17 ideas
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
6215 | 'Contingent' means that the cause is unperceived, not that there is no cause [Hobbes] |