17 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] |
| 10190 | From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki] |
| 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] |
| 3282 | The general form of moral reasoning is putting yourself in other people's shoes [Nagel] |
| 3278 | An egalitarian system must give priority to those with the worst prospects in life [Nagel] |
| 3275 | Equality was once opposed to aristocracy, but now it opposes public utility and individual rights [Nagel] |
| 3281 | The ideal of acceptability to each individual underlies the appeal to equality [Nagel] |
| 3277 | In judging disputes, should we use one standard, or those of each individual? [Nagel] |
| 3274 | Equality can either be defended as good for society, or as good for individual rights [Nagel] |
| 3273 | Equality nowadays is seen as political, social, legal and economic [Nagel] |
| 3276 | A morality of rights is very minimal, leaving a lot of human life without restrictions or duties [Nagel] |