33 ideas
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] |
19566 | Epistemology does not just concern knowledge; all aspects of cognitive activity are involved [Kvanvig] |
19261 | Understanding is seeing coherent relationships in the relevant information [Kvanvig] |
19568 | Making sense of things, or finding a good theory, are non-truth-related cognitive successes [Kvanvig] |
19567 | The 'defeasibility' approach says true justified belief is knowledge if no undermining facts could be known [Kvanvig] |
19679 | 'Access' internalism says responsibility needs access; weaker 'mentalism' needs mental justification [Kvanvig] |
19730 | Epistemic virtues: love of knowledge, courage, caution, autonomy, practical wisdom... [Kvanvig] |
19731 | If epistemic virtues are faculties or powers, that doesn't explain propositional knowledge [Kvanvig] |
19732 | The value of good means of attaining truth are swamped by the value of the truth itself [Kvanvig] |
19678 | Strong foundationalism needs strict inferences; weak version has induction, explanation, probability [Kvanvig] |
19570 | Reliabilism cannot assess the justification for propositions we don't believe [Kvanvig] |
9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |