5 Categorical Syllogisms 5.1 Standard Form, Mood, and Figure

Standard Form A Categorical Syllogism is a deductive argument (what makes it deductive?) that always has: Three categorical statements Three different terms All A are B All B are C All A are C In all categorical syllogisms, the term shared between the premises is called the middle term. The predicate of the conclusion is called the major term, and the subject of the conclusion is called the minor term.

Standard Form (continued) All A are B All B are C All A are C The major premise is the premise containing the major term. The minor premise contains the minor term. So, we can now define ‘Standard Form’: All three statements are standard form categorical propositions The two occurrences of each term are identical Each term is used in the same sense throughout The major premise is listed first, the minor second, conclusion last

Standard Form (continued) How about: Some A are B No B are non-C Some A are not non-C Is this a categorical syllogism? (Yes, but it is not in standard form until its statements are)

Standard Form (continued) Some A are B All B are C (by obversion) Some A are C (by obversion) Is this standard form now? (No. What’s wrong?) All the statements are categorical and in standard form There are only three terms (they’re identical and for all we can tell, non-equivocal) The middle term doesn’t appear in the conclusion The major premise is first … oh, wait.

Standard Form (continued) All B are C Some A are B Some A are C Now we have a Standard Form Categorical Syllogism What mood and figure is it?

Mood and Figure All B are C Some A are B Some A are C We can tell if this argument is valid or invalid by identifying its mood and figure. Mood is simple: it is just the letter names of the propositions in order of appearance: (A) All B are C (I) Some A are B (I) Some A are C Mood = AII

Mood and Figure (continued) All B are C Some A are B Some A are C Figure is determined by the arrangement of the appearances of the middle term Figure 1 Figure 2 Figure 3 Figure 4 M P P M M P P M S M S M M S M S S P S P S P S P

Mood and Figure (continued) So our syllogism All B are C Some A are B Some A are C is AII-1 To determine validity or invalidity we have to look at a list of valid forms to see if AII-1 appears.