24 ideas
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
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] |
8840 | There are five possible responses to the problem of infinite regress in justification [Cleve] |
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] |
8841 | Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve] |
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] |