46 ideas
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
12154 | Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry] |
10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
10735 | Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach] |
8780 | Attributes are functions, not objects; this distinguishes 'square of 2' from 'double of 2' [Geach] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
8969 | We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne] |
16075 | Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach] |
12152 | Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach] |
16073 | Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman] |
11910 | Being 'the same' is meaningless, unless we specify 'the same X' [Geach] |
8775 | A big flea is a small animal, so 'big' and 'small' cannot be acquired by abstraction [Geach] |
8776 | We cannot learn relations by abstraction, because their converse must be learned too [Geach] |
10732 | If concepts are just recognitional, then general judgements would be impossible [Geach] |
2567 | You can't define real mental states in terms of behaviour that never happens [Geach] |
2568 | Beliefs aren't tied to particular behaviours [Geach] |
8781 | The mind does not lift concepts from experience; it creates them, and then applies them [Geach] |
10731 | For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach] |
8769 | If someone has aphasia but can still play chess, they clearly have concepts [Geach] |
8770 | 'Abstractionism' is acquiring a concept by picking out one experience amongst a group [Geach] |
8771 | 'Or' and 'not' are not to be found in the sensible world, or even in the world of inner experience [Geach] |
8772 | We can't acquire number-concepts by extracting the number from the things being counted [Geach] |
8773 | Abstractionists can't explain counting, because it must precede experience of objects [Geach] |
8774 | The numbers don't exist in nature, so they cannot have been abstracted from there into our languages [Geach] |
8778 | Blind people can use colour words like 'red' perfectly intelligently [Geach] |
8777 | If 'black' and 'cat' can be used in the absence of such objects, how can such usage be abstracted? [Geach] |
8779 | We can form two different abstract concepts that apply to a single unified experience [Geach] |
10733 | The abstractionist cannot explain 'some' and 'not' [Geach] |
10734 | Only a judgement can distinguish 'striking' from 'being struck' [Geach] |
22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |