Combining Texts

All the ideas for 'Realism in Mathematics', 'Elements of Set Theory' and 'Troubles with Functionalism'

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25 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8755 Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10718 A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
8756 Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17733 We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
15. Nature of Minds / B. Features of Minds / 5. Qualia / a. Nature of qualia
2584 Lobotomised patients can cease to care about a pain [Block]
15. Nature of Minds / B. Features of Minds / 5. Qualia / c. Explaining qualia
2582 A brain looks no more likely than anything else to cause qualia [Block]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
2574 Behaviour requires knowledge as well as dispositions [Block]
17. Mind and Body / C. Functionalism / 1. Functionalism
2575 Functionalism is behaviourism, but with mental states as intermediaries [Block]
2576 In functionalism, desires are internal states with causal relations [Block]
2583 You might invert colours, but you can't invert beliefs [Block]
17. Mind and Body / C. Functionalism / 8. Functionalism critique
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]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
2579 Physicalism is prejudiced in favour of our neurology, when other systems might have minds [Block]
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / b. Turing Machines
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]
19. Language / C. Assigning Meanings / 1. Syntax
2581 Intuition may say that a complex sentence is ungrammatical, but linguistics can show that it is not [Block]