41 ideas
11159 | My account shows how the concept works, rather than giving an analysis [Fine,K] |
11157 | Modern philosophy has largely abandoned real definitions, apart from sortals [Fine,K] |
11171 | Defining a term and giving the essence of an object don't just resemble - they are the same [Fine,K] |
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] |
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] |
11151 | An object is dependent if its essence prevents it from existing without some other object [Fine,K] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
11152 | Essences are either taken as real definitions, or as necessary properties [Fine,K] |
11161 | Essentially having a property is naturally expressed as 'the property it must have to be what it is' [Fine,K] |
11160 | Simple modal essentialism refers to necessary properties of an object [Fine,K] |
11158 | Essentialist claims can be formulated more clearly with quantified modal logic [Fine,K] |
11167 | Metaphysical necessity is a special case of essence, not vice versa [Fine,K] |
16537 | Essence as necessary properties produces a profusion of essential properties [Fine,K, by Lowe] |
11163 | The nature of singleton Socrates has him as a member, but not vice versa [Fine,K] |
11164 | It is not part of the essence of Socrates that a huge array of necessary truths should hold [Fine,K] |
10935 | An essential property of something must be bound up with what it is to be that thing [Fine,K, by Rami] |
10936 | Essential properties are part of an object's 'definition' [Fine,K, by Rami] |
11165 | If Socrates lacks necessary existence, then his nature cannot require his parents' existence [Fine,K] |
11166 | The subject of a proposition need not be the source of its necessity [Fine,K] |
11169 | Conceptual necessities rest on the nature of all concepts [Fine,K] |
11162 | Socrates is necessarily distinct from the Eiffel Tower, but that is not part of his essence [Fine,K] |
11168 | Metaphysical necessities are true in virtue of the nature of all objects [Fine,K] |
11170 | Analytic truth may only be true in virtue of the meanings of certain terms [Fine,K] |
11172 | The meaning of 'bachelor' is irrelevant to the meaning of 'unmarried man' [Fine,K] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
6610 | I believe because it is absurd [Tertullian] |