Dear Ben, lists, I strongly appreciate the persistent work Ben has been doing in tracing out, over many postings, the implications of Peirce's problems with the "strange rule". I think Ben is quite correct in locating the ambiguity in the quantifier "some", taken to mean sometimes "a certain one", sometimes "some - one or several". But I think there may lie a further reason behind this - linked to Ben's reinterpretation in terms of modal logic where a necessity operator distinguishes the two cases otherwise identified by the "strange rule". When introducing his discussion of the "strange rule" in the April 1906 note, Peirce connects it to a modal observation: " … I soon discovered, upon a critical analysis, that it was absolutely necessary to insist upon and bring to the front, the truth that a mere possibility may be quite real." Why does he do that, as the bankruptcy-suicide inference is ordinary first order logic without any modal semantics on the surface? I think it is because what Peirce would like to catch is the meaning of that sentence (taken in ordinary language) that there is a causal-tendency link between the bankruptcy of husbands and the suicides of their wives. So that the wife-suicide is a "real possibility" actualized by the husband-bankruptcy. This is obviously indicated by saying that a "certain one" wife commits suicide if HER husband etc. This is not full necessity, but "real possibility" (because other wives with bankrupt husbands may escape suicide even if threatened by it as a real possibility). So - I think - Peirce's idea is that the strange rule equates the "mere possibility" of "There is some married woman who will commit suicide in case A husband fails in business." with the real possibility in the claim connecting the two: "There is some married woman who will commit suicide in case HER husband fails in business." - which he did not like because he wanted to distinguish those two types of possibilities. Of course, real possibility is not logic, it is material ontology not even captured by standard modal logic. As Ben rightly indicated, this unease comes from reading more (ordinary language) meaning into logical expressions than their formal definition allows for. But simultaneously, this excessive meaning is scientifically important - the mature Peirce, after 1897, seeing "real possibilities" as implied by scientific laws, regularities, tendencies, patterns etc., regarding how certain predicates, more or less strongly, determine others. This can not be logically expressed in any simple way, and I think that was what tormented Peirce …
Best F Den 18/02/2015 kl. 15.41 skrev Benjamin Udell <bud...@nyc.rr.com>: > Peirce said "there is some one individual of which one or other of two > predicates is true" ABOUT a specific proposition that he was discussing. So > you need to read that specific proposition in order to understand what Peirce > meant by "there is some one individual" etc.: "There is some married woman > who will commit suicide in case her husband fails in business." which, Peirce > finds, turns out to be equivalent to "if every married man fails in business > some married woman will commit suicide".
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