26 ideas
15647 | Truth definitions don't produce a good theory, because they go beyond your current language [Halbach] |
15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
15655 | Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach] |
15654 | If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach] |
15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach] |
15656 | Deflationists say truth merely serves to express infinite conjunctions [Halbach] |
15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
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] |
5637 | Nowadays logic is seen as the science of extensions, not intensions [Scruton] |
15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
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] |
5636 | Cartesian 'ideas' confuse concepts and propositions [Scruton] |
5660 | Allegiance is prior to the recognition of individual rights [Scruton] |
5653 | A right is a power which is enforced in the name of justice [Scruton] |