Syllogistic fallacies Using canons to test syllogisms for validity or invalidity
Canons • Another word for ‘rule’ (Gk. κανων, “rule”; OED 2b), but to be distinguished from ‘rules’ of inference, etc. that you’ll learn about in PHIL 305. • Think about how a scripture becomes a “ruling” scripture by canonization. • A syllogism is valid if & only if all canons are satisfied. • Different authors may list a few additional canons (derivable from more limited lists), or perhaps list them in different orders, but they are essentially the same. • The canons apply only to syllogisms with matching occurrences of terms (i.e., no complement classes)
Distribution • In logic, to say something is ‘distributed’ means that something has been said about (or ‘distributed over/to’) an entire class. • For a claim to be necessarily true of a class, it must be true of the entire class. • So, somewhere in the argument, there must be a properly reasoned claim about an entire class if the argument is going to lay any claim to necessity and, ultimately, to validity. • Distributing a claim over one class, however, doesn’t guarantee the validity of a syllogistic argument; rather, reasoning about all such claims in an argument must be done validly. • Each kind of categorical proposition (A,E,I,O) distributes a claim in a unique way over one or more of the classes (the subject or predicate) in the claim. • For each kind of proposition (A, E, I, O), the distribution always happens the same way for that proposition. • That is, an A proposition is always distributed in the same way; an E proposition is always distributed in the same way, etc., as illustrated in the next slide.
Distribution, cont’d.**Each method of distribution can be demonstrated by Venn diagrammingNote that, conveniently, each type of distribution is a “mirror image” of it’s contradictory statement.
HSL* Canons (aka ‘fallacies’) • Existential: A particular conclusion cannot follow from two universal premises. • Affirmative/Negative: # of ~ premises = # of ~ conclusions (i.e., 0:0, 1:1). • Illicit process: If an ET is distributed in conclusion, it must be so in a premise (illicit major/minor). • Four Terms: Exactly 3 unequivocal terms. • Undistributed middle: MT distributed at least once. *Howard-Snyder Logic: These canons are not in the HSL order, the reason for which will become apparent in the next slide.
Really stupid demonic devices for HSL canon/fallacies • existentia-l Looks like Roman numeral I, pretty much. • a-ff-irmative / negative Looks like Roman numeral II, sort of—maybe written by a Roman calligrapher. • Ill-icit process Looks like Roman numeral III, sort of—particularly if you squint. • IV terms Looks like Roman numeral IV, sort of—although the likeness is really very good in this case. • u-ndistributed middle Looks like Roman numeral V, sort of—especially if we were carving it in marble, in which case a “u” would be a “v.” A couple of really stupid, demonic “tools” (i.e., demonic devices)
Carter’s canons and fallacies • The middle term must be distributed exactly once (and its corollary, the fallacy of undistributed middle) • Each end term must be distributed twice or not at all. • Either all three statements are affirmative, or the conclusion and exactly one premise are negative. • False converse: any syllogism in which any A-statement is the converse of the actual statement required for validity.
Copi’s canons (fallacies)(from which Carter’s and Layman’s canons can be derived, and vice versa) • Existential fallacy: From two universal premises, no particular conclusion may be drawn. Corollary: valid syllogisms are either completely universal, or they consist of a particular conclusion and exactly one particular premise: no valid syllogism contains all particular premises. (implication of Carter 2, Layman 5) • Affirmative/negative fallacy: if either premise is negative, the conclusion must be negative; if the conclusion is negative, at least one premise must be negative; one cannot draw positive conclusions from negative premises and vice versa. (cf. Carter 3, Layman 4) • Fallacy of illicit process: any term distributed in the conclusion must be distributed in the premises. (cf. Carter 2, Layman 3) • Exclusive premises fallacy: no two negative premises. (cf Carter 3, Layman 4) • Fallacy of undistributed middle: the middle term must be distributed at least once. (cf. Carter 1 & fallacy of undistributed middle, Layman 2) • Four-term fallacy: the syllogism must contain exactly three consistent terms. (cf. Carter’s definition of syllogisms, Layman 1) • Fallacy of false converse: if syllogism is not one of 15 valid forms but meets all of the above and contains an A or O proposition, converting the A or O will yield a valid argument and demonstrate the false conversion. (cf. Carter’s fallacy of false conversion)