17 ideas
| 14782 | Philosophy is an experimental science, resting on common experience [Peirce] |
| 14787 | Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
| 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] |
| 14788 | Mathematics is close to logic, but is even more abstract [Peirce] |
| 527 | Everything exists which anyone perceives [Metrodorus of Chios] |
| 14786 | Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce] |
| 14789 | Experience is indeed our only source of knowledge, provided we include inner experience [Peirce] |
| 14785 | The world is one of experience, but experiences are always located among our ideas [Peirce] |
| 14784 | Ethics is the science of aims [Peirce] |