64 ideas
4588 | There is no such thing as 'science'; there are just many different sciences [Heil] |
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] |
17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
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] |
4616 | A higher level is 'supervenient' if it is determined by lower levels, but has its own natural laws [Heil] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
4603 | Functionalists in Fodor's camp usually say that a genuine property is one that figures in some causal laws [Heil] |
4617 | A stone does not possess the property of being a stone; its other properties make it a stone [Heil] |
4615 | Complex properties are not new properties, they are merely new combinations of properties [Heil] |
4612 | Complex properties are just arrangements of simple properties; they do not "emerge" as separate [Heil] |
4587 | From the property predicates P and Q, we can get 'P or Q', but it doesn't have to designate another property [Heil] |
4611 | The supporters of 'tropes' treat objects as bundles of tropes, when I think objects 'possess' properties [Heil] |
4592 | If you can have the boat without its current planks, and the planks with no boat, the planks aren't the boat [Heil] |
4586 | You can't embrace the formal apparatus of possible worlds, but reject the ontology [Heil] |
4591 | Idealism explains appearances by identifying appearances with reality [Heil] |
4610 | Different generations focus on either the quality of mind, or its scientific standing, or the content of thought [Heil] |
4618 | If minds are realised materially, it looks as if the material laws will pre-empt any causal role for mind [Heil] |
4621 | Whatever exists has qualities, so it is no surprise that states of minds have qualities [Heil] |
4623 | Propositional attitudes are not the only intentional states; there is also mental imagery [Heil] |
4626 | The widespread externalist view says intentionality has content because of causal links of agent to world [Heil] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
4622 | Error must be possible in introspection, because error is possible in all judgements [Heil] |
4590 | If causation is just regularities in events, the interaction of mind and body is not a special problem [Heil] |
4614 | Disposition is a fundamental feature of reality, since basic particles are capable of endless possible interactions [Heil] |
4595 | No mental state entails inevitable behaviour, because other beliefs or desires may intervene [Heil] |
4599 | Hearts are material, but functionalism says the property of being a heart is not a material property [Heil] |
4624 | If you are a functionalist, there appears to be no room for qualia [Heil] |
4601 | Higher-level sciences cannot be reduced, because their concepts mark boundaries invisible at lower levels [Heil] |
4602 | Higher-level sciences designate real properties of objects, which are not reducible to lower levels [Heil] |
4593 | 'Property dualism' says mind and body are not substances, but distinct families of properties [Heil] |
4597 | Early identity theory talked of mind and brain 'processes', but now the focus is properties [Heil] |
4609 | It seems contradictory to be asked to believe that we can be eliminativist about beliefs [Heil] |
4596 | The appeal of the identity theory is its simplicity, and its solution to the mental causation problem [Heil] |
4598 | Functionalists emphasise that mental processes are not to be reduced to what realises them [Heil] |
4619 | 'Multiple realisability' needs to clearly distinguish low-level realisers from what is realised [Heil] |
4620 | Multiple realisability is not a relation among properties, but an application of predicates to resembling things [Heil] |
4594 | A scientist could know everything about the physiology of headaches, but never have had one [Heil] |
4625 | Is mental imagery pictorial, or is it propositional? [Heil] |
4607 | Folk psychology and neuroscience are no more competitors than cartography and geology are [Heil] |
4605 | Truth-conditions correspond to the idea of 'literal meaning' [Heil] |
4606 | To understand 'birds warble' and 'tigers growl', you must also understand 'tigers warble' [Heil] |
4604 | If propositions are abstract entities, how do human beings interact with them? [Heil] |