28 ideas
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] |
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] |
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] |
16014 | It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan] |
16024 | I could have died at five, but the summation of my adult stages could not [Noonan] |
16023 | Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan] |
16015 | Problems about identity can't even be formulated without the concept of identity [Noonan] |
16017 | Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan] |
16016 | Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan] |
16020 | Identity can only be characterised in a second-order language [Noonan] |
16018 | Indiscernibility is basic to our understanding of identity and distinctness [Noonan] |
16019 | Leibniz's Law must be kept separate from the substitutivity principle [Noonan] |
19718 | Indefeasibility does not imply infallibility [Grundmann] |
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] |
19719 | 'Moderate' foundationalism has basic justification which is defeasible [Grundmann] |