31 ideas
| 23657 | The existence of tensed verbs shows that not all truths are necessary truths [Reid] |
| 23655 | An ad hominem argument is good, if it is shown that the man's principles are inconsistent [Reid] |
| 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] |
| 12427 | All of mathematics is properties of the whole numbers [Kronecker] |
| 10091 | God made the integers, all the rest is the work of man [Kronecker] |
| 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] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 23659 | If someone denies that he is thinking when he is conscious of it, we can only laugh [Reid] |
| 23662 | The existence of ideas is no more obvious than the existence of external objects [Reid] |
| 23661 | We are only aware of other beings through our senses; without that, we are alone in the universe [Reid] |
| 23654 | In obscure matters the few must lead the many, but the many usually lead in common sense [Reid] |
| 23660 | The theory of ideas, popular with philosophers, means past existence has to be proved [Reid] |
| 23658 | Consciousness is an indefinable and unique operation [Reid] |
| 23656 | The structure of languages reveals a uniformity in basic human opinions [Reid] |
| 23653 | If you can't distinguish the features of a complex object, your notion of it would be a muddle [Reid] |
| 23663 | There are axioms of taste - such as a general consensus about a beautiful face [Reid] |