33 ideas
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 17771 | How we evaluate evidence depends on our background beliefs [Bayne] |
| 17770 | Clifford's dictum seems to block our beliefs in morality, politics and philosophy [Bayne] |
| 4020 | The modern self has disengaged reason, self-exploration, and personal commitment [Taylor,C] |
| 4002 | My aim is to map the connections between our sense of self and our moral understanding [Taylor,C] |
| 4006 | I can only be aware of myself as a person who changes by means of my personal history [Taylor,C] |
| 17766 | Physicalism correlates brain and mind, explains causation by thought, and makes nature continuous [Bayne] |
| 17768 | Perception reveals what animals think, but humans can disengage thought from perception [Bayne] |
| 17769 | Some people centre space on themselves; others centre space on the earth [Bayne] |
| 17767 | The alternative to a language of thought is map-like or diagram-like thought [Bayne] |
| 4003 | Selfhood and moral values are inextricably intertwined [Taylor,C] |
| 4021 | Willingness to risk life was the constitutive quality of the man of honour [Taylor,C] |
| 4005 | To have respect for people, you must feel their claims, or their injustices, or hold them in awe [Taylor,C] |
| 4004 | Consistency presupposes intrinsic description [Taylor,C] |
| 4010 | In later utilitarianism the modern stress on freedom leads to the rejection of paternalism [Taylor,C] |
| 4009 | Nominalists defended the sovereignty of God against the idea of natural existing good and evil [Taylor,C] |