61 ideas
9449 | The plausible Barcan formula implies modality in the actual world [Bird] |
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] |
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] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [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] |
9501 | If all existents are causally active, that excludes abstracta and causally isolated objects [Bird] |
9500 | If naturalism refers to supervenience, that leaves necessary entities untouched [Bird] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
9502 | There might be just one fundamental natural property [Bird] |
9477 | Categorical properties are not modally fixed, but change across possible worlds [Bird] |
9490 | The categoricalist idea is that a property is only individuated by being itself [Bird] |
9495 | If we abstractly define a property, that doesn't mean some object could possess it [Bird] |
9492 | Categoricalists take properties to be quiddities, with no essential difference between them [Bird] |
9503 | To name an abundant property is either a Fregean concept, or a simple predicate [Bird] |
14540 | Only real powers are fundamental [Bird, by Mumford/Anjum] |
9450 | If all properties are potencies, and stimuli and manifestation characterise them, there is a regress [Bird] |
9498 | The essence of a potency involves relations, e.g. mass, to impressed force and acceleration [Bird] |
9474 | A disposition is finkish if a time delay might mean the manifestation fizzles out [Bird] |
9475 | A robust pot attached to a sensitive bomb is not fragile, but if struck it will easily break [Bird] |
9499 | Megarian actualists deny unmanifested dispositions [Bird] |
9486 | Why should a universal's existence depend on instantiation in an existing particular? [Bird] |
9472 | Resemblance itself needs explanation, presumably in terms of something held in common [Bird] |
9482 | If the laws necessarily imply p, that doesn't give a new 'nomological' necessity [Bird] |
9481 | Logical necessitation is not a kind of necessity; George Orwell not being Eric Blair is not a real possibility [Bird] |
9505 | Empiricist saw imaginability and possibility as close, but now they seem remote [Bird] |
9491 | Haecceitism says identity is independent of qualities and without essence [Bird] |
9487 | We can't reject all explanations because of a regress; inexplicable A can still explain B [Bird] |
8130 | Qualities of experience are just representational aspects of experience ('Representationalism') [Harman, by Burge] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
9493 | We should explain causation by powers, not powers by causation [Bird] |
9494 | Singularism about causes is wrong, as the universals involved imply laws [Bird] |
9507 | Laws are explanatory relationships of things, which supervene on their essences [Bird] |
9488 | Laws are either disposition regularities, or relations between properties [Bird] |
9496 | That other diamonds are hard does not explain why this one is [Bird] |
9479 | Dispositional essentialism says laws (and laws about laws) are guaranteed regularities [Bird] |
9473 | Laws cannot offer unified explanations if they don't involve universals [Bird] |
9484 | If the universals for laws must be instantiated, a vanishing particular could destroy a law [Bird] |
9506 | Salt necessarily dissolves in water, because of the law which makes the existence of salt possible [Bird] |
23713 | Most laws supervene on fundamental laws, which are explained by basic powers [Bird, by Friend/Kimpton-Nye] |
9489 | Essentialism can't use conditionals to explain regularities, because of possible interventions [Bird] |
9504 | The relational view of space-time doesn't cover times and places where things could be [Bird] |