Hao Wang. The formalization of mathematics. The journal of symbolic logic, vol. 19 (1954), pp. 241–266.

The difference between the transcendent Coleridgean symbol and the unreliable conventional symbol was of explicit concern in Victorian mathematics, where the former was aligned with Euclidean geometry and the latter with algebra. Rather than trying to bridge this divide, practitioners of modern algebra and the pioneers of symbolic logic made it the founding principle of their work. Regarding the content of claims as a matter of “indifference,” they concerned themselves solely with the formal interrelations of the symbolic systems devised to represent those claims. In its celebration of artificial algorithmic structures, symbolic logician Lewis Carroll’s Sylvie and Bruno dramatizes the power of this new formalist ideal not only to revitalize the moribund field of Aristotelian logic but also to redeem symbolism itself, conceived by Carroll and his mathematical, philosophical, and symbolist contemporaries as a set of harmonious associative networks rather than singular organic correspondences.

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Frege and Wittgenstein: The Limits of the Analytic Style

Elements ◽

10.6017/eurj.v6i1.9022 ◽

2010 ◽

Vol 6 (1) ◽

Author(s):

Christopher Sheridan

Keyword(s):

Twentieth Century ◽

Logical Analysis ◽

Linguistic Meaning ◽

Bertrand Russell ◽

Gottlob Frege ◽

Symbolic Logic ◽

Scientific Language ◽

German Mathematician ◽

Broad Application ◽

Analytic Tradition

The analytic tradition in philosophy stems from the work of German mathematician and logician Gottlob Frege. Bertrand Russell brough Frege's program to render language-particularly scientific language-in formal logical terms to the forefront of philosophy in the early twentieth century. The quest to clarify language and parse out genuine philosophical problems remains a cornerstone of analytic philosophy, but investigative programs involving the broad application of formal symbolic logic to language have largely been abandoned due to the influence of Ludwig Wittgenstein's later work. This article identifies the key philosophical moves that must be performed successfully in order for Frege's "conceptual notation" and other similar systems to adequately capture syntax and semantics. These moves ultimately fail as a result of the nature of linguistic meaning. The shift away from formal logical analysis of language and the emergence of the current analytic style becomes clearer when this failure is examined critically.

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