Figures of Syllogism
6. In illustration of this progress from guess-work to science, [1] I will give an example of the three Aristotelian figures of the Syllogism. I omit the fourth. I assume that the heavier term, or the term most like a “thing,” is fitted to be the Subject, and the term more like an attribute to be the Predicate. The syllogistic rules depend practically on the fact that common Logic, following common speech and thought, treats the Predicate as wider than the Subject, which corresponds to Mill’s view (also the common scientific view), that the same effect may have several alternative causes (not a compound cause, but different possible causes), and that consequent is wider than antecedent. [2] It is this assumption that prevents affirmative propositions from being simply convertible, i.e. prevents “All men are mortal” from being identical with “All mortals are men,” and but for it there would be no difference of figure at all, as there is not for inference by equation.
[1] Cf. Plato’s Republic, Bk. VI., end. [2] See p. 141, note.
This progression is here merely meant to illustrate the universal or systematic connection of particulars in process of disengaging itself. But I do not say that the first {147} figure with a major premise is a natural form for all arguments.
I take the scheme of the first three figures from Jevons, and suggest their meaning as follows:—
X denotes the major term.
Y denotes the middle term.
Z denotes the minor term.
1st Fig. 2nd Fig. 3rd Fig.
Major Premise YX XY YX
Minor Premise ZY ZY YZ
Conclusion ZX ZX ZX
Fig. 3. An observation and a guess.
Yesterday it rained in the evening.
All yesterday the smoke tended to sink.
∴ The smoke sinking ( may be ) a sign of rain.
( is sometimes )
The conclusion cannot be general in this figure, because nothing general has been said in the premisses about the subject of the conclusion. So it is very suitable for a mere suggested connection given in a single content—that of the time “yesterday,” implying moreover that both the points in question have something to do with the state of the atmosphere on that single day.