Dictionary of Arguments


Philosophical and Scientific Issues in Dispute
 
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Convention T Tarski Berka I 476f
Def Convention T/original place/Tarski: We will call a true definition of truth a formally correct definition of the symbol "Wr" ("class of all true statements") formulated in terms of the metalanguage if it leads to the following conclusions:
I 477
α) all sentences that are gained from the expression "x ε Wr iff "p" by inserting for the symbol x a structurally descriptive name of an arbitrary statement in the considered language ((s) of the object language) and for the symbol "p" the expression that is the translation of this statement in the meta language; β) the statement "for an arbitrary x - if x ε Wr, then x ε AS" (or in other words ""Wr < AS").

New in relation to Chapter 1: introduction of the meta language.(1)
>Object language, >Metalanguage.
I 451
Definition structural-descriptive name/Tarski: ((s) different category than the quotation names): describe, of what words the expression, designated by the name, consists and of which characters each individual word consists and in what order they follow one another - goes without quotation marks. Method: introduce single names for all letters and other characters ((s) no quotation names).
E.g. for letters f, j, P, etc.: Ef, Jay, Pee,
E.g. to the quotation name ""snow"" ((s) quotation marks twice) corresponds the structural-descriptive name: the word that consists of the six consecutive letters Es, En, O, double-u - ((s) letter names without quotation marks).

1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935

Tarski I
A. Tarski
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983


Berka I
Karel Berka
Lothar Kreiser
Logik Texte Berlin 1983
Formal Language Tarski Berka I 458
Formal language/Tarski: in a formal language the meaning of each term is uniquely determined by its shape.
I 459
Variables: variables have no independent meaning. - Statements remain statements after translation into everyday language.
Variable/Tarski: variables represent for us always names of classes of individuals.
>Class name.
Berka I 461
Formal language/terminology/abbreviations/spelling/Tarski: here: the studied language (object language). Symbols: N, A, I, P: negation, alternation, inclusion, quantifier - metalanguage: Symbols ng (negation), sm (sum = alternation), in (inclusion) - this is the language in which the examination is performed. ng, sm, etc. correspond to the colloquial expressions ((s) the formal symbols N, A, etc. do not).
I 464
E.g. object language: Example expression: Nixi, xll: - meta language: translation of this expression: (structural-descriptive name, symbolic expression): name: "((ng ^ in) ^ v1) ^ v2" - but: see below: difference name/translation.(1) >Structural-descriptive name, >Quotation name, >Metalanguage.

1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935
---
Horwich I 112
Formal language/Tarski: in it all assertible sentences are theorems. - There may be a language with exactly specified structure, which is not formalized. - Then the assertibility may depend on extra-linguistic factors.(2) >Assertibility.


2. A. Tarski, The semantic Conceptions of Truth, Philosophy and Phenomenological Research 4, pp. 341-75

Tarski I
A. Tarski
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983


Berka I
Karel Berka
Lothar Kreiser
Logik Texte Berlin 1983

Horwich I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Functors Tarski I Berka 455
Functor/Tarski: quotation marks: quotation marks are name-forming functors.
"extensional"/"intensional": these expressions name assertion-forming functors.(1)
((s) There is no "intensional "name.)
>Intensionality, >Extensionality, >Functions/Tarski, >Quotation name, >Structural-descriptive name, >Terminology/Tarski.

1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935

Tarski I
A. Tarski
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983

Method Tarski Berka I 401
Consistent-proof/Gödel: cannot be performed if the meta language does not contain variables of higher type. >Metalanguage, >Expressivity, cf. >Type theory.
Undecidability: Undecidability is eliminated when one enriches the examined theory (object language) with variables of higher type.(1)
>Decidability.

1. A.Tarski, „Grundlegung der wissenschaftlichen Semantik“, in: Actes du Congrès International de Philosophie Scientifique, Paris 1935, VOl. III, ASI 390, Paris 1936, pp. 1-8
---
I 462
Meta language/Tarski: is our real examination object. ((s) because of the application conditions of the truth concept).
I 464
Meta language/Tarski: 2nd category of expressions: specific terms of structural-descriptive character.
>Structural-descriptive name.
Names of specific signs and expressions of the class calculus,
names of classes
names of sequences of such expressions and
of structural relations between them,
Any expression of the considered language (object language) one can allocate - on the one hand an individual name of this expression, and - on the other hand an expression that is the translation of this expression in the meta language.
That is decisive for the construction of the truth-definition.
>Truth definition/Tarski.
I 464
Name/translation/meta language/object language/Tarski: difference: an expression of the object language can in the meta language a) be given a name, or
b) be a translation.
Berka I 525
Morphology/Tarski: our meta language includes here the entire object language - that is, for us only logical expressions of the general class theory. - That is, only structural-descriptive terms. >Homophony.
So we have the morphology of the language, that is, even the concept of inference is traced back.
I 526
Thus we have justified the logic of this studied science as a part of the morphology.(2) >Description levels, >Semantic closure.


2. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935

Tarski I
A. Tarski
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983


Berka I
Karel Berka
Lothar Kreiser
Logik Texte Berlin 1983
Proper Names Tarski Berka I 451
Def quotation name/Tarski: any name of a statement (or even meaningless expression) consisting of quotes and the expression, and which is precisely the signified through the considered name. E.g. the name ""it snows"". ((s) Quotation marks twice)
N.B.: identical configured expressions must not be identified. - Therefore quotation names are general, not individual names (classes of character strings).
>Description levels, >Quotation marks, cf. >Names of sentences.
I 453
Syntactically simple expressions - such as letters - have no independent meaning.
I 451
Def structural-descriptive name/Tarski: (different category than the quotation names): they describe, of what words the expression, designated by the name, consists and of which characters each individual word consists and in what order they follow one another. - This goes without quotation marks. Method: introduce single names for all letters and other characters (No quotation names).
E.g. for letters f, j, P, etc.: Ef, Jay, Pee, ex - E.g. to the quotation name ""snow"" (quotation marks twice) corresponds the structural-descriptive name: word that consists of the six consecutive letters Es, En, O, double-u - (letter names without quotation marks).
I 451
Semantically ambiguous/Russell/Tarski: E.g. name, designating: a) with respect to items
b) to classes, relations, etc.
I 464
Name/translation/metalanguage/object language/Tarski: difference: an expression of the object language in the metalanguage may a) be given a name,
or b) a translation.
>Object language, >Metalanguage.
I 496
Names/variables/constants/Tarski: variables represent names
constants are names.
>Representation, >Proxy.
For each constant and each variable of the object language (except for the logical constants of propositional calculus) can form a fundamental function that contains this character (the statement variables neither occur into the fundamental functions as functors nor as arguments).
Statement variable: any ((s) individual) of them is regarded as an independent fundamental function.(1)
>Constants/Tarski, >Functions/Tarski.


1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935

Tarski I
A. Tarski
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983


Berka I
Karel Berka
Lothar Kreiser
Logik Texte Berlin 1983
Quote/Disquotation Kripke III 362
Quote/relation/Kripke: the quote process Q (x1, a1) does not define a relation. For each t, which can be used for x1, the result is a monadic predicate with free referential variables whose extension is (t). On the other hand: denotation: induces a relation, if the formula is transparent. The quote-name of a term works radically different from a structural-descriptive name. >structural-descriptive name, >Denotation/Kripke.
III 364
A quote-name contains the term as part, a structural-descriptive name does not.

Kripke I
S.A. Kripke
Naming and Necessity, Dordrecht/Boston 1972
German Edition:
Name und Notwendigkeit Frankfurt 1981

Kripke II
Saul A. Kripke
"Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276
In
Eigennamen, Ursula Wolf Frankfurt/M. 1993

Kripke III
Saul A. Kripke
Is there a problem with substitutional quantification?
In
Truth and Meaning, G. Evans/J McDowell Oxford 1976

Kripke IV
S. A. Kripke
Outline of a Theory of Truth (1975)
In
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg) Oxford/NY 1984

Terminology Tarski I 451
Def structural-descriptive name/Tarski: ((s) different category than the quotation names): describe, of what words the expression, designated by the name, consists and of which characters each individual word consists and in what order they follow one another - goes without quotation marks. Method: introduce single names for all letters and other characters ((s) no quotation names).
E.g. for letters f, j, P, etc.: Ef, Jay, Pee,
E.g. to the quotation name ""snow"" ((s) quotation marks twice) corresponds the structural-descriptive name: the word that consists of the six consecutive letters Es, En, O, double-u - ((s) letter names without quotation marks).
Berka I 454
Def Quotation function/Tarski: the in Tarski schema (or variants) occurring expression ""p"" (quotes twice) must be regarded as a function whose argument is a propositional variable and the values constant leading names of statements. So the quotation marks become separate words (like the word "name") with the syntactic role of functors.


Tarski I
A. Tarski
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983


Berka I
Karel Berka
Lothar Kreiser
Logik Texte Berlin 1983


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