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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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XI. Philosophical Reflections on Logic, Proof and Truth

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XIPhilosophical Reflections on Logic, Proof and Truth

Let us agree that logic (for simplicity, I limit my further considerations to classical first-order logic and theories; thus, non-classical, deviant or alternative logics, including infinitary systems, and respective theories based on such logical systems are entirely ignored) codifies the methodology of mathematics. For Frege, logical laws are inherently connected with truth. He says (Frege 1979a, p. 128 and Frege 1979b, p. 3):

   How must I think in order to reach the goal, truth? We expect logic to give us the answer to this question, but we do not demand that it should go into what is peculiar to each branch of knowledge and its subject-matter. On the contrary, the task we assign logic is only that of saying what holds with the utmost generality, whatever its subject-matter. We must assume that the rules for our thinking and for our holding something to be true are prescribed by the laws of truth. The former are given along with the latter. Consequently we can also say: logic is the science of the most general laws of truth.

   Logic is concerned only with those grounds of judgment which are truths. To make a judgment because we are cognizant of other truths as providing a justification for it is known as inferring. There are laws governing this kind of justification, and to set up these laws of valid inference is the goal of logic.

However, Frege’s view appears...

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