Abstract
One might look for connections between the notion of analyticity and the problems of semantics or—in broader terms — semiotics in the definition of analytic judgements deriving from Kant, which, as it is known, involves the inclusion of the meaning of the predicate in the meaning of the subject. The above mentioned connections manifest themselves at present in numerous current definitions of the term ‘analytic sentence’, which, as a rule, involve such semantic terms as: ‘meaning’, ‘definition’, ‘synonymy’ and others. Many authors express the opinion that the concept of analyticity is indispensable in order to define certain semantic concepts. The concept of meaning comes to the foreground here. Rudolf Carnap, the author of one of the most important attemps to explicate this concept has used the concept of logical truth which —according to his intentions— is supposed to correspond to the old notion of analyticity.
A fragment of Ph.D. dissertation (1967). Translated by E. Ronowicz.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
K. Ajdukiewicz, Jezyk i poznanie (Language and Knowledge), PWN, Warszawa, vol. I 1960, vol. II 1965.
K. Ajdukiewicz, ‘Le problème du fondement des propositions analytiques’, Studia Logica VIII (1958), included in the present volume as: ‘The Problem of Justifying Analytic Sentences’.
K. Ajdukiewicz, ‘Logika a doświadczenie’ (‘Logic and Experience’), Przeglad Filozoficzny XLIII (1947) (also in [1]).
K. Ajdukiewicz, ‘O znaczeniu wyrazen’ (‘On the Meaning of Expressions’), in: Ksiega Pamiatkowa Polskiego Towarzystwa Filozoficznego we Lwowie, Lwów 1931.
K. Ajdukiewicz, ‘Sprache und Sinn’, Erkenntnis IV (1934) (also in [1]).
K. Ajdukiewicz, ‘Axiomatic Systems From the Methodological Point of View’, Studia Logica IX (1960) (also in [1]), included in the present volume.
R. Carnap, ