Combining Texts

All the ideas for 'Issues of Pragmaticism', 'On the Ultimate Origination of Things' and 'Alfred Tarski: life and logic'

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20 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
19336 Wisdom involves the desire to achieve perfection [Leibniz]
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
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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
7696 Leibniz first asked 'why is there something rather than nothing?' [Leibniz, by Jacquette]
19341 There must be a straining towards existence in the essence of all possible things [Leibniz]
19428 Because something does exist, there must be a drive in possible things towards existence [Leibniz]
10. Modality / A. Necessity / 7. Natural Necessity
5047 The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz]
19. Language / A. Nature of Meaning / 1. Meaning
19087 The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
19343 We follow the practical rule which always seeks maximum effect for minimum cost [Leibniz]
26. Natural Theory / A. Speculations on Nature / 1. Nature
19429 The principle of determination in things obtains the greatest effect with the least effort [Leibniz]