Reason and Logic

2014

Abstract: This paper discusses the approaches of Frege, Nagel, Hanna and Cooper to reason, logic and their relationship, it points out their limitations and outlines an alternative approach hopefully not subject to those limitations. 1. The Reduction of Reason to Logic The relation between reason and logic goes back at least to 1292-1075 BC, when the so-called Memphite Theology stated that the Memphis God Ptah created everything through his mind and by his word. 1 This is the remotest origin of the dictum: “In the beginning was the logos ” and “through it everything was made. ” 2 It is also the remotest origin of the relation between reason and logic. For, on the one hand, the Greek word logos was translated into Latin as ‘ratio’, which originated the Italian ‘ragione’, the French ‘raison ’ and then the English ‘reason’. On the other hand, logos is the root of ‘logic’.

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.

2015

Modern logic has the tools for becoming a broad science of reasoning and other information directed behavior that plays an important role in connecting the humanities, exact sciences and social sciences at the university, and which is part of the bedrock of our information society. This paper is a revised version of a valedictory lecture delivered on 26 September 2014 as a University Professor of Pure and Applied Logic in the main auditorium of the University of Amsterdam. It traces the history of modern logic, illustrates the emergence of new trends in logic and agency, and discusses the most important future challenges facing it.

Bulletin of Symbolic Logic 19: 145-98, 2013

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Critical Views of Logic, 2023

This volume 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. Challenging the logic-first view 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. What, then, might justify a law of logic? We could of course consult logic itself: As to the question, why and with what right we acknowledge a logical law to be true, logic can respond only by reducing it to other logical laws. Where this is not possible, it can give no answer. (Frege 1893 (2013), p. xvii) But this will not take us very far, for logic too will need some fundamental laws. Frege therefore continues by asking whether there are extralogical considerations to which we can appeal: Stepping outside logic, one can say: our nature and external circumstances force us to judge, and when we judge we cannot discard this law-of identity, for example-but have to acknowledge it if we do not want to lead our thinking into confusion and in the end abandon judgement altogether. I neither want to dispute nor to endorse this opinion, but merely note that what we have here is not a logical conclusion. What is offered here is not a ground of being true but of our taking to be true. (ibid.) Thus, there is no help to be had from extralogical considerations either. Whereas in the Grundlagen (Frege 1884 (1974)) Frege seemed attracted to the idea that logic is constitutive of our thinking or judging, he is now unwilling to endorse this as a reason for the truth of the laws of logic, seeing it only as a reason for our taking the laws of logic to be true. It will also not help to look to other sciences:

New Ideas in Psychology 16 (1998) 125-139

This is our response to the commentaries on the paper on the logical substantiation of our theory.

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.

The current dominant view about logic is that there is a single paradigm of logic, logic as justification, according to which logic is a means of justification and consists in a theory of deduction. The paradigm originated with Aristotle's logic and its current form is mathematical logic. The latter was created to justify mathematics by putting it on a firm foundation, it includes Aristotle's logic as a small fragment, and is adequate as a logic of justification. This paper, however, argues that this view is not valid. Aristotle's logic does not belong to the paradigm of logic as justification because it is a method of discovery, and mathematical logic is inadequate as a means of justification. Besides the paradigm of logic as justification, there is the paradigm of logic as discovery, according to which logic is a method of discovery and consists in the analytic method. The latter is adequate as a means of discovery, and hence also as a means of justification, because in the analytic method justification is part of discovery.

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.