## Tuesday, February 22, 2011

### On proving logic

Siris has some interesting posts on a method of representing the four types of proposition (universal affirmative, universal negative, particular affirmative, particular negative) but I found it hard going. Propositions are represented by ‘stacking ‘ one term on top of another. But you wouldn’t really understand this unless it were explained that the stacking relation means ‘every’ or ‘some’ or whatever. I.e. this

Animal
Man

means ‘every man is an animal’. So, what is the advantage? Since you need the quantifier ‘every’ to explain it, why not just use the quantifier itself? Thomas Reid in his essay on Aristotle’s logic considered a similar method used by Aristotle and his followers to demonstrate the validity of the syllogism (the ‘dici de omni’). But he objects that when the axioms of this method are put in plain English, they does not seem to have that degree of evidence which axioms ought to have. He says

It may even be suspected, that an attempt, by any method, to demonstrate that a
syllogism is conclusive, is an impropriety somewhat like that of attempting to
demonstrate an axiom. In a just syllogism, the connection between the premises
and the conclusion is not only real, but immediate; so that no proposition can
come between them to make their connection more apparent. The very intention of
a syllogism is to leave nothing to be supplied that is necessary to a complete
demonstration. Therefore, a man of common understanding, who has a perfect
comprehension of the premises, finds himself under a necessity of admitting the
conclusion, supposing the premises to be true; and the conclusion is connected
with the premises with all the force of intuitive evidence. In a word, an
immediate conclusion is seen in the premises by the light of common sense; and,
where that is wanting, no kind of reasoning will supply its place.

Brandon said...

I'm not sure I follow; the point wasn't to use the word 'every' to explain it because the point of stacking is to represent propositions in a way closely connected to one particular philosophical view of the syllogism. A full discussion requires showing how a proposition with (e.g.) universal quantity would be put in a stack; as it happens we often use 'every' to describe such propositions in English. The stacking relation doesn't mean 'every' or 'some'; there is no exact correspondence to those words in the stack because such words actually serve two functions (ordering terms according to inclusion and allowing or not allowing exceptions) that are separated in the stacking method.

I'm glad it's reminiscent of Aristotle, though; that's precisely the point, as noted in the precursor post.

Edward Ockham said...

>>the point wasn't to use the word 'every' to explain

But my point was I was only able to understand it when I realised that the stacking relation means 'every'. Perhaps other people found it easier!

>>The stacking relation doesn't mean 'every' or 'some'

OK I see now I didn't understand it. I did read your previous post though.