150 ideas
23890 | For Plato true wisdom is supernatural [Plato, by Weil] |
7170 | 'Wisdom' attempts to get beyond perspectives, making it hostile to life [Nietzsche] |
3060 | Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius] |
7167 | Words such as 'I' and 'do' and 'done to' are placed at the point where our ignorance begins [Nietzsche] |
7196 | Pessimism is laughable, because the world cannot be evaluated [Nietzsche] |
7137 | Is a 'philosopher' now impossible, because knowledge is too vast for an overview? [Nietzsche] |
7132 | Philosophers should create and fight for their concepts, not just clean and clarify them [Nietzsche] |
23891 | Two contradictories force us to find a relation which will correlate them [Plato, by Weil] |
15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
7188 | Logic tries to understand the world according to a man-made scheme [Nietzsche] |
7145 | Logic is not driven by truth, but desire for a simple single viewpoint [Nietzsche] |
7144 | Logic must falsely assume that identical cases exist [Nietzsche] |
10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
18176 | Pure mathematics is pure set theory [Cantor] |
8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
7153 | We can't be realists, because we don't know what being is [Nietzsche] |
7174 | Categories are not metaphysical truths, but inventions in the service of needs [Nietzsche] |
7175 | Philosophers find it particularly hard to shake off belief in necessary categories [Nietzsche] |
14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
20906 | Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle] |
17948 | Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas] |
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] |
7189 | Maybe there are only subjects, and 'objects' result from relations between subjects [Nietzsche] |
7207 | Counting needs unities, but that doesn't mean they exist; we borrowed it from the concept of 'I' [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] |
7161 | The essence of a thing is only an opinion about the 'thing' [Nietzsche] |
7134 | Something can be irrefutable; that doesn't make it true [Nietzsche] |
7186 | There are no necessary truths, but something must be held to be true [Nietzsche] |
7154 | We can't use our own self to criticise our own capacity for knowledge! [Nietzsche] |
7146 | Belief in the body is better established than belief in the mind [Nietzsche] |
7156 | Sense perceptions contain values (useful, so pleasant) [Nietzsche] |
7181 | Pain shows the value of the damage, not what has been damaged [Nietzsche] |
7129 | Perception is unconscious, and we are only conscious of processed perceptions [Nietzsche] |
7149 | Comprehending everything is impossible, because it abolishes perspectives [Nietzsche] |
7169 | Is the perspectival part of the essence, or just a relation between beings? [Nietzsche] |
7182 | 'Perspectivism': the world has no meaning, but various interpretations give it countless meanings [Nietzsche] |
7183 | 'Subjectivity' is an interpretation, since subjects (and interpreters) are fictions [Nietzsche] |
7133 | There are different eyes, so different 'truths', so there is no truth [Nietzsche] |
7139 | Explanation is just showing the succession of things ever more clearly [Nietzsche] |
17085 | A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben] |
7131 | The intellect and senses are a simplifying apparatus [Nietzsche] |
7152 | With protoplasm ½+½=2, so the soul is not an indivisible monad [Nietzsche] |
7130 | Unity is not in the conscious 'I', but in the organism, which uses the self as a tool [Nietzsche] |
7155 | Consciousness exists to the extent that consciousness is useful [Nietzsche] |
7143 | Consciousness is a 'tool' - just as the stomach is a tool [Nietzsche] |
7157 | We think each thought causes the next, unaware of the hidden struggle beneath [Nietzsche] |
7148 | The 'I' is a conceptual synthesis, not the governor of our being [Nietzsche] |
7138 | The 'I' is a fiction used to make the world of becoming 'knowable' [Nietzsche] |
7135 | 'Freedom of will' is the feeling of having a dominating force [Nietzsche] |
1651 | Plato wanted to somehow control and purify the passions [Vlastos on Plato] |
7171 | Rationality is a scheme we cannot cast away [Nietzsche] |
8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
