25 ideas
8820 | Rules of reasoning precede the concept of truth, and they are what characterize it [Pollock] |
8819 | We need the concept of truth for defeasible reasoning [Pollock] |
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] |
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] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
8822 | Statements about necessities need not be necessarily true [Pollock] |
8818 | Defeasible reasoning requires us to be able to think about our thoughts [Pollock] |
8811 | What we want to know is - when is it all right to believe something? [Pollock] |
8817 | Logical entailments are not always reasons for beliefs, because they may be irrelevant [Pollock] |
8814 | Epistemic norms are internalised procedural rules for reasoning [Pollock] |
8823 | Reasons are always for beliefs, but a perceptual state is a reason without itself being a belief [Pollock] |
8813 | If we have to appeal explicitly to epistemic norms, that will produce an infinite regress [Pollock] |
8812 | Norm Externalism says norms must be internal, but their selection is partly external [Pollock] |
8816 | Externalists tend to take a third-person point of view of epistemology [Pollock] |
8815 | Belief externalism is false, because external considerations cannot be internalized for actual use [Pollock] |
3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |