38 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] |
| 10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
| 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] |
| 10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
| 10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
| 10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
| 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] |
| 10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
| 10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
| 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] |
| 10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
| 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] |
| 10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
| 20961 | What is considered a priori changes as language changes [Habermas, by Bowie] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
| 10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
| 10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
| 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] |
| 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] |