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Hamilton's Theory of Quantifying the Predicate—A Correction
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Published:April 1992
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“Hamilton's Theory of Quantifying the Predicate—A Correction,” Philosophical Quarterly, 26 (1976). Reprinted by permission of the publisher.
My account1 of Hamilton's theory of the quantification of the predicate contains a fundamental mistake. Following De Morgan (and others who have written on Hamilton), I interpreted the proposition “All A is all B” to mean “All A is B and all B is A.” This, after all, produces the correct distributional assignments, i.e., both terms are distributed. I next treated Hamilton's eighth proposition “Some A is not some B” to be the denial of the first proposition, interpreting it as “Some A is not B or some B is not A.” Again this yields the correct distributional assignments, i.e., neither term is distributed.
Although these interpretations seem plausible and in line with Hamilton's intentions, they in fact render his system inconsistent. To see this, consider the following argument that the Hamiltonian system declares valid.
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