Thought Itself

One of the many strange things encountered in studying Aristotle’s work on logic is the ability to derive the truth of a particular statement (some or some not) from a universal statement (all or none).  If we know that all cows have horns, we also know that some cows have horns, and if we know that no cows play the accordion, we also know that some cows do not play the accordion.

While we know that this is technically true, many a student of logic becomes lost here, as it sounds odd to make a statement only about some when we could make a statement about all.  If I know that cows never play the accordion, it almost sounds like a deliberate misrepresentation to say that some cows do not.

However, if we are strictly empirical, and investigating things with the idea that there can always be counter examples we have yet to encounter, we can only say that some cows, those we have encountered, cannot play the accordion.  Aristotle himself believed that all swans are white and all crows are black, and used these as examples of universal statements, but he was wrong, as both black swans and white crows existed at the time in Australia.

Why, then, do we feel more comfortable making the universal claim then the particular one?  The particular statement, only about some, is more cautious than the universal statement, about all.  When we make universal claims, we are stating with confidence that there are, effectively, no counter examples, much as one could say, in Aristotle’s world, there effectively were no black swans or white crows, as Aristotle’s world did not include Australia.  When we are skeptical and doubt we are cautious, only feeling safe making particular claims, but when we are dogmatic and believe we are confident, feeling safe in making universal claims.  This is why making a cautious particular claim about some sounds odd when we have already assumed the universal claim about all to be true.