Frege's Begriffsschrift and Logicism (original) (raw)
Related papers
Formality of Logic and Frege's Begriffsschrift
Canadian Journal of Philosophy, 2019
This paper aims to challenge what I call the 'standard interpretation' of Frege's conception of logic, according to which Frege's view of logic (early and late) is at odds with the contemporary one, because on the latter's view logic is formal, while on Frege's view it is not, given that logic's subject matter is reality's most general features. I show evidence that, contra the standard interpretation, the early Frege – in his Begriffsschrift – retained the idea that logic is formal; Frege assigns logic the task of providing the 'logical cement' (the formal – structural – scaffolding) that ties up together the contentful concepts used in specific sciences, not that of providing the most general truths. I finally connect this task with what Frege says about the application of his Begriffsschrift and, relatedly, I provide an alternative reading – to the standard interpretation – of what Frege means by saying that Begriffsschrift is a 'lingua characteristica'.
Debating (Neo)logicism: Frege and the Neo-Fregeans
Between Logic and Reality, 2011
The paper's aim is to determine and discuss in which sense, if any, Frege's and neo-Fregean logicism are responding to the epistemological challenge concerning our arithmetical knowledge. More precisely the paper analyses what the epistemological significance of Frege's logicist programme amounts to, namely, the objective justificatory connections obtaining between arithmetical and logical statements. It then contrasts this result with the self-understanding of the neo-Fregeans who allegedly follow Frege's steps, but in fact take a rather different direction.
Frege's Conception of Logic: From Kant to Grundgesetze
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.
Philosophia Mathematica (III) The Ins and Outs of Frege's Way Out
Confronted with Russell's Paradox, Frege wrote an appendix to volume II of his Grundgesetze der Arithmetik. In it he offered a revision to Basic Law V, and proclaimed with confidence that the major theorems for arithmetic are recoverable. This paper shows that Frege's revised system has been seriously undermined by interpretations that transcribe his system into a predicate logic that is inattentive to important details of his concept-script. By examining the revised system as a concept-script, we see how Frege imagined that minor modifications of his former proofs would recover arithmetic. † Special thanks to Kevin Klement, Ed Mares, Francesco Orilia, and anonymous referees for helpful comments on this paper.
Comments on Patricial Blanchette's Book: Frege's Conception of Logic
Journal for the History of Analytical Philosophy, 2015
All contributions included in the present issue were originally presented at an 'Author Meets Critics' session organised by Richard Zach at the Pacific Meeting of the American Philosophical Association in San Diego in the Spring of 2014.
Frege, his Logic and his Philosophy Interview with Michael Beaney
Journal of the graduate school of letters, 2010
The interview begins with an outline of Gottlob Freges lifeacademic career and the reception of his ideas by later philosophers such as Bertrand Russell and Ludwig Wittgenstein. Freges main contributions to logic and philosophy are summarizedand the key ideas of his three main booksBegriffsschriftDie Grundlagen der Arithmetik and Grundgesetze der Arithmetik � are explained. Particular attention is paid to Freges fundamental claim thata statement of number contains an assertion about a conceptand to theCantor‑Hume Principlewhich play a central role in his logicist projectthe attempt to show that arithmetic can be reduced to logic. Also discussed are three of Freges important essayswhich elucidate his view of concepts as functions and his distinctions between concept and object and betweenSinnandBedeutung� . Here particular attention is paid to problems concerning his notion of an extension of a concept (or more generallyhis notion of a value‑range of a functionthe translation ofBedeu...