3324 | Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato] |
7209 | There is no will; weakness of will is splitting of impulses, strong will is coordination under one impulse [Nietzsche] |
7194 | Experiencing a thing as beautiful is to experience it wrongly [Nietzsche] |
7136 | Morality is a system of values which accompanies a being's life [Nietzsche] |
7163 | Morality is merely interpretations, which are extra-moral in origin [Nietzsche] |
7503 | Plato never refers to examining the conscience [Plato, by Foucault] |
7147 | Values are innate and inherited [Nietzsche] |
7190 | Our values express an earlier era's conditions for survival and growth [Nietzsche] |
2173 | As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato] |
7201 | Knowledge, wisdom and goodness only have value relative to a goal [Nietzsche] |
7205 | Altruism is praised by the egoism of the weak, who want everyone to be looked after [Nietzsche] |
7141 | A living being is totally 'egoistic' [Nietzsche] |
9274 | Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray] |
94 | Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle] |
7168 | Modest people express happiness as 'Not bad' [Nietzsche] |
17947 | Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas] |
7159 | The only happiness is happiness with illusion [Nietzsche] |
7197 | Pleasure needs dissatisfaction, boundaries and resistances [Nietzsche] |
6015 | Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut] |
7165 | Virtue is wasteful, as it reduces us all to being one another's nurse [Nietzsche] |
7193 | Virtue for everyone removes its charm of being exceptional and aristocratic [Nietzsche] |
7191 | What does not kill us makes us stronger [Nietzsche] |
7151 | Courage, compassion, insight, solitude are the virtues, with courtesy a necessary vice [Nietzsche] |
7185 | Replace the categorical imperative by the natural imperative [Nietzsche] |
7164 | Not feeling harnessed to a system of 'ends' is a wonderful feeling of freedom [Nietzsche] |
7198 | Nihilism results from measuring the world by our categories which are purely invented [Nietzsche] |
2912 | Plato is boring [Nietzsche on Plato] |
7150 | By developing herd virtues man fixes what has up to now been the 'unfixed animal' [Nietzsche] |
7177 | Virtues from outside are dangerous, and they should come from within [Nietzsche] |
7172 | Existence without meaning or goal or end, eternally recurring, is a terrible thought [Nietzsche] |
7166 | Man is above all a judging animal [Nietzsche] |
7204 | The upholding of the military state is needed to maintain the strong human type [Nietzsche] |
7173 | Rights arise out of contracts, which need a balance of power [Nietzsche] |
7176 | 'Purpose' is like the sun, where most heat is wasted, and a tiny part has 'purpose' [Nietzsche] |
7195 | If the world aimed at an end, it would have reached it by now [Nietzsche] |
7206 | Things are strong or weak, and do not behave regularly or according to rules or compulsions [Nietzsche] |
7140 | Chemical 'laws' are merely the establishment of power relations between weaker and stronger [Nietzsche] |
7142 | All motions and 'laws' are symptoms of inner events, traceable to the will to power [Nietzsche] |
10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |
7178 | The utility of an organ does not explain its origin, on the contrary! [Nietzsche] |
7179 | Survival might undermine an individual's value, or prevent its evolution [Nietzsche] |
7180 | Darwin overestimates the influence of 'external circumstances' [Nietzsche] |
13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
7192 | Remove goodness and wisdom from our concept of God. Being the highest power is enough! [Nietzsche] |
7158 | Morality kills religion, because a Christian-moral God is unbelievable [Nietzsche] |
7199 | It is dishonest to invent a being containing our greatest values, thus ignoring why they exist and are valuable [Nietzsche] |
7162 | Morality can only be upheld by belief in God and a 'hereafter' [Nietzsche] |
7208 | Paganism is a form of thanking and affirming life? [Nietzsche] |
7160 | Christian belief is kept alive because it is soothing - the proof based on pleasure [Nietzsche] |
7203 | In heaven all the interesting men are missing [Nietzsche] |
7200 | A combination of great power and goodness would mean the disastrous abolition of evil [Nietzsche] |