105 ideas
7001 | If you begin philosophy with language, you find yourself trapped in it [Heil] |
7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
7004 | The view that truth making is entailment is misguided and misleading [Heil] |
18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
18114 | There is no single agreed structure for set theory [Bostock] |
18107 | A 'proper class' cannot be a member of anything [Bostock] |
18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
7035 | God does not create the world, and then add the classes [Heil] |
18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
18109 | The completeness of first-order logic implies its compactness [Bostock] |
18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
18097 | The Peano Axioms describe a unique structure [Bostock] |
18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
18149 | There are many criteria for the identity of numbers [Bostock] |
18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
18140 | The best version of conceptualism is predicativism [Bostock] |
18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
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] |
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] |
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] |
7030 | Properties don't possess ways they are, because that just is 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] |
7458 | The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking] |
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] |
3441 | If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace] |
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] |
18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
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] |