Logicism and its Philosophical Legacy

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inspirarte-qa-fabercastell.gingaone.com/smut-sequence-one-perspective-series-book.php Frege and the rigorization of analysis; 8. The philosophical basis of our knowledge of number; 9. The Principia's theory of functions and classes; Ramsey's extensional propositional functions.

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  • Origins and Varieties of Logicism;

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Write your review. One of the more famous comes from the Oxford philosopher A. Philosophy of Mathematics. Add a tag Cancel Be the first to add a tag for this edition. Nor does he hold the view that truth reduces to empirical adequacy.

Add to Wishlist. USD Sign in to Purchase Instantly. Overview The idea that mathematics is reducible to logic has a long history, but it was Frege who gave logicism an articulation and defense that transformed it into a distinctive philosophical thesis with a profound influence on the development of philosophy in the twentieth century. Average Review.

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By focusing on recent works on Frege, Dedekind, Peano, Russell, and Carnap, the workshop aims at both an historical and theoretical exploration of the main figures in the philosophical and mathematical milieu in which logicist views were first expounded, in order to shed new light on their legacy for contemporary philosophy of mathematics.

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Kurt Gödel & the Limits of Mathematics

Beyond his anachronistic use of Ramsey sentences the import of which he elegantly extracts via a comparison with Craig transcriptions [] to articulate the commitments of Russell's structuralism, Demopoulos offers a phenomenalist reconstruction of Ramsey's remarks in "Theories" to provide a striking antirealist contrast to Russell's realism. This enables him to draw out some important philosophical implications of the technical contrast between extensions and expansions Demopoulos makes these points using a "toy theory" T which has true observational consequences in the standard model of the natural numbers, but which is only true in nonstandard models.

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Whereas extensions of the domain of observational consequences and so, theories that can be modeled only in such extensions are licensed under Russell's realist structuralism since its point is to show how we can extend our knowledge beyond percepts to things existing in the material world , Demopoulos maintains that they are ontologically extravagant under Ramsey's antirealist structuralism. Demopoulos enlists Carnap to help clear an attractive middle ground, emphasizing his passing remark that the theoretical entities to which the Ramsey sentence of a theory refer are "purely logico-mathematical.

Bertrand Russell

For if a theory's theoretical vocabulary is only fixed up to its logical category, Demopoulos proves that it can be interpreted in an arbitrary model of the right cardinality. The upshot is that the non-observational part of a theory is trivialized, being true "as a matter of metalogic," not as a matter of the world being a certain way Demopoulos deploys variations of this core insight repeatedly in the essays critiquing structuralism.

Some repetition is of course to be expected in collections where a view is being refined over several decades. Readers will find similar discussions of the toy theory in essays four and seven, and of Frege's logicism in essays one, eight, and nine.

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While specialists may find it valuable to work through Demopoulos' refinements, framed as they are against the developing literature on Newman's objection, others should focus on his view's culmination in essay seven, "Three Views of Theoretical Knowledge. On Gupta's view, experience does not yield epistemically privileged observational propositions even ones capable of being rationally rejected, as naturalists following Quine might say but hypothetical entitlements to further beliefs given one's current view.

Accordingly, an account of rationality should explain which outlook an agent ought to adopt having contemplated the features of the various belief revision sequences licensed by her experiences. This appealing proposal, informed as it is by Gupta and Nuel Belnap's technical machinery on revision rules, and like the structuralist tradition Demopoulos usefully sets it against, demonstrates the value of employing logical methods in epistemological investigations. Demopoulos and Friedman end their essay with a conjecture that Newman's problem reveals logicism incapable of simultaneously capturing the "distinctive character" of pure and applied mathematics In the new and provocative essays on the epistemic significance of fundamental identity criteria that open the book, Demopoulos argues against this conjecture.

Bertrand Russell (Stanford Encyclopedia of Philosophy)

Demopoulos begins his argument with a thought-provoking reconstruction of the goal of Frege's logicism. Frege gives rigorous gap-free derivations of arithmetical theorems not to solidify their justification but to establish that their proof does not require an appeal to spatial or temporal intuition. This point is not new, but Demopoulos argues that a Fregean could build upon it to answer "the problem of apriority," namely, how, without invoking Frege's inconsistent theory of extensions, the justification for arithmetical truths can be shown to depend only on general laws Demopoulos' idea is to distinguish Frege's argument for and use of Hume's principle as the criterion of identity for number from his logicist argument for the existence of logical objects to be identified with the numbers.

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Buy Logicism and its Philosophical Legacy on fejacudobemo.tk ✓ FREE SHIPPING on qualified orders. Jul 1, William Demopoulos, Logicism and its Philosophical Legacy, Cambridge University Press, , pp., $ (hbk), ISBN

Since Hume's principle is not logical but arithmetical, it cannot serve Frege's logicist argument. However, its generality in mentioning no objects makes it an appropriate ground for arithmetic's apriority, and Frege shows how to use it to derive the Dedekind infinity of the natural numbers. Since the cardinality operator acts on concepts, Demopoulos takes Frege to reveal a "basis.