Combining Texts

Ideas for 'Metaphysics', 'Apology of Socrates' and 'Ethics and the Limits of Philosophy'

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4 ideas

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic

17851	Number is plurality measured by unity [Aristotle]
	Full Idea: Number is plurality as measured by unity.
	From: Aristotle (Metaphysics [c.324 BCE], 1057a04)

17843	The idea of 'one' is the foundation of number [Aristotle]
	Full Idea: One is the principle of number qua number.
	From: Aristotle (Metaphysics [c.324 BCE], 1052b21)

17850	Each many is just ones, and is measured by the one [Aristotle]
	Full Idea: The reason for saying of each number that it is many is just that it is ones and that each number is measured by the one.
	From: Aristotle (Metaphysics [c.324 BCE], 1056b16)

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

9793	Mathematics studies abstracted relations, commensurability and proportion [Aristotle]
	Full Idea: Mathematicians abstract perceptible features to study quantity and continuity ...and examine the mutual relations of some and the features of those relations, and commensurabilities of others, and of yet others the proportions.
	From: Aristotle (Metaphysics [c.324 BCE], 1061a32)
	A reaction: This sounds very much like the intuition of structuralism to me - that the subject is entirely about relations between things, with very little interest in the things themselves. See Aristotle on abstraction (under 'Thought').