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Logic and Its Philosophy

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Jan Woleński

This collection of essays examines logic and its philosophy. The author investigates the nature of logic not only by describing its properties but also by showing philosophical applications of logical concepts and structures. He evaluates what logic is and analyzes among other aspects the relations of logic and language, the status of identity, bivalence, proof, truth, constructivism, and metamathematics. With examples concerning the application of logic to philosophy, he also covers semantic loops, the epistemic discourse, the normative discourse, paradoxes, properties of truth, truth-making as well as theology, being and logical determinism. The author concludes with a philosophical reflection on nothingness and its modelling.

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XIII. Rule-Following and Logic

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XIIIRule-Following and Logic

1. Introduction

If you type the phrase ‘rule-following problem’ in Google and click, more than 66 millions of results is displayed. Of course, not all are related to the question formulated by Wittgenstein several years ago and widely popularized by Kripke in recent times. I did not calculate the number of items in the Google-list related to the views of Kripkenstein and their variations. Anyway, few first pages are almost entirely related to Wittgenstein and Kripke. What is fairly surprising is that we do not find too many attempts to clarify the concept of rule in the context of rule-following. Most authors take for granted that normativity and correctness are involved in thinking about rules as followed. Although this intuition is certainly right, its insufficiency for a satisfactory account of rule-following immediately turns out to be obvious. The first part of this paper offers an analysis of rule-following based on a more complex foundation. In particular, some devices taken from deontic logic are employed in my proposed solution of the issue. The second part considers the problem of rules of pure logic and their following in making inferences.

2. The concept of rule-following and Wittgenstein’s paradox

As it is customary, I will start with Wittgenstein’s formulation of the paradox concerning rule-following. Wittgenstein says (see Wittgenstein 1953, sections 201, 202, 203, pp. 81e, 82e):

   This was our paradox: no course of action could be determined by a rule,...

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