Logical operations and iterated infinitely deep languages

We discuss an abstract notion of a logical operation and corresponding logics. It is shown that if all the logical operations considered are implicitely definable in a logic ?*, then the same holds also for the logic obtained from these operations. As an application we show that certain iterated forms of infinitely deep languages are implicitely definable in game quantifier languages. We consider also relations between structures and show that Karttunen's characterization of elementary equivalence for the ordinary infinitely deep languages can be generalized to hold for the iterated infinitely deep languages. An early version of this work was presented in the Abstracts Section of ICM '78.     

Logical Truth and Tarskian Logical Truth

This paper examines the question of the extensional correctness of Tarskian definitions of logical truth and logical consequence. I identify a few different informal properties which are necessary for a sentence to be an informal logical truth and look at whether they are necessary properties of Tarskian logical truths. I examine arguments by John Etchemendy and Vann McGee to the effect that some of those properties are not necessary properties of some Tarskian logical truths, and find them unconvincing. I stress the point that since the hypothesis that Tarski's definitions are extensionally correct is deeply entrenched, the burden of proof is still on the shoulders of Tarski's critics, who have not lifted the burden. This revised version was published online in June 2006 with corrections to the Cover Date.     

Logical Knowledge

It seems obvious that our beliefs are logically imperfect in two ways: they are neither deductively closed nor logically consistent. But this common-sense truism has been judged erroneous by some philosophers in the light of various arguments. In defence of common sense I consider and rebut interpretative arguments for logical perfection and show that the assumption espoused by common sense is theoretically superior, and capable - unlike its rival - of accounting for the informativeness of mathematics. Finally, I suggest that common sense opens the way to genuine disputes about the correct logic.     

Logical feedback

Just as non-well-founded sets extend the usual sets of ZF, so do root reflexive propositional formulas extends the usual class of Boolean expressions. Though infinitary, these formulas are generated by finite patterns. They possess transition functions instead of truth values and have applications in electric circuit theory.     

Logical Partisanhood

Philosophical Studies - A natural suggestion and increasingly popular account of how to revise our logical beliefs treats revision of logic analogously to the revision of scientific...     

Logical Predictivism

Journal of Philosophical Logic - Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention has been paid recently to the view, known as anti-exceptionalism...     

Logical Luck

Is guilt always part of the pain of contradiction? If I equivocate, is it always my fault? These issues about blame in logic (and perhaps the logic of blame) bear on central issues in philosophy of mind and language. One focus is the distinction between ignorance and incoherence drawn by Saul Kripke in his Pierre puzzle. The second focus is the challenge to privileged access mounted by Hilary Putnam in his twin earth 'thought-experiment'. I shall argue that some logical misdeeds are unavoidable. Often this lack of control excuses the misdeed. But not always – for reasons presaged by Bernard Williams in his discussion of moral luck.     

Explicating Logical Independence

Journal of Philosophical Logic - Accounts of (complete) logical independence which coincide when applied in the case of classical logic diverge elsewhere, raising the question of what a...     

Translating Logical Terms

The is an old question over whether there is a substantial disagreement between advocates of different logics, as they simply attach different meanings to the crucial logical terminology. The purpose of this article is to revisit this old question in light a pluralism/relativism that regards the various logics as equally legitimate, in their own contexts. We thereby address the vexed notion of translation, as it occurs between mathematical theories. We articulate and defend a thesis that the notion of “same meaning” is itself context-sensitive, depending on the purposes of a given conversation.

     

Reinflating Logical Consequence

Shapiro (Philos Q 61:320–342, 2011) argues that, if we are deflationists about truth, we should be deflationists about logical consequence. Like the truth predicate, he claims, the logical consequence predicate is merely a device of generalisation and more substantial characterisation, e.g. proof- or model-theoretic, is mistaken. I reject his analogy between truth and logical consequence and argue that, by appreciating how the logical consequence predicate is used as well as the goals of proof theory and model theory, we can be deflationists about truth but not logical consequence.