logicism वाक्य
उदाहरण वाक्य
मोबाइल
- With the benefit of hindsight, we can see that Couturat was in broad agreement with the logicism of Russell and Whitehead, while Poincar?anticipated Brouwer's intuitionism.
- Dedekind's path to logicism had a turning point when he was able to reduce the theory of real numbers to the rational number system by means of set theory.
- Kant's often brief remarks about mathematics influenced the mathematical school known as intuitionism, a movement in philosophy of mathematics opposed to formalism, and the logicism of Frege and Bertrand Russell.
- Kurt G�del's incompleteness theorem is sometimes alleged to undermine logicism because it shows that no particular axiomatization of mathematics can decide all statements, although such theorem itself is based in logic.
- Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.
- In an observation pertinent to Russell's brand of logicism, Perry remarks that Russell went through three phases of realism-- extreme, moderate and constructive ( Perry 1997 : xxv ).
- Hilbert dismissed logicism as a " false path " : " Some tried to define the numbers purely logically; others simply took the usual number-theoretic modes of inference to be self-evident.
- Philosophical rationalism in its most extreme form is the doctrine that knowledge can ultimately be founded on pure reason, while logicism is the doctrine that mathematical concepts, among others are reducible to pure logic.
- Pursuing both Bertrand Russell's logical atomism deconstructing language into supposedly elementary parts and Russell's logicism reducing swaths of mathematics to symbolic logic, logical positivists envisioned both Carnap of the most flagrant " pseudostatements ".
- However, he also conceived of the mathematical community as carrying on a kind of dialectic to decide which mathematical proofs are Russell's logicism, which defines proof simply in terms of " formal " validity.
- The incompleteness theorem is sometimes thought to have severe consequences for the program of logicism proposed by Gottlob Frege and Bertrand Russell, which aimed to define the natural numbers in terms of logic ( Hellman 1981, p . 451 468 ).
- Frege in particular sought to demonstrate ( see Gottlob Frege, The Foundations of Arithmetic, 1884, and Logicism in Philosophy of mathematics ) that arithmetical truths can be derived from purely logical axioms and therefore are, in the end, logical truths.
- This started a period of expansion of logicism, with Dedekind and Frege as its main exponents, which however was brought to a deep crisis with the discovery of the classical paradoxes of set theory ( Cantor 1896, Zermelo and Russell 1900 1901 ).
- In the " Principia Mathematica ", Bertrand Russell and Alfred North Whitehead advanced the philosophical program known as logicism, and attempted to prove that all mathematical concepts, statements, and principles can be defined and proved entirely in terms of symbolic logic.
- The importance to logicism of the construction of the natural numbers derives from Russell's contention that " That all traditional pure mathematics can be derived from the natural numbers is a fairly recent discovery, though it had long been suspected " ( 1919 : 4 ).
- Russell continued to defend logicism, the view that mathematics is in some important sense reducible to logic, and along with his former teacher, Alfred North Whitehead, wrote the monumental " Principia Mathematica ", an axiomatic system on which all of mathematics can be built.
- Having exhibited this possibility, Frege's larger purpose was to defend the view that arithmetic is a branch of logic, a view known as logicism : unlike geometry, arithmetic was to be shown to have no basis in " intuition ", and no need for non-logical axioms.
- Gottlob Frege began the program of reducing mathematics to logic, continued it with Bertrand Russell, but lost interest in this logicism, and Russell continued it with Alfred North Whitehead in their monumental " Principia Mathematica ", inspiring some of the more mathematical logical posivists, such as Hans Hahn and Rudolf Carnap.
- This has not been the definition taken in this article, but the idea that logic treats special forms of argument, deductive argument, rather than argument in general, has a history in logic that dates back at least to logicism in mathematics ( 19th and 20th centuries ) and the advent of the influence of mathematical logic on philosophy.
- About same time as Carnap ( 1929 ), but apparently independently, Fraenkel ( 1928 ) used the word : " Without comment he used the name'logicism'to characterise the Whitehead / Russell position ( in the title of the section on p . 244, explanation on p . 263 ) " ( G-G 2002 : 269 ).
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