, this assumption is incidental to my present argument, which can accommodate the contrary assumption just as easily.

Universal de possibili propositions of this type embody assertions about "every possible such-and-such." (45), for example, makes an assertion about every possible man. It tells us, to put it somewhat vaguely, something necessary about men. This intuition is, I think, adequately captured if we take 'Every A is possibly B', where 'A' is taken to supposit for what is possibly

A, as equivalent to (49) This ispossible: 'Some being is A', and this is necessary: 'If a being is A, then it is possibly B'.

Note that in 'If a being is A, then it is possibly B', the subject of the consequent is taken to supposit for what is actually A.

The second conjunct of (49) in effect asserts that a proposition of the form 'This is A' entails a proposition of the form 'This A is possibly B', when 'this' and 'this A' supposit for the same thing. The second of these propositions is then explicated in accordance with (P39) above.

Similarly, 'Every A is possibly not B', where 'A' is taken to supposit for what is possibly A, is equivalent to (50) Either (i) this is necessary: 'No being is A' or (ii) this is possible: 'Some being is A', and this is necessary:

'If a being is A, then it is possibly not B'.

Comments analogous to those in the previous paragraph apply to Theory of Truth Conditions the second conjunct of (ii) in (50). Here (P40) above is relevant.

Particular de possibili propositions of this type can be handled as follows. 'Some A is possibly B', where 'A' is taken to supposit for what is possibly A, is equivalent to (51) This is possible: 'Some A is possibly B', where 'A' in the embedded proposition is taken to suppositfor what is actually A. The truth conditions for this embedded proposition are explicated as in (P47) above.

Lastly, 'Some A is possibly not B', where 'A' is taken to supposit for what is possibly A, is equivalent to (52) Either (i) this is necessary: 'No being is A' or (ii) this is possible: 'Some being is A', and this is possible:

'SomeA is possibly not B'.

The truth conditions for the second of conjunct of (ii) in (52) are explicated as in (P48) above.

As should be expected, (52) follows from (50), and (51) follows from (49). Again, as one should expect, each of (49)-(52) is compatible with each of the others.

As I noted, the truth conditions for each of the de possibili propositions without a dictum that is embedded in (49)-(52) can be explicated without presupposing that there are merely possible beings. For in each of these propositions the subject term is taken to supposit for what is actually such-and-such.

The only remaining question is this: does Ockham's treatment of de necessario and de possibili propositions taken in the sense of composition presuppose that there are merely possible beings?

Take the following proposition, which Ockham admits as true when it is taken in the sense of composition:

(53) It is necessary that no man is a donkey.

What does the term 'man' supposit for in (53)? It cannot be the case that it supposits just for all actual men, since one cannot validly infer (53) from the proposition 'No man is a donkey'.

Likewise, (53) cannot be inferred from the conjunctive proposition 'No man is a donkey and no man was a donkey and no man will be a donkey', where the last two conjuncts are taken in the sense of composition. For the sense of (53) is this: it has never

Theory of Truth Conditions been true, is not now true, and never will be true that some man is a donkey, and even if there were men other than those that now exist, have existed, and will exist, it would still not be true that some man is a donkey. That is, even if God had chosen, as he could have, to create human beings other than those whom he has created or will create, it would still be true that no man js a donkey. Hence, it seems that 'man' in (53) supposits for all possible men, including some that are merely possible.

Nevertheless, it is clear upon reflection that Ockham's account of the truth conditions of (53) does not commit him irrevocably to the thesis that there are merely possible things. For he explicates those truth conditions in terms of a present-tense nonmodal proposition, in which the term 'man' supposits only for actually existing human beings. Thus, (54) 'It is necessary that no man is a donkey', taken in the sense of composition, is true if and only if this is necessary: 'No man is a donkey'.

An Ockhamistic semantics need not assign supposition directly to the terms of a modal proposition taken in the sense of composition. Rather, the terms of the dicta of such propositions point, as it were, to their own occurrence in present-tense non-modal propositions and to the semantic relations which they have entered into, now enter into, will enter into, or might have entered into in virtue of their use in such propositions. Thus, Ockham might accept the following as a full explication of the truth conditions of (53):

(55) 'It is necessary that no man is a donkey', taken in the sense of composition, is true if and only if it is impossible that there be something for which 'man' and 'donkey' both supposit in the present-tense non-modal proposition 'No man is a donkey'.

In general, discourse about merely possible beings can be dispensed with in favor of discourse about the semantic relations that terms might have entered into. Consider the following:

(56) 'There might have been beings other than those which have existed, now exist, or will exist' is true if and only if the term 'being' might have supposited in a present-tense non-modal proposition for beings

Theory of Truth Conditions other than those which it has supposited for, now supposits for, or will supposit for in such a proposition.

Ockham would presumably find the metaphysical basis for the truth that there might have been other beings in the operation of God's will and intellect. However, this is one metaphysical problem which a semantic account of the modalities of necessity and possibility should not be expected to address."

The above interpretation of Ockham's semantics for modal propositions taken in the composed sense might seem strained to some.

