Combining Texts

All the ideas for 'Wiener Logik', 'Alfred Tarski: life and logic' and 'Defining 'Intrinsic' (with Rae Langton)'

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19 ideas

2. Reason / D. Definition / 1. Definitions
15457 Interdefinition is useless by itself, but if we grasp one separately, we have them both [Lewis]
2. Reason / D. Definition / 2. Aims of Definition
18261 A simplification which is complete constitutes a definition [Kant]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
22275 Logic gives us the necessary rules which show us how we ought to think [Kant]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10159 Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
10160 Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10161 If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 7. Decidability
10156 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
10155 Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
15400 We must avoid circularity between what is intrinsic and what is natural [Lewis, by Cameron]
15458 A property is 'intrinsic' iff it can never differ between duplicates [Lewis]
15459 Ellipsoidal stars seem to have an intrinsic property which depends on other objects [Lewis]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
18260 If we knew what we know, we would be astonished [Kant]