Combining Texts

All the ideas for 'Alfred Tarski: life and logic', 'Phil Applications of Cognitive Science' and 'Defeasibility Theory'

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25 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]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
4045 Children may have three innate principles which enable them to learn to count [Goldman]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
4044 Rat behaviour reveals a considerable ability to count [Goldman]
7. Existence / E. Categories / 2. Categorisation
4048 Infant brains appear to have inbuilt ontological categories [Goldman]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
19718 Indefeasibility does not imply infallibility [Grundmann]
12. Knowledge Sources / B. Perception / 3. Representation
4043 Elephants can be correctly identified from as few as three primitive shapes [Goldman]
12. Knowledge Sources / B. Perception / 5. Interpretation
4049 The way in which colour experiences are evoked is physically odd and unpredictable [Goldman]
12. Knowledge Sources / D. Empiricism / 2. Associationism
4047 Gestalt psychology proposes inbuilt proximity, similarity, smoothness and closure principles [Goldman]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
19717 Can a defeater itself be defeated? [Grundmann]
19716 Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann]
19715 You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann]
19713 Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann]
19714 Knowledge requires that there are no facts which would defeat its justification [Grundmann]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
19719 'Moderate' foundationalism has basic justification which is defeasible [Grundmann]