79 ideas
18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
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] |
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] |
3005 | 'Jocasta' needs to be distinguished from 'Oedipus's mother' because they are connected by different properties [Fodor] |
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] |
18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [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] |
18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
7014 | A particle and a coin heads-or-tails pick out to perfectly well-defined predicates and properties [Fodor] |
3008 | Evolution suggests that innate knowledge of human psychology would be beneficial [Fodor] |
2990 | Contrary to commonsense, most of what is in the mind seems to be unlearned [Fodor] |
3009 | Sticklebacks have an innate idea that red things are rivals [Fodor] |
2994 | In CRTT thought may be represented, content must be [Fodor] |
15494 | We can't use propositions to explain intentional attitudes, because they would need explaining [Fodor] |
7326 | Intentionality doesn't go deep enough to appear on the physicists' ultimate list of things [Fodor] |
3001 | Behaviourism has no theory of mental causation [Fodor] |
2993 | Any piece of software can always be hard-wired [Fodor] |
3011 | Causal powers must be a crucial feature of mental states [Fodor] |
5498 | Mind is a set of hierarchical 'homunculi', which are made up in turn from subcomponents [Fodor, by Lycan] |
2995 | Supervenience gives good support for mental causation [Fodor] |
2991 | Hume's associationism offers no explanation at all of rational thought [Fodor] |
3002 | If mind is just physical, how can it follow the rules required for intelligent thought? [Fodor] |
2992 | We may be able to explain rationality mechanically [Fodor] |
2988 | Folk psychology is the only explanation of behaviour we have [Fodor] |
3010 | Belief and desire are structured states, which need mentalese [Fodor] |
2999 | Obsession with narrow content leads to various sorts of hopeless anti-realism [Fodor] |
3012 | Do identical thoughts have identical causal roles? [Fodor] |
2998 | Grice thinks meaning is inherited from the propositional attitudes which sentences express [Fodor] |
3006 | Whatever in the mind delivers falsehood is parasitic on what delivers truth [Fodor] |
3007 | Many different verification procedures can reach 'star', but it only has one semantic value [Fodor] |
3004 | The meaning of a sentence derives from its use in expressing an attitude [Fodor] |
3000 | Meaning holism is a crazy doctrine [Fodor] |
3003 | Very different mental states can share their contents, so content doesn't seem to be constructed from functional role [Fodor] |
2996 | Mental states may have the same content but different extensions [Fodor] |
18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
21991 | The middle class gain freedom through property, but workers can only free all of humanity [Marx, by Singer] |
21990 | Theory is as much a part of a revolution as material force is [Marx] |
7128 | Religion is the opium of the people, and real happiness requires its abolition [Marx] |