Recall from my earlier post that the quantifiers in formal syllogism are represented by the letters “A,” “E,” “I,” and “O.” The choice of these letters has to do with millenia of tradition, and so is not the kind of thing one will casually change to make more readily memorable. The letters stand for:
A = All
E = None (or “There is no …”)
I = Some
O = Some Not
I want to expand a bit on my earlier discussion regarding authoritarian thinking and the syllogism by using these scripts to illuminate another common piece of fallacious reasoning, one that especially lends itself to the form of the syllogism, and which is often advanced by persons who score high on Altemeyer’s authoritarian spectrum. I’ll will introduce the simplifying symbolism in parentheses as I pose the argument itself.
So here it goes: It is frequently claimed that “There is no” ( = “E”) “Mention in the Constitution” ( = “M”) of a “Right to Privacy” ( = “P”). Therefore, The “Right to Privacy” ( = “P”) is not ( = “E”) a “Right that exists” ( = “R”). I’m taking for granted the reader’s ability to follow over my formalization above. In simplified form, this argument looks like:
E M P
(← Something is missing here!)
E P R (Notice that the quantifier “E” has been pushed to the front of the sentence. This is necessitated by the form of the syllogism, but it leads to somewhat awkward phrasing: “There is no right to privacy that is a right that exists.” This type of not-quite idiomatic phrasing is sometimes unavoidable when formalizing an argument.)
The above is not a valid syllogism, because in order to be valid it would need a second premise. Not every formal, logical argument has just and only two premises, but this is the necessary structure of a formal syllogism. However, one could fill in that missing premise, making it a valid syllogism. This kind of incomplete, but theoretically completable syllogism, is what is known as an “enthymeme.” Moreover, if one understands the formal structures of syllogisms, one can construct the missing premise, and make the whole thing a valid argument, just from the above formalized schema, without knowing anything about the interpretations the non-logical (that is, non-quantifier) symbols. Thus, without even knowing how the “M,” “P,” or “R” are intended to be interpreted, that valid syllogism is:
E M P
A R M
E P R
The presence of an “E” quantifier in the first premise and the conclusion requires that an “A” (“All”) quantifier lead in the second, previously missing premise. The “middle term” – the “M” – must be distributed, that is diagonalized, in the second premise. And the final term that appears in the conclusion, the “R”, must appear between the quantifier and the now distributed middle term, the “M”. This gives us the “A R M” premise. Given that the “M,” “P,” and “R” do have interpretations, and knowing what we know about the quantifiers, we can read the now provided premise as, “All rights that exist are mentioned in the Constitution.”
The above is now a formally valid syllogism, which means that IF the premises are true, THEN the conclusion follows by logical necessity.
But here’s the rub: the premises are not true. In particular, the second premise, the one that was conveniently skipped over, makes a claim that is explicitly denied by the 9th Amendment! Specifically, “The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.” Which is to say, no conclusion may be drawn about the existence of a right from its failure to be explicitly mentioned in the Constitution! This comes from both an understanding of the actual text of the Constitution, and a grasp of basic principles of logical reasoning. It is with such reasoning that Altemeyer’s authoritarians struggle so “inexplicably” — “inexplicably,” at least, from the purely logical point of view.
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