Ideas of Volker Halbach, by Theme
[German, fl. 2010, Reader at the University of Oxford.]
green numbers give full details |
back to list of philosophers |
expand these ideas
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
|
16325
|
Analysis rests on natural language, but its ideal is a framework which revises language
|
2. Reason / D. Definition / 2. Aims of Definition
|
16292
|
An explicit definition enables the elimination of what is defined
|
2. Reason / E. Argument / 3. Analogy
|
16307
|
Don't trust analogies; they are no more than a guideline
|
3. Truth / A. Truth Problems / 1. Truth
|
16339
|
Truth axioms prove objects exist, so truth doesn't seem to be a logical notion
|
|
16330
|
Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth
|
3. Truth / A. Truth Problems / 2. Defining Truth
|
15647
|
Truth definitions don't produce a good theory, because they go beyond your current language
|
|
16324
|
Any definition of truth requires a metalanguage
|
|
16293
|
Traditional definitions of truth often make it more obscure, rather than less
|
|
16301
|
If people have big doubts about truth, a definition might give it more credibility
|
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
|
15649
|
In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage
|
|
16297
|
Semantic theories avoid Tarski's Theorem by sticking to a sublanguage
|
3. Truth / F. Semantic Truth / 2. Semantic Truth
|
16337
|
Disquotational truth theories are short of deductive power
|
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
|
15648
|
Instead of a truth definition, add a primitive truth predicate, and axioms for how it works
|
|
15650
|
Axiomatic theories of truth need a weak logical framework, and not a strong metatheory
|
|
15654
|
If truth is defined it can be eliminated, whereas axiomatic truth has various commitments
|
|
15655
|
Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms?
|
|
16294
|
Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage
|
|
16311
|
To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction'
|
|
16318
|
Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents
|
|
16326
|
The main semantic theories of truth are Kripke's theory, and revisions semantics
|
|
16299
|
Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory
|
|
16340
|
Truth axioms need a base theory, because that is where truth issues arise
|
|
16305
|
We know a complete axiomatisation of truth is not feasible
|
|
16313
|
A theory is 'conservative' if it adds no new theorems to its base theory [PG]
|
|
16315
|
The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals
|
|
16314
|
Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free'
|
|
16322
|
CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA
|
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
|
16327
|
Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth
|
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
|
16329
|
Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts
|
|
16331
|
The KF is much stronger deductively than FS, which relies on classical truth
|
|
16332
|
The KF theory is useful, but it is not a theory containing its own truth predicate
|
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
|
15656
|
Deflationists say truth merely serves to express infinite conjunctions
|
|
16338
|
Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge
|
|
16316
|
Deflationists say truth is just for expressing infinite conjunctions or generalisations
|
|
16317
|
The main problem for deflationists is they can express generalisations, but not prove them
|
|
16319
|
Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism
|
|
16320
|
Some say deflationism is axioms which are conservative over the base theory
|
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
|
16335
|
In Strong Kleene logic a disjunction just needs one disjunct to be true
|
|
16334
|
In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value
|
4. Formal Logic / F. Set Theory ST / 1. Set Theory
|
15657
|
To prove the consistency of set theory, we must go beyond set theory
|
|
16309
|
Every attempt at formal rigour uses some set theory
|
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
|
16333
|
The underestimated costs of giving up classical logic are found in mathematical reasoning
|
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
|
15652
|
We can use truth instead of ontologically loaded second-order comprehension assumptions about properties
|
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
|
15651
|
Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true'
|
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
|
16310
|
A theory is some formulae and all of their consequences
|
5. Theory of Logic / K. Features of Logics / 3. Soundness
|
16341
|
Normally we only endorse a theory if we believe it to be sound
|
|
16342
|
You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system
|
|
16344
|
Soundness must involve truth; the soundness of PA certainly needs it
|
5. Theory of Logic / L. Paradox / 1. Paradox
|
16347
|
Many new paradoxes may await us when we study interactions between frameworks
|
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
|
16336
|
The liar paradox applies truth to a negated truth (but the conditional will serve equally)
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
|
16321
|
The compactness theorem can prove nonstandard models of PA
|
|
16343
|
The global reflection principle seems to express the soundness of Peano Arithmetic
|
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
|
16312
|
To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
|
16308
|
Set theory was liberated early from types, and recent truth-theories are exploring type-free
|
7. Existence / C. Structure of Existence / 2. Reduction
|
16345
|
That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction
|
10. Modality / A. Necessity / 2. Nature of Necessity
|
16346
|
Maybe necessity is a predicate, not the usual operator, to make it more like truth
|
19. Language / D. Propositions / 4. Mental Propositions
|
16298
|
We need propositions to ascribe the same beliefs to people with different languages
|