Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'Truth and the Past' and 'Alfred Tarski: life and logic'

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27 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 / D. Assumptions for Logic / 1. Bivalence
8195 Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett]
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]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
8194 Surely there is no exact single grain that brings a heap into existence [Dummett]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10580 Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
10579 Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8190 Intuitionists rely on the proof of mathematical statements, not their truth [Dummett]
7. Existence / B. Change in Existence / 1. Nature of Change
8198 A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
10577 Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
10578 We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
7. Existence / D. Theories of Reality / 4. Anti-realism
8192 I no longer think what a statement about the past says is just what can justify it [Dummett]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
8199 The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
8193 Verification is not an individual but a collective activity [Dummett]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
8189 Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett]
8191 The truth-conditions theory must get agreement on a conception of truth [Dummett]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
8197 Maybe past (which affects us) and future (which we can affect) are both real [Dummett]
27. Natural Reality / D. Time / 2. Passage of Time / k. Temporal truths
8196 The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett]