21 ideas
18851 | Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen] |
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] |
14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
18852 | A Meinongian principle might say that there is an object for any modest class of properties [Rosen] |
18850 | 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen] |
18849 | Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen] |
18857 | Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen] |
18858 | Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen] |
18856 | Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen] |
18848 | Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen] |
18855 | Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen] |
18853 | A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
18854 | The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen] |