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Ideas of Alfred Tarski, by Text

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

1933 The Concept of Truth for Formalized Languages
p.1 Tarski's had the first axiomatic theory of truth that was minimally adequate [Horsten]
p.4 Tarski proved that truth cannot be defined from within a given theory [Halbach]
p.5 Tarski's Theorem renders any precise version of correspondence impossible [Halbach]
p.9 Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess]
p.15 Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Horsten]
p.15 Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Halbach]
p.15 Tarski defined truth for particular languages, but didn't define it across languages [Davidson]
p.17 Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson]
p.17 Tarski made truth respectable, by proving that it could be defined [Halbach]
p.18 Tarski proved that any reasonably expressive language suffers from the liar paradox [Horsten]
p.19 Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach]
p.22 Tarski had a theory of truth, and a theory of theories of truth [Read]
p.23 Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Halbach]
p.27 Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson]
p.31 Tarski's 'truth' is a precise relation between the language and its semantics [Walicki]
p.32 Tarski made truth relative, by only defining truth within some given artificial language [O'Grady]
p.37 Tarski built a compositional semantics for predicate logic, from dependent satisfactions [McGee]
p.38 Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Fisher]
p.42 Identity is invariant under arbitrary permutations, so it seems to be a logical term [McGee]
p.60 Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith]
p.62 Taste is the capacity to judge an object or representation which is thought to be beautiful [Schellekens]
p.72 Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Rumfitt]
p.74 We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Horsten]
p.111 Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Haack]
p.123 Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman]
p.141 Tarksi invented the first semantics for predicate logic, using this conception of truth [Kirkham]
p.142 For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Kirkham]
p.146 The object language/ metalanguage distinction is the basis of model theory [Halbach]
p.152 Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Kirkham]
p.160 Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Davidson]
p.172 Tarski has to avoid stating how truths relate to states of affairs [Kirkham]
p.377 Physicalists should explain reference nonsemantically, rather than getting rid of it [Field,H]
p.381 A physicalist account must add primitive reference to Tarski's theory [Field,H]
p.417 Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Hossack]
1 p.165 'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless
p.194 p.382 A name denotes an object if the object satisfies a particular sentential function
1936 The Establishment of Scientific Semantics
p.401 p.401 Semantics is the concepts of connections of language to reality, such as denotation, definition and truth
p.402 p.402 A language containing its own semantics is inconsistent - but we can use a second language
p.402 p.402 A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules
p.404 p.404 '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth
p.405 p.405 A sentence is satisfied when we can assert the sentence when the variables are assigned
p.406 p.406 Satisfaction is the easiest semantical concept to define, and the others will reduce to it
p.407 p.407 Using the definition of truth, we can prove theories consistent within sound logics
1936 The Concept of Logical Consequence
p.73 Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Rumfitt]
p.417 p.417 X follows from sentences K iff every model of K also models X
p.417 p.417 A 'model' is a sequence of objects which satisfies a complete set of sentential functions
p.418 p.418 Sentences are 'analytical' if every sequence of objects models them
1936 works
p.6 Logical consequence is when in any model in which the premises are true, the conclusion is true [Beall/Restall]
p.9 Logical consequence: true premises give true conclusions under all interpretations [Hodges,W]
p.31 Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Davidson]
p.103 There is no clear boundary between the logical and the non-logical
p.112 In everyday language, truth seems indefinable, inconsistent, and illogical
p.230 Tarski improved Hilbert's geometry axioms, and without set-theory [Feferman/Feferman]
1944 The Semantic Conception of Truth
01 p.13 Definitions of truth should not introduce a new version of the concept, but capture the old one
01 p.13 A definition of truth should be materially adequate and formally correct
01 p.14 For a definition we need the words or concepts used, the rules, and the structure of the language
02 p.14 It is convenient to attach 'true' to sentences, and hence the language must be specified
04 p.15 In the classical concept of truth, 'snow is white' is true if snow is white
04 p.16 Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate'
04 p.16 Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction
04 p.387 If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs [Field,H]
05 p.17 The best truth definition involves other semantic notions, like satisfaction (relating terms and objects)
05 p.17 Semantics is a very modest discipline which solves no real problems
06 p.19 A rigorous definition of truth is only possible in an exactly specified language
07 p.20 The Liar makes us assert a false sentence, so it must be taken seriously
08-09 p.20 We can't use a semantically closed language, or ditch our logic, so a meta-language is needed
09 p.22 The metalanguage must contain the object language, logic, and defined semantics
10 p.24 We need an undefined term 'true' in the meta-language, specified by axioms
11 p.25 Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects
12 p.26 The truth definition proves semantic contradiction and excluded middle laws (not the logic laws)
14 p.27 Disputes that fail to use precise scientific terminology are all meaningless
14 p.28 We may eventually need to split the word 'true' into several less ambiguous terms
15 p.29 Scheme (T) is not a definition of truth
15 p.29 Truth tables give prior conditions for logic, but are outside the system, and not definitions
16 p.31 Truth can't be eliminated from universal claims, or from particular unspecified claims
18 p.33 We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true
19 p.35 Some say metaphysics is a highly generalised empirical study of objects
1965 talk
p.52 Set theory and logic are fairy tales, but still worth studying
p.52 I am a deeply convinced nominalist