48 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] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
24137 | Mathematics is just accurate inferences from definitions, and doesn't involve objects [Nietzsche] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
10763 | Completeness and compactness together give axiomatizability [Tharp] |
10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
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] |
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] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
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] |
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] |