31 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] |
10494 | Several words may label a category; one word can name several categories; some categories lack words [Ellen] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
4608 | Minds are hard-wired, or trial-and-error, or experimental, or full self-aware [Dennett, by Heil] |
4880 | Sentience comes in grades from robotic to super-human; we only draw a line for moral reasons [Dennett] |
4873 | What is it like to notice an uncomfortable position when you are asleep? [Dennett] |
4881 | Being a person must involve having second-order beliefs and desires (about beliefs and desires) [Dennett] |
4875 | We descend from robots, and our intentionality is composed of billions of crude intentional systems [Dennett] |
4879 | There is no more anger in adrenaline than silliness in a bottle of whiskey [Dennett] |
4876 | Maybe there is a minimum brain speed for supporting a mind [Dennett] |
4878 | The materials for a mind only matter because of speed, and a need for transducers and effectors [Dennett] |
4874 | The predecessor and rival of the language of thought hypothesis is the picture theory of ideas [Dennett] |
4882 | Concepts are things we (unlike dogs) can think about, because we have language [Dennett] |
4872 | Most people see an abortion differently if the foetus lacks a brain [Dennett] |
4877 | Maybe plants are very slow (and sentient) animals, overlooked because we are faster? [Dennett] |