71 ideas
13786 | Wisdom is called 'beautiful', because it performs fine works [Plato] |
13780 | Good people are no different from wise ones [Plato] |
23183 | Different abilities are needed for living in an incomplete and undogmatic system [Nietzsche] |
23188 | Bad writers use shapeless floating splotches of concepts [Nietzsche] |
23212 | A text has many interpretations, but no 'correct' one [Nietzsche] |
13778 | A dialectician is someone who knows how to ask and to answer questions [Plato] |
23199 | What is the search for truth if it isn't moral? [Nietzsche] |
23202 | Like all philosophers, I love truth [Nietzsche] |
13776 | Truths say of what is that it is, falsehoods say of what is that it is not [Plato] |
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] |
23196 | Logic is a fiction, which invents the view that one thought causes another [Nietzsche] |
13777 | A name is a sort of tool [Plato] |
13790 | A name-giver might misname something, then force other names to conform to it [Plato] |
13791 | Things must be known before they are named, so it can't be the names that give us knowledge [Plato] |
13789 | Anyone who knows a thing's name also knows the thing [Plato] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
23186 | Numbers enable us to manage the world - to the limits of counting [Nietzsche] |
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] |
2063 | How can beauty have identity if it changes? [Plato] |
23211 | Events are just interpretations of groups of appearances [Nietzsche] |
13775 | We only succeed in cutting if we use appropriate tools, not if we approach it randomly [Plato] |
13787 | Doesn't each thing have an essence, just as it has other qualities? [Plato] |
13774 | Things don't have every attribute, and essence isn't private, so each thing has an essence [Plato] |
13772 | Is the being or essence of each thing private to each person? [Plato] |
13788 | If we made a perfect duplicate of Cratylus, there would be two Cratyluses [Plato] |
23201 | The 'I' does not think; it is a construction of thinking, like other useful abstractions [Nietzsche] |
23207 | Appearance is the sole reality of things, to which all predicates refer [Nietzsche] |
23197 | Memory is essential, and is only possible by means of abbreviation signs [Nietzsche] |
23206 | Schematic minds think thoughts are truer if they slot into a scheme [Nietzsche] |
13792 | There can't be any knowledge if things are constantly changing [Plato] |
23209 | Each of our personal drives has its own perspective [Nietzsche] |
23184 | The mind is a simplifying apparatus [Nietzsche] |
13781 | Soul causes the body to live, and gives it power to breathe and to be revitalized [Plato] |
23190 | Consciousness is our awareness of our own mental life [Nietzsche] |
23191 | Minds have an excluding drive to scare things off, and a selecting one to filter facts [Nietzsche] |
23213 | The greatest drive of life is to discharge strength, rather than preservation [Nietzsche] |
23210 | That all events are necessary does not mean they are compelled [Nietzsche] |
23189 | Concepts are rough groups of simultaneous sensations [Nietzsche] |
23192 | Concepts don’t match one thing, but many things a little bit [Nietzsche] |
23187 | Whatever their origin, concepts survive by being useful [Nietzsche] |
23205 | Thought starts as ambiguity, in need of interpretation and narrowing [Nietzsche] |
23198 | Aesthetics can be more basic than morality, in our pleasure in certain patterns of experience [Nietzsche] |
23208 | Caesar and Napoleon point to the future, when they pursue their task regardless of human sacrifice [Nietzsche] |
23193 | Napoleon was very focused, and rightly ignored compassion [Nietzsche] |
13785 | 'Arete' signifies lack of complexity and a free-flowing soul [Plato] |
23214 | For the strongest people, nihilism gives you wings! [Nietzsche] |
23203 | The great question is approaching, of how to govern the earth as a whole [Nietzsche] |
23200 | The controlling morality of aristocracy is the desire to resemble their ancestors [Nietzsche] |
23194 | People feel united as a nation by one language, but then want a common ancestry and history [Nietzsche] |
23204 | To be someone you need property, and wanting more is healthy [Nietzsche] |
23195 | Laws of nature are actually formulas of power relations [Nietzsche] |
23185 | In chemistry every substance pushes, and thus creates new substances [Nietzsche] |
13779 | The natural offspring of a lion is called a 'lion' (but what about the offspring of a king?) [Plato] |
13783 | Even the gods love play [Plato] |