29 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
2584 | Lobotomised patients can cease to care about a pain [Block] |
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] |
2581 | Intuition may say that a complex sentence is ungrammatical, but linguistics can show that it is not [Block] |
8659 | The gods alone live forever with Shamash. The days of humans are numbered. [Anon (Gilg)] |