17 ideas
| 20771 | Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 13831 | Logic is based on transitions between sentences [Prawitz] |
| 13827 | Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz] |
| 13825 | Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz] |
| 13823 | In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz] |
| 13826 | Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz] |
| 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] |
| 6028 | Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius] |
| 20831 | The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes] |
| 5993 | The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman] |