65 ideas
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] |
17774 | Definitions make our intuitions mathematically useful [Mayberry] |
17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
23199 | What is the search for truth if it isn't moral? [Nietzsche] |
23202 | Like all philosophers, I love truth [Nietzsche] |
17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
17803 | Limitation of size is part of the very conception of a set [Mayberry] |
17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
23196 | Logic is a fiction, which invents the view that one thought causes another [Nietzsche] |
17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
23186 | Numbers enable us to manage the world - to the limits of counting [Nietzsche] |
17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
23211 | Events are just interpretations of groups of appearances [Nietzsche] |
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
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] |
23209 | Each of our personal drives has its own perspective [Nietzsche] |
23184 | The mind is a simplifying apparatus [Nietzsche] |
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] |
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] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
23195 | Laws of nature are actually formulas of power relations [Nietzsche] |
23185 | In chemistry every substance pushes, and thus creates new substances [Nietzsche] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |