Ideas of Leon Horsten, by Theme

[Belgian, fl. 2007, Professor at the Catholic University of Leuven, then at University of Bristol.]

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1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
15357 Philosophy is the most general intellectual discipline
2. Reason / D. Definition / 2. Aims of Definition
15352 A definition should allow the defined term to be eliminated
2. Reason / D. Definition / 8. Impredicative Definition
10882 Predicative definitions only refer to entities outside the defined collection
3. Truth / A. Truth Problems / 1. Truth
15323 Truth is a property, because the truth predicate has an extension
15324 Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles
3. Truth / A. Truth Problems / 2. Defining Truth
15374 Truth has no 'nature', but we should try to describe its behaviour in inferences
3. Truth / A. Truth Problems / 5. Truth Bearers
15348 Propositions have sentence-like structures, so it matters little which bears the truth
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
15333 Modern correspondence is said to be with the facts, not with true propositions
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
15337 The correspondence 'theory' is too vague - about both 'correspondence' and 'facts'
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
15334 The coherence theory allows multiple coherent wholes, which could contradict one another
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
15336 The pragmatic theory of truth is relative; useful for group A can be useless for group B
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
15354 Tarski's hierarchy lacks uniform truth, and depends on contingent factors
15340 Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
15345 Semantic theories have a regress problem in describing truth in the languages for the models
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
15373 Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models
15332 'Reflexive' truth theories allow iterations (it is T that it is T that p)
15346 Axiomatic approaches to truth avoid the regress problem of semantic theories
15361 A good theory of truth must be compositional (as well as deriving biconditionals)
15371 An axiomatic theory needs to be of maximal strength, while being natural and sound
15350 The Naďve Theory takes the bi-conditionals as axioms, but it is inconsistent, and allows the Liar
15351 Axiomatic theories take truth as primitive, and propose some laws of truth as axioms
15367 By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content!
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
15330 Friedman-Sheard theory keeps classical logic and aims for maximum strength
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
15331 Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
15325 Inferential deflationism says truth has no essence because no unrestricted logic governs the concept
15344 Deflationism skips definitions and models, and offers just accounts of basic laws of truth
15356 Deflationism concerns the nature and role of truth, but not its laws
15368 This deflationary account says truth has a role in generality, and in inference
15358 Deflationism says truth isn't a topic on its own - it just concerns what is true
15359 Deflation: instead of asserting a sentence, we can treat it as an object with the truth-property
4. Formal Logic / E. Nonclassical Logics / 1. Nonclassical Logics
15329 Nonclassical may accept T/F but deny applicability, or it may deny just T or F as well
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
15326 Doubt is thrown on classical logic by the way it so easily produces the liar paradox
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
15341 Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
15328 A theory is 'non-conservative' if it facilitates new mathematical proofs
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
15349 It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F)
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
15366 Satisfaction is a primitive notion, and very liable to semantical paradoxes
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10884 A theory is 'categorical' if it has just one model up to isomorphism
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
15353 The first incompleteness theorem means that consistency does not entail soundness
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
15355 Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
15364 English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10881 The concept of 'ordinal number' is set-theoretic, not arithmetical
15360 ZFC showed that the concept of set is mathematical, not logical, because of its existence claims
15369 Set theory is substantial over first-order arithmetic, because it enables new proofs
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
15370 Predicativism says mathematical definitions must not include the thing being defined
7. Existence / D. Theories of Reality / 7. Facts / b. Types of fact
15338 We may believe in atomic facts, but surely not complex disjunctive ones?
7. Existence / D. Theories of Reality / 9. Vagueness / f. Supervaluation for vagueness
15363 In the supervaluationist account, disjunctions are not determined by their disjuncts
15362 If 'Italy is large' lacks truth, so must 'Italy is not large'; but classical logic says it's large or it isn't
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
15372 Some claim that indicative conditionals are believed by people, even though they are not actually held true
19. Language / C. Assigning Meanings / 1. Syntax
15347 A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding