20 ideas
9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
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] |
9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
9342 | Understanding needs a priori commitment [Horwich] |
9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
7073 | I am a creative nothing, out of which I myself create everything [Stirner] |