33 ideas
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] |
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] |
3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
2584 | Lobotomised patients can cease to care about a pain [Block] |
6172 | The Inverted Earth example shows that phenomenal properties are not representational [Block, by Rowlands] |
2582 | A brain looks no more likely than anything else to cause qualia [Block] |
2574 | Behaviour requires knowledge as well as dispositions [Block] |
2576 | In functionalism, desires are internal states with causal relations [Block] |
2575 | Functionalism is behaviourism, but with mental states as intermediaries [Block] |
2583 | You might invert colours, but you can't invert beliefs [Block] |
2578 | Could a creature without a brain be in the right functional state for pain? [Block] |
2585 | Not just any old functional network will have mental states [Block] |
2586 | In functionalism, what are the special inputs and outputs of conscious creatures? [Block] |
2579 | Physicalism is prejudiced in favour of our neurology, when other systems might have minds [Block] |
2577 | Simple machine-functionalism says mind just is a Turing machine [Block] |
2580 | A Turing machine, given a state and input, specifies an output and the next state [Block] |
3178 | A fast machine could pass all behavioural tests with a vast lookup table [Block, by Rey] |
18033 | The meaning of a representation is its role in thought, perception or decisions [Block] |
2581 | Intuition may say that a complex sentence is ungrammatical, but linguistics can show that it is not [Block] |