28 ideas
7396 | Hobbes created English-language philosophy [Hobbes, by Tuck] |
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] |
19393 | What is not active is nothing [Leibniz] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
16638 | The qualities of the world are mere appearances; reality is the motions which cause them [Hobbes] |
7405 | Experience can't prove universal truths [Hobbes] |
16688 | Evidence is conception, which is imagination, which proceeds from the senses [Hobbes] |
7408 | It is an error that reason should control the passions, which give right guidance on their own [Hobbes, by Tuck] |
7407 | Good and evil are what please us; goodness and badness the powers causing them [Hobbes] |
7410 | Self-preservation is basic, and people judge differently about that, implying ethical relativism [Hobbes, by Tuck] |
7409 | Hobbes shifted from talk of 'the good' to talk of 'rights' [Hobbes, by Tuck] |
7411 | The attributes of God just show our inability to conceive his nature [Hobbes] |