Combining Texts

All the ideas for 'Matters of Mind', 'Elements of Set Theory' and 'fragments/reports'

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17 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
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
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
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
We can only define functions if Choice tells us which items are involved [Enderton]
5. Theory of Logic / L. Paradox / 1. Paradox
If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
15. Nature of Minds / A. Nature of Mind / 1. Mind / e. Questions about mind
Mindless bodies are zombies, bodiless minds are ghosts [Sturgeon]
Types are properties, and tokens are events. Are they split between mental and physical, or not? [Sturgeon]
15. Nature of Minds / B. Features of Minds / 5. Qualia / b. Qualia and intentionality
Intentionality isn't reducible, because of its experiential aspect [Sturgeon]
17. Mind and Body / D. Property Dualism / 1. Reductionism critique
Rule-following can't be reduced to the physical [Sturgeon]
17. Mind and Body / E. Mind as Physical / 5. Causal Argument
The main argument for physicalism is its simple account of causation [Sturgeon]
18. Thought / C. Content / 10. Causal Semantics
Do facts cause thoughts, or embody them, or what? [Sturgeon]