50 ideas
| 22438 | Philosophy is largely concerned with finding the minimum that science could get by with [Quine] |
| 22436 | Logicians don't paraphrase logic into language, because they think in the symbolic language [Quine] |
| 22431 | Good algorithms and theories need many occurrences of just a few elements [Quine] |
| 22317 | Truth does not admit of more and less [Frege] |
| 22435 | The logician's '→' does not mean the English if-then [Quine] |
| 22433 | It is important that the quantification over temporal entities is timeless [Quine] |
| 13455 | Frege did not think of himself as working with sets [Frege, by Hart,WD] |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| 16895 | The null set is indefensible, because it collects nothing [Frege, by Burge] |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| 13044 | Infinity: There is at least one limit level [Potter] |
| 3328 | Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA] |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| 9179 | Frege frequently expressed a contempt for language [Frege, by Dummett] |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| 22437 | Logical languages are rooted in ordinary language, and that connection must be kept [Quine] |
| 13473 | Frege thinks there is an independent logical order of the truths, which we must try to discover [Frege, by Hart,WD] |
| 22434 | Reduction to logical forms first simplifies idioms and grammar, then finds a single reading of it [Quine] |
| 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] |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| 16884 | Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge] |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| 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] |
| 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] |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| 3318 | Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' [Frege, by Benardete,JA] |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| 22432 | Normally conditionals have no truth value; it is the consequent which has a conditional truth value [Quine] |
| 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] |
| 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] |
| 22430 | If we understand a statement, we know the circumstances of its truth [Quine] |
| 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] |
| 13713 | Quine holds time to be 'space-like': past objects are as real as spatially remote ones [Quine, by Sider] |
| 3307 | Frege put forward an ontological argument for the existence of numbers [Frege, by Benardete,JA] |