107 ideas
| 19359 | Leibniz aims to give coherent rational support for empiricism [Leibniz, by Perkins] |
| 13086 | Metaphysics is a science of the intelligible nature of being [Leibniz, by Cover/O'Leary-Hawthorne] |
| 16710 | Leibniz tried to combine mechanistic physics with scholastic metaphysics [Leibniz, by Pasnau] |
| 16897 | Reason is the faculty for grasping apriori necessary truths [Leibniz, by Burge] |
| 3346 | For Leibniz rationality is based on non-contradiction and the principle of sufficient reason [Leibniz, by Benardete,JA] |
| 3347 | Leibniz said the principle of sufficient reason is synthetic a priori, since its denial is not illogical [Leibniz, by Benardete,JA] |
| 8627 | Leibniz is inclined to regard all truths as provable [Leibniz, by Frege] |
| 9161 | Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H] |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| 9147 | Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction [Fine,K on Leibniz] |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| 19375 | The continuum is not divided like sand, but folded like paper [Leibniz, by Arthur,R] |
| 18081 | Nature uses the infinite everywhere [Leibniz] |
| 18080 | A tangent is a line connecting two points on a curve that are infinitely close together [Leibniz] |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| 7565 | Leibniz proposes monads, since there must be basic things, which are immaterial in order to have unity [Leibniz, by Jolley] |
| 10419 | If relations can be reduced to, or supervene on, monadic properties of relata, they are not real [Leibniz, by Swoyer] |
| 13078 | Relations aren't in any monad, so they are distributed, so they are not real [Leibniz] |
| 12713 | Forms have sensation and appetite, the latter being the ability to act on other bodies [Leibniz, by Garber] |
| 13087 | The essence of a thing is its real possibilities [Leibniz, by Cover/O'Leary-Hawthorne] |
| 12701 | Leibniz moved from individuation by whole entity to individuation by substantial form [Leibniz, by Garber] |
| 13105 | The laws-of-the-series plays a haecceitist role [Leibniz, by Cover/O'Leary-Hawthorne] |
| 16513 | Identity of a substance is the law of its persistence [Leibniz] |
| 12035 | Leibniz bases pure primitive entities on conjunctions of qualitative properties [Leibniz, by Adams,RM] |
| 13091 | Leibnizian substances add concept, law, force, form and soul [Leibniz, by Cover/O'Leary-Hawthorne] |
| 7561 | Substances are essentially active [Leibniz, by Jolley] |
| 12715 | Leibniz strengthened hylomorphism by connecting it to force in physics [Leibniz, by Garber] |
| 11878 | Leibniz's view (that all properties are essential) is extreme essentialism, not its denial [Leibniz, by Mackie,P] |
| 11862 | Leibniz was not an essentialist [Leibniz, by Wiggins] |
| 16504 | Two eggs can't be identical, because the same truths can't apply to both of them [Leibniz] |
| 8650 | Things are the same if one can be substituted for the other without loss of truth [Leibniz] |
| 13828 | Necessary truths are those provable from identities by pure logic in finite steps [Leibniz, by Hacking] |
| 13084 | How can things be incompatible, if all positive terms seem to be compatible? [Leibniz] |
| 4307 | A reason must be given why contingent beings should exist rather than not exist [Leibniz] |
| 15883 | Leibniz narrows down God's options to one, by non-contradiction, sufficient reason, indiscernibles, compossibility [Leibniz, by Harré] |
| 18822 | Each monad expresses all its compatible monads; a possible world is the resulting equivalence class [Leibniz, by Rumfitt] |
| 7837 | Leibniz proposed possible worlds, because they might be evil, where God would not create evil things [Leibniz, by Stewart,M] |
| 13080 | Leibniz has a counterpart view of de re counterfactuals [Leibniz, by Cover/O'Leary-Hawthorne] |
| 19332 | For Leibniz, divine understanding grasps every conceivable possibility [Leibniz, by Perkins] |
| 5509 | Leibniz said dualism of mind and body is illusion, and there is only mind [Leibniz, by Martin/Barresi] |
| 7568 | Leibniz is an idealist insofar as the basic components of his universe are all mental [Leibniz, by Jolley] |
| 9160 | Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H] |
| 9164 | We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H] |
| 9165 | Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H] |
| 9162 | Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H] |
| 9166 | People vary in their epistemological standards, and none of them is 'correct' [Field,H] |
| 9163 | If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H] |
| 13092 | The essence of substance is the law of its changes, as in the series of numbers [Leibniz] |
| 19354 | Leibniz introduced the idea of degrees of consciousness, essential for his monads [Leibniz, by Perkins] |
| 7841 | We think we are free because the causes of the will are unknown; determinism is a false problem [Leibniz] |
| 5510 | Leibniz has a panpsychist view that physical points are spiritual [Leibniz, by Martin/Barresi] |
| 7564 | Occasionalism give a false view of natural laws, miracles, and substances [Leibniz, by Jolley] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 19372 | Concepts are ordered, and show eternal possibilities, deriving from God [Leibniz, by Arthur,R] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 13467 | Leibniz was the first modern to focus on sentence-sized units (where empiricists preferred word-size) [Leibniz, by Hart,WD] |
| 19365 | Limited awareness leads to bad choices, and unconscious awareness makes us choose the bad [Leibniz, by Perkins] |
| 8110 | Leibniz identified beauty with intellectual perfection [Leibniz, by Gardner] |
| 7569 | Humans are moral, and capable of reward and punishment, because of memory and self-consciousness [Leibniz, by Jolley] |
| 7574 | Natural law theory is found in Aquinas, in Leibniz, and at the Nuremberg trials [Leibniz, by Jolley] |
| 12728 | Leibniz rejected atoms, because they must be elastic, and hence have parts [Leibniz, by Garber] |
| 19374 | Microscopes and the continuum suggest that matter is endlessly divisible [Leibniz] |
| 7560 | Leibniz struggled to reconcile bodies with a reality of purely soul-like entities [Jolley on Leibniz] |
| 16683 | Leibniz eventually said resistance, rather than extension, was the essence of body [Leibniz, by Pasnau] |
| 12725 | Leibniz wanted to explain motion and its laws by the nature of body [Leibniz, by Garber] |
| 16507 | The law within something fixes its persistence, and accords with general laws of nature [Leibniz] |
| 7859 | Leibniz had an unusual commitment to the causal completeness of physics [Leibniz, by Papineau] |
| 15307 | Leibniz uses 'force' to mean both activity and potential [Leibniz] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| 3889 | God's existence is either necessary or impossible [Leibniz, by Scruton] |
| 7842 | Leibniz was closer than Spinoza to atheism [Leibniz, by Stewart,M] |