Torsten Odland

The object language of Kripke’s 1975 semantic theory of truth, based on the Strong Kleene valuation scheme, cannot contain a predicate that expresses the notion "ungroundedness" that Kripke provides an analysis of. This is unfortunate; it means that, in the object language of Kripke’s theory, there is no obvious way to express Kripke’s diagnostic insight about what causes semantic pathology. This paper shows how to introduce a “groundedness” predicate, G, to a Kripkean theory of truth that can fill this expressive gap. In the fixed-point construction that gives an interpretation for G, G’s anti-extension tracks networks of sentences that, due to predications of truth, result in non-terminating graphs of semantic dependence. In the fixed-point models that provide a class of intended interpretations for G: (i) every sentence with a classical semantic value is in the extension of G, (ii) every sentence in the anti-extension of G receives the value $$\frac{1}{2}$$, and (iii) the anti-extension of G includes all the sentences that receive $$\frac{1}{2}$$ in the corresponding model of Kripke’s original theory. A language augmented with predicates for truth and groundedness possesses sufficient expressive resources to articulate Kripke’s diagnostic insight as it applies to itself.

ABSTRACT The traditional view of propositional content presupposes that there is a privileged classification of token representations that partitions them with respect to sameness of content. I argue that there is no such thing: we utilize multiple distinct standards of sameness of content, none of which is privileged. My argument is based on the existence of semantic underdetermination. Plausibly, we use expressions (e.g. ‘sandwich’) that do not have determinate extensions and that are open to precisification in multiple directions. This gives rise to indefinitely many possible cases of content fission, where a semantically underdetermined token is identified as having the same content as two tokens that are precisified in opposite ways. Content fission requires recognizing a huge variety of legitimate notions of sameness of content.

In recent years, a variety of philosophers have argued that the fundamental bearers of representational properties like truth are concrete particulars produced by cognitive agents—representational vehicles (“RVs”), as I will call them. This view apparently conflicts with other judgments that are part of our common sense understanding of truth. For instance, it is plausible that there are truths about the Milky Way that have and never will never be articulated by anyone. Whatever these truths are, it looks like they cannot be RVs, because an RV is articulated just in case it exists. In this paper, I argue that it is consistent to hold that the fundamental truth-bearers are representational vehicles, while also acknowledging the existence of unarticulated truths. I argue that truth is a property that derivatively holds of kinds of RVs, that these provide the basis for our judgments that there are unarticulated truths, and I defend the view against putative counter-examples.