35 ideas
18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
18182 | The extension of concepts is not important to me [Maddy] |
18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
1635 | Mathematics reduces to set theory (which is a bit vague and unobvious), but not to logic proper [Quine] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
7627 | You can't reduce epistemology to psychology, because that presupposes epistemology [Maund on Quine] |
8871 | We should abandon a search for justification or foundations, and focus on how knowledge is acquired [Quine, by Davidson] |
8826 | If we abandon justification and normativity in epistemology, we must also abandon knowledge [Kim on Quine] |
8827 | Without normativity, naturalized epistemology isn't even about beliefs [Kim on Quine] |
8899 | Epistemology is a part of psychology, studying how our theories relate to our evidence [Quine] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
8898 | Inculcations of meanings of words rests ultimately on sensory evidence [Quine] |
8900 | In observation sentences, we could substitute community acceptance for analyticity [Quine] |