Combining Philosophers

All the ideas for Dougherty,T/Rysiew,P, R Martin / J Barresi and Feferman / Feferman

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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]
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]
11. Knowledge Aims / A. Knowledge / 2. Understanding
19542 It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew]
19543 To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew]
11. Knowledge Aims / A. Knowledge / 7. Knowledge First
19541 Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
19540 Don't confuse justified belief with justified believers [Dougherty/Rysiew]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
19539 If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
5504 Maybe we should see persons in four dimensions, with stages or time-slices at an instant [Martin/Barresi]
5503 Maybe personal identity is not vital in survival, and other continuations would suffice [Martin/Barresi]
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
5502 Locke's intrinsic view of personal identity has been replaced by an externalist view [Martin/Barresi]
19. Language / C. Assigning Meanings / 2. Semantics
19538 Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
5505 For Aristotle the psyche perishes with the body (except possibly 'nous') [Martin/Barresi]