Online research in philosophy

Tarski’s Convention T is often taken to claim that it is both sufficient and necessary for adequacy in a definition of truth that it imply instances of the T-schema where the embedded sentence translates the mentioned sentence. However, arguments against the necessity claim have recently appeared, and, furthermore, the necessity claim is actually not required for the indefinability results for which Tarski is justly famous; indeed, Tarski’s own presentation of the results in the later Undecidable Theories makes no mention of an assumption to the effect that the definition of truth implies the biconditionals. This raises a question: was Tarski in fact committed to the necessity claim in the important papers of the 1930s and 40s? I argue that he was not. The discussion of this apparently esoteric interpretive issue in fact gets to the heart of many important questions about truth, and in the final sections of the paper I discuss the importance of the T-biconditionals in the theory of meaning and the relation of deflationary and inflationary theories of truth to the semantic paradoxes.

This is a review of Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena, by Jon Barwise and Lawrence Moss, published by CSLI (Center for the Study of Language and Information) Publications in 1996.

Response-dependence theses are usually formulated in terms of a priori true biconditionals of roughly the form ‘something, x, falls under the concept ‘F’ ↔ x would elicit response R from subjects S under conditions C’. Such formulations are vulnerable to conditional fallacy problems; counterexamples threaten whenever the C-conditions’ coming to obtain might alter the object with respect to F. Crispin Wright has suggested that such problems can be avoided by placing the C-conditions in a proviso. This ensures that any changes triggered by the C-conditions’ coming to obtain will be irrelevant to the truth of the biconditional. I argue that this move leaves the equations vulnerable to counterexamples of a slightly different kind: Cases where the change is triggered, not by the C-conditions’ coming to obtain, but by the response. I consider two ways to resist these counterexamples, and argue that both are insufficient. The upshot is a challenge that must be met if provisoed biconditionals are to serve their purpose.

This paper explores a distinction between two types of response-dependence (RD) account (shallow vs. deep). This distinction is inherent in much of the existing literature, however it is neither widely nor well understood, and has never been drawn explicitly. The distinction is often taken to be a metaphysical, or ‘realism-relevant’ one—i.e. deep RD accounts entail qualified realism (or perhaps anti-realism), while shallow RD accounts are metaphysically neutral. I argue that the distinction is not reliably realism-relevant. I formulate a weaker version of the distinction that may help prevent some common and understandable confusion about RD biconditionals and their relationship to realism. The weaker distinction rests on the different roles assigned to RD biconditionals by the two types of account.

In introductory logic courses the authors often limit their considerations to the truth-value operators. Then they write that conditionals and biconditionals of natural language ("if" and "if and only if") may be represented as material implications and equivalences ("⊃" and "≡"), respectively. Yet material implications are not suitable for conditionals. Lewis' strict implications are much better for this purpose. Similarly, strict equivalences are better for representing biconditionals (than material equivalences). In this paper we prove that the methods from standard first courses in logic can be used for testing arguments with strict implications, strict equivalences and other operators which may represent connectives from natural language.

A common objection against deflationism is that it cannot account for the fact that truth depends on reality. Consider the question ‘On what does the truth of the proposition that snow is white depend?’ An obvious answer is that it depends on whether snow is white. Now, consider what answer, if any, a deflationist can offer. The problem is as follows. A typical deflationary analysis of truth consists of biconditionals of the form ‘The proposition that p is true iff p’. Such biconditionals tell us nothing about what the truth of the proposition that p might depend on. Therefore, it seems that a typical deflationist cannot give an answer. Since we know that an answer is available, this throws doubt over the adequacy of deflationism as an account of truth. Articulated here is a defence of deflationism against this objection. It is argued that although biconditionals of the sort mentioned do not explicitly state a dependency between truth and reality, they nevertheless convey one. The reason is that, given the context in which a deflationist invokes the biconditionals, such a dependency is implicated. A potential problem with this defence is that it leaves the deflationist still unable to give an account of what it is for truth to depend on reality. One might think that a deflationist can offer such an account by appealing to truthmaker theory but, it is argued below, truthmaker theory is unavailable to a deflationist. Instead, the deflationist should question the assumption that an account is available.

Minimalists about truth say that the important properties of the truth predicate are revealed in the class of T -biconditionals. Most minimalists demur from taking all of the T -biconditionals of the form “ p is true if and only if p”, to be true, because to do so leads to paradox. But exactly which biconditionals turn out to be true? I take a leaf out of the epistemic account of vagueness to show how the minimalist can avoid giving a comprehensive answer to that question. I also show that this response is entailed by taking minimalism seriously, and that objections to this position may be usefully aided and abetted by Gupta and Belnap’s revision theory of truth.

The T-biconditionals, also known as T-sentences or T-equivalences, play a very prominent role in contemporary work on truth. It is widely held that they are so central to our understanding of truth that conformance with them is indispensable to any account of truth that aspires to be adequate. Even “deflationists” and “inflationists” tend to agree on this point; their debate turns largely on just how central a role these biconditionals can play in a theory of truth. In the present paper, I want to bracket this debate about their “theoretical role” and focus on the T- biconditionals themselves. They are typically presented as entirely unproblematic, as models of simplicity, clarity, and obviousness. I confess that I find them rather more puzzling than that. The main purpose of the paper is to reflect on some of these biconditionals and to survey and explore some doubts one might have about their virtues.

Practical philosophy and ethics -- Practical tortise raising -- Truth, beauty, and goodness -- Dilemmas: dithering, plumping, and grief -- Group minds and expressive harm -- Trust, cooperation, and human psychology -- Must we weep for sentimentalism? -- Through thick and thin -- Perspectives, fictions, errors, play -- The steps from doing to saying -- Success semantics -- Wittgenstein's irrealism -- Circles, finks, smells, and biconditionals -- The absolute conception: Putnam vs. Williams -- Julius Caesar and George Berkeley play leapfrog -- The majesty of reason -- Fiction and conviction.