48 ideas
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
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] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
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] |