48 ideas
| 4456 | Epistemological Ockham's Razor demands good reasons, but the ontological version says reality is simple [Moreland] |
| 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] |
| 4474 | Existence theories must match experience, possibility, logic and knowledge, and not be self-defeating [Moreland] |
| 4461 | Tropes are like Hume's 'impressions', conceived as real rather than as ideal [Moreland] |
| 4463 | In 'four colours were used in the decoration', colours appear to be universals, not tropes [Moreland] |
| 4462 | A colour-trope cannot be simple (as required), because it is spread in space, and so it is complex [Moreland] |
| 4451 | If properties are universals, what distinguishes two things which have identical properties? [Moreland] |
| 4453 | One realism is one-over-many, which may be the model/copy view, which has the Third Man problem [Moreland] |
| 4464 | Realists see properties as universals, which are single abstract entities which are multiply exemplifiable [Moreland] |
| 4450 | The traditional problem of universals centres on the "One over Many", which is the unity of natural classes [Moreland] |
| 4449 | Evidence for universals can be found in language, communication, natural laws, classification and ideals [Moreland] |
| 4454 | The One-In-Many view says universals have abstract existence, but exist in particulars [Moreland] |
| 4452 | Maybe universals are real, if properties themselves have properties, and relate to other properties [Moreland] |
| 4467 | A naturalist and realist about universals is forced to say redness can be both moving and stationary [Moreland] |
| 4469 | There are spatial facts about red particulars, but not about redness itself [Moreland] |
| 4468 | How could 'being even', or 'being a father', or a musical interval, exist naturally in space? [Moreland] |
| 4472 | Redness is independent of red things, can do without them, has its own properties, and has identity [Moreland] |
| 4459 | Moderate nominalism attempts to embrace the existence of properties while avoiding universals [Moreland] |
| 4458 | Unlike Class Nominalism, Resemblance Nominalism can distinguish natural from unnatural classes [Moreland] |
| 4457 | There can be predicates with no property, and there are properties with no predicate [Moreland] |
| 4471 | We should abandon the concept of a property since (unlike sets) their identity conditions are unclear [Moreland] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 12066 | Aristotelian and Kripkean essentialism are very different theories [Witt] |
| 12067 | An Aristotelian essence is a nonlinguistic correlate of the definition [Witt] |
| 12082 | If unity is a matter of degree, then essence may also be a matter of degree [Witt] |
| 12089 | Essences mainly explain the existence of unified substance [Witt] |
| 12102 | Essential properties of origin are too radically individual for an Aristotelian essence [Witt] |
| 4476 | Most philosophers think that the identity of indiscernibles is false [Moreland] |
| 4460 | Abstractions are formed by the mind when it concentrates on some, but not all, the features of a thing [Moreland] |
| 4455 | It is always open to a philosopher to claim that some entity or other is unanalysable [Moreland] |
| 12085 | Reality is directional [Witt] |
| 4473 | 'Presentism' is the view that only the present moment exists [Moreland] |