19 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] |
5163 | Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer] |
5167 | The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer] |
5164 | A statement is meaningful if observation statements can be deduced from it [Ayer] |
5165 | Directly verifiable statements must entail at least one new observation statement [Ayer] |
5166 | The principle of verification is not an empirical hypothesis, but a definition [Ayer] |
5162 | Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer] |
5168 | Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer] |
6012 | We must choose in which of the virtues we wish to excel [Panaetius] |
6013 | Panaetius said we should live according to our natural starting-points [Panaetius, by Asmis] |
6014 | Panaetius identified courage with great-mindedness, preferring civic courage to military [Panaetius, by Asmis] |
5888 | Souls are born, since they are sensitive and inherited, so they must perish [Panaetius, by Cicero] |