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BISSELL ON DIMPART IISubmitted by seddon on Fri, 20131227 16:41
In this post, I want to talk about the section “Syllogisms and DIM Mixtures: A Not So Ominous Parallel” in Roger Bissell’s review of DIM in the December, 2013 issue of JARS. My problems concerns the first sentence in the paragraph that occurs on 171 immediately below Figure 3. It reads, “Now, in a categorical proposition of BARBARA form (All S is M, All M is P, therefore All S is P) in which the premises may be true or false or meaningless, there are a total of twentyseven permutations, but only fourteen of them are logically valid.” Let enumerate the problems. Second, BARBARA is not a form, but a mood. In order to have a syllogistic form, one needs both the mood and the figure. (Mood has to do with the quantity of the propositions in a syllogism; Figure with the location of the middle term in the premises.) Since BARBARA is a mood that can take four figures, we can’t be sure what form Bissell is referring to, but from the example given in parenthesis, he seems to be referring to BARBARA1. And this holds, not only for the example in the sentence we are examining, but for every example he gives of BARBARA. All fourteen of them. Henceforth, I will assume he has BARBARA1 in mind. Third, he seems to think that syllogistic logic is trivalent, i.e., propositions are either true or false or meaningless. But syllogistic logic is not trivalent, but bivalent. All propositions are either true or false. To see this, consider an example Bissell gives of a “meaningless” proposition, “All cows are krelnicks.” I assume he thinks this is a meaningless proposition because there are no krelnicks, the class of krelnicks is empty. But as Kelley points out in his THE ART OF REASONING, 4TH edition, if the objects referred to by a term “do not exist, the statement is false.” (156) While we have Kelley before us, a look at the index of his book reveals not one occurrence of the concept “meaningless.” If Bissell tries to say he is using modern logic, recall that for modern logic the universal affirmative proposition has NO existential import, so the nonexistence of krelnicks does not make the proposition meaningless. Finally, he claims to give 27 permutations of BARBARA1 of which only 14 are valid. But this is wrong. BARBARA1 always valid; never invalid. In fact, of all 256 syllogistic forms, all of them are either valid or invalid. No syllogism is sometimes valid, sometimes invalid. BARBARA2, BARBARA3, and BARBARA4 are always invalid. Any syllogism that can have true premises and a false conclusion is invalid. That is the defining characteristic of an invalid syllogism. If you insert true premises in BARBARA1, you automatically get a true conclusion. In example 2 (of the 27), Bissell writes, “True + true = false: INVALID.” But this is simply impossible in BARBARA1. Let’s take a look. Fred
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