Ideas of Alfred Tarski, by Theme

[Polish, 1902 - 1983, Taught in Warsaw 1925-1939, then University of California at Berkeley from 1942 to 1968.]

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1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
19199 Some say metaphysics is a highly generalised empirical study of objects
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
19193 Disputes that fail to use precise scientific terminology are all meaningless
2. Reason / D. Definition / 1. Definitions
19179 For a definition we need the words or concepts used, the rules, and the structure of the language
3. Truth / A. Truth Problems / 2. Defining Truth
16295 Tarski proved that truth cannot be defined from within a given theory [Halbach]
15342 Tarski proved that any reasonably expressive language suffers from the liar paradox [Horsten]
19069 'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless
10153 In everyday language, truth seems indefinable, inconsistent, and illogical
19178 Definitions of truth should not introduce a new version of the concept, but capture the old one
19177 A definition of truth should be materially adequate and formally correct
19186 A rigorous definition of truth is only possible in an exactly specified language
19194 We may eventually need to split the word 'true' into several less ambiguous terms
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
16296 Tarski's Theorem renders any precise version of correspondence impossible [Halbach]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
15339 Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Horsten]
16302 Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Halbach]
19135 Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson]
19138 Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson]
4699 Tarski made truth relative, by only defining truth within some given artificial language [O'Grady]
19324 Tarski has to avoid stating how truths relate to states of affairs [Kirkham]
10672 Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Hossack]
13338 '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth
19180 It is convenient to attach 'true' to sentences, and hence the language must be specified
19181 In the classical concept of truth, 'snow is white' is true if snow is white
19182 Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate'
19183 Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction
19198 We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true
19196 Scheme (T) is not a definition of truth
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
15410 Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess]
18811 Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Rumfitt]
15365 We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Horsten]
19314 For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Kirkham]
19316 Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Kirkham]
19175 Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Davidson]
19184 The best truth definition involves other semantic notions, like satisfaction (relating terms and objects)
19191 Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
19188 We can't use a semantically closed language, or ditch our logic, so a meta-language is needed
19189 The metalanguage must contain the object language, logic, and defined semantics
3. Truth / F. Semantic Truth / 2. Semantic Truth
19134 Tarski defined truth for particular languages, but didn't define it across languages [Davidson]
16304 Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach]
17746 Tarski's 'truth' is a precise relation between the language and its semantics [Walicki]
10904 Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith]
2571 Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Haack]
10821 Physicalists should explain reference nonsemantically, rather than getting rid of it [Field,H]
10822 A physicalist account must add primitive reference to Tarski's theory [Field,H]
16303 Tarski made truth respectable, by proving that it could be defined [Halbach]
10969 Tarski had a theory of truth, and a theory of theories of truth [Read]
10824 If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs [Field,H]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
16306 Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Halbach]
15322 Tarski's had the first axiomatic theory of truth that was minimally adequate [Horsten]
19141 Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Davidson]
19190 We need an undefined term 'true' in the meta-language, specified by axioms
3. Truth / H. Deflationary Truth / 1. Redundant Truth
19197 Truth can't be eliminated from universal claims, or from particular unspecified claims
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
19185 Semantics is a very modest discipline which solves no real problems
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
19195 Truth tables give prior conditions for logic, but are outside the system, and not definitions
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
10152 Set theory and logic are fairy tales, but still worth studying
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10048 There is no clear boundary between the logical and the non-logical
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
13337 A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
18812 Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Rumfitt]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10694 Logical consequence is when in any model in which the premises are true, the conclusion is true [Beall/Restall]
10479 Logical consequence: true premises give true conclusions under all interpretations [Hodges,W]
13344 X follows from sentences K iff every model of K also models X
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
19192 The truth definition proves semantic contradiction and excluded middle laws (not the logic laws)
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
18759 Identity is invariant under arbitrary permutations, so it seems to be a logical term [McGee]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
10823 A name denotes an object if the object satisfies a particular sentential function
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
18756 Tarski built a compositional semantics for predicate logic, from dependent satisfactions [McGee]
19313 Tarksi invented the first semantics for predicate logic, using this conception of truth [Kirkham]
13335 Semantics is the concepts of connections of language to reality, such as denotation, definition and truth
13336 A language containing its own semantics is inconsistent - but we can use a second language
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
13339 A sentence is satisfied when we can assert the sentence when the variables are assigned
13340 Satisfaction is the easiest semantical concept to define, and the others will reduce to it
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
16323 The object language/ metalanguage distinction is the basis of model theory [Halbach]
13343 A 'model' is a sequence of objects which satisfies a complete set of sentential functions
5. Theory of Logic / K. Features of Logics / 2. Consistency
13341 Using the definition of truth, we can prove theories consistent within sound logics
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
8940 Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Fisher]
19187 The Liar makes us assert a false sentence, so it must be taken seriously
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
10157 Tarski improved Hilbert's geometry axioms, and without set-theory [Feferman/Feferman]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
10154 Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
10151 I am a deeply convinced nominalist
19. Language / E. Analyticity / 1. Analytic Propositions
13345 Sentences are 'analytical' if every sequence of objects models them
21. Aesthetics / A. Aesthetic Experience / 3. Taste
20407 Taste is the capacity to judge an object or representation which is thought to be beautiful [Schellekens]