29 ideas
12780 | We can grasp the wisdom of God a priori [Leibniz] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
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] |
12774 | Without a substantial chain to link monads, they would just be coordinated dreams [Leibniz] |
12777 | Monads do not make a unity unless a substantial chain is added to them [Leibniz] |
12782 | Monads control nothing outside of themselves [Leibniz] |
12778 | There is active and passive power in the substantial chain and in the essence of a composite [Leibniz] |
12783 | Primitive force is what gives a composite its reality [Leibniz] |
12775 | Things seem to be unified if we see duration, position, interaction and connection [Leibniz] |
12776 | Every substance is alive [Leibniz] |
12753 | A substantial bond of powers is needed to unite composites, in addition to monads [Leibniz] |
12781 | A composite substance is a mere aggregate if its essence is just its parts [Leibniz] |
12779 | There is a reason why not every possible thing exists [Leibniz] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
12785 | Truth is mutually agreed perception [Leibniz] |
9284 | Reasons are 'internal' if they give a person a motive to act, but 'external' otherwise [Williams,B] |
12784 | Allow no more miracles than are necessary [Leibniz] |