35 ideas
| 20962 | Habermas seems to make philosophy more democratic [Habermas, by Bowie] |
| 15670 | The aim of 'post-metaphysical' philosophy is to interpret the sciences [Habermas, by Finlayson] |
| 15665 | We can do social philosophy by studying coordinated action through language use [Habermas, by Finlayson] |
| 20573 | Rather than instrumental reason, Habermas emphasises its communicative role [Habermas, by Oksala] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 20961 | What is considered a priori changes as language changes [Habermas, by Bowie] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 15667 | To understand a statement is to know what would make it acceptable [Habermas] |
| 15668 | Meaning is not fixed by a relation to the external world, but a relation to other speakers [Habermas, by Finlayson] |
| 15666 | To understand language is to know how to use it to reach shared understandings [Habermas] |
| 15677 | Moral right is linked to validity and truth, so morality is a matter of knowledge, not an expression of values [Habermas, by Finlayson] |
| 15672 | Actions norms are only valid if everyone possibly affected is involved in the discourse [Habermas] |
| 15671 | Move from individual willing of a general law, to willing norms agreed with other people [Habermas] |
| 15669 | People endorse equality, universality and inclusiveness, just by their communicative practices [Habermas, by Finlayson] |
| 23416 | Political involvement is needed, to challenge existing practices [Habermas, by Kymlicka] |