64 ideas
24146 | All the major problems were formulated before Socrates [Nietzsche] |
24142 | What matters is how humans can be developed [Nietzsche] |
24143 | Thinkers might agree some provisional truths, as methodological assumptions [Nietzsche] |
24125 | Aristotle enjoyed the sham generalities of a system, as the peak of happiness! [Nietzsche] |
24147 | Thoughts are uncertain, and are just occasions for interpretation [Nietzsche] |
17774 | Definitions make our intuitions mathematically useful [Mayberry] |
17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
17796 | There is a semi-categorical axiomatisation of set-theory [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] |
24137 | Mathematics is just accurate inferences from definitions, and doesn't involve objects [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] |
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] |
24131 | There is no 'being'; it is just the opposition to nothingness [Nietzsche] |
24151 | I only want thinking that is anchored in body, senses and earth [Nietzsche] |
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
24150 | We can only understand through concepts, which subsume particulars in generalities [Nietzsche] |
24138 | Strongly believed a priori is not certain; it may just be a feature of our existence [Nietzsche] |
24130 | An affirmative belief is present in every basic sense impression [Nietzsche] |
24124 | We now have innumerable perspectives to draw on [Nietzsche] |
24145 | Mind is a mechanism of abstraction and simplification, aimed at control [Nietzsche] |
24144 | A cognitive mechanism wanting to know itself is absurd! [Nietzsche] |
24139 | A 'person' is just one possible abstraction from a bundle of qualities [Nietzsche] |
24133 | I have perfected fatalism, as recurrence and denial of the will [Nietzsche] |
24152 | Fate is inspiring, if you understand you are part of it [Nietzsche] |
24129 | We start with images, then words, and then concepts, to which emotions attach [Nietzsche] |
24127 | Judging actions by intentions - like judging painters by their thoughts! [Nietzsche] |
24149 | Values need a perspective, of preserving some aspect of life [Nietzsche] |
24148 | If you love something, it is connected with everything, so all must be affirmed as good [Nietzsche] |
24135 | Egoism should not assume that all egos are equal [Nietzsche] |
24132 | After Socrates virtue is misunderstood, as good for all, not for individuals [Nietzsche] |
24126 | We contain multitudes of characters, which can brought into the open [Nietzsche] |
24136 | Who can endure the thought of eternal recurrence? [Nietzsche] |
24154 | If you want one experience repeated, you must want all of them [Nietzsche] |
24153 | Humans are determined by community, so its preservation is their most valued drive [Nietzsche] |
24134 | There is always slavery, whether we like it or not [Nietzsche] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
24128 | After history following God, or a people, or an idea, we now see it in terms of animals [Nietzsche] |
24140 | Cause and effect is a hypothesis, based on our supposed willing of actions [Nietzsche] |
24141 | Having a sense of time presupposes absolute time [Nietzsche] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |