40 ideas
| 4642 | No fact can be real and no proposition true unless there is a Sufficient Reason (even if we can't know it) [Leibniz] |
| 2115 | Everything in the universe is interconnected, so potentially a mind could know everything [Leibniz] |
| 15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 2111 | Falsehood involves a contradiction, and truth is contradictory of falsehood [Leibniz] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
| 15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| 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] |
| 7644 | The monad idea incomprehensibly spiritualises matter, instead of materialising soul [La Mettrie on Leibniz] |
| 11857 | He replaced Aristotelian continuants with monads [Leibniz, by Wiggins] |
| 7843 | Is a drop of urine really an infinity of thinking monads? [Voltaire on Leibniz] |
| 12751 | It is unclear in 'Monadology' how extended bodies relate to mind-like monads. [Garber on Leibniz] |
| 19363 | Changes in a monad come from an internal principle, and the diversity within its substance [Leibniz] |
| 19352 | A 'monad' has basic perception and appetite; a 'soul' has distinct perception and memory [Leibniz] |
| 7931 | If a substance is just a thing that has properties, it seems to be a characterless non-entity [Leibniz, by Macdonald,C] |
| 17554 | There must be some internal difference between any two beings in nature [Leibniz] |
| 2112 | Truths of reason are known by analysis, and are necessary; facts are contingent, and their opposites possible [Leibniz] |
| 9344 | Mathematical analysis ends in primitive principles, which cannot be and need not be demonstrated [Leibniz] |
| 2110 | We all expect the sun to rise tomorrow by experience, but astronomers expect it by reason [Leibniz] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
| 2109 | Increase a conscious machine to the size of a mill - you still won't see perceptions in it [Leibniz] |
| 19362 | We know the 'I' and its contents by abstraction from awareness of necessary truths [Leibniz] |
| 12707 | The true elements are atomic monads [Leibniz] |
| 2114 | This is the most perfect possible universe, in its combination of variety with order [Leibniz] |
| 2113 | God alone (the Necessary Being) has the privilege that He must exist if He is possible [Leibniz] |