47 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] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [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] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [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] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic 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] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
16554 | Activities have place, rate, duration, entities, properties, modes, direction, polarity, energy and range [Machamer/Darden/Craver] |
3509 | Externalism may be the key idea in philosophical naturalism [Papineau] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
16556 | Penicillin causes nothing; the cause is what penicillin does [Machamer/Darden/Craver] |
16562 | We understand something by presenting its low-level entities and activities [Machamer/Darden/Craver] |
16563 | The explanation is not the regularity, but the activity sustaining it [Machamer/Darden/Craver] |
16555 | Functions are not properties of objects, they are activities contributing to mechanisms [Machamer/Darden/Craver] |
16529 | Mechanisms are systems organised to produce regular change [Machamer/Darden/Craver] |
16530 | A mechanism explains a phenomenon by showing how it was produced [Machamer/Darden/Craver] |
16553 | Our account of mechanism combines both entities and activities [Machamer/Darden/Craver] |
16559 | Descriptions of explanatory mechanisms have a bottom level, where going further is irrelevant [Machamer/Darden/Craver] |
16528 | Mechanisms are not just push-pull systems [Machamer/Darden/Craver] |
16564 | There are four types of bottom-level activities which will explain phenomena [Machamer/Darden/Craver] |
16561 | We can abstract by taking an exemplary case and ignoring the detail [Machamer/Darden/Craver] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
3513 | How does a dualist mind represent, exist outside space, and be transparent to itself? [Papineau] |
3514 | Functionalism needs causation and intentionality to explain actions [Papineau] |
3510 | Epiphenomenalism is supervenience without physicalism [Papineau] |
3511 | Supervenience requires all mental events to have physical effects [Papineau] |
3515 | Knowing what it is like to be something only involves being (physically) that thing [Papineau] |
3512 | If a mental state is multiply realisable, why does it lead to similar behaviour? [Papineau] |
3516 | The Private Language argument only means people may misjudge their experiences [Papineau] |
16558 | Laws of nature have very little application in biology [Machamer/Darden/Craver] |