Combining Texts

All the ideas for 'Events and Their Names', 'Frege Philosophy of Language (2nd ed)' and 'The Concept of Truth for Formalized Languages'

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61 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
What matters in mathematics is its objectivity, not the existence of the objects [Dummett]
3. Truth / A. Truth Problems / 2. Defining Truth
Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach]
Tarski proved that any reasonably expressive language suffers from the liar paradox [Tarski, by Horsten]
'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless [Tarski]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Tarski's Theorem renders any precise version of correspondence impossible [Tarski, by Halbach]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Tarski, by Hossack]
Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Tarski, by Horsten]
Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Tarski, by Halbach]
Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson on Tarski]
Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson on Tarski]
Tarski made truth relative, by only defining truth within some given artificial language [Tarski, by O'Grady]
Tarski has to avoid stating how truths relate to states of affairs [Kirkham on Tarski]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski]
Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt]
We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten]
For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham]
Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham]
Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson]
3. Truth / F. Semantic Truth / 2. Semantic Truth
Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach]
Tarski defined truth for particular languages, but didn't define it across languages [Davidson on Tarski]
Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach on Tarski]
Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Tarski, by Haack]
Physicalists should explain reference nonsemantically, rather than getting rid of it [Tarski, by Field,H]
A physicalist account must add primitive reference to Tarski's theory [Field,H on Tarski]
Tarski had a theory of truth, and a theory of theories of truth [Tarski, by Read]
Tarski's 'truth' is a precise relation between the language and its semantics [Tarski, by Walicki]
Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith on Tarski]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Tarski's had the first axiomatic theory of truth that was minimally adequate [Tarski, by Horsten]
Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
A name denotes an object if the object satisfies a particular sentential function [Tarski]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Tarski built a compositional semantics for predicate logic, from dependent satisfactions [Tarski, by McGee]
Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
Events are made of other things, and are not fundamental to ontology [Bennett]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale]
The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett]
We don't need a sharp concrete/abstract distinction [Dummett]
We can't say that light is concrete but radio waves abstract [Dummett]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
The context principle for names rules out a special philosophical sense for 'existence' [Dummett]
The objects we recognise the world as containing depends on the structure of our language [Dummett]
8. Modes of Existence / D. Universals / 1. Universals
We can understand universals by studying predication [Dummett]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett]
9. Objects / A. Existence of Objects / 1. Physical Objects
Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Abstract objects may not cause changes, but they can be the subject of change [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects must have names that fall within the range of some functional expression [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale]
Abstract objects can never be confronted, and need verbal phrases for reference [Dummett]
9. Objects / A. Existence of Objects / 3. Objects in Thought
There is a modern philosophical notion of 'object', first introduced by Frege [Dummett]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Since abstract objects cannot be picked out, we must rely on identity statements [Dummett]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Facts are about the world, not in it, so they can't cause anything [Bennett]