Combining Philosophers

All the ideas for Michael Burke, E Conee / R Feldman and Leon Horsten

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62 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is the most general intellectual discipline [Horsten]
2. Reason / D. Definition / 2. Aims of Definition
A definition should allow the defined term to be eliminated [Horsten]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
3. Truth / A. Truth Problems / 1. Truth
Truth is a property, because the truth predicate has an extension [Horsten]
Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles [Horsten]
3. Truth / A. Truth Problems / 2. Defining Truth
Truth has no 'nature', but we should try to describe its behaviour in inferences [Horsten]
3. Truth / A. Truth Problems / 5. Truth Bearers
Propositions have sentence-like structures, so it matters little which bears the truth [Horsten]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Modern correspondence is said to be with the facts, not with true propositions [Horsten]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
The correspondence 'theory' is too vague - about both 'correspondence' and 'facts' [Horsten]
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
The coherence theory allows multiple coherent wholes, which could contradict one another [Horsten]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
The pragmatic theory of truth is relative; useful for group A can be useless for group B [Horsten]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa [Horsten]
Tarski's hierarchy lacks uniform truth, and depends on contingent factors [Horsten]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
Semantic theories have a regress problem in describing truth in the languages for the models [Horsten]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
The Naďve Theory takes the bi-conditionals as axioms, but it is inconsistent, and allows the Liar [Horsten]
Axiomatic theories take truth as primitive, and propose some laws of truth as axioms [Horsten]
A good theory of truth must be compositional (as well as deriving biconditionals) [Horsten]
An axiomatic theory needs to be of maximal strength, while being natural and sound [Horsten]
By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! [Horsten]
'Reflexive' truth theories allow iterations (it is T that it is T that p) [Horsten]
Axiomatic approaches to truth avoid the regress problem of semantic theories [Horsten]
Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models [Horsten]
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
Friedman-Sheard theory keeps classical logic and aims for maximum strength [Horsten]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationism concerns the nature and role of truth, but not its laws [Horsten]
Deflationism says truth isn't a topic on its own - it just concerns what is true [Horsten]
Deflation: instead of asserting a sentence, we can treat it as an object with the truth-property [Horsten]
This deflationary account says truth has a role in generality, and in inference [Horsten]
Deflationism skips definitions and models, and offers just accounts of basic laws of truth [Horsten]
Inferential deflationism says truth has no essence because no unrestricted logic governs the concept [Horsten]
4. Formal Logic / E. Nonclassical Logics / 1. Nonclassical Logics
Nonclassical may accept T/F but deny applicability, or it may deny just T or F as well [Horsten]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
The first incompleteness theorem means that consistency does not entail soundness [Horsten]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
ZFC showed that the concept of set is mathematical, not logical, because of its existence claims [Horsten]
Set theory is substantial over first-order arithmetic, because it enables new proofs [Horsten]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Predicativism says mathematical definitions must not include the thing being defined [Horsten]
7. Existence / D. Theories of Reality / 7. Facts / b. Types of fact
We may believe in atomic facts, but surely not complex disjunctive ones? [Horsten]
7. Existence / D. Theories of Reality / 9. Vagueness / f. Supervaluation for vagueness
In the supervaluationist account, disjunctions are not determined by their disjuncts [Horsten]
If 'Italy is large' lacks truth, so must 'Italy is not large'; but classical logic says it's large or it isn't [Horsten]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]
The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]
Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten]
If the only aim is to believe truths, that justifies recklessly believing what is unsupported (if it is right) [Conee/Feldman]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
We don't have the capacity to know all the logical consequences of our beliefs [Conee/Feldman]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
Evidentialism says justifications supervene on the available evidence [Conee/Feldman]
19. Language / C. Assigning Meanings / 1. Syntax
A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Rational decisions are either taken to be based on evidence, or to be explained causally [Conee/Feldman]