Classical second-order intensional logic with maximal propositions

Conclusion By the standards presented in the Introduction, CMFC2 is deficient on at least one ontological ground: ‘∀’ is a syncategorematic expression and so CMFC2 is not an ideal language. To some there may be an additional difficulty: any two wffs provably equivalent in the classical sense are provably identical. We hope in sequel to present systems free of these difficulties, free either of one or the other, or perhaps both. This work was done with the aid of Canada Council Grant S74-0551-S1.     

Defending truth values for indicative conditionals

Philosophical Studies - There is strong disagreement about whether indicative conditionals have truth values. In this paper, I present a new argument for the conclusion that indicative conditionals...     

Language, truth and logic

Ohne Zusammenfassung

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Language, truth and logic Alfred J. Ayer: 254 S. London 1936. Victor Gollancz Ltd.

     

Paradox,truth and logic part I: Paradox and truth

Conclusion The discussion of the semantics of inconsistent truth theories now comes to a pause. The preceding is of course but a sketch; many interesting questions remain to be answered. The second part of this essay, however, will not seek to answer them. Rather, I will turn to the discussion of the proof theory of truth theory: the local and global logic of truth.Under the first heading, I show how to replace the inductive construction of models with an appropriate infinitary proof theory, and relate this on the one hand to the so-called dependence approach to inductive truth theories (Davis, 1979; Yablo, 1982) and on the other to van Fraassen's fact semantics for relevance logic.Under the second heading, I offer formals systems which capture the inferences valid in all approximate models. Not surprisingly, these turn out to be relevant logics.With formalism in hand, I discuss finally the extent to which the gap and/or glut approach can in fact be said to solve the paradoxes; that is, to allow us to say that the very language we are speaking is of the sort described in our theory.     

A note on three-valued logic and Tarski theorem on truth definitions

We introduce a notion of semantical closure for theories by formalizing Nepeivoda notion of truth. [10]. Tarski theorem on truth definitions is discussed in the light of Kleene's three valued logic (here treated with a formal reinterpretation of logical constants). Connections with Definability Theory are also established.A first version was prepared for sec. 5-Gnsaga-CNR and presented at the Logic Seminar, Institute of Philosophy, University of Firenze, in the academic year 1978–79. The author would like to thank the referee for his criticism and the Alexander von Humboldt-Stiftung for the support during the revision of the paper.     

Reasoning with contrary-to-fact propositions

In the initial study, the ability of subjects at four age levels (10, 13, 15, 18 years) (1) to accept if-then premises as a basis for reasoning and (2) to reason correctly with if-then premises was examined. Half the subjects were assessed with four reasoning problems involving factually accurate premises. The other half received factually inaccurate premises which were derived from the preceding ones by altering a single term. Both tests included an abstract problem which preceded the concrete propositions. Results indicate that the 10 year olds, and to a lesser extent the 13 year olds, did have difficulty in accepting contrary-to-fact premises as a basis for reasoning. The 15 and 18 year olds did not, but did find reasoning correctly more difficult with contrary-to-fact premises. The second study examined the ability of 5 and 7 year olds to accept contrary-to-fact premises. Subjects were given factually false premises either alone or within a fantasy context. Results indicate that the fantasy context decreases the extent to which empirical knowledge interferes with accepting contrary-to-fact premises. This result supports the notion that a representational process may be involved in accepting contrary-to-fact premises.