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 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.     

Logical operations

Tarski and Mautner proposed to characterize the logical operations on a given domain as those invariant under arbitrary permutations. These operations are the ones that can be obtained as combinations of the operations on the following list: identity; substitution of variables; negation; finite or infinite disjunction; and existential quantification with respect to a finite or infinite block of variables. Inasmuch as every operation on this list is intuitively logical, this lends support to the Tarski-Mautner proposal.Thanks to Shaughan Levine, Gila Sher, and the referee for their help.     

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.     

Resurrecting Logical Probability

The logical interpretation of probability, or ``objective Bayesianism'– the theory that (some) probabilitiesare strictly logical degrees of partial implication – is defended.The main argument against it is that it requires the assignment ofprior probabilities, and that any attempt to determine them by symmetryvia a ``principle of insufficient reason' inevitably leads to paradox.Three replies are advanced: that priors are imprecise or of little weight, sothat disagreement about them does not matter, within limits; thatit is possible to distinguish reasonable from unreasonable priorson logical grounds; and that in real cases disagreement about priorscan usually be explained by differences in the background information.It is argued also that proponents of alternative conceptions ofprobability, such as frequentists, Bayesians and Popperians, areunable to avoid committing themselves to the basic principles oflogical probability.