28 ideas
15134 | The truthmaker principle requires some specific named thing to make the difference [Williamson] |
15140 | The converse Barcan formula will not allow contingent truths to have truthmakers [Williamson] |
15141 | Truthmaker is incompatible with modal semantics of varying domains [Williamson] |
15131 | If metaphysical possibility is not a contingent matter, then S5 seems to suit it best [Williamson] |
15135 | If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson] |
15139 | Converse Barcan: could something fail to meet a condition, if everything meets that condition? [Williamson] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
18492 | Not all quantification is either objectual or substitutional [Williamson] |
15136 | Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson] |
15138 | Not all quantification is objectual or substitutional [Williamson] |
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] |
15137 | If 'fact' is a noun, can we name the fact that dogs bark 'Mary'? [Williamson] |
15142 | Our ability to count objects across possibilities favours the Barcan formulas [Williamson] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
20751 | As a young girl assumes her status as feminine, she acts in a more fragile immobile way [Young,IM] |
15133 | A thing can't be the only necessary existent, because its singleton set would be as well [Williamson] |