Russell's reasons for logicism

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Russell: the Journal of Bertrand Russell Studies, 1994

1994

Innovations in the History of Analytical Philosophy, 2017

One of the most significant events in the emergence of analytic philosophy was Bertrand Russell's rejection of the idealist philosophy of mathematics contained in his An Essay on the Foundations of Geometry [EFG] (1897) in favor of the logicism that he developed and defended in his Principles of Mathematics [POM] (1903). Russell's language in POMand in the sharp and provocative paper, "Recent Work on the Principles of Mathematics" (1901a), which is the first public presentation of many of the doctrines of POM-is deliberately revolutionary. "The proof that all pure mathematics, including Geometry, is nothing but formal logic, is a fatal blow to Kantian philosophy" (1901a, 379)-including, of course, the Kantian philosophy that he defended just four years earlier in EFG. "The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age" (POM, §4), a discovery that will initiate a new era in philosophy: "[T]here is every reason to hope that the near

2019

Bertrand Arthur William Russell (1872-1970) was a prolific, versatile and prominent British philosopher/mathematician who has been active in every major area of philosophy except aesthetics. While simultaneously having been notably prolific in the fields of metaphysics, philosophy of language, ethics and epistemology, Russell came to be widely regarded as one of the 20th century’s foremost logicians to such an extent that his name has become inseparable from any mention of mathematical logic. The principal goal of this present exposition will be the introduction of and expounding upon the intricate details of Russell’s lifelong logical output, as well as briefly sketching the historical progression and the contextual overview of the then-contemporary logic leading up to Russell’s efforts.

Noûs, 2007

The paper examines the widespread idea that Russell subscribes to a "Universalist Conception of Logic". Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results are, by an large, unfavorable to the Universalist interpretation.

According to Quine, Charles Parsons, Mark Steiner, and others, Russell's logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as a prioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell's explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of logicism? Building on recent work by Andrew Irvine and Martin Godwyn, I argue that Russell thought a systematic reduction of mathematics increases the certainty of known mathematical theorems (even basic arithmetical facts) by showing mathematical knowledge to be coherently organized. The paper outlines Russell's theory of coherence, and discusses its relevance to logicism and the certainty attributed to mathematics.

Russell: the Journal of Bertrand Russell Studies, 2017

Dialectica, 2005

In the unpublished work Theory of Knowledge† a complex is assumed to be “anything analyzable, any- thing which has constituents” (p. 79), and analysis is presented as the “discovery of the constituents and the manner of combination of a given complex” (p. 119). The notion of complex is linked in various ways with the notions of relating relation, logical form and proposition, taken as a linguistic expression provided with meaning. This paper mainly focuses on these notions, on their links and, more widely, on the role of logical form, by offering a new way of understanding what Russell was doing in TK as concerns the logical-ontological matter of this manuscript. In particular, a new account of Russell's theory of judgment will be given, by taking a stand with respect to the main accounts already given, and it will be argued for the presence in TK of a notion of type different from the one applied to propositional functions in ML and PM.