display all the ideas for this combination of texts
5 ideas
10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
From: JC Beall / G Restall (Logical Consequence [2005], 3) |
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) |
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'). |