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 s… - Hilary Putnam
" "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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About 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 changing his own position.
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Hilary Whitehall Putnam
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Additional quotes by Hilary Putnam
I might try to save the view that 'future contingents' have no truth value by saying that even present-tense statements have no truth value if they refer to the outcome of events that are so far away that a causal signal informing me of the outcome could not have reached me-now without traveling faster than light. In other words, I might attempt saying that statements about events that are in neither the upper half nor the lower half of my light-cone have no truth value. In addition, statements about events in the upper half of my light-cone have no truth value, since they are in my future according to every coordinate system. So only statements about events in the lower half of my light-cone have a truth value; only events that are in 'my past* according to all observers are determined.
Even if we consider not words by themselves but rules deciding what words may appropriately be produced in certain contexts — even if we consider, in computer jargon, programs for using words — unless those programs themselves refer to something extra-linguistic there is still no determinate reference that those words possess. This will be a crucial step in the process of reaching the conclusion that the Brain-in-a-Vat Worlders cannot refer to anything external at all (and hence cannot say that they are Brain-in-a-Vat Worlders).
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