Ideas of Alfred Tarski, by Theme
[Polish, 1902  1983, Taught in Warsaw 19251939, 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

19177

A definition of truth should be materially adequate and formally correct

19178

Definitions of truth should not introduce a new version of the concept, but capture the old one

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

19183

Each interpreted Tsentence is a partial definition of truth; the whole definition is their conjunction

19182

Use 'true' so that all Tsentences can be asserted, and the definition will then be 'adequate'

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 physicalpluslogic [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. Metalanguage for truth
19188

We can't use a semantically closed language, or ditch our logic, so a metalanguage is needed

19189

The metalanguage must contain the object language, logic, and defined semantics

3. Truth / F. Semantic Truth / 2. Semantic Truth
10821

Physicalists should explain reference nonsemantically, rather than getting rid of it [Field,H]

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 noncontradiction [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]

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 witchvictim pairs [Field,H]

3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
15322

Tarski's had the first axiomatic theory of truth that was minimally adequate [Horsten]

16306

Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Halbach]

19141

Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Davidson]

19190

We need an undefined term 'true' in the metalanguage, 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 nonlogical

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 settheory [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]
