12 ideas
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] |
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] |
12750 | The question is whether force is self-sufficient in bodies, and essential, or dependent on something [Lenfant] |
7876 | Even if we identify pain with neural events, we can't explain why those neurons cause that feeling [Levine, by Papineau] |
7877 | Only phenomenal states have an explanatory gap; water is fully explained by H2O [Levine, by Papineau] |
7878 | Materialism won't explain phenomenal properties, because the latter aren't seen in causal roles [Papineau on Levine] |