20 ideas
9208 | Philosophers with a new concept are like children with a new toy [Fine,K] |
14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
9210 | Possible objects are abstract; actual concrete objects are possible; so abstract/concrete are compatible [Fine,K] |
9211 | A non-standard realism, with no privileged standpoint, might challenge its absoluteness or coherence [Fine,K] |
14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
9202 | Objects, as well as sentences, can have logical form [Fine,K] |
9206 | We must distinguish between the identity or essence of an object, and its necessary features [Fine,K] |
9205 | The three basic types of necessity are metaphysical, natural and normative [Fine,K] |
9209 | Metaphysical necessity may be 'whatever the circumstance', or 'regardless of circumstances' [Fine,K] |
9200 | Empiricists suspect modal notions: either it happens or it doesn't; it is just regularities. [Fine,K] |
9207 | If sentence content is all worlds where it is true, all necessary truths have the same content! [Fine,K] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |