58 ideas
11147 | Naturalistic philosophers oppose analysis, preferring explanation to a priori intuition [Margolis/Laurence] |
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
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] |
10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
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] |
9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
11141 | Modern empiricism tends to emphasise psychological connections, not semantic relations [Margolis/Laurence] |
11142 | Body-type seems to affect a mind's cognition and conceptual scheme [Margolis/Laurence] |
11121 | Language of thought has subject/predicate form and includes logical devices [Margolis/Laurence] |
11120 | Concepts are either representations, or abilities, or Fregean senses [Margolis/Laurence] |
11122 | A computer may have propositional attitudes without representations [Margolis/Laurence] |
11124 | Do mental representations just lead to a vicious regress of explanations [Margolis/Laurence] |
11123 | Maybe the concept CAT is just the ability to discriminate and infer about cats [Margolis/Laurence] |
11125 | The abilities view cannot explain the productivity of thought, or mental processes [Margolis/Laurence] |
11140 | Concept-structure explains typicality, categories, development, reference and composition [Margolis/Laurence] |
11128 | Classically, concepts give necessary and sufficient conditions for falling under them [Margolis/Laurence] |
11130 | Typicality challenges the classical view; we see better fruit-prototypes in apples than in plums [Margolis/Laurence] |
11129 | The classical theory explains acquisition, categorization and reference [Margolis/Laurence] |
11131 | It may be that our concepts (such as 'knowledge') have no definitional structure [Margolis/Laurence] |
11132 | The prototype theory is probabilistic, picking something out if it has sufficient of the properties [Margolis/Laurence] |
11133 | Prototype theory categorises by computing the number of shared constituents [Margolis/Laurence] |
11134 | People don't just categorise by apparent similarities [Margolis/Laurence] |
11135 | Complex concepts have emergent properties not in the ingredient prototypes [Margolis/Laurence] |
11136 | Many complex concepts obviously have no prototype [Margolis/Laurence] |
11137 | The theory theory of concepts says they are parts of theories, defined by their roles [Margolis/Laurence] |
11138 | The theory theory is holistic, so how can people have identical concepts? [Margolis/Laurence] |
11139 | Maybe concepts have no structure, and determined by relations to the world, not to other concepts [Margolis/Laurence] |
11146 | People can formulate new concepts which are only named later [Margolis/Laurence] |
9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |