33 ideas
23326 | In the third century Stoicism died out, replaced by Platonism, with Aristotelian ethics [Frede,M] |
23335 | In late antiquity nearly all philosophers were monotheists [Frede,M] |
16137 | Earlier views of Aristotle were dominated by 'Categories' [Frede,M] |
23249 | The early philosophers thought that reason has its own needs and desires [Frede,M] |
9921 | 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen] |
13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
9924 | Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen] |
9933 | The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen] |
9928 | Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen] |
13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
9926 | A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen] |
13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
9932 | The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen] |
9923 | We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen] |
9925 | Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen] |
9934 | Number words became nouns around the time of Plato [Burgess/Rosen] |
9918 | Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen] |
9929 | Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen] |
9927 | Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen] |
9930 | Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen] |
16157 | Insurance on the original ship would hardly be paid out if the plank version was wrecked! [Frede,M] |
23334 | For Christians man has free will by creation in God's image (as in Genesis) [Frede,M] |
23337 | The Stoics needed free will, to allow human choices in a divinely providential cosmos [Frede,M] |
23333 | The idea of free will achieved universal acceptance because of Christianity [Frede,M] |
9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
23336 | There is no will for Plato or Aristotle, because actions come directly from perception of what is good [Frede,M] |
9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |
23313 | The Gnostic demiurge (creator) is deluded, and doesn't care about us [Frede,M] |