Developing parallel to, and sometimes overlapping with, uses of the notion of supposition in accounts of truth, there is a very rich tradition of theories of truth in the fourteenth century to be found in treatises on Insolubilia, that is, treatises on paradoxes. They are semantic correspondence theories of truth, and thus illustrate that correspondence theories of truth need not be metaphysical (in the sense presented here).
A watershed is widely recognized to be Thomas Bradwardine’s treatise, written in the first half of the 1320s. Until then, the most popular solutions to such paradoxes had little to offer as theories of truth: the restringentes approach, for example, consisted only in a ban or restriction to self-reference in general, and for propositions containing the predicate ‘‘true’’ in particular. By contrast, the apparatus presented by Bradwardine in his Insolubilia is the germinal state of a full-fledged theory of truth. Bradwardine’s starting point is the Aristotelian formula propositio vera est oratio significans sicut est, that is, a correspondence view on truth with a semantic emphasis on the signification of the proposition - the second relatum of the relation of correspondence is minimally referred to as sicut est with no further elaboration on what must obtain in reality for a proposition to be true. The truth of a proposition depends primarily on its signification, not on how things are.
In order to prove that Liar propositions and other paradoxical propositions are false, Bradwardine modifies this formula and posits that ‘‘A true proposition is an utterance signifying only [tantum] as things are’’ (first definition in chap. 6, 6.2 in Read’s edition and translation). He then goes on to prove that a Liar proposition says (at least) two things, namely, that it is false and that it is true. Since both things cannot obtain, he concludes that a Liar proposition does not signify only as things are; it signifies partially as things are (that it is false), but since it also signifies something that does not obtain (that it is true), it is not a true proposition (see Read 2002).
This definition of truth implies a few important assumptions: propositions may (in fact typically do) signify several things, and true propositions are only those whose total signification obtains, that is, if each and every thing that a proposition signifies is the case. It is thus what we could call a quantificational definition of truth, and truth is associated with universal quantification (see Dutilh Novaes 2008). Accordingly, a proposition is false if it fails to comply with the peak of success associated with a true proposition, that is, if at least one of the things it says is false. Therefore, while truth is associated with universal quantification, falsity is associated with existential quantification.
A variation of this approach to truth can be found in Buridan’s treatment of insolubles. While his main theory of truth is based on the concept of supposition, following the same lines of Ockham’s theory, Buridan recognizes that, in the case of Liar propositions, the co-suppositional criterion is not sufficient to determine their truth-value (cf. Sophismata ch. 8, 7th sophism). In such cases, not only the proposition itself must satisfy the co-suppositional criterion to be true, but also all of its implications. But since Buridan thinks that all propositions virtually imply their own truth, Liar propositions imply that they are true and that they are not true, and thus cannot satisfy the criterion for truth and are simply false (see Read 2002, Klima 2004 and Dutilh Novaes forthcoming for details).
In Albert of Saxony, writing shortly after Buridan, one finds a hybrid of the quantificational and the supposition approaches to truth. Albert’s first definition is a reformulation of Bradwardine’s definition of truth: ‘‘A true proposition is one which, in whatever way [qualitercumque] it signifies, so it is’’ (in Pozzi 1978:316). It replaces the term tantum in Bradwardine’s definition by one which is even more explicit with respect to the universal quantification implied in the definition, qualitercumque (also to be found in Buridan’s treatise on consequences (TC) to define the truth and the modality of propositions; however, he adds that this is just a way of speaking (TC, 21), a shorthand way to refer to the different truth-conditions of propositions on the basis of the supposition of their terms, which he discusses earlier in the text.). Albert then goes on to add a few theses equating the truth or falsity of propositions to the co-supposition (or lack thereof) of their terms. From these definitions and suppositions he then draws the conclusion (third thesis) that all propositions signify their own truth. So with Albert (as with Buridan) we have something of a forerunner of one of the directions of the Tarskian T-convention: here the relation between a proposition and the assertion of its truth is that of signification, while with Buridan it is a relation of (virtual) implication.
World History
