19 ideas
| 19304 | The rules of reasoning are not the rules of logic [Harman] |
| 19306 | It is a principle of reasoning not to clutter your mind with trivialities [Harman] |
| 19307 | If there is a great cost to avoiding inconsistency, we learn to reason our way around it [Harman] |
| 19309 | Logic has little relevance to reasoning, except when logical conclusions are immediate [Harman] |
| 19303 | Implication just accumulates conclusions, but inference may also revise our views [Harman] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 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] |
| 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] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| 19305 | The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence [Harman] |
| 19310 | High probability premises need not imply high probability conclusions [Harman] |
| 19308 | We strongly desire to believe what is true, even though logic does not require it [Harman] |
| 19311 | In revision of belief, we need to keep track of justifications for foundations, but not for coherence [Harman] |
| 19312 | Coherence is intelligible connections, especially one element explaining another [Harman] |
| 4316 | Either all action is rational, or reason dominates, or reason is only concerned with means [Cottingham] |