Introduction to "Critical Views of Logic"

Inquiry

This special issue explores what we call 'critical views of logic'. Following Frege, logic is often regarded as epistemologically and methodologically fundamental. All disciplines-including mathematics-are answerable to logic rather than vice versa. Critical views of logic disagree with this 'logic first' view. The logical principles that govern some subject matter may depend on the metaphysics of this subject matter or on the semantics of our discourse about it. General overview According to Frege, logic codifies 'the basic laws' of all rational thought, and the laws of logic must therefore be presupposed by all other sciences. He writes: I take it to be a sure sign of error should logic have to rely on metaphysics and psychology, sciences which themselves require logical principles. (Frege 1893, p. xix.

Philosophy Compass, 2015

This two-part paper reviews a scholarly debate on an alleged tension in Frege’s philosophy of logic. In section 1 of Part 1 I discuss Frege’s view that logic is concerned with establishing norms for correct thinking, and is therefore a normative science. In section 2 I explore a different understanding of the role of logic that Frege seems to advance: logic is constitutive of the very possibility of thought, because it sets forth necessary conditions for thought. Hence the tension: the view according to which logic is normative for thought seems to be incompatible with the idea that abiding by the laws of logic forms a precondition for thought. In section 1 of Part 2 I survey a number of interpretations of Frege’s conception of logic that deal with this question. I show that they are for the most part either normative readings (emphasising the former understanding of the nature of logic) or constitutive readings (emphasising the latter). Finally in section 2 I adjudicate the debate and aim at reconciling the normative and the constitutive strands in Frege’s conception of logic.

New Essays on Frege

Frege's conception of science includes three features: (1) a science is applicable to other sciences, or even to itself, (2) a science consists of a more or less rigid system of judgements and (3) a science presupposes elucidations, illustrative examples and a "catch on" among scientists. Together, I label these three features "The scientific Picture". Both logic and mathematics are included among the sciences and are covered by the scientific picture. As I understand Frege, this picture guides his logical and philosophical reflections. Here it is invoked in a treatment of two well-known and controversial Fregean topics: His claim, often repeated, that the axioms of Begriffsschrift and Grundgesetze are obvious and stand in no need of justification, and his use of a Kantian terminology in classifying judgements as analytic or synthetic, a priori or a posteriori. The most significant consequence of my reading is that it underscores the epistemological nature of Frege's thinking and, at the same time, downplays a current, and in my mind unfortunate, trend of ascribing to Frege a rather "thick" metaphysics. Towards the end, I discuss different aspects of the notion of a judgment at play in Frege's discussions: judgement as movement from thought to truth-value and judgement as represented by the judgement-stroke. These aspects point back to the distinction, so nicely illustrated by Frege's own writings, between a scientist, engaged in scientific research, and a philosopher, explicating the scientific activity and its general presuppositions, respectively.

2012

Philosophy Compass, 2015

This two-part paper reviews a scholarly debate on an alleged tension in Frege’s philosophy of logic. In section 1 of Part 1 I discuss Frege’s view that logic is concerned with establishing norms for correct thinking, and is therefore a normative science. In section 2 I explore a different understanding of the role of logic that Frege seems to advance: logic is constitutive of the very possibility of thought, because it sets forth necessary conditions for thought. Hence the tension: the view according to which logic is normative for thought seems to be incompatible with the idea that abiding by the laws of logic forms a precondition for thought. In section 1 of Part 2 I survey a number of interpretations of Frege’s conception of logic that deal with this question. I show that they are for the most part either normative readings (emphasising the former understanding of the nature of logic) or constitutive readings (emphasising the latter). Finally in section 2 I adjudicate the debate and aim at reconciling the normative and the constitutive strands in Frege’s conception of logic.

2003

The last few decades have brought impressive new technical insights regarding Frege's logicism and his "reduction of arithmetic to logic." 1 This paper, however, deals with the complementary but far less investigated question how Frege understood the nature of logical truth and of logical knowledge. I shall examine Frege's conception of logic as it developed and matured, beginning with his early Begriffsschrift from 1879 and following it up through to Grundgesetze I from 1893. 2 I shall make two main claims. My first main claim is that Frege started out with a view of logic that is closer to Kant's than is generally recognized, but that he gradually came to reject this Kantian view, or at least totally to transform it. My second main claim concerns Frege's reasons for distancing himself from the Kantian conception of logic. It is natural to speculate that this change in Frege's view of logic may have been spurred by a desire to establish the logicality of the axiom system he needed for his logicist reduction, including the infamous Basic Law V. I admit this may have been one of Frege's motives. But I shall argue that Frege also had a deeper and more interesting reason to reject his early Kantian view of logic, having to do with his increasingly vehement anti-psychologism.

Mind, 2008

Since its publication in 1967, Jean 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 1930. 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.

History and Philosophy of Logic, 2024

In many accounts of the history of logic, especially from the second half of the twentieth century and partly still today, Frege's rst book, Begri sschrift (1879), is singled out as the beginning of modern logic. In the English-speaking literature, this assessment goes back to the 1950s-60s when Frege's logical writings were rediscovered, after an initial period of neglect (although thinkers like Russell, Wittgenstein, and Carnap had paid close attention to it earlier). This is also the period during which modern logic consolidated itself, with its now standard sub elds: set theory, proof theory, model theory, and recursion theory. Good illustrations of this assessment of Frege's contributions can be found in William and Martha Kneale's book, The Development of Logic (1962), and in Jean van Heijenoort's revealingly entitled collection, From Frege to Gödel: A Source Book in Mathematical Logic. 1879-1931 (1967). The assessment was grounded in writings by a number of in uential logicians, including Alonzo Church, W.V.O. Quine, and Michael Dummett. Some of these writings, especially those by Dummett, include strong claims about how utterly original Frege's logical ideas were, thus representing a radical new beginning (cf. Reck 2023). Within the last 30-40 years such claims about the originality of Frege's views have been challenged and partly refuted in a number of ways. Thus, interpreters such as Christian Thiel, Gottfried Gabriel, Hans Sluga, etc. have pointed out the roots of some of Frege's logical ideas, including aspects of his logicist project, in neo-Kantian or post-Kantian philosophers like Hermann Lotze, J. F Herbart, and Wilhelm Windelband (cf. Gabriel 2002, Gabriel and, also the literature mentioned in them). Other interpreters of Frege, including Mark Wilson, Jamie Tappenden, and I, have discussed sources for Fregean ideas in mathematics, especially in nineteenth-century geometry, Bernhard Riemann's writings, and other works to which Frege was exposed in his mathematical education (cf. Tappenden 2008. Similarly, logical and mathematical in uences on Frege in works by Hermann and Robert Grassmann, Hermann Hankel, etc. may be worth exploring further, partly to clarify what Frege was reacting against (cf. Kreiser 2001). Yet another way in which the claim that modern logic started abruptly in 1879, with Begri sschrift, has been called into question is by rediscovering and highlighting earlier contributions by other logicians, such as George Boole, members of the Boolean school, as well as Bernard Bolzano (cf. Peckhaus 1997, Rusnock and. As this shows, it CONTACT Erich H. Reck