Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'The Ultimate Constituents of Matter' and 'Alfred Tarski: life and logic'

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22 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10147 The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman]
10148 Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman]
10149 Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman]
10150 The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman]
10146 Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
7548 Classes, grouped by a convenient property, are logical constructions [Russell]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10158 A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
10162 Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10160 Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
10159 Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10161 If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 7. Decidability
10156 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
10155 Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
7. Existence / D. Theories of Reality / 4. Anti-realism
7545 Visible things are physical and external, but only exist when viewed [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
7553 Sense-data are purely physical [Russell]
7549 If my body literally lost its mind, the object seen when I see a flash would still exist [Russell]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
7546 A man is a succession of momentary men, bound by continuity and causation [Russell]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
7550 We could probably, in principle, infer minds from brains, and brains from minds [Russell]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
7551 Matter is a logical construction [Russell]
7547 Matter requires a division into time-corpuscles as well as space-corpuscles [Russell]
27. Natural Reality / C. Space / 2. Space
7552 Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell]