25 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] |
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] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
1212 | Replacing timbers on Theseus' ship was the classic illustration of the problem of growth and change [Plutarch] |
5958 | The sun is always bright; it doesn't become bright when it emerges [Plutarch] |
22110 | Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump] |
5960 | When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch] |
5959 | Some philosophers say the soul is light [Plutarch] |
5952 | Rather than being the whole soul, maybe I am its chief part? [Plutarch] |
5951 | If atoms have no qualities, they cannot possibly produce a mind [Plutarch] |
5963 | Some say emotion is a sort of reason, and others say virtue concerns emotion [Plutarch] |
20796 | Action needs an affinity for a presentation, and an impulse toward the affinity [Plutarch] |
1477 | Being manly and brave is the result of convention, not of human nature [Plutarch] |
1478 | Animals don't value pleasure, as they cease sexual intercourse after impregnation [Plutarch] |
5948 | The good life involves social participation, loyalty, temperance and honesty [Plutarch] |
1479 | Animals have not been led into homosexuality, because they value pleasure very little [Plutarch] |
5950 | If only atoms exist, how do qualities arise when the atoms come together? [Plutarch] |
5974 | People report seeing through rocks, or over the horizon, or impossibly small works [Plutarch] |
5957 | Absurd superstitions make people atheist, not disharmony in nature [Plutarch] |
5955 | No one will ever find a city that lacks religious practices [Plutarch] |