16 ideas
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
1507 | We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea] |
5109 | The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle] |
1512 | Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does? [Aristotle on Zeno of Elea] |
1508 | Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
6303 | Sets are positions in patterns [Resnik] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
454 | If there are many things they must have a finite number, but there must be endless things between them [Zeno of Elea] |
455 | That which moves, moves neither in the place in which it is, nor in that in which it is not [Zeno of Elea] |
1511 | If everything is in a place, what is the place in? Place doesn't exist [Zeno of Elea, by Simplicius] |