30 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] |
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
2111 | Falsehood involves a contradiction, and truth is contradictory of falsehood [Leibniz] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
6303 | Sets are positions in patterns [Resnik] |
6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
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] |
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] |
17371 | Some kinds are very explanatory, but others less so, and some not at all [Devitt] |
17373 | Species pluralism says there are several good accounts of what a species is [Devitt] |
17372 | The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt] |
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] |