Nonetheless, it is clearly suggested by the fact that Ockham himself explicates the truth conditions of such propositions in terms of the modal status of non-modal propositions—and not directly in terms of the supposition of subjects and predicates in the modal propositions themselves.

Moreover, as we have seen, he ultimately explicates the truth conditions of propositions of all types in terms of the truth

(past, present, or future) and/or modal status of present-tense non-modal propositions." And this indicates that he could easily dispense with all discourse about non-actual beings in favor of discourse about the semantic relations which terms did enter into, will enter into, or might have entered into when used in presenttense non-modal propositions.

In fact, Ockham's general strategy in dealing with past-tense, future-tense, and modal propositions suggests the thesis that, strictly speaking, terms other than modal terms (construed broadly to include 'true' and 'false') and the names of propositions have supposition only in present-tense non-modal propositions." For the latter are the only propositions whose truth conditions are explicated directly in terms of the notion of supposition. Further, the truth conditions for more complex propositions can be explicated entirely in terms of the semantic properties of present-tense non-modal propositions. This picture of Ockham's semantics is the basis of my somewhat vague assertion that terms in more complex propositions 'point to" their past or future or possible uses in present-tense non-modal propositions.

The only serious objection to this view of Ockham's semantics is that he himself explicitly speaks of the supposition of subject

Theory of Truth Conditions terms in certain past-tense, future-tense, and modal propositions.

But I pointed out before that in the case of past-tense and futuretense propositions such talk can be eliminated in favor of talk about scope distinctions. My suspicion is that the same holds true in the case of modal propositions as well.

After treating modal propositions Ockham goes on to deal with exponible propositions, i.e. propositions which, though categorical in appearance, are really equivalent to disjunctive and conjunctive propositions. At this point in Part II he has already provided us with the basics of a semantic account of the truth conditions for all types of non-exponible categorical propositions.

Now he wants to show that exponible categorical propositions are equivalent to conjunctions or disjunctions of the sorts of propositions already treated."*> Hence, the sort of analysis in which he now engages differs in kind from the sort of analysis found in previous sections of Part II. We have already seen the distinction between these types of analysis in the discussion of predication above. I will now elaborate on it a bit further.

Until now Ockham has been formulating the truth conditions of categorical propositions by using the following schema:

(57) 'P is true if and only if ___—_, where the quotes surround an indicative sentence and the blank is filled by a proposition which is strictly equivalent to '''P' is true" and which provides the necessary and sufficient semantic conditions for the truth of 'P'. Further, as we have just seen, a full characterization of these truth conditions can ultimately be formulated in terms of how the subject and predicate of the proposition to be explicated do supposit or did supposit or will supposit or might supposit in one or more relevant present-tense propositions.

The sort of analysis which Ockham now engages in, by contrast, has the following form:

(58) 'P is true if and only if 'Q and (or) R' is true, where 'P' is replaced by an exponible categorical proposition and where the hypothetical proposition on the right-hand side has as its parts the "exponents" of 'P'. This hypothetical proposition

Theory of Truth Conditions typically contains no allusion—either explicit or implicit—to semantic properties. In fact, if a biconditional of the form of (58) is true, then a corresponding biconditional, namely, one of the form (59) P if and only if (Q and [or] R), which lacks the semantic trappings of (58), will also be true. On the other hand, a biconditional of the form of (57) has no such counterpart in the object language. Further, a hypothetical proposition which occurs in an analysis of the form of (58) still stands in need of the sort of semantic analysis illustrated by (57).

One might even make the stronger claim that the two sides of an analysis of the form of (58) are, if the analysis is correct, strictly synonymous with one another, whereas it is fairly clear that this is not the case in an analysis of the form of (57). Within the framework of Ockham's theory of language, such a claim

'is tantamount to the assertion that the mental language contains no exponible propositions. I will not discuss this suggestion here, but only note that it is rather controversial."

It is not difficult to see that Ockham's analysis of exponible propositions is similar to Russell's analysis of sentences containing definite descriptions. The analyzanda, it is claimed, do not perspicuously exhibit their true logical form. Thus, they must be expounded in terms of simpler sentences in order for their truth conditions to be explicated fully.

I will not attempt to survey all the types of exponible propositions which Ockham discusses. Instead I will merely try to illustrate his method by examining briefly his treatment of two types of exponible propositions, namely, those containing infinite terms and those containing figment terms.

An infinite term is formed by prefixing the particle 'non-' to a categorematic term, as in 'non-man', 'non-white', etc. Such terms do not affect the quality of a proposition, i.e. its being affirmative or negative. In this way they are similar to positive terms. Thus, we must distinguish 'Socrates is a non-donkey' from 'Socrates is not a donkey', and 'Some animal is a nonman' from 'Some animal is not a man'. The first member of each of these pairs is an affirmative proposition and hence is true only if there is something for which its subject term supTheory of Truth Conditions posits. The second member of each pair, on the other hand, is a negative proposition which is true if there is nothing for which its subject term supposits.

Ockham uses as an example the indefinite proposition 'A donkey is a non-man'. The nominal definition of 'non-man' is 'something that is not a man'. The proposition in question, he tells us, is thus equivalent to the conjunctive proposition 'A donkey is something and a donkey is not a man'. The force of 'A donkey is something' is clearly existential. In fact, given Ockham's insistence, noted above, that 'being' supposits for all and only those things which actually exist when it is used in a present-tense nonmodal proposition, we may read 'A donkey is something' as 'A donkey is a being'. Thus (60) 'A donkey is a non-man' is true if and only if 'A donkey is a being and a donkey is not a man' is true.

Hence, 'Every donkey is a man' and 'A donkey is a non-man', though contraries, are not contradictories, for they are both false if there are no donkeys. Likewise, 'Socrates is a man' and 'Socrates is a non-man', though contraries, are not contradictories, since they are both false if Socrates does not exist. Again, 'Some man is a non-man' is true only if there is a man who is not a man— and for this reason it is impossible. However, 'Some man is not a man' is possible, since it is true if there are no men.

As noted in previous discussions, this account has the consequence that every proposition of the form ' is a non-being' is necessarily false. For the nominal definition of 'non-being' is

'something that is not a being'. Using (60) above as a guide, we can expound the proposition 'The Antichrist is a non-being' as follows:

(61) 'The Antichrist is a non-being' is true if and only if 'The Antichrist is a being and the Antichrist is not a being' is true.

But the proposition embedded in the right-hand side of (61) is a straightforward contradiction. Hence, 'The Antichrist is a nonbeing' is impossible.

Thus, Ockham's logical theory recognizes the distinction between propositional negation and terminal negation, which is not captured by standard first-order predicate logic as normally preTheory of Truth Conditions sented. Further, this distinction is philosophically important. For instance, in The Nature of Necessity Alvin Plantinga claims that in order to understand singular negative existential propositions we must distinguish between what he calls the predicative and impredicative senses of sentences like 'Socrates does not exist'.7§

And this distiaction corresponds exactly to the distinction which Ockham draws between 'Socrates is a non-being', which is impossible, and 'Socrates is not a being', which is possible.

Figment terms are categorematic terms which are such that it is impossible that there be anything for which they supposit personally in a present-tense non-modal proposition. 'Chimera' is Ockham's favorite example of such a term. As noted above, its nominal definition is 'animal composed of a goat and a cow'. Although this example is rather controversial, my purpose here is not to specify just which terms are figment terms but merely to outline Ockham's analysis of propositions in which figment terms occur. One who objects to Ockham's example may substitute a more obvious instance of a figment term, e.g. 'round square'.

Since figment terms are necessarily empty, there is no true affirmative proposition in which such a term has personal supposition. For each such proposition implies that there is or was or will be or might be something of which the figment term in question is truly predicable. Take, for example, the affirmative proposition 'A chimera is a non-being'. Although this proposition radiates an aura of truth, it is necessarily false, since it entails the necessarily false proposition 'An animal composed of a goat and a cow is a being'. On the other hand, each negative proposition in which a figment term has personal supposition is necessarily true, since there can be nothing for which such a term supposits. For example, 'A chimera is not a man' is necessarily true, even though 'A chimera is a non-man' is necessarily false.

Thus, as Ockham emphasizes, there is no need to posit a universe of impossible entities in order to explicate the truth conditions of propositions containing figment terms. For all such affirmative propositions are false and all such negative propositions are true simply in virtue of the fact that there can be no such entities. Still, figment terms do have signification, namely, secondary signification, and thus differ in signification from one another insofar as their nominal definitions differ from one

Theory of Truth Conditions another. On Ockham's view, then, the fact that no figment term can personally supposit for anything does not entail that all such terms are equivalent in signification. This way of dealing with figment terms is surely elegant if nothing else.

One further feature of this section of Part II merits comment here. In the chapters on exclusive propositions, exceptive propositions, and propositions containing the verbs 'begin' and 'cease',

Ockham assigns modes of common personal supposition to the subjects and predicates of the propositions in question. He does so, however, only after analyzing them into their exponents.

Thus, it is clear that the account of the modes of common personal supposition plays no essential role in the explication of the truth conditions of these propositions—or of any others.

For the three chapters just alluded to contain the only substantive discussion of the modes of common personal supposition in Part II. However, I wish to suggest, without pursuing the matter here, that a close study of these chapters might provide a clue to the mystery of just what role the account of the modes of common personal supposition is meant to play in the Summa

In the last section of Part II Ockham deals with hypothetical propositions, i.e. propositions composed of two or more categorical propositions joined by one or more propositionforming conjunctions or adverbs. Since exponible categorical propositions, as we have seen, are equivalent to hypothetical propositions, this section of Part II also constitutes a necessary step in the formulation of a complete semantic account of the truth conditions of exponible propositions.

Ockham divides hypothetical propositions into six species: conditional, conjunctive, disjunctive, causal, temporal, and local.

I will concentrate here on the first three types. (Ockham's treatment of the last three types is, in any case, open to serious objections which go beyond the scope of this introduction.)

