35 ideas
| 6161 | Structuralism is neo-Kantian idealism, with language playing the role of categories of understanding [Rowlands] |
| 8083 | Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin] |
| 7727 | Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner] |
| 8686 | Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend] |
| 6163 | If bivalence is rejected, then excluded middle must also be rejected [Rowlands] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 22277 | Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter] |
| 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] |
| 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] |
| 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] |
| 6155 | Supervenience is a one-way relation of dependence or determination between properties [Rowlands] |
| 6154 | It is argued that wholes possess modal and counterfactual properties that parts lack [Rowlands] |
| 6157 | Tokens are dated, concrete particulars; types are their general properties or kinds [Rowlands] |
| 6159 | Strong idealism is the sort of mess produced by a Cartesian separation of mind and world [Rowlands] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 6152 | Minds are rational, conscious, subjective, self-knowing, free, meaningful and self-aware [Rowlands] |
| 6173 | Content externalism implies that we do not have privileged access to our own minds [Rowlands] |
| 6174 | If someone is secretly transported to Twin Earth, others know their thoughts better than they do [Rowlands] |
| 6158 | Supervenience of mental and physical properties often comes with token-identity of mental and physical particulars [Rowlands] |
| 6168 | The content of a thought is just the meaning of a sentence [Rowlands] |
| 6167 | Action is bodily movement caused by intentional states [Rowlands] |
| 6177 | Moral intuition seems unevenly distributed between people [Rowlands] |
| 6156 | The 17th century reintroduced atoms as mathematical modes of Euclidean space [Rowlands] |
| 6170 | Natural kinds are defined by their real essence, as in gold having atomic number 79 [Rowlands] |
| 6178 | It is common to see the value of nature in one feature, such as life, diversity, or integrity [Rowlands] |