Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'Alfred Tarski: life and logic' and 'On Concept and Object'

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24 ideas

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 / E. Structures of Logic / 1. Logical Form
4975 A thought can be split in many ways, so that different parts appear as subject or predicate [Frege]
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
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]
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]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
9949 There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman]
7. Existence / A. Nature of Existence / 5. Reason for Existence
19400 Possibles demand existence, so as many of them as possible must actually exist [Leibniz]
19401 God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18995 Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
10317 It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale]
9. Objects / A. Existence of Objects / 3. Objects in Thought
10535 Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
19402 The actual universe is the richest composite of what is possible [Leibniz]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9839 Frege equated the concepts under which an object falls with its properties [Frege, by Dummett]
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
4973 As I understand it, a concept is the meaning of a grammatical predicate [Frege]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
9167 Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
4974 For all the multiplicity of languages, mankind has a common stock of thoughts [Frege]