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5. Theory of Logic / E. Structures of Logic / 1. Logical Form

4730	For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
	Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality.
	From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4
	A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional.

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

16865	'Theorems' are both proved, and used in proofs [Frege]
	Full Idea: Usually a truth is only called a 'theorem' when it has not merely been obtained by inference, but is used in turn as a premise for a number of inferences in the science. ….Proofs use non-theorems, which only occur in that proof.
	From: Gottlob Frege (Logic in Mathematics [1914], p.204)