47 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] |
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
2111 | Falsehood involves a contradiction, and truth is contradictory of falsehood [Leibniz] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
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] |
2526 | Philosophers regularly confuse failures of imagination with insights into necessity [Dennett] |
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] |
2523 | That every mammal has a mother is a secure reality, but without foundations [Dennett] |
2528 | Does consciousness need the concept of consciousness? [Dennett] |
2525 | Maybe language is crucial to consciousness [Dennett] |
2109 | Increase a conscious machine to the size of a mill - you still won't see perceptions in it [Leibniz] |
2527 | Unconscious intentionality is the foundation of the mind [Dennett] |
19362 | We know the 'I' and its contents by abstraction from awareness of necessary truths [Leibniz] |
2530 | Could a robot be made conscious just by software? [Dennett] |
2524 | A language of thought doesn't explain content [Dennett] |
2529 | Maybe there can be non-conscious concepts (e.g. in bees) [Dennett] |
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] |