Paradoxes of truth-in-context-X

We may suppose that the truth predicate that we utilize in our semantic metalanguage is a two-place predicate relating sentences to contexts, the truth-in-context-X predicate. Seeming paradoxes pertaining to the truth-in-context-X predicate can be blocked by placing restrictions on the structure of contexts. While contexts must specify a domain of contexts, and what a context constant denotes relative to a context must be a context in the context domain of that context, no context may belong to its own context domain. A generalization of that restriction appears to block all of the paradoxes of truth-in-context-X. This restriction entails that, in a certain sense, we cannot talk about the context we are in. This result will be defended, up to a point, on broadly ontological grounds. It will also be conjectured that our semantic metalanguage can be regarded as semantically closed.

The Epistemic Conception of Vagueness

This chapter challenges Epistemicism. It rebuts Williamson’s arguments for unrestricted Bivalence, based on the Disquotational Scheme for the truth predicate, and Sorensen’s arguments that the idea of a predicate’s being of limited sensitivity is itself incoherent. The chapter nevertheless proposes a broadly epistemic conception of what a definite case of a vague predicate is—namely, a case where at least one of two conflicting verdicts about a vague predication must involve some kind of cognitive shortcoming, and proposes a corresponding notion of a borderline case—one where each of a pair of conflicting verdicts can be unexceptionable—and sides with Epistemicism in rejecting the idea of such cases as truth-value gaps. It is contended that Williamson’s explanation of why we cannot know where the putative sharp cut-offs in Sorites series come at best explains too little, since it has nothing plausible to say about our ignorance throughout a borderline area, nor about vagueness induced by deliberate approximation—‘roughly six feet tall’, ‘about a metre long’.

Assessment Relativism and the Truth-Predicate

The purpose of this paper is to argue that assessment relativism entails the assessment-sensitivity of the sentential truth-predicate, but not of the propositional truth-predicate. The central idea of assessment relativism is that a single token claim evaluated within a single world can have different truth-values when considered in different contexts of assessment. John MacFarlane in Assessment Sensitivity: Relative Truth and its Applications (2014) and also Max Kölbel in the article ‘Global relativism and self-refutation’ (2011) have argued that this position leads to relativism about the propositional truth-predicate. I argue that this is not the case—it entails relativism only about the sentential truth-predicate.

Does Frege Have a Metalinguistic Truth-Predicate in Begriffsschrift?

In the explanations of logical laws and inference rules of the mature version of Begriffsschrift in Grundgesetze, Frege uses the predicate “… is the True.” Scholars like Greimann maintain that this predicate is a metalinguistic truth-predicate for Frege. This paper examines an argument for this claim that is based on the “nominal reading” of Frege’s conception of sentences—the claim that for Frege a sentence “ $ p $ ” is equivalent to a nonsentential phrase like “the truth-value of the thought that $ p $ .” In particular, this paper attempts to establish two points concerning this argument based on the nominal reading. First, the argument implies a claim about the nature of assertion which Frege repeatedly denies in his mature works. Secondly, the nominal reading on which the argument depends is false. A sentence “ $ p $ ” is not equivalent to a nonsentential phrase like “the truth-value of the thought that $ p $ ” for Frege. Our discussion will lead to an important lesson about Frege’s conception of sentences and of assertion.

Another Look at Reflection

Reflection principles are of central interest in the development of axiomatic theories. Whereas they are independent statements they appear to have a specific epistemological status. Our trust in those principles is as warranted as our trust in the axioms of the system itself. This paper is an attempt in clarifying this special epistemic status. We provide a motivation for the adoption of uniform reflection principles by their analogy to a form of the constructive $$\omega $$ ω -rule. Additionally, we analyse the role of informal arithmetic and the conception of natural numbers as an inductive structure, also with regard to extra conceptual resources such as a primitive truth predicate.

Interpreting the compositional truth predicate in models of arithmetic

We present a construction of a truth class (an interpretation of a compositional truth predicate) in an arbitrary countable recursively saturated model of first-order arithmetic. The construction is fully classical in that it employs nothing more than the classical techniques of formal proof theory.

Soundness, Epistemology, and Frege’s Project

Insofar as the use of natural language to introduce, discuss, and argue about features of a formal system is metatheoretic, there can be no doubt: Frege has a metatheory. But what kind of metatheory? Although the model theoretic semantics with which we are familiar today is a post-Fregean development, most believe that Frege offers a proto-soundness proof for his logic that intrinsically exploits a truth predicate and metalinguistic variables. In this chapter it is argued that he neither uses, nor has any need to use, a truth predicate or metalinguistic variables in justifications of his basic laws and rules. The purpose of the discussions that are typically understood as constituting Frege’s metatheory is, rather, elucidatory. And once we see what the aim of these particular elucidations is, we can explain Frege’s otherwise puzzling eschewal of the truth predicate in his discussions of the justification of the laws and rules of inference.

The Subject and the Quest for Truth: Heidegger and Lonergan on Truth

Since the “elimination of the subject” from truth discourse by Frege, by identifying the subject—or rather the subjective—with the private and personal, philosophical investigations of truth have consciously or unconsciously truncated the role of the knowing subject in the quest for truth. The neglect of the subject has turned the exploration of truth into logical, semantic, conceptual or linguistic analysis of the truth predicate. The consequence of this is that some philosophers tend to treat truth as if it does not really matter; as is shown by their deflationary attitude towards truth or even the total denial of truth. Despite the prevalent elimination of the subject from truth discourses, two thinkers that acknowledge the importance of the subject in the exposition of the concept of truth are Martin Heidegger and Bernard Lonergan. In this paper I explore their positions and argue that Heidegger’s situating of the centrality of Dasein in relation to truth in disclosedness—as the basic state of Dasein’s ontological constitution—is inadequate. Following Lonergan, I argue that an adequate account of the centrality of the role of the subject can only be situated in the cognitional acts of the subject within the context of the human quest for knowledge, and that the pivotal cognitional act is the act of judgment.

Truth and the Quest for Definition

The controversies in contemporary truth discourses can be traced directly or indirectly to the Fregean choice of “thought” as the truth bearer, Ramsey’s redundancy thesis, Tarskian semantic conception, and Davidson’s defence of the indefinability of truth. The common feature of these four positions is an inadequate treatment of the “what is” question. Because of the neglect of this kind of question, the consequence is that truth has been reduced to a thin concept (that is a reduction of truth to logical, semantic or linguistic analysis of the truth predicate, or analysis of intentional signs at the expense of intentional acts) and subsequent quest for the deflation of truth. I argue that such an approach to the philosophical investigation of truth is at best inadequate and at worst bound to fail. Hence, I propose that an adequate exploration of truth must first address the “what is” question, rather than just assuming it. Further, I argue that to realise this, it is vital to take into consideration the wider context in which the truth question arises, that is, the human quest for knowledge and self-transcendence; and it is the conception of truth as critical correspondence that is capable of sufficiently answering the question.