81 ideas
20947 | Thoughts are learnt through words, so language shows the limits and shape of our knowledge [Herder] |
7001 | If you begin philosophy with language, you find yourself trapped in it [Heil] |
7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
7004 | The view that truth making is entailment is misguided and misleading [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] |
7035 | God does not create the world, and then add the classes [Heil] |
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] |
7017 | The reductionist programme dispenses with levels of reality [Heil] |
7003 | There are levels of organisation, complexity, description and explanation, but not of reality [Heil] |
7045 | Realism says some of our concepts 'cut nature at the joints' [Heil] |
7065 | Anti-realists who reduce reality to language must explain the existence of language [Heil] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
7020 | Concepts don't carve up the world, which has endless overlooked or ignored divisions [Heil] |
7007 | I think of properties as simultaneously dispositional and qualitative [Heil] |
7015 | A predicate applies truly if it picks out a real property of objects [Heil] |
7042 | A theory of universals says similarity is identity of parts; for modes, similarity is primitive [Heil] |
7023 | Powers or dispositions are usually seen as caused by lower-level qualities [Heil] |
7025 | Are a property's dispositions built in, or contingently added? [Heil] |
7034 | Universals explain one-over-many relations, and similar qualities, and similar behaviour [Heil] |
7039 | How could you tell if the universals were missing from a world of instances? [Heil] |
7009 | Similarity among modes will explain everthing universals were for [Heil] |
7041 | Similar objects have similar properties; properties are directly similar [Heil] |
7032 | Objects join sets because of properties; the property is not bestowed by set membership [Heil] |
7008 | Trope theorists usually see objects as 'bundles' of tropes [Heil] |
7018 | Objects are substances, which are objects considered as the bearer of properties [Heil] |
7019 | Maybe there is only one substance, space-time or a quantum field [Heil] |
7046 | Rather than 'substance' I use 'objects', which have properties [Heil] |
7047 | Statues and bronze lumps have discernible differences, so can't be identical [Heil] |
7048 | Do we reduce statues to bronze, or eliminate statues, or allow statues and bronze? [Heil] |
7030 | Properties don't possess ways they are, because that just is the property [Heil] |
7028 | If properties were qualities without dispositions, they would be undetectable [Heil] |
7029 | Can we distinguish the way a property is from the property? [Heil] |
7051 | Objects only have secondary qualities because they have primary qualities [Heil] |
7044 | Secondary qualities are just primary qualities considered in the light of their effect on us [Heil] |
7052 | Colours aren't surface properties, because of radiant sources and the colour of the sky [Heil] |
7053 | Treating colour as light radiation has the implausible result that tomatoes are not red [Heil] |
7066 | If the world is just texts or social constructs, what are texts and social constructs? [Heil] |
7021 | If the world is theory-dependent, the theories themselves can't be theory-dependent [Heil] |
7026 | Science is sometimes said to classify powers, neglecting qualities [Heil] |
7060 | One form of explanation is by decomposition [Heil] |
7010 | Dispositionality provides the grounding for intentionality [Heil] |
7054 | Intentionality now has internalist (intrinsic to thinkers) and externalist (environment or community) views [Heil] |
7011 | Qualia are not extra appendages, but intrinsic ingredients of material states and processes [Heil] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
7061 | Philosophers' zombies aim to show consciousness is over and above the physical world [Heil] |
7063 | Zombies are based on the idea that consciousness relates contingently to the physical [Heil] |
7064 | Functionalists deny zombies, since identity of functional state means identity of mental state [Heil] |
7027 | Functionalists say objects can be the same in disposition but differ in quality [Heil] |
7062 | Functionalism cannot explain consciousness just by functional organisation [Heil] |
7059 | The 'explanatory gap' is used to say consciousness is inexplicable, at least with current concepts [Heil] |
7012 | If a car is a higher-level entity, distinct from its parts, how could it ever do anything? [Heil] |
7043 | Multiple realisability is actually one predicate applying to a diverse range of properties [Heil] |
7058 | Externalism is causal-historical, or social, or biological [Heil] |
7057 | Intentionality is based in dispositions, which are intrinsic to agents, suggesting internalism [Heil] |
7013 | The Picture Theory claims we can read reality from our ways of speaking about it [Heil] |
7002 | If propositions are states of affairs or sets of possible worlds, these lack truth values [Heil] |
7016 | The standard view is that causal sequences are backed by laws, and between particular events [Heil] |
7036 | The real natural properties are sparse, but there are many complex properties [Heil] |