25 ideas
| 15163 | The interest of quantified modal logic is its metaphysical necessity and essentialism [Soames] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 15158 | Indefinite descriptions are quantificational in subject position, but not in predicate position [Soames] |
| 15157 | Recognising the definite description 'the man' as a quantifier phrase, not a singular term, is a real insight [Soames] |
| 15156 | The universal and existential quantifiers were chosen to suit mathematics [Soames] |
| 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] |
| 15161 | There are more metaphysically than logically necessary truths [Soames] |
| 15162 | We understand metaphysical necessity intuitively, from ordinary life [Soames] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 15152 | To study meaning, study truth conditions, on the basis of syntax, and representation by the parts [Soames] |
| 15153 | Tarski's account of truth-conditions is too weak to determine meanings [Soames] |
| 15154 | We should use cognitive states to explain representational propositions, not vice versa [Soames] |