73 ideas
19579 | The history of philosophy is just experiments in how to do philosophy [Novalis] |
19583 | Philosophy only begins when it studies itself [Novalis] |
22026 | Philosophy is homesickness - the urge to be at home everywhere [Novalis] |
19588 | The highest aim of philosophy is to combine all philosophies into a unity [Novalis] |
19598 | Philosophy relies on our whole system of learning, and can thus never be complete [Novalis] |
19586 | Philosophers feed on problems, hoping they are digestible, and spiced with paradox [Novalis] |
19587 | Philosophy aims to produce a priori an absolute and artistic world system [Novalis] |
9136 | The paradox of analysis says that any conceptual analysis must be either trivial or false [Sorensen] |
9131 | Two long understandable sentences can have an unintelligible conjunction [Sorensen] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
19574 | If man sacrifices truth he sacrifices himself, by acting against his own convictions [Novalis] |
9139 | If nothing exists, no truthmakers could make 'Nothing exists' true [Sorensen] |
9140 | Which toothbrush is the truthmaker for 'buy one, get one free'? [Sorensen] |
19571 | Delusion and truth differ in their life functions [Novalis] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
19597 | Logic (the theory of relations) should be applied to mathematics [Novalis] |
9119 | No attempt to deny bivalence has ever been accepted [Sorensen] |
9135 | We now see that generalizations use variables rather than abstract entities [Sorensen] |
19581 | A problem is a solid mass, which the mind must break up [Novalis] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
9125 | Denying problems, or being romantically defeated by them, won't make them go away [Sorensen] |
9137 | Banning self-reference would outlaw 'This very sentence is in English' [Sorensen] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
19584 | Whoever first counted to two must have seen the possibility of infinite counting [Novalis] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
22025 | Novalis thought self-consciousness cannot disclose 'being', because we are temporal creatures [Novalis, by Pinkard] |
9116 | Vague words have hidden boundaries [Sorensen] |
9132 | An offer of 'free coffee or juice' could slowly shift from exclusive 'or' to inclusive 'or' [Sorensen] |
19575 | Refinement of senses increasingly distinguishes individuals [Novalis] |
22067 | Poetry is true idealism, and the self-consciousness of the universe [Novalis] |
9128 | It is propositional attitudes which can be a priori, not the propositions themselves [Sorensen] |
9130 | Attributing apriority to a proposition is attributing a cognitive ability to someone [Sorensen] |
9118 | The colour bands of the spectrum arise from our biology; they do not exist in the physics [Sorensen] |
9124 | We are unable to perceive a nose (on the back of a mask) as concave [Sorensen] |
19572 | Experiences tests reason, and reason tests experience [Novalis] |
19590 | Empiricists are passive thinkers, given their philosophy by the external world and fate [Novalis] |
9126 | Bayesians build near-certainty from lots of reasonably probable beliefs [Sorensen] |
9121 | Illusions are not a reason for skepticism, but a source of interesting scientific information [Sorensen] |
19594 | General statements about nature are not valid [Novalis] |
19591 | Desire for perfection is an illness, if it turns against what is imperfect [Novalis] |
19596 | The whole body is involved in the formation of thoughts [Novalis] |
19573 | The seat of the soul is where our inner and outer worlds interpenetrate [Novalis] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
19577 | Everything is a chaotic unity, then we abstract, then we reunify the world into a free alliance [Novalis] |
9134 | The negation of a meaningful sentence must itself be meaningful [Sorensen] |
9133 | Propositions are what settle problems of ambiguity in sentences [Sorensen] |
19585 | Every person has his own language [Novalis] |
19578 | Only self-illuminated perfect individuals are beautiful [Novalis] |
19582 | Morality and philosophy are mutually dependent [Novalis] |
22027 | Life isn't given to us like a novel - we write the novel [Novalis] |
19589 | The whole point of a monarch is that we accept them as a higher-born, ideal person [Novalis] |
9129 | I can buy any litre of water, but not every litre of water [Sorensen] |
19580 | If the pupil really yearns for the truth, they only need a hint [Novalis] |
19593 | Persons are shaped by a life history; splendid persons are shaped by world history [Novalis] |
19595 | Nature is a whole, and its individual parts cannot be wholly understood [Novalis] |
19592 | The basic relations of nature are musical [Novalis] |
9122 | God cannot experience unwanted pain, so God cannot understand human beings [Sorensen] |
19576 | Religion needs an intermediary, because none of us can connect directly to a godhead [Novalis] |