30 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] |
| 22744 | Parts are not parts if their whole is nothing more than the parts [Sext.Empiricus] |
| 22748 | Some say motion is perceived by sense, but others say it is by intellect [Sext.Empiricus] |
| 22746 | If we try to conceive of a line with no breadth, it ceases to exist, and so has no length [Sext.Empiricus] |
| 22741 | The incorporeal is not in the nature of body, and so could not emerge from it [Sext.Empiricus] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 22747 | A man walking backwards on a forwards-moving ship is moving in a fixed place [Sext.Empiricus] |
| 22749 | Time doesn't end with the Universe, because tensed statements about destruction remain true [Sext.Empiricus] |
| 22750 | Time is divisible, into past, present and future [Sext.Empiricus] |
| 22742 | Socrates either dies when he exists (before his death) or when he doesn't (after his death) [Sext.Empiricus] |
| 22751 | If the present is just the limit of the past or the future, it can't exist because they don't exist [Sext.Empiricus] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| 22730 | All men agree that God is blessed, imperishable, happy and good [Sext.Empiricus] |
| 22739 | God must suffer to understand suffering [Sext.Empiricus] |
| 22738 | The Divine must lack the virtues of continence and fortitude, because they are not needed [Sext.Empiricus] |
| 22734 | God is defended by agreement, order, absurdity of denying God, and refutations [Sext.Empiricus] |
| 22736 | God's sensations imply change, and hence perishing, which is absurd, so there is no such God [Sext.Empiricus] |
| 22740 | God without virtue is absurd, but God's virtues will be better than God [Sext.Empiricus] |
| 22735 | The original substance lacked motion or shape, and was given these by a cause [Sext.Empiricus] |
| 22732 | The perfections of God were extrapolations from mankind [Sext.Empiricus] |
| 22728 | Gods were invented as watchers of people's secret actions [Sext.Empiricus] |
| 22737 | An incorporeal God could do nothing, and a bodily god would perish, so there is no God [Sext.Empiricus] |
| 22731 | It is mad to think that what is useful to us, like lakes and rivers, are gods [Sext.Empiricus] |