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 diagramming

Note that, conveniently, each type of distribution is a “mirror image” of it ’s contradictory statement.

A

(subject only)

E

(both)

I (neither)

O

(predicate only)

HSL* Canons (aka ‘fallacies’)① Existential: A particular conclusion cannot

follow from two universal premises.

② Affirmative/Negative: # of ~ premises = # of ~ conclusions (i.e., 0:0, 1:1).

③ Illicit process: If an ET is distributed in conclusion, it must be so in a premise (illicit major/minor).

④ Four Terms: Exactly 3 unequivocal terms.

⑤ 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

I. existentia-lLooks like Roman numeral I, pretty much.

II. a-ff-irmative / negativeLooks like Roman numeral II, sort of—maybe written by a Roman calligrapher.

III. Ill-icit processLooks like Roman numeral III, sort of—particularly if you squint.

IV. IV termsLooks like Roman numeral IV, sort of—although the likeness is really very good in this case.

V. u-ndistributed middleLooks 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

1. The middle term must be distributed exactly once (and its corollary, the fallacy of undistributed middle)

2. Each end term must be distributed twice or not at all.

3. Either all three statements are affirmative, or the conclusion and exactly one premise are negative.

4. 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)

I. 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)

II. 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)

III. Fallacy of illicit process: any term distributed in the conclusion must be distributed in the premises. (cf. Carter 2, Layman 3)

IV. Exclusive premises fallacy: no two negative premises. (cf Carter 3, Layman 4)V. Fallacy of undistributed middle: the middle term must be distributed at least once. (cf.

Carter 1 & fallacy of undistributed middle, Layman 2)VI. Four-term fallacy: the syllogism must contain exactly three consistent terms. (cf.

Carter’s definition of syllogisms, Layman 1)VII. 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)