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Single Idea 10823
[filed under theme 5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
]
Full Idea
To say that the name x denotes a given object a is the same as to stipulate that the object a ... satisfies a sentential function of a particular type.
Gist of Idea
A name denotes an object if the object satisfies a particular sentential function
Source
Alfred Tarski (The Concept of Truth for Formalized Languages [1933], p.194)
Book Ref
'The Nature of Truth', ed/tr. Lynch, Michael P. [MIT 2001], p.382
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]
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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]
|