Combining Texts

All the ideas for 'Through the Looking Glass', 'The Mysterious Flame' and 'Elements of Set Theory'

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17 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Philosophy is a magnificent failure in its attempt to overstep the limits of our knowledge [McGinn]
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 / E. Structures of Logic / 1. Logical Form
Thoughts have a dual aspect: as they seem to introspection, and their underlying logical reality [McGinn]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Mental modules for language, social, action, theory, space, emotion [McGinn]
16. Persons / F. Free Will / 1. Nature of Free Will
Free will is mental causation in action [McGinn]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
Brains aren't made of anything special, suggesting panpsychism [McGinn]
17. Mind and Body / D. Property Dualism / 6. Mysterianism
Examining mind sees no brain; examining brain sees no mind [McGinn]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
There is information if there are symbols which refer, and which can combine into a truth or falsehood [McGinn]
26. Natural Theory / C. Causation / 4. Naturalised causation
Causation in the material world is energy-transfer, of motion, electricity or gravity [McGinn]