In each instance Ockham's strategy is to explicate the truth conditions of the hypothetical proposition in question in terms of the truth or modal status of its components or in terms of the logical relations of those components to one another. When one or more of these components are themselves hypothetical

Theory of Truth Conditions propositions, the same procedure applies to them. Hence, ultimately the truth conditions for any hypothetical proposition can be spelled out in terms of the truth or modal status of categorical propositions or in terms of the logical relations of given categorical propositions to one another. Ockham's account of hypothetical propositions, then, is continuous with and builds upon his treatment of categorical propositions.

There has been some debate about whether Ockham had the notion of material implication."* This issue will not be discussed here, since such a discussion would take us far beyond Part II to Ockham's fullest treatment of conditional propositions (or consequences) in Part III-3 of the Summa Logicae. In Part II he consistently treats conditional propositions as strict implications, i.e. as propositions which are true if and only if it is impossible both that the antecedent be true and the consequent false. I believe, in fact, that it can be shown that Ockham treats all conditional propositions along these lines, although such a claim requires support. However, even if he does treat some conditional propositions as material implications, the truth conditions for such propositions can still be formulated in terms of the truth of negative conjunctive propositions. So I will proceed directly to a consideration of conjunctive propositions.

Let 'P' and 'Q' stand for propositions and let 'not-P' and 'notQ stand for their respective negations. Ockham gives the following rules for conjunctive propositions:

(P49) An affirmative non-modal conjunctive proposition, 'P and Q', is true if and only if (i) 'P' is true and (ii) 'Q' is true.

(P50) A negative non-modal conjunctive proposition, 'It is not the case that P and Q,, is true if and only if either (i) 'not-P' is true or (ii)

(P51) An affirmative de necessario conjunctive proposition, 'It is necessary that P and Q', is true if and only if (i) 'P' is necessary and (ii) 'Q' is necessary.

(P52) An affirmative de possibili conjunctive proposition, 'It is possible that P and Q', is true if and only if (i) 'P' is possible and (ii) 'Q' is possible and (iii) 'P' and 'Q' are neither contraries nor contradictories.

(P53) An affirmative de impossibili conjunctive proposition, 'It is impos sible that P and Q', is true if and only if either (i) 'P' is not posTheory of Truth Conditions sible or (ii) 'Q' is not possible or (iii) 'P' and 'Q' are either contraries or'contradictories.

~ Ockham gives the following rules for disjunctive propositions:

(P54) An affirmative non-modal disjunctive proposition, 'P or Q', is true if and only if either (i) 'P' is true or (ii) 'Q' is true.

(P55) A negative non-modal disjunctive proposition, 'It is not the case that P or Q', is true if and only if (i) 'not-P' is true and (ii) 'notQ' is true.

(P56) An affirmative de necessario disjunctive proposition, 'It is necessary that P or Q', is true if and only if either (i) 'P' is necessary or (ii)

'Q' is necessary or (iii) 'P' and 'Q' are either subcontraries or contradictories.

(P57) An affirmative de possibili disjunctive proposition, 'It is possible that P or Q', is true if and only if either (i) 'P' is possible or (ii)

(P58) An affirmative de impossibili disjunctive proposition, 'It is impossible that P or Q', is true if and only if (i) 'P' is not possible and (ii) 'Q' is not possible.

(P50) and (P55) are actually somewhat misleading, since Ockham never mentions propositions of the form 'It is not the case that P and Q' or 'It is not the case that P or Q'. Rather, he simply says that the contradictory of a conjunctive proposition is a disjunctive proposition whose: parts are the contradictories of the parts of that conjunctive proposition, and that the contradictory of a disjunctive proposition is a conjunctive proposition whose parts are the contradictories of the parts of that disjunctive proposition. This point is perhaps significant, since it may explain why

Ockham makes no mention of past-tense and future-tense conjunctive or disjunctive propositions, e.g. 'It was the case that Socrates is white and Plato is black' or 'It will be the case that Socrates is white or Plato is black'. Perhaps conjunctive propositions of this sort could be treated as temporal propositions, while disjunctive propositions of this type could be treated as disjunctive propositions in which each disjunct is past-tense or futuretense.

In any case, it should be clear from this brief discussion how Ockham's treatment of hypothetical propositions is related to his earlier treatment of categorical propositions.

Finally, I do not wish to leave the impression that Ockham has Theory of Truth Conditions successfully completed in every respect the project on which he embarked in Part II of the Summa Logicae. His theory of predication, for instance, has been characterized by some as one of the most catastrophic mistakes in the history of logic." Again, he spends depressingly little time discussing the truth conditions of relational propositions, i.e. propositions in which one extreme includes a term in an oblique case. His account of reduplicative propositions has been called inadequate" and his treatment of exceptive propositions question begging."? The list of complaints goes on.

Nevertheless, the project itself is of enduring philosophical importance. And in view of the renewed interest among contemporary philosophers in the theory of truth conditions, Ockham's attempt to carry out this project warrants close study.

NOTES 1. Ockham's most extensive treatment of the problem of universals occurs in the Ordinatio I, dist. 2, ques. IV-VIII. This section of the Ordinatio is found in Stephen Brown and Gedeon Gal, eds., Ockham: Opera Theologica, vol. II (St. Bonaventure, N.Y., 1970), pp. 99-292.

2. These three distinctions are discussed in chapters 3, 4, and 10, respectively, of Part I of the Summa Logicae (hereafter: SL). For excellent expositions of the first and third of these distinctions, cf. Trentman (30) and Spade (25).

3. This revision of (P1) would consist of three principles. The first captures the first sense of "primarily signify" found in SL I, chap. 33:

(a) A term 'T' primarily signifies a thing x if and only if 'This is (a) T' is true, where 'this' indicates x.

In order to accommodate the objection that on (a) the signification of a common term might constantly change in virtue of changes in things, Ockham gives a second sense to "primarily signify'? which (P1) is meant to capture. On the proposed revision the point of this second sense would be captured by the following:

(b) A term 'T' has primary signification if and only if it is possible that there be an x such that 'T' primarily signifies x.

(c) Term 'T' differs in primary signification from term 'T*' if and only if (i) both 'T' and 'T*' have primary signification and (ii) it is possible that there be an x such that 'T' but not 'T*" primarily signifies x, or 'T*' but not 'T' primarily signifies x.

The objection in question is thus avoided, since, for instance, the term 'man' as used on one occasion will never differ in primary signification from the same term as used on another occasion, even though two uses of the same term may primarily signify, in the sense defined by (a), different individuals. Note also that although terms like 'triangular' and 'trilateral' would not differ in primary signification, they would still differ in secondary signification in the sense characterized by (P2) below. If my contention, argued below, that Ockham's semantics is not commited irrevocably to the existence or subsistence of merely past, merely future or merely possible things is correct, then the above account may be taken as a possible—and perhaps even plausible—interpretation of the first part of SL

4, On this point and others in the discussion of secondary signification Ihave borrowed heavily from Spade (25).

5. Cf. Spade (25), p. 73.

6. This claim is itself somewhat problematic, as Spade notes in (24), esp. pp. 66-68.

7. (P3) can be simplified by replacing condition (ii) with the stipulation that 'T' is a categorematic term. I have chosen this more clumsy condition in order to emphasize that a demonstrative pronoun may have personal

Theory of Truth Conditions supposition, even though it is not clear whether such a term can properly be said to signify anything primarily.

8. Some may object to the claim that a mental term can have material supposition, but it is clear that Ockham holds this view. See SL I, chap.

64, lines 59-62. (Line references are to the critical edition of the Summa Logicae found in Philotheus Boehner, G. Gal, and S. Brown, eds., Ockham:

Opera Philosophice, vol. I (St. Bonaventure, N.Y., 1974].) Also, Loux in (14), p. 44, fn. 2 mentions a somewhat technical difficulty with what Ockham says about material supposition in SL I, chap. 63. I will not discuss this problem here, although (P4) might have to be amended slightly to accommodate precisely what Ockham says about propositional dicta which have material supposition.

9. This seems to be what Ockham has in mind in SL I, chap. 65, lines 8-10, when he claims that a term can have material or simple supposition

"tantum quando terminus talis comparatur alteri extremo quod respicit intentionem animam vel vocem vel scriptum." It is tempting—though not unproblematic—to take "respicit"' here as equivalent to "'significat." For in a subsequent passage Ockham claims that 'man' in 'Man is a species' may have simple supposition, since 'species' signifies ("'significat"') intentions of the soul. If this suggestion is correct, then it seems that in (2), p. 382 Adams is mistaken in claiming that the term 'man' may have material supposition in both 'This is man' (where 'this' indicates a term) and 'Man is man', For 'this', as noted above, does not appear to signify anything primarily, and 'man' signifies only human beings primarily. Ockham does occasionally use propositions like 'The term "man" is the term ''man''', But in such a proposition the whole extreme, namely, 'the term "'man''', has personal supposition. One might be tempted to say that at least part of this extreme has material supposition, but in SL I, chap. 72, lines 155-161 Ockham denies that a part of an extreme can properly be said to have supposition. (On this point, however, cf. Spade (26), pp. 265-268.)

10. An account of predication of this sort is proposed by Bergmann in (6), p. 208.

11. See Trentman (29), pp. 362-363; Geach (11), p. 300; and Tweedale (32), pp. 307-327.

12. SL Il, chap. 2, lines 22-31.

13. See Boehner (8), p. 260. In (31) Turnbull agrees that Ockham is attempting to define truth.

14. This shortcoming of Boehner's proposal is noted by Adams in (2), p. 388, fn. 12.

15. See, for example, SL I, chap. 72, lines 121-126 and SL II, chap.

16. See Adams (2), esp. pp. 375-381. Although Adams believes that .

Ockham's characterization of supposition does not fall victim to the circularity charge, she does not distinguish the two versions of that objection which are developed below.

17. Adams indicates that neither the notion of supposition nor the notion of a term's being posited for a thing in a proposition is a suitable candidate for a primitive notion. See (2), p. 384. However, it is clear that an appeal to speakers' intentions, discussed briefly at the conclusion of (2), will not help here. For although Ockham sometimes appeals to speakers'

Theory of Truth Conditions intentions in order to disambiguate equivocal propositions in which the same term can be taken to supposit in two or more ways, such intentions only help determine which thing or things a speaker intends the term in question to stand for. The basic notion of a term's standing for or being posited for a thing remains itself undefined.

