57 ideas
| 12104 | All ideas must be understood historically [Comte] |
| 12105 | Our knowledge starts in theology, passes through metaphysics, and ends in positivism [Comte] |
| 12112 | Metaphysics is just the oversubtle qualification of abstract names for phenomena [Comte] |
| 12106 | Positivism gives up absolute truth, and seeks phenomenal laws, by reason and observation [Comte] |
| 12111 | Positivism is the final state of human intelligence [Comte] |
| 12114 | Science can drown in detail, so we need broad scientists (to keep out the metaphysicians) [Comte] |
| 12116 | Only positivist philosophy can terminate modern social crises [Comte] |
| 22317 | Truth does not admit of more and less [Frege] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 13455 | Frege did not think of himself as working with sets [Frege, by Hart,WD] |
| 16895 | The null set is indefensible, because it collects nothing [Frege, by Burge] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 3328 | Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA] |
| 9179 | Frege frequently expressed a contempt for language [Frege, by Dummett] |
| 13473 | Frege thinks there is an independent logical order of the truths, which we must try to discover [Frege, by Hart,WD] |
| 6076 | For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn] |
| 3319 | Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA] |
| 9871 | Frege always, and fatally, neglected the domain of quantification [Dummett on Frege] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 16884 | Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge] |
| 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] |
| 3331 | If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege] |
| 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] |
| 16880 | Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge] |
| 8689 | Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend] |
| 5657 | Frege's logic showed that there is no concept of being [Frege, by Scruton] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 3318 | Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' [Frege, by Benardete,JA] |
| 16885 | To understand a thought, understand its inferential connections to other thoughts [Frege, by Burge] |
| 16887 | Frege's concept of 'self-evident' makes no reference to minds [Frege, by Burge] |
| 16894 | An apriori truth is grounded in generality, which is universal quantification [Frege, by Burge] |
| 12108 | All real knowledge rests on observed facts [Comte] |
| 12109 | We must observe in order to form theories, but connected observations need prior theories [Comte] |
| 16882 | The building blocks contain the whole contents of a discipline [Frege] |
| 12107 | Positivism explains facts by connecting particular phenomena with general facts [Comte] |
| 12115 | Introspection is pure illusion; we can obviously observe everything except ourselves [Comte] |
| 5816 | Frege said concepts were abstract entities, not mental entities [Frege, by Putnam] |
| 7307 | A thought is not psychological, but a condition of the world that makes a sentence true [Frege, by Miller,A] |
| 7309 | Frege's 'sense' is the strict and literal meaning, stripped of tone [Frege, by Miller,A] |
| 7312 | 'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness [Frege, by Miller,A] |
| 7725 | 'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate [Frege, by Weiner] |
| 7316 | Analytic truths are those that can be demonstrated using only logic and definitions [Frege, by Miller,A] |
| 12113 | The search for first or final causes is futile [Comte] |
| 12110 | We can never know origins, purposes or inner natures [Comte] |
| 3307 | Frege put forward an ontological argument for the existence of numbers [Frege, by Benardete,JA] |