Combining Texts

All the ideas for 'Alfred Tarski: life and logic', 'A Philosophy of Boredom' and 'Counting and the Natural Numbers'

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26 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
9307 Modern Western culture suddenly appeared in Jena in the 1790s [Svendsen]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
9297 You can't understand love in terms of 'if and only if...' [Svendsen]
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 / 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 / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
17423 The essence of natural numbers must reflect all the functions they perform [Sicha]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17425 To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha]
17424 Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
9308 If subjective and objective begin to merge, then so do primary and secondary qualities [Svendsen]
18. Thought / A. Modes of Thought / 3. Emotions / b. Types of emotion
9309 Emotions have intentional objects, while a mood is objectless [Svendsen]
22. Metaethics / B. Value / 2. Values / e. Death
9304 Death appears to be more frightening the less one has lived [Svendsen]
23. Ethics / F. Existentialism / 4. Boredom
9298 We can be unaware that we are bored [Svendsen]
9301 Boredom is so radical that suicide could not overcome it; only never having existed would do it [Svendsen]
9302 We are bored because everything comes to us fully encoded, and we want personal meaning [Svendsen]
9310 The profoundest boredom is boredom with boredom [Svendsen]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
9311 We have achieved a sort of utopia, and it is boring, so that is the end of utopias [Svendsen]
24. Political Theory / D. Ideologies / 9. Communism
9303 The concept of 'alienation' seems no longer applicable [Svendsen]