18 ideas
| 9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
| 9984 | We can have a series with identical members [Tait] |
| 13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
| 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] |
| 9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
| 9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
| 9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
| 9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
| 9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
| 1743 | The greatest deterrence for injustice is if uninjured parties feel as much indignation as those who are injured [Solon, by Diog. Laertius] |