Contrasting with Aquinas’ metaphysical approach to truth and stemming from entirely different sources, the thirteenth century witnessed, within the terminist tradition (represented by Peter of Spain, William of Sherwood, etc.), the emergence of a new and subsequently very influential approach to truth founded on the notion of supposition. It is perhaps the best example in the history of philosophy of a theory of truth that is genuinely not based on correspondence.
The notion of supposition was developed within the general framework of medieval properties of terms (see Read (2006) and the entry on Supposition Theory in this volume). In the thirteenth century, supposition was one among other equally important properties of terms, but in the fourteenth century it came to occupy a privileged position. It particular, it was used for the analysis of the truth-conditions of the basic types of categorical propositions (the A, E, I, and O Aristotelian logical forms). This approach had among its proponents Ockham (in the first chapters of the second part of his Summa logicae) and Buridan (e. g. in the first chapters of his Treatise on Consequences). Its main idea is that an affirmative proposition is true iff there is identity between the supposita of the subject and of the predicate, while a negative proposition is true if this does not occur (the supposita are the entities which a given term in a proposition supposits or stands for). But this general principle must be refined by means of truth-conditional clauses for propositions of different logical categories:
• ‘‘Every A is B’’ is true iff ‘‘the predicate supposits for all those things that the subject supposits for, so that it is truly predicated of them’’ (Ockham 1998:96).
• ‘‘No A is B’’ is true if the predicate supposits for none of the things that the subject supposits for, or if the subject does not supposit for anything.
• ‘‘Some A is B’’ is true iff ‘‘the subject and predicate supposit for some same thing’’ (Ockham 1998:92).
• ‘‘Some A is not B’’ is true if ‘‘the subject supposits for something that the predicate does not supposit for’’ (Ockham 1998:92), or if the subject does not supposit for anything.
Notice that negative propositions have two causes oftruth, as Ockham puts it: either if there is no co-supposition of their terms in the appropriate case (universal or particular), or if the subject does not supposit for anything at all, then the proposition is true, since in the latter case the absence of co-supposition obtains trivially. Moreover, the same procedure can be applied mutatis mutandis to propositions whose verb is tensed or accompanied by a modality (see chaps. 7, 9, and 10 of part II of Ockham’s Summa logicae).
These definitions can also be formulated as recursive definitions of truth-conditions on the basis of the truth of more fundamental propositions, namely, singular propositions whose subject is a demonstrative and whose predicate is one of the terms of the proposition whose truth-conditions are being established. This is because for a term A to supposit for something amounts to the truth of a singular proposition ‘‘This is A,’’ where ‘‘This’’ supposits for the thing in question, and so does ‘‘A’’.
A problem for Ockham’s account is the threat of circularity: while the truth of propositions, including singular propositions with demonstratives as their subjects, is defined in terms of the supposition of their terms in the first chapters of part II of the Summa logicae, elsewhere the supposition of terms is in turn defined in terms of the truth of such singular propositions. It is clear that one of the two notions, either supposition or the truth of singular demonstrative propositions, must be taken as primitive if the theory is to avoid circularity.
Besides the technical aspect of formulating precise truth-conditions for different logical forms of propositions, Ockham’s theory of truth is also a rejection of a metaphysical approach in favor of a semantic approach to truth (see Perler 1992: chaps 1 and 2, Moody 1953:chap. III and Dutilh Novaes forthcoming). The fundamental cause of truth of propositions is a semantic property of their terms, namely their supposition, and not actual properties of the objects in question. Ockham stresses this idea in several passages, for example in
> Thus, for the truth of'This is an angel' it is not required that the common term 'angel' be really identical with what is posited as the subject, or that it be really in that subject, or anything of this sort. Rather, it is sufficient and necessary that the subject and predicate supposit for the same thing (Ockham 1998:86).
Another significant aspect of Ockham’s account of truth is that truth-bearers are the actually formed propositions of a language, be they spoken, written, or mental; he (as well as Buridan) is what we could call an inscriptionalist with respect to truth-bearers. Truth is a monadic predicate attributed to them, and this attribution is formulated with the special dictum construction: a proposition whose subject is the nominalized form of the proposition to which truth is attributed (terms in the accusative case and verb in the infinitive mode) and the predicate is the term for true, 'verum” - for example, Socratem esse hominem est verum. So truth is nothing more than a predicate of propositions, namely those that are true, and this in turn depends solely on the supposition of their terms.
In sum, theories of truth based on the concept of supposition, Ockham’s in particular, have the distinctive trait of rejecting metaphysical foundations for truth; the burden here is to be borne exclusively by semantic properties. Moreover, in contrast with Anselm and Aquinas, truth is attributed exclusively to complex linguistic and, more importantly, mental entities. Indeed, the primary bearers of truth-value for Ockham as well as for Buridan are mental propositions; spoken and written propositions are only derivatively true, insofar as they are related to true mental propositions.
World History
