31 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] |
14664 | Necessary beings (numbers, properties, sets, propositions, states of affairs, God) exist in all possible worlds [Plantinga] |
14666 | Socrates is a contingent being, but his essence is not; without Socrates, his essence is unexemplified [Plantinga] |
15161 | There are more metaphysically than logically necessary truths [Soames] |
15162 | We understand metaphysical necessity intuitively, from ordinary life [Soames] |
14662 | Possible worlds clarify possibility, propositions, properties, sets, counterfacts, time, determinism etc. [Plantinga] |
16472 | Plantinga's actualism is nominal, because he fills actuality with possibilia [Stalnaker on Plantinga] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |
16469 | Plantinga has domains of sets of essences, variables denoting essences, and predicates as functions [Plantinga, by Stalnaker] |
16470 | Plantinga's essences have their own properties - so will have essences, giving a hierarchy [Stalnaker on Plantinga] |
14663 | Are propositions and states of affairs two separate things, or only one? I incline to say one [Plantinga] |
15154 | We should use cognitive states to explain representational propositions, not vice versa [Soames] |