Anssi Korhonen

Logic as a Science and Logic as a Theory: Remarks on Frege, Russell and the Logocentric Predicament

Since its publication in 1967, van Heijenoort’s paper, “Logic as Calculus and Logic as Language” has become a classic in the historiography of modern logic. According to van Heijenoort, the contrast between the two conceptions of logic provides the key to many philosophical issues underlying the entire classical period of modern logic, the period from Frege’s Begriffsschrift (1879) to the work of Herbrand, Gödel and Tarski in the late 1920s and early 1930s. The present paper is a critical reflection on some aspects of van Heijenoort’s thesis. I concentrate on the case of Frege and Russell and the claim that their philosophies of logic are marked through and through by acceptance of the universalist conception of logic, which is an integral part of the view of logic as language. Using the so-called “Logocentric Predicament” (Henry M. Sheffer) as an illustration, I shall argue that the universalist conception does not have the consequences drawn from it by the van Heijenoort tradition. The crucial element here is that we draw a distinction between logic as a universal science and logic as a theory. According to both Frege and Russell, logic is first and foremost a universal science, which is concerned with the principles governing inferential transitions between propositions; but this in no way excludes the possibility of studying logic also as a theory, i.e., as an explicit formulation of (some) of these principles. Some aspects of this distinction will be discussed.

Frege, the Normativity of Logic, and the Kantian Tradition

This paper considers the role of constitutivity and normativity in Frege’s conception of logic. It outlines an historical interpretation with two goals. First, it traces these concepts back to their origins in Kant’s philosophy. Second, it considers some of the different ways in which the issue of normativity and its proper grounding was addressed in the neo-Kantian tradition and in early analytic philosophy. Some neo-Kantians worked out an epistemic-normative conception of objective judgment, according to which the objectivity of cognition is constituted by distinctively logical norms. In Frege we find an original and sophisticated version of this line of thought. For Frege, the normative and constitutive roles of logic come to the fore in the articulation of scientific reason which follows the classical model of demonstrative science as cognitio ex principiis (cognition from principles). Wittgenstein’s Tractatus then opens up a fresh Kantian perspective on the constitutivity of logic, one that grounds logic in structure rather than norms, and does so in conscious opposition to Frege and his normative science. Logic is transcendental, according to Wittgenstein, being the essence of the world and of all description. Hence, the normative function of logic becomes, in a way, superfluous.

Other Logics: Alternatives to Formal Logic in the History of Thought and Contemporary Philosophy

Criticism of formal logic is a familiar topic from the history of philosophy, where it has often been coupled by constructive proposals advocating either replacement or supplementation. The essays ...

Russell’s Ontological Logic

The single most important ingredient in the conception of logic that informs PoM is the notion of proposition. It combines familiar elements with others which are much less so (although these less familiar elements, or something similar to them, also have advocates among contemporary philosophers). The familiar elements are two:

Kant and Russell on the Mathematical Method

Russell’s reasons for emphasizing rigour were primarily semantic rather than epistemic; he wanted to find out what was really involved in mathematical concepts, propositions and reasonings, and this, he thought, should be accomplished in agreement with ‘modern mathematics’.

Russell on Kant and the Synthetic a priori

In this chapter we shall be concerned with Russell’s criticism of Kant’s explanation of the synthetic a priori. Much of what Russell has to say here is based on the well-known interpretation of transcendental idealism as a species of psychologism. Attending to the details of what Russell has to say about Kant, however, helps us to see that there is more to it than just a rather simplistic misreading of Kant. Ultimately, what is at stake here is the contrast between two radically different perspectives on the synthetic a priori: epistemic (Kant) and metaphysical (Russell).

Russell and the Bolzanian Conception of Logic

In Chapter 3 we examined, from Russell’s point of view, Kant’s account of how propositions that are synthetic can nevertheless be known a priori. Russell’s argument, it will be recalled, was directed against Kant’s model of explanation, which seeks to derive a number of properties of a priori propositions from features characterizing the cognition of these propositions; this was referred to as the relativized model of the a priori (r-model). Russell’s own view is that the source of the synthetic a priori in mathematics is to be found in logic. Since logic is a priori, an acceptable account of its propositions is constrained, among other things, by conditions revealed through an examination of the r-model. On the face of it, apriority implies that the propositions of logic must be true, universal and necessary. Insofar as these characteristics are present, moreover, they should be genuine rather than proxy as in Kant’s theory, according to Russell.