Analyticity (New Problems of Philosophy) by Cory Juhl

By Cory Juhl

Analyticity, or the 'analytic/synthetic' contrast is likely one of the most vital and debatable difficulties in modern philosophy. it's also necessary to knowing many advancements in common sense, philosophy of language, epistemology and metaphysics. during this notable advent to analyticity Cory Juhl and Eric Loomis conceal the next key themes: The origins of analyticity within the philosophy of Hume and Kant Carnap's arguments pertaining to analyticity within the early 20th century Quine's well-known objections to analyticity in his vintage 'Two Dogmas of Empiricism' essay the connection among analyticity and valuable concerns in metaphysics, reminiscent of ontology the connection among analyticity and epistemology Analyticity within the context of the present debates in philosophy, together with arithmetic and ontology during the publication the authors express what number philosophical controversies hinge at the challenge of analyticity. extra positive aspects comprise bankruptcy summaries, annotated additional interpreting and a thesaurus of technical phrases making the ebook perfect to these coming to the matter for the 1st time.

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And to the extent that mathematics could be reduced to logic following Frege and Russell, a similar account could be given of mathematical truths as well – they too express implication relations between statements. CONC E P T I O N S O F A N A LY T I C T RUT H There thus emerged a new conception of analytic truths as expressions of the conventions governing language. Some of the core ideas behind this conception were outlined in Schlick’s General Theory of Knowledge (Schlick 1985). There, Schlick adopted discoveries in axiomatic theory made by the mathematician David Hilbert.

The significance of Gödel’s result for Carnap’s philosophy was immense. C A RN A P A N D Q UI N E By proving that no consistent formal system could allow the derivation of every true arithmetical formula, Gödel’s result undermined Carnap’s belief in a universal logic, for it made clear that at least some formulas of any consistent formal system of sufficient strength to express standard arithmetic would fall ‘outside’ what was derivable (provable or disprovable) in any given system of logic. Furthermore, Gödel’s result seemed to raise serious doubts about the extent to which truths of arithmetic could be regarded as analytic in the way that Frege and the Vienna Circle had hoped.

Russell noticed that Frege’s basic axioms entail the existence of C. Yet consider the question whether the set C is a member of itself or not. If C is not a member of itself, then since it is the set of all and only things that are not members of themselves, it is a member of itself. Conversely, if it is a member of itself, then it must not be a member of itself. So either a yes or no answer to the question yields a contradiction. Russell’s Paradox undermined Frege’s logicism. It also CONC E P T I O N S O F A N A LY T I C T RUT H undermined Frege’s idea that the apparently obvious truth of the basic laws could serve as an indicator of their analyticity.

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