Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'Axiomatic Theories of Truth (2013 ver)' and 'The Structure of Empirical Knowledge'

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24 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
19125 If we define truth, we can eliminate it [Halbach/Leigh]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
19128 If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
19120 Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh]
3. Truth / F. Semantic Truth / 2. Semantic Truth
19127 The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
19124 A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]
19126 If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
19129 The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
19130 KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
8. Modes of Existence / B. Properties / 12. Denial of Properties
19121 We can reduce properties to true formulas [Halbach/Leigh]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
19122 Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
21506 A coherence theory of justification can combine with a correspondence theory of truth [Bonjour]
21509 There will always be a vast number of equally coherent but rival systems [Bonjour]
21503 Empirical coherence must attribute reliability to spontaneous experience [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
21511 A well written novel cannot possibly match a real belief system for coherence [Bonjour]
21510 The objection that a negated system is equally coherent assume that coherence is consistency [Bonjour]
21505 A coherent system can be justified with initial beliefs lacking all credibility [Bonjour]
21504 The best explanation of coherent observations is they are caused by and correspond to reality [Bonjour]
14. Science / A. Basis of Science / 5. Anomalies
21508 Anomalies challenge the claim that the basic explanations are actually basic [Bonjour]