31 ideas
| 22358 | Scientific objectivity lies in inter-subjective testing [Popper] |
| 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] |
| 17744 | De Morgan started the study of relations and their properties [De Morgan, by Walicki] |
| 13501 | De Morgan found inferences involving relations, which eluded Aristotle's syllogistic [De Morgan, by Hart,WD] |
| 17743 | De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki] |
| 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] |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [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] |
| 11946 | Propensities are part of a situation, not part of the objects [Popper] |
| 12177 | Human artefacts may have essences, in their purposes [Popper] |
| 5451 | Popper felt that ancient essentialism was a bar to progress [Popper, by Mautner] |
| 22188 | Give Nobel Prizes for really good refutations? [Gorham on Popper] |
| 18284 | Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper] |
| 7780 | Falsification is the criterion of demarcation between science and non-science [Popper, by Magee] |
| 16830 | We don't only reject hypotheses because we have falsified them [Lipton on Popper] |
| 6794 | If falsification requires logical inconsistency, then probabilistic statements can't be falsified [Bird on Popper] |
| 6795 | When Popper gets in difficulties, he quietly uses induction to help out [Bird on Popper] |
| 3856 | Good theories have empirical content, explain a lot, and are not falsified [Popper, by Newton-Smith] |
| 7779 | There is no such thing as induction [Popper, by Magee] |
| 3860 | Science cannot be shown to be rational if induction is rejected [Newton-Smith on Popper] |
| 12176 | Science does not aim at ultimate explanations [Popper] |
| 12175 | Galilean science aimed at true essences, as the ultimate explanations [Popper] |
| 12179 | Essentialist views of science prevent further questions from being raised [Popper] |