42 ideas
| 22317 | Truth does not admit of more and less [Frege] |
| 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] |
| 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] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 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] |
| 16884 | Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge] |
| 10245 | One geometry cannot be more true than another [Poincaré] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 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] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 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] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 5657 | Frege's logic showed that there is no concept of being [Frege, by Scruton] |
| 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] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 16882 | The building blocks contain the whole contents of a discipline [Frege] |
| 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] |
| 3307 | Frege put forward an ontological argument for the existence of numbers [Frege, by Benardete,JA] |