18. A complete account of quantification would also include a treatment of singular propositions in which the predicate is determined by a universal sign, e.g. 'Socrates is every man' and 'This substance is not every animal'.

The truth conditions for such propositions parallel exactly those given here for I'- and O'- propositions. Also, it is not clear whether Ockham's theory of truth conditions can successfully deal with relational statements containing multiple quantifiers, e.g. 'Some boy loves every girl'. On this point see

Priest and Read (20), p. 113 and Geach (10), chap. 4. My own suspicion is that this problem is parasitic on the problem of how Ockham's theory can adequately deal with relational propositions in general. A solution to this latter difficulty would, I believe, yield a solution to the former.

19, This view is either suggested or presupposed in Boehner (7), p. 38; Turnbull (31), pp. 321-322; Scott (22), p. 586; Swiniarski (28), pp. 205 ff.;

Loux (14), p. 30; Priest and Read (10), p. 310; and Spade (26), It is tentatively accepted by Adams in (2), p. 387, fn. 2. Matthews held this view in (15), but later rejected it in (16). In (9) I presupposed this picture of Ockham's account of the MCPS but have since come to reject it in light of my study of Part II and comments made on (9) by Calvin Normore at the APA West meetings in April 1978.

20. See Loux (14), p. 25.

21. See SZ I, chap. 74, lines 12-15. This feature of Ockham's account was noted in the early 1970s by both Matthews in (16) and Swiniarski in (28), although only the former urged that the thesis that Ockham's account

. of the MCPS is his theory of quantification ought to be abandoned.

22. See Priest and Read (20) and Spade (26).

23. In (28) Swiniarski discusses the possibility of using this fourth mode of common personal supposition to solve the problem posed by O-propositions but correctly rejects it in that' context. Such a mode of reference is discussed in some detail by Geach in (10), pp. 71 ff.

24. In (28) Swiniarski proposes such a rule to solve the problem posed by O-propositions, even though he admits that Ockham never mentions a tule of this type. For a response to this strategy, see Spade (26).

25. See SL I, chap. 74, lines 29-30.

26. See SL I, chap. 74, lines 23-29.

27. This problem is similar to the one raised by Matthews in his discussion of 'monoreferential' terms in (16), p. 21.

28. See Spade (27), p. 86.

29. Expositio in Librum Praedicamentorum Aristotelis, chap. 10, lines 116-118. (Line references here are taken from the critical edition of this work edited by Gedeon Gal and found in Ockham: Opera Philosophica, vol. II [St. Bonaventure, N.Y., 1978], pp. 135-339.)

30. See SL I, chap. 50, lines 14-35.

31. See SL II, chap. 6.

32. Loux (14), p. 46, fn. 13.

33. See Priest and Read (20), pp. 109-110. In (3) Adams claims that Theory of Truth Conditions Ockham is committed to the existence of infinitely many possibilia and that he has no obviousty consistent way of reducing possibilia to anything actual, e.g. mental acts. See Adams (3), pp. 163-175.

34. See section 5 below.

35. SL Il, chap. 3, lines 16-17, 36. SL II, chap. 4, lines 57-60.

37. SL Il-3, chap. 32, lines 5-8.

38. See Loux (14), esp. pp. 33-37.

39. The thesis that the account of the MCPS is best relegated to the theory of inference was first suggested to me by Calvin Normore.

40. Ockham discusses this point in the Summa Logicae at II, chap. 33, lines 6-11 and III-3, chap. 32, lines 46-163. Both of these passages are. found in translation in Adams and Kretzmann (4).

41. SL Il, chap. 7, lines 36-40.

42. In (14), pp. 38-40 Loux claims in effect that even if the subject of a proposition of the form 'This A was this B' is taken to supposit for what was A, 'this A' does not appear as the subject of the relevant present-tense proposition.

43. Expositio in Librum Praedicamentorum Aristotelis, chap. 10, lines 164-166.

44. SL Ill-4, chap. 13, lines 16-17, 20-23.

45. In (3) 4.°ams discusses at length the two theories of intentionality which Ockham «eld during his philosophical career, namely, the "'objectiveexistence" theory and the "mental act" theory.

46. This question is important in its own right, since Adams looks to SL Ul for evidence that Ockham retained a commitment to possibilia even in his later philosophical writings. See Adams (3), p. 173.

47, At the end of section 5 I will try to make clearer the force of the expression "points back to" as I am using it here.

48. As noted above, propositions of the sort in question are still ambiguous even after it is made clear that the subject term is taken to supposit for what was such-and-such. This indicates that the scope of a pasttense verb may be understood in three distinct ways when its subject is or includes a common term.

49. It should be mentioned at this point that there is a type-token ambiguity in Ockham's use of the term 'proposition'. In what follows I am assuming that a proposition-type may be said to exist just in case at least one proposition-token of that type exists. For more on the use of the term

'proposition' by medieval logicians, see Kretzmann (12).

