Disproof: Counterexamples and Terms
Aristotle proves invalidity by constructing counterexamples.
This is very much in the spirit of modern logical theory:
– all that it takes to show that a certain form is invalid is a single instance of that form with true premises and a false conclusion. [NB]
However, Aristotle states his results not by saying that certain premise-conclusion combinations are invalid but by saying that certain premise pairs DO NOT “syllogize”:
– that is, that, given the pair in question, examples can be constructed in which premises of that form are true and a conclusion of any of the four possible forms is false.
When possible, he does this by a clever and economical method:
– he gives two triplets of terms, one of which makes the premises true and a universal affirmative “conclusion” true, and the other of which makes the premises true and a universal negative “conclusion” true.
The first is a counterexample for an argument with either an E or an O conclusion, and the second is a counterexample for an argument with either an A or an I conclusion.
via: http://plato.stanford.edu/archives/spr2012/entries/aristotle-logic/
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