16 ideas
10185 | Set theory is the standard background for modern mathematics [Burgess] |
10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
14193 | 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA] |
14195 | If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA] |
14196 | Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA] |
14198 | Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA] |
14190 | Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA] |
14191 | Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA] |
14192 | Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA] |
14197 | An object's modal properties don't determine its possibilities [Paul,LA] |
14189 | 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA] |
20698 | Irenaeus says evil is necessary for perfect human development [Irenaeus, by Davies,B] |