Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'Alfred Tarski: life and logic' and 'On Propositions: What they are, and Meaning'

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24 ideas

3. Truth / A. Truth Problems / 5. Truth Bearers
5784 In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell]
3. Truth / B. Truthmakers / 1. For Truthmakers
5777 The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
5783 Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell]
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
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]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
19402 The actual universe is the richest composite of what is possible [Leibniz]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
5780 The three questions about belief are its contents, its success, and its character [Russell]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
5778 If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
5779 There are distinct sets of psychological and physical causal laws [Russell]
19. Language / D. Propositions / 1. Propositions
5781 Our important beliefs all, if put into words, take the form of propositions [Russell]
5782 A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell]
5776 A proposition is what we believe when we believe truly or falsely [Russell]