15 ideas
2661 | Dialectic is speech cast in the form of logical argument [Cicero] |
2673 | There cannot be more than one truth [Cicero] |
17824 | The master science is physical objects divided into sets [Maddy] |
2669 | Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero] |
17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
2664 | If we have complete healthy senses, what more could the gods give us? [Cicero] |
2665 | How can there be a memory of what is false? [Cicero] |
20800 | Every true presentation can have a false one of the same quality [Cicero] |
2672 | Virtues must be very detached, to avoid being motivated by pleasure [Cicero] |