50. The claim here is that the propositions said to be formulated by God would be proposition-tokens and that the corresponding proposition-type would exist eternally in virtue of the fact that God either formulates a token of that type at every moment or conserves a token of that type in existence at every moment.

51. See especially the Tractatus De Praedestinatione et De Praescientia Dei et De Futuris Contingentibus, ques. 2. This work can now be found in a critical edition in Ockham: Opera Philosophica, vol. Il (St. Bonaventure,

N.Y., 1978). This edition is based on the edition previously published by Philotheus Boehner, with some corrections made by Stephen Brown. Also, this entire work is found in English translation in Adams and Kretzmann (4).

Theory of Truth Conditions 52. Ockham does not explicitly deal with propositions containing iterated modalities. However, it is clear that what he says can be extended to accommodate such propositions,

53. Loux in (14), p. 43 notes that Ockham tends to take propositions of the form '"'P" is necessary' as singular propositions, whether or not the proposition substituted for 'P' is itself a singular proposition. This seems to me essentially correct despite what Ockham says at SL II, chap. 9, lines 50-66.

However, on p. 46, fn. 17, Loux goes on to suggest that such a move "'effectively denies that the proposition 'Every A is B' has any internal structure in '"BEvery A is B" is necessary' [and thus] makes it difficult to explain just how the proposition figures in inferential contexts." Nevertheless, it is not obvious that Ockham has a problem here. For on his view '""Q" is necessary' follows from 'If P, then Q' and '"'P" is necessary' via the following rule of inference: 'If the antecedent is necessary, then the consequent is necessary'.

54. These characterizations of necessity and impossibility are found at SL Il, chap. 9, lines 72-74 and 80-81.

55. I wish to thank Paul Spade for pointing out to me that this problem is more serious than its analogue in the case of past-tense and future-tense propositions.

56. Again I am assuming that a proposition-type is a necessary being just jin case it is necessary that one of its tokens exist.

57. See Scott (23), chap. 8.

58. See esp. Prior (21), pp. 202-214.

59. See Adams and Kretzmann (4), p. 36.

60. See SL III-3, chap. 13, esp. lines 39-43 for Ockham's own characterization of this distinction. He then applies the distinction to de necessario and de possibili propositions in chap. 14.

61. See, e.g., SL-II-2, chap. 5, lines 26-34.

62. Ockham's examples at various points in the Summa Logicae indicate that the existential implications of (33)-(36) are correctly rendered by (P41)- (P44). But if.that is so, then the subjects of the de possibili derived forms of (33)-(36) are such that they are taken to supposit for what is actually

A. For this reason I have assumed that the logical relations just noted hold when the subject terms of (37)-(40) are taken to supposit for what is actually such-and-such.

63. SL I, chap. 38, lines 54-66. Someone may object to my parenthetical insertion of the word 'terms' into the translation, since Ockham says only that the term 'being' is predicated of something (''de aliquo") actually and of something potentially. However, the insertion of the word 'term' here is necessary to preserve his point and is in any case consistent with his often repeated insistence that only terms are predicable and that they are predicable only of other terms. See, e.g., SL I, chap. 30, lines 20 ff. Unfortunately,

Ockham himself sometimes talks in a way which indicates that extramental things are the subjects of propositions and of predication. But it is clear that he does not believe this.

64. SL III-1, chap. 31, lines 85-86.

65. SL II, chap. 14, lines 33-35.

66. SL Il, chap. 25, lines 31-32. Although Ockham explicitly says only that the second of these propositions follows from the first, it is clear from the rules governing conversion that in this case the conversion is mutual as Theory of Truth Conditions long as the subject of the first proposition is taken to supposit for what is possibly someone who is living on earth.

67. SL IlI-1, chap. 31, lines 70-72.

68. SL Ill-1, chap. 34, lines 39-42.

69. SL IN-1, chap. 23, lines 27-28. A similar point is made less clearly at SL II, chap. 27, lines 170-178.

70. Such a question is tantamount to asking, for instance, why it is that a necessary truth is true in all possible worlds. However, philosophers of Ockham's time were discussing the following question: Is something possible because God can bring it about or is it rather that God can bring it about because it is possible? For an account of the debate over this question and Ockham's opinion on this matter, see Wolter (33).

71. A complete Ockhamistic semantics would, of course, need rules to deal with propositions which are both modal and past-tense or future-tense.

Such rules would establish orderings of the operations already discussed.

72. It is not clear from what Ockham says in Part II just how he would formulate the truth conditions for the metalinguistic propositions in terms of which the truth conditions for object-language propositions are formuJated. This is why I have excluded modal terms and names of propositions from the thesis suggested here. However, it seems reasonable to believe that Ockham would extend the strategies outlined above to metalinguistic propositions. For instance, the proposition 'This was true: 'Socrates is white"' would be true if and only if this was true: 'This is true: "Socrates is white"'.

In that case it would also be true that modal terms and names of propositions have supposition, strictly speaking, only in present-tense propositions— although such propositions would still be modal in Ockham's sense. Also, a full defense of this thesis, especially if it is taken as an interpretation of what Ockham says, should include a discussion of passages such as SL

I, chap. 72, lines 37-57, where he explicitly speaks of the supposition of terms in past-tense, future-tense, and modal propositions.

73. This is not entirely accurate, since in certain cases conditional propositions occur as parts of such conjunctive or disjunctive propositions.

74. See Ashworth (5), esp. pp. 137-142.

75. See Plantinga (19), pp. 144-152.

76. Cf. Boehner (8), pp. 319-351; Moody (17), pp. 64-80; Adams (1); and Mullick (18).

77. Geach makes this claim in several places, e.g. (10), pp. 34-36 and (11), pp. 44-61 and 289 ff.

78. See Geach (11), p. 295.

79. See Leff (13), p. 263, fn. 126.

SEMEY Theory of Truth Conditions REFERENCES (1) Adams, Marilyn McCord. "Did Ockham Know of Material and Strict Implication? A Reconsideration." Franciscan Studies 33 (1973),

5-37, (2) ——. "What Does Ockham Mean by 'Supposition'?"" Notre Dame Journal of Formal Logic 17 (1976), 375-391.

(3) ——. "Ockham's Nominalism and Unreal Entities." Philosophical Review 76 (1977), 144-176.

(4) —— and Kretzmann, Norman, trans. Predestination, God's Foreknowledge, and Future Contingents. 'New York, 1967.

(5) Ashworth, E. J. "The Doctrine of Exponibilia in the Fifteenth and Sixteenth Centuries." Vivarium 11 (1973), 137-167.

(6) Bergmann, Gustav. Meaning and Existence. Madison, Wisc. 1967.

(7) Boehner, Philotheus. Medieval Logic. Manchester, England, 1952.

(8) ——. Collected Articles on Ockham, E. Buytaert, ed. St. Bonaventure, N.Y., 1958.

(9) Freddoso, Alfred J. "O-Propositions and Ockham's Theory of Supposition." Notre Dame Journal of Formal Logic 20 (1979), 741-750.

(10) Geach, Peter T. Reference and Generality. Ithaca, N.Y., 1962.

(11) ——. Logic Matters, Berkeley, Calif., 1972.

(12) Kretzmann, Norman. "Medieval Logicians on the Meaning of 'Propositio'."". Journal of Philosophy 67 (1970), 767-787.

(13) Leff, Gordon. William of Ockham. Manchester, England, .1975.

(14) Loux, Michael J., trans. Ockham's Theory of Terms: Part I of the Summa Logicae. Notre Dame, Ind., 1974.

(15) Matthews, Gareth. ""Ockham's Supposition Theory and Modern Logic."

Philosophical Review 73 (1964), 91-99.

(16) ——. "Supposition and Quantification in Ockham." Nous 7 (1973), 13-24.

(17) Moody, Ernest A. Truth and Consequence in Medieval Logic. Amsterdam, 1953.

(18) Mullick, Mohini. "Does Ockham Accept Material Implication?" Notre Dame Journal of Formal Logic 12 (1971), 117-124.

(19) Plantinga, Alvin. The Nature of Necessity. Oxford, 1974.

(20) Priest, Graham, and Read, Stephen. 'The Formalization of Ockham's Theory of Supposition." Mind 87 (1977), 109-113.

(21) Prior, A. N. Papers in Logic and Ethics, P. T, Geach and A. J. P.

Kenny, eds. Amherst, Mass., 1976.

(22) Scott, T. K. "Geach on Supposition Theory."' Mind 75 (1966), 586588.

(23) ——. trans. John Buridan: Sophisms on Meaning and Truth. New York, -1966.

(24) Spade, Paul Vincent. ""Ockham's Rule of Supposition: Two Conflicts in his Theory." Vivarium 12 (1974), 63-73.

(25) ——. '"'Ockham's Distinctions between Absolute and Connotative Terms." Vivarium 13 (1975), 55-76.

(26) ——. "Priority of Analysis and the Predicates of O-form Sentences."

Franciscan Studies 36 (1976), 263-270.

Theory of Truth Conditions (27) ——. "Review of Michael J. Loux, trans., Ockham's Theory of Terms:

Part I of the Summa Logicae." Nous 12 (1978), 82-87.

(28) Swiniarski, John. "A New Presentation of Ockham's Theory of Supposition and an Evaluation of Some Contemporary Criticisms."

Franciscan Studies 30 (1970), 181-217.

(29) Trentman, John. '"Lesniewski's Ontology and Some Medieval Logicians." Notre Dame Journal of Formal Logic 7 (1966), 361-364,

(30) ——. "Ockham on Mental." Mind 79 (1970), 586-590.

(31) Turnbull, Robert G. "Ockham's Nominalistic Logic: Some Twentieth Century Reflections." New Scholasticism 36 (1962), 313-329.

(32) Tweedale, Martin. Abailard on Universals. Amsterdam, 1976.

(33) Wolter, Allan B. "Ockham and the Textbooks: On the Origin of Possibility."" Franziskanische Studien 32 (1950), 70-96.

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