31 ideas
22659 | It is wisdom to believe what you desire, because belief is needed to achieve it [James] |
22657 | All good philosophers start from a dumb conviction about which truths can be revealed [James] |
22647 | A complete system is just a classification of the whole world's ingredients [James] |
22648 | A single explanation must have a single point of view [James] |
22644 | Our greatest pleasure is the economy of reducing chaotic facts to one single fact [James] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
22649 | Classification can only ever be for a particular purpose [James] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
22655 | Scientific genius extracts more than other people from the same evidence [James] |
22658 | Experimenters assume the theory is true, and stick to it as long as result don't disappoint [James] |
22654 | We can't know if the laws of nature are stable, but we must postulate it or assume it [James] |
22656 | Trying to assess probabilities by mere calculation is absurd and impossible [James] |
22646 | We have a passion for knowing the parts of something, rather than the whole [James] |
22652 | The mind has evolved entirely for practical interests, seen in our reflex actions [James] |
22651 | Dogs' curiosity only concerns what will happen next [James] |
22650 | How can the ground of rationality be itself rational? [James] |
22643 | It seems that we feel rational when we detect no irrationality [James] |
22660 | Evolution suggests prevailing or survival as a new criterion of right and wrong [James] |
22645 | Understanding by means of causes is useless if they are not reduced to a minimum number [James] |
22653 | Early Christianity says God recognises the neglected weak and tender impulses [James] |