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NAIVE TRUTH AND NAIVE LOGICAL PROPERTIES

Published online by Cambridge University Press:  04 March 2014

ELIA ZARDINI
ELIA ZARDINI*
Affiliation:
LOGOS, Logic, Language and Cognition Research Group, Department of Logic, History and Philosophy of Science, University of Barcelona and Northern Institute of Philosophy, Department of Philosophy, University of Aberdeen
*
*LOGOS, LOGIC, LANGUAGE AND COGNITION RESEARCH GROUP DEPARTMENT OF LOGIC, HISTORY AND PHILOSOPHY OF SCIENCE UNIVERSITY OF BARCELONA and NORTHERN INSTITUTE OF PHILOSOPHY DEPARTMENT OF PHILOSOPHY UNIVERSITY OF ABERDEEN E-mail:[email protected]
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Abstract

A unified answer is offered to two distinct fundamental questions: whether a nonclassical solution to the semantic paradoxes should be extended to other apparently similar paradoxes (in particular, to the paradoxes of logical properties) and whether a nonclassical logic should be expressed in a nonclassical metalanguage. The paper starts by reviewing a budget of paradoxes involving the logical properties of validity, inconsistency, and compatibility. The author’s favored substructural approach to naive truth is then presented and it is explained how that approach can be extended in a very natural way so as to solve a certain paradox of validity. However, three individually decisive reasons are later provided for thinking that no approach adopting a classical metalanguage can adequately account for all the features involved in the paradoxes of logical properties. Consequently, the paper undertakes the task to do better, and, building on the system already developed, introduces a theory in a nonclassical metalanguage that expresses an adequate logic of naive truth and of some naive logical properties.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 7 , Issue 2 , June 2014 , pp. 351 - 384
Copyright
Copyright © Association for Symbolic Logic 2014 

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