Combining Philosophers

All the ideas for Archimedes, Oswald Veblen and Eustachius a Sancto Paulo

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4 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

10247	We have no adequate logic at the moment, so mathematicians must create one [Veblen]
	Full Idea: Formal logic has to be taken over by mathematicians. The fact is that there does not exist an adequate logic at the present time, and unless the mathematicians create one, no one else is likely to do so.
	From: Oswald Veblen (Presidential Address of Am. Math. Soc [1924], 141), quoted by Stewart Shapiro - Philosophy of Mathematics
	A reaction: This remark was made well after Frege, but before the advent of Gödel and Tarski. That implies that he was really thinking of meta-logic.

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

13007	Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
	Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
	From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
	A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.

9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance

16616	Substances 'substand' (beneath accidents), or 'subsist' (independently) [Eustachius]
	Full Idea: It is proper to substance both to stretch out or exist beneath accidents, which is to substand, and to exist per se and not in another, which is to subsist.
	From: Eustachius a Sancto Paulo (Summa [1609], I.1.3b.1.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 06.2
	A reaction: This reflects Aristotle wavering between 'ousia' being the whole of a thing, or the substrate of a thing. In current discussion, 'substance' still wavers between a thing which 'is' a substance, and substance being the essence.

9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism

16585	Prime matter is free of all forms, but has the potential for all forms [Eustachius]
	Full Idea: Everyone says that prime matter, considered in itself, is free of all forms and at the same time is open to all forms - or, that matter is in potentiality to all forms.
	From: Eustachius a Sancto Paulo (Summa [1609], III.1.1.2.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1
	A reaction: This is the notorious doctrine developed to support the hylomorphic picture derived from Aristotle. No one could quite figure out what prime matter was, so it faded away.