128 ideas
23890 | For Plato true wisdom is supernatural [Plato, by Weil] |
18330 | Judging by the positive forces, the Renaissance was the last great age [Nietzsche] |
3060 | Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius] |
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] |
23891 | Two contradictories force us to find a relation which will correlate them [Plato, by Weil] |
2897 | With dialectics the rabble gets on top [Nietzsche] |
18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
2898 | Anything which must first be proved is of little value [Nietzsche] |
18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
18114 | There is no single agreed structure for set theory [Bostock] |
18107 | A 'proper class' cannot be a member of anything [Bostock] |
18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
18109 | The completeness of first-order logic implies its compactness [Bostock] |
18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
18097 | The Peano Axioms describe a unique structure [Bostock] |
18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
18149 | There are many criteria for the identity of numbers [Bostock] |
18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
18140 | The best version of conceptualism is predicativism [Bostock] |
18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
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] |
14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
17948 | Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas] |
20906 | Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle] |
3039 | When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius] |
556 | If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato] |
563 | If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato] |
557 | A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato] |
565 | The Forms cannot be changeless if they are in changing things [Aristotle on Plato] |
9607 | The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato] |
13263 | We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki] |
18314 | In language we treat 'ego' as a substance, and it is thus that we create the concept 'thing' [Nietzsche] |
13265 | Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki] |
13261 | Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki] |
593 | Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle] |
13260 | Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki] |
11237 | Only universals have essence [Plato, by Politis] |
11238 | Plato and Aristotle take essence to make a thing what it is [Plato, by Politis] |
18309 | The evidence of the senses is falsified by reason [Nietzsche] |
17085 | A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben] |
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] |
1651 | Plato wanted to somehow control and purify the passions [Vlastos on Plato] |
2899 | The fanatical rationality of Greek philosophy shows that they were in a state of emergency [Nietzsche] |
3324 | Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato] |
18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
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] |
7503 | Plato never refers to examining the conscience [Plato, by Foucault] |
2173 | As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato] |
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] |
9274 | Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray] |
2903 | A good human will be virtuous because they are happy [Nietzsche] |
94 | Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle] |
2891 | Only the English actually strive after happiness [Nietzsche] |
17947 | Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas] |
18327 | A wholly altruistic morality, with no egoism, is a thoroughly bad thing [Nietzsche] |
6015 | Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut] |
15606 | Military idea: what does not kill me makes me stronger [Nietzsche] |
18328 | Invalids are parasites [Nietzsche] |
2912 | Plato is boring [Nietzsche on Plato] |
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] |
1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |
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] |