A logic by which the imagination might illumine what the intellect is doing in a categorical syllogism

In speaking about categorical syllogisms, we too easily get tricked by imagination into seeing them as arrangements of terms in space.  Such arrangement is an accident of language, and not a particularly helpful one. The trickery of imagination is inevitable, so we might as well try to exploit it to our advantage, and arrange the terms in space in such a way as to better illuminate what is going on in a categorical syllogism.

Since categorical syllogisms express certain relationships of universality among terms, it would be more illuminating to arrange the terms in a way that reflected this universality, and to call the syllogism whatever order we make in space. The argument that all men are mortal, and all Greeks are men, could be arranged with the most universal terms on top, the least universal on the bottom, and so the syllogism would look like this:




or, following the convention of reading left to right

Mortal, Men, Greeks.

 On this sort of logic, the first figure would be a syllogism pure and simple, since it is the only figure were what is called “most” [universal] (major) and “least” [universal] (minor) is really such. A simple order of the terms would be taken as a first figure Barbara syllogism. Other syllogisms would be makde by adding marks to this: “some” could be indicated in some way or another of the last term (I’d like an asterisk), and some way of indicating whether someone was affirming or denying. No adverbs, copulae, or adjectives of quantity (all, every, some, no) would be used.

The second figure would, following this, put the middle term on the top or on the left, and then find some way of placing the major term closer to it. The third figure would reverse this (major on top, middle on bottom). Any other figure would be self-evidently impossible.

On this arrangement, the term on the top or left could not have an asterisk, indicating that the mind always moves from something unqualified and universal as opposed to particular. We would distinguish affirmation and negation (indicated in speech by is… is not… and in a sense by “all” and “no”) from universality and particularity (indicated by “some” as opposed to “all” or “no”).

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