"The real significance of the Russell paradox, from the standpoint of the modal-logic picture, is this: it shows that no concrete structure can be a standard model for the naive conception of the totality of all sets; for any concrete structure has a possible extension that contains more 'sets'. (If we identify sets with the points that represent them in the various possible concrete structures, we might say: it is not possible for all possible sets to exist in any one world!) Yet set theory does not become impossible. Rather, set theory becomes the study of what must hold in, e.g. any standard model for Zermelo set theory."
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Computer scientists from the United StatesWomen academics from the United StatesCognitive scientistsMathematicians from the United StatesPrinceton University faculty
Original Language: English
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"Mathematics without foundations" (1967)
https://en.wikiquote.org/wiki/Hilary_Putnam
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Hilary Putnam
Hilary Whitehall Putnam (July 31, 1926 - March 13, 2016) was an American philosopher who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, and philosophy of science. He is known for his willingness to apply an equal degree of scrutiny to his own philosophical positions as to those of others, subjecting each position to rigorous analysis until he exposes its flaws. As a result, he has acquired a reputation for frequently ch
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