20 ideas
9327 | Organisms understand their worlds better if they understand themselves [Gulick] |
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] |
9325 | In contrast with knowledge, the notion of understanding emphasizes practical engagement [Gulick] |
9326 | Knowing-that is a much richer kind of knowing-how [Gulick] |
9319 | Is consciousness a type of self-awareness, or is being self-aware a way of being conscious? [Gulick] |
9320 | Higher-order theories divide over whether the higher level involves thought or perception [Gulick] |
9321 | Higher-order models reduce the problem of consciousness to intentionality [Gulick] |
9322 | Maybe qualia only exist at the lower level, and a higher-level is needed for what-it-is-like [Gulick] |
9324 | From the teleopragmatic perspective, life is largely an informational process [Gulick] |