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Single Idea 18759

[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic ]

Full Idea

Tarski showed that the only binary relations invariant under arbitrary permutations are the universal relation, the empty relation, identity and non-identity, thus giving us a reason to include '=' among the logical terms.

Gist of Idea

Identity is invariant under arbitrary permutations, so it seems to be a logical term

Source

report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Vann McGee - Logical Consequence 6

Book Ref

'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.42

A Reaction

Tarski was looking for a criterion to distinguish logical from non-logical terms, since his account of logical validity depended on it. This idea lies behind whether a logic is or is not specified to be 'with identity' (i.e. using '=').

Related Idea

Idea 18755 Validity is explained as truth in all models, because that relies on the logical terms [McGee]

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]
19179 For a definition we need the words or concepts used, the rules, and the structure of the language [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]
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]
19183 Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction [Tarski]
19182 Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate' [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]
19193 Disputes that fail to use precise scientific terminology are all meaningless [Tarski]
19194 We may eventually need to split the word 'true' into several less ambiguous terms [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]
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]
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]
16306 Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach]
18759 Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee]
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]
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]
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]
16296 Tarski's Theorem renders any precise version of correspondence impossible [Tarski, by Halbach]
10672 Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Tarski, by Hossack]
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]
10969 Tarski had a theory of truth, and a theory of theories of truth [Tarski, by Read]
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]
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]