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Single Idea 19191

[filed under theme 3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth ]

Full Idea

To define satisfaction we indicate which objects satisfy the simplest sentential functions, then state the conditions for compound functions. This applies automatically to sentences (with no free variables) so a true sentence is satisfied by all objects.

Gist of Idea

Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects

Source

Alfred Tarski (The Semantic Conception of Truth [1944], 11)

Book Ref

'Semantics and the Philosophy of Language', ed/tr. Linsky,Leonard [University of Illinois 1972], p.25

A Reaction

I presume nothing in the domain of objects can conflict with a sentence that has been satisfied by some of them, so 'all' the objects satisfy the sentence. Tarski doesn't use the word 'domain'. Basic satisfaction seems to be stipulated.

Related Idea

Idea 19174 Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson]

The 79 ideas from Alfred Tarski

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