Aldo antonelli and others published freges conception of logic by patricia a. Thus, the object reading is still arguably a tenable reading of freges conception of truth. An introduction to formal logic open textbook library. However, this attack leaves the picture of the relation between the normative and the explanatory intact. But crispin wright claimed, in his book freges conception of numbers as objects 1983, that. But, of course, freges view and kants view contradict each other only if they have the same conception of logic. Goldfarb depicts salient differences between freges and the contemporary philosophical conceptions of logic. I recommend it for courses on frege, philosophy of language, philosophy of logic, and analytic philosophy. Starting from this simple principle, frege formulated a complex and powerful notation, a sample of which is shown in figure 1.
He worked as a mathematics professor at the university of jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. The last few decades have brought impressive new technical insights regarding freges logicism and his reduction of arithmetic to logic. His work of a more purelyphilosophical kind includes the articulation and persuasive defense of antipsychologism in mathematics and logic, the. 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. Freges new science antonelli, aldo and may, robert, notre dame journal of formal logic, 2000. Contemporary logic has close ties with philosophy, but it. Some reflections on freges constraint wright, crispin, notre dame journal of formal logic, 2000.
However, in the present paper, we shall be focusing on those systems which try to reconstruct freges theory of logical objects by. So far as i know, noone has really been tempted by that claim. Logical segmentation and generality in wittgenstein s. The logic of frege s theorem richard g heck jr department of philosophy, brown university 1 opening as is now wellknown, axioms for arithmetic can be interpreted in secondorder logic plus humes princi.
Frege essentially reconceived the discipline of logic by constructing a formal system which, in effect, constituted the first predicate calculus. In this paper, i focus my attention on clarifying the latter claim and freges motivations for making it, exposing what i take to be a fundamental tension in freges conception of logic. Frege, kant, and the logic in logicism john macfarlane. The lectures will provide a broadly historical introduction to various themes in the philosophy of logic and language, focusing on the work of frege and tarski. The history of logic as a subject has been characterised by many disputes over what the topic deals with, and the main article logic has as a result been hesitant to commit to a particular definition of logic. Frege and wittgenstein, truth and negation springerlink.
Blanchette explores the relationship between gottlob freges understanding of conceptual analysis and his understanding of logic. First, she examines freges understanding and use of conceptual analysis, and how this notion plays out methodologically in freges logicist philosophy of mathematics. Also, the object reading provides a plausible understanding of freges remarks. Frege, kant, and the logic in logicism 27 would have been open to kant to claim that freges begriffsschrift is not a proper logic at all, but a kind of abstract combinatorics, and that the meaning of the iterated quantifiers can only be grasped through construction in pure intuition.
Gottlob frege 18481925 made significant contributions to pure mathematics and philosophy. See heck and may for further discussion of freges contribution to the philosophy of language. Freges changing conception of number 147 a orded by geometrical and temporal sources is still a priori. Freges judgement stroke and the conception of logic as the study of inference not consequence nicholas j. On the contemporary conception, logical properties such as validity and consequence are metalinguistic properties of schemata determined by the truth values that result from interpretations of their placeholders. Frege s reasons for distancing himself from the kantian conception of logic. What drives this development is freges confrontation with the work of george boole. Freges theorem and foundations for arithmetic first published wed jun 10, 1998. He was wykeham professor of logic in the university of oxford, and was a fellow of new college, oxford, from 1959 until 1978. Freges conception of logic oxford scholarship online. Greimanns criticisms are not sufficient to refute the object reading of freges conception of truth. It is easily readable by graduates or advanced under graduates. The fortysix page introduction and notes to the translations make it useful also for frege scholars. In this paper i examine the question of logics normative status in the light of carnaps principle of tolerance.
To use freges theorem to reinstate logicism, for example, one would have to claim that hp was a logical truth. In addition he is a fellow of the british academy, an hon. In his most pointed discussions of sense and reference, e. The rst premise asserts bimplies ain freges notation, the second premise asserts b, and the conclusion asserts a. Although freges conception of truth is a central component of his. Frege s conception of logic specified formal system, but with ordinary sentences of natural language. Critical remarks on freges conception of logic by patricia blanchette. Freges coneption of logic explores the relationship between freges understanding of conceptual analysis and his understanding. Below is the provisional schedule for a course of lectures for the final honour school paper 108, philosophy of logic and language.
Frege, boolos, and logical objects the metaphysics research lab. New essays on frege between science and literature. Freges work became the starting point for numerous new formulations of logic. Crispin wright, freges conception of numbers as objects. He thought, in particular, that the psychologistic view of logic put forward by the majority of the logicians of his time is based on a misunderstanding of the nature of truth. Logical segmentation and generality in wittgensteins tractatus thomas ricketts how does wittgenstein understand quanti. His most important technical contribution, of both mathematical and philosophical significance, is the introduction of a formal system of quantified logic. She argues that the fruitfulness of freges conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop. Frege is of course an important progenitor of modern logic. Frege and carnap on the normativity of logic florian steinberger forthcoming in a special issue on carnap on logic in synthese, g.
Freges reasons for distancing himself from the kantian conception of logic. Logic, sense, and reference in frege will begin by describing an incertitude which clearly emerges from freges texts concerning the determination of the object of logic. From 1978 to 1983 he was a fellow of wolfson college, oxford. Blanchette explores the relationship between gottlob frege s understanding of conceptual analysis and his understanding of logic. It will help philosophers, researchers, and students better understand the nuances of this great thinker. This article surveys various definitions of the subject that have appeared over the centuries through to modern times, and puts them in context as reflecting rival conceptions of the. Meanwhile, logic was also enjoying a conceptual revolution due to gottlob frege, who maintained that with the impredicative comprehension of functions, logic that is, comprehension principle logic, cplogic hereafter is an informative science. It is a theorem of logic that nothing falls under this concept. Finally, i discuss whether freges deployment of the horizontal in his. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading. This paper challenges a standard interpretation according to which freges conception of logic early and late is at odds with the contemporary one, because on the latters view logic is. The evolution of freges mature conception begins soon after the publication of the former volume, and is largely in place by 1882. Frege and carnap on the normativity of logic springerlink.
Patricia blanchettes excellent freges conception of logic is focused, for the most part, on two interrelated questions. The volume elucidates this conception as well as the relation between natural language and the begriffsschrift. Fregean logic and russellian logic jaroslav peregrin. Many deep mathematical structures, of extreme importance and beauty, have been unearthed in it. Freges conception of the use of begri sschrifts formal system as a tool. It was to provide rigorous, gapless proofs that arithmetic was just logic further. They thus require a truth predicate for their expression, and, moreover. What is distinctive about my conception of logic wrote frege in july 19191 is that i. The debate has a starting point in freges specific conception of logic. Freges judgement stroke and the conception of logic as.
Pdf critical remarks on freges conception of logic by. It is natural to speculate that this change in freges 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. Frege grundgesetze pdf grundgesetze, as mentioned, was to be freges magnum opus. Numerical abstraction via the frege quantifier antonelli, g.
Freges theorem and foundations for arithmetic stanford. Freges coneption of logic explores the relationship between freges understanding of conceptual analysis and his understanding of logic. I begin by contrasting carnaps conception of the normativity of logic with that of his teacher, frege. Philosophers today still find that work insightful. Smith the university of sydney to appear in philosophy compass abstract one of the most striking differences between freges begriffsschrift logical system and. Second, she carefully explicates freges views on logic. Freges conception of logic chapter 3 the cambridge. It is argued that the fruitfulness of freges conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop of a clear account of the. The fact that the logical vocabulary can be used to state apparently nonlogical truths is.