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of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic." Nowhere in these 2 articles is there any proof to how logicism is disproven by
Russell's paradox. So I ask, how is logicism, as stricly defined by the above excerpt, false?
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In the article "Reductionism" under the heading "Set-Theoretic
Reductionism" it states the following: " then proposed his own form of reductionism, logicism, which in turn was famously disproven by Russell's Paradox." According to wikipedia "Logicism is one of the schools of thought in the philosophy
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article. I took a look at it and tried to figure out how to fix the "set-theoretic reductionism" section, but decided it was so badly flawed that all I could do was delete it. Could be an interesting addition if someone could source it and explain it clearly and accurately, but I saw nothing worth
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These are not the sorts of questions that are really susceptible to final proof or disproof in the ordinary mathematical sense. However, mathematical discoveries do shed light on how difficult these metamathematical positions are to hold, how much sense they make, and how much they accomplish.
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The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the
134:, at least, might be reduced to logic, even if sets could not be. Many mathematical logicians now feel that this hope was rendered untenable by
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Russell's paradox. But it was definitely dealt a severe blow. Frege's logicist project for set theory attempted to identify sets with purely
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entities (extensions of definable properties). That didn't work, or at the very least, Frege's version of it didn't work.
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saving in the existing text and didn't have a source that would allow me to rewrite it. My specific criticisms are on
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There was still a logicist school after
Russell; it was still possible to hope that the
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didn't think so, and even today there are logicians who call themselves "neo-logicist".
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Welcome to the
Knowledge Mathematics Reference Desk Archives
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I wouldn't say that logicism was, strictly speaking,
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