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Additional info for Carnap, Tarski, and Quine at Harvard: Conversations on Logic, Mathematics, and Science
So he would certainly be sympathetic to the motivation behind (FN 3) as well: in Introduction to M athematical Philosophy , he says that we do not know whether the axiom of infinity is true in our world or not, and that physical space and time may be discrete and finite (Russell 1920, 140–41). 3 Logical Empiricists skeptical of infinity Finally, I wish to consider very briefly a few remarks concerning infinity that logical empiricists and their allies made during the first part of the twentieth century.
Thus we see that (FN 1) and (FN 2) are both consequences of reism. Kotarbi´ nski says that we could declare utterances containing such words either false or nonsensical. Kotarbi´ nski calls ‘roundness,’ ‘property,’ etc. ‘onomatoids,’ that is, merely apparent names, not genuine names. ’ In places, Kotarbi´ nski suggests that the reist’s paraphrase is in fact what was really meant all along (Kotarbi´ nski 1929/1966, 432): a hermaneutic reconstruction of everyday language, instead of a revolutionary one, in the terminology of Burgess and Rosen (1996).
Creath 1990, 410) Two points about this quotation are relevant for present purposes. First, for Quine, ‘intelligibility’ and ‘clarity’ are (at least roughly) synonymous. ’ Carnap does not, as far as I could find, tie intelligibility to clarity. Second, for Quine, the standard of intelligibility is ultimate or fundamental: not only is it irreducible to ‘mere convenience,’ but it is not reducible to anything else either. A similar sentiment is expressed in Goodman and Quine’s “Steps Toward a Constructive Nominalism”: “Why do we refuse to admit the abstract objects that mathematics needs?