Online research in philosophy

We define a propositionally quantified intuitionistic logic Hπ + by a natural extension of Kripke's semantics for propositional intutionistic logic. We then show that Hπ+ is recursively isomorphic to full second order classical logic. Hπ+ is the intuitionistic analogue of the modal systems S5π +, S4π +, S4.2π +, K4π +, Tπ +, Kπ + and Bπ +, studied by Fine.

We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson's logic takes both truth and falsity as constructive notions, in the falsification logic truth is essentially non-constructive as opposed to falsity that is conceived constructively. We also briefly clarify the relationships of our falsification logic to some other logical systems.

Classical logic -- Temporal logic -- Modal logic -- Conditional logic -- Relevantistic logic -- Intuitionistic logic.

The main purpose of this note is to present difficult embeddings of minimal and full intuitionistic logic into classical linear logic, and to prove their soundness and faithfulness. Moreover, it is also pointed out that Girard's translation of intuitionistic logic into classical linear logic is provably equivalent to one of the translations considered in this paper.

We give a syntactic translation from first-order intuitionistic predicate logic into second-order intuitionistic propositional logic IPC2. The translation covers the full set of logical connectives ∧, ∨, →, ⊥, ∀, and ∃, extending our previous work, which studied the significantly simpler case of the universal-implicational fragment of predicate logic. As corollaries of our approach, we obtain simple proofs of nondefinability of ∃ from the propositional connectives and nondefinability of ∀ from ∃ in the second-order intuitionistic propositional logic. We also show that the ∀-free fragment of IPC2 is undecidable.

Only propositional logics are at issue here. Such a logic is contra-classical in a superficial sense if it is not a sublogic of classical logic, and in a deeper sense, if there is no way of translating its connectives, the result of which translation gives a sublogic of classical logic. After some motivating examples, we investigate the incidence of contra-classicality (in the deeper sense) in various logical frameworks. In Sections 3 and 4 we will encounter, originally as an example of what (in Section 2) we call a contra-classical modal logic, an unusual logic boasting a connective (" demi-negation" ) whose double application is equivalent to a single application of the negation connective. Pondering the example points the way to a general characterization of contra-classicality (Theorems 3.3 and 4.6). In an Appendix (Section 5), we look at one alternative to classical logic as the target for such translational assimilation, intuitionistic logic, calling logics which resist the assimilation, in this case, contra- intuitionistic. We will show that one such logic is classical logic itself, thereby strengthening a result of Wojcicki's to the effect that the consequence relation of classical logic cannot be faithfully embedded by any connective-by-connective translation into that of intuitionistic logic. (What the "faithfully" means here is that not only is the translation of anything provable in the 'source' logic..

Chomsky’s conception of semantics must contend with both philosophical skepticism and contrary traditions in linguistics. In “Two Dogmas” Quine argued that “...it is non-sense, and the root of much non-sense, to speak of a linguistic component and a factual component in the truth of any individual statement.” If so, it follows that language as the object of semantic investigation cannot be separated from collateral information. F. R. Palmer pursues a similar contention in his recent survey of issues in semantic theory: “...it is impossible even in theory to draw a clear line between the meaning of a word or sentence and all possible relevant information about it.” In spite of such skepticism, and through a variety of theories, devotion to lexical decomposition and truth dependent on language has not abated. The purpose of this paper is to focus related criticism and briefly put forward an alternative conception of empirical semantics.

Anti-realism is a doctrine about logic, language, and meaning that is based on the work of Wittgenstein and Frege. In this book, Professor Tennant clarifies and develops Dummett's arguments for anti-realism and ultimately advocates a radical reform of our logical practices.

This is my expository and critical review of Jerry Fodor's Psychosemantics. See also Callaway 1992, Meaning Holism and Semantic Realism.

Reconciliation of semantic holism with interpretation of individual expressions is advanced here by means of a relativization of sentence meaning to object language theories viewed as idealizations of belief-systems. Fodor's view of the autonomy of the special sciences is emphasized and this is combined with detailed replies to his recent criticisms of meaning holism. The argument is that the need for empirical evidence requires a holistic approach to meaning. Thus, semantic realism requires semantic holism.