Neil Tennant

Using a quantified propositional logic involving the operators it is known that and it is possible to know that, we formalize various interesting philosophical claims involved in the realism debate. We set out inferential rules for the epistemic modalities, ranging from ones that are obviously analytic, to ones that are epistemologically more substantive or even controversial. Then we investigate various aporias for the realism debate. These are constructively inconsistent triads of claims from our list: a claim expressing some sort of common ground in the debate; a characteristically anti-realist thesis about truth and knowability; and a characteristically realist thesis about determinacy of truth value. Various patterns of reductio proof for these inconsistent triads are generated, so as to display their variety. The reductio proofs use only the inferential rules set out earlier. The philosophical utility of each aporia for the anti-realist is then assessed. This involves consideration of the acceptability of the premiss expressing common ground; the strength and plausibility of the anti-realist premiss; the strength of the realist premiss that is the ultimate target of the reductio; and the analytic status of the inferential rules applied within the proof.

This is Part I of a two-part study of the foundations of mathematics through the lenses of (i) apriority and analyticity, and (ii) the resources supplied by Core Logic. Here we explain what is meant by apriority, as the notion applies to knowledge and possibly also to truths in general. We distinguish grounds for knowledge from grounds of truth, in light of our recent work on truthmakers. We then examine the role of apriority in the realism/anti-realism debate. We raise a hitherto unnoticed problem for any Orthodox Realist who attempts to explain the a priori

This paper rebuts criticisms by Hintikka of the author's account of game-theoretic semantics for classical logic. At issue are (i) the role of the axiom of choice in proving the equivalence of the game-theoretic account with the standard truth-theoretic account; (ii) the alleged need for quantification over strategies when providing a game-theoretic semantics; and (iii) the role of Tarski's Convention T. As a result of the ideas marshalled in response to Hintikka, the author puts forward a new conjecture concerning the relationship among truth, meaning and translation

We present a logically detailed case-study of explanation and prediction in Newtonian mechanics. The case in question is that of a planet's elliptical orbit in the Sun's gravitational field. Care is taken to distinguish the respective contributions of the mathematics that is being applied, and of the empirical hypotheses that receive a mathematical formulation. This enables one to appreciate how in this case the overall logical structure of scientific explanation and prediction is exactly in accordance with the hypotheticodeductive model

The Theory of theory change has contraction and revision as its central notions. Of these, contraction is the more fundamental. The best-known theory, due to Alchourrón, Gärdenfors, and Makinson, is based on a few central postulates. The most fundamental of these is the principle of recovery: if one contracts a theory with respect to a sentence, and then adds that sentence back again, one recovers the whole theory. Recovery is demonstrably false. This paper shows why, and investigates how one can nevertheless characterize contraction in a theoretically fruitful way. The theory proposed lends itself to implementation, which in turn could yield new theoretical insights. The Main proposal is a ‘staining algorithm’ which identifies which sentences to reject when contracting a theory. The algorithm requires one to be clear about the structure of reasons one has for including sentences within one's theory.

Brian Skyrms has studied the evolutionary dynamics of a simple bargaining game. Fair-dealing is the strategy 'demand 1/2', competing with the more modest strategy 'demand 1/3' and the greedier strategy 'demand 2/3'. Individuals leave offspring in proportion to their accumulated payoffs. The rules for payoffs from encounters penalize low- and high-demanders. The result is a significant basin of attraction for fair-dealing as an evolutionarily stable strategy. From these considerations Skyrms concludes that a disposition to fair-dealing could have evolved. A very different picture emerges, however, when one considers genetic bases for the dispositions involved. A simple two-allele sexual model produces very different stable equilibria in the distribution of behavioral phenotypes. The equilibria for Skyrms's purely phenotypic selection process will not in general be attainable once one enters some simple genetic considerations

Michael Friedman maintains that Carnap did not fully appreciate the impact of Gödel's first incompleteness theorem on the prospect for a purely syntactic definition of analyticity that would render arithmetic analytically true. This paper argues against this claim. It also challenges a common presumption on the part of defenders of Carnap, in their diagnosis of the force of Gödel's own critique of Carnap in his Gibbs Lecture. The author is grateful to Michael Friedman for valuable comments. Part of the research towards this paper was carried out while the author was a Visiting Fellow at the Center for Philosophy of Science at the University of Pittsburgh. The paper was presented to the Center's Fellowship Reunion Conference in Athens in 1992. It was committed for publication in the Proceedings of that conference, but those Proceedings never appeared. By the time it became evident that they would never appear, both the hard copy and the source file had been mislaid. The hard copy re-surfaced in 2007. The literature on this topic since 1992 appears to leave some space for the ideas and arguments presented here. Although the paper has been updated in light of the more recent literature, its basic thesis, presented in 1992, remains the same. Only 3 is new, questioning a basic presumption made by more recent commentators in their presentation of Gödel's criticism of Carnap in his Gibbs Lecture. For helpful comments on the current version, the author is indebted to Robert Kraut, Stewart Shapiro, and Adam Podlaskowski. CiteULike    Connotea    Del.icio.us    What's this?

Christopher Peacocke, in A Study of Concepts, motivates his account of possession conditions for concepts by means of an alleged parallel with the conditions under which numbers are abshacted to give the numerosity of a predicate. There are, however, logical mistakes in Peacocke's treatment of numbers, which undermine his intended analogy. Nevertheless Peacocke's account of possession conditions for concepts is not rendered inadequate simply by virtue of being deprived of the intended analogy and the motivation it was supposed to afford. His account of concepts deserves still to be considered on its own merits, even if it is more idiosyncratic for being isolated from the paradigm case of numerical abstraction. Peacocke's own account of concepts as abstract objects turns out, though, not to have the logical form that he himself was seeking for it. We show how to re-cast it in an equivalent form of the kind he requires. Then we re-formulate it so as to achieve complete generality. This exercise helps to clarify the central theses in Peacocke's account of concepts. It invites the conclusion that his account of content-determination is rather platitudinous and unoriginal — except for a claim of 'doxastic sufficiency' for content-determination, which emerges at the end of the discussion.

This paper treats entailment as a subrelation of classical consequence and deducibility. Working with a Gentzen set-sequent system, we define an entailment as a substitution instance of a valid sequent all of whose premisses and conclusions are necessary for its classical validity. We also define a sequent Proof as one in which there are no applications of cut or dilution. The main result is that the entailments are exactly the Provable sequents. There are several important corollaries. Every unsatisfiable set is Provably inconsistent. Every logical consequence of a satisfiable set is Provable therefrom. Thus our system is adequate for ordinary mathematical practice. Moreover, transitivity of Proof fails upon accumulation of Proofs only when the newly combined premisses are inconsistent anyway, or the conclusion is a logical truth. In either case Proofs that show this can be effectively determined from the Proofs given. Thus transitivity fails where it least matters — arguably, where it ought to fail! We show also that entailments hold by virtue of logical form insufficient either to render the premisses inconsistent or to render the conclusion logically true. The Lewis paradoxes are not Provable. Our system is distinct from Anderson and Belnap''s system of first degree entailments, and Johansson''s minimal logic. Although the Curry set paradox is still Provable within naive set theory, our system offers the prospect of a more sensitive paraconsistent reconstruction of mathematics. It may also find applications within the logic of knowledge and belief.