69 ideas
18330 | Judging by the positive forces, the Renaissance was the last great age [Nietzsche] |
2900 | I revere Heraclitus [Nietzsche] |
2913 | Thucydides was the perfect anti-platonist sophist [Nietzsche] |
2909 | Thinking has to be learned in the way dancing has to be learned [Nietzsche] |
2892 | Wanting a system in philosophy is a lack of integrity [Nietzsche] |
2896 | I want to understand the Socratic idea that 'reason equals virtue equals happiness' [Nietzsche] |
2897 | With dialectics the rabble gets on top [Nietzsche] |
2898 | Anything which must first be proved is of little value [Nietzsche] |
13520 | A 'tautology' must include connectives [Wolf,RS] |
13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
18317 | The 'real being' of things is a nothingness constructed from contradictions in the actual world [Nietzsche] |
18315 | We get the concept of 'being' from the concept of the 'ego' [Nietzsche] |
18316 | The grounds for an assertion that the world is only apparent actually establish its reality [Nietzsche] |
18314 | In language we treat 'ego' as a substance, and it is thus that we create the concept 'thing' [Nietzsche] |
18309 | The evidence of the senses is falsified by reason [Nietzsche] |
18323 | Any explanation will be accepted as true if it gives pleasure and a feeling of power [Nietzsche] |
18310 | The 'highest' concepts are the most general and empty concepts [Nietzsche] |
20368 | There are no 'individual' persons; we are each the sum of humanity up to this moment [Nietzsche] |
2899 | The fanatical rationality of Greek philosophy shows that they were in a state of emergency [Nietzsche] |
18313 | The big error is to think the will is a faculty producing effects; in fact, it is just a word [Nietzsche] |
20133 | The 'motive' is superficial, and may even hide the antecedents of a deed [Nietzsche] |
18326 | The beautiful never stands alone; it derives from man's pleasure in man [Nietzsche] |
20101 | Without music life would be a mistake [Nietzsche] |
2902 | Healthy morality is dominated by an instinct for life [Nietzsche] |
18311 | Philosophers hate values having an origin, and want values to be self-sufficient [Nietzsche] |
18324 | There are no moral facts, and moralists believe in realities which do not exist [Nietzsche] |
2904 | The doctrine of free will has been invented essentially in order to blame and punish people [Nietzsche] |
4375 | Evaluations are not disguised emotions; instead, emotion is a type of evaluation [Achtenberg] |
2895 | The value of life cannot be estimated [Nietzsche] |
18322 | When we establish values, that is life itself establishing them, through us [Nietzsche] |
2893 | In every age the wisest people have judged life to be worthless [Nietzsche] |
18308 | A philosopher fails in wisdom if he thinks the value of life is a problem [Nietzsche] |
2894 | Value judgements about life can never be true [Nietzsche] |
18321 | To evaluate life one must know it, but also be situated outside of it [Nietzsche] |
18319 | Love is the spiritualisation of sensuality [Nietzsche] |
2903 | A good human will be virtuous because they are happy [Nietzsche] |
2891 | Only the English actually strive after happiness [Nietzsche] |
18327 | A wholly altruistic morality, with no egoism, is a thoroughly bad thing [Nietzsche] |
15606 | Military idea: what does not kill me makes me stronger [Nietzsche] |
18328 | Invalids are parasites [Nietzsche] |
18331 | Democracy is organisational power in decline [Nietzsche] |
18332 | The creation of institutions needs a determination which is necessarily anti-liberal [Nietzsche] |
2911 | True justice is equality for equals and inequality for unequals [Nietzsche] |
18320 | To renounce war is to renounce the grand life [Nietzsche] |
2908 | There is a need for educators who are themselves educated [Nietzsche] |
18329 | Sometimes it is an error to have been born - but we can rectify it [Nietzsche] |
2905 | 'Purpose' is just a human fiction [Nietzsche] |
18312 | The supreme general but empty concepts must be compatible, and hence we get 'God' [Nietzsche] |
2906 | By denying God we deny human accountability, and thus we redeem the world [Nietzsche] |
2901 | How could the Church intelligently fight against passion if it preferred poorness of spirit to intelligence? [Nietzsche] |
18325 | Christians believe that only God can know what is good for man [Nietzsche] |
18318 | People who disparage actual life avenge themselves by imagining a better one [Nietzsche] |