23 ideas
19115 | You can 'rebut' an argument's conclusion, or 'undercut' its premises [Antonelli] |
19119 | We infer that other objects are like some exceptional object, if they share some of its properties [Antonelli] |
19111 | Reasoning may be defeated by new premises, or by finding out more about the given ones [Antonelli] |
19113 | Weakest Link Principle: prefer the argument whose weakest link is the stronger [Antonelli] |
19114 | Should we accept Floating Conclusions, derived from two arguments in conflict? [Antonelli] |
19116 | Non-monotonic core: Reflexivity, Cut, Cautious Monotonicity, Left Logical Equivalence, Right Weakening [Antonelli] |
19117 | We can rank a formula by the level of surprise if it were to hold [Antonelli] |
19118 | People don't actually use classical logic, but may actually use non-monotonic logic [Antonelli] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [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] |
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] |
19110 | In classical logic the relation |= has Monotony built into its definition [Antonelli] |
19112 | Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved [Antonelli] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |