Rebirth of Reason


by Fred Seddon

Bissell on DIM-Part II
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 twenty-seven permutations, but only fourteen of them are logically valid.” Let enumerate the problems.
First, BARBARA is not a proposition. It is a syllogism (actually a mood, more on that in due course.)
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 BARBARA-1. 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 BARBARA-1 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 non-existence of krelnicks does not make the proposition meaningless.
Finally, he claims to give 27 permutations of BARBARA-1 of which only 14 are valid. But this is wrong. BARBARA-1 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. BARBARA-2, BARBARA-3, and BARBARA-4 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 BARBARA-1, you automatically get a true conclusion. In example 2 (of the 27), Bissell writes, “True + true = false: INVALID.” But this is simply impossible in BARBARA-1. Let’s take a look.
Major Premise – All mammals are animals
Minor Premise – All cows are mammals
The only conclusion one can draw is “All cows are animals.” Why? The predicate of the major is by definition the predicate of the conclusion; the subject of the minor is the subject of the conclusion. If this is true, then we cannot draw a false conclusion (or even a meaningless one if such existed). But let’s try. Try “All animals are cows” which is false. But this violates Rule 2 that says if we distribute a term in the conclusion, it must be distributed in the premise. “Animal” is distributed in the conclusion but not in the premise. To distribute it we would have to switch the subject and predicate of the major to read “All animals are mammals.” We now have
Major Premise – All animals are mammals
Minor Premise – All cows are mammals
for our premises. But we no longer have BARBARA-1, but rather BARBARA-2, which is always invalid. One cannot make BARBARA-1 invalid. Since Bissell does that repeatedly in his 27 permutations, he must be wrong.
With a starting sentence like this, I cannot see how he can produce anything of value in the remainder of this section.
His main problem seems to me to be a lack of understanding of what validity is. As Kelley points out, validity is the relationship between the premises and the conclusion, not between the premises and reality. In my words, validity is purely a matter of syntax, not semantics. That is why we can know, say, BARBARA-2 is invalid without knows what words we are going to replace the variables with. I know the IIA mood in invalid in every figure because I can see it will fail to distribute the middle term. I don’t need or care (as a logician) to know whether you are talking about “cows” “krelnicks” or whatever.
For me, however, this is not a major flaw. As I wrote in a previous post, what Bissell has to say about Kant makes this review a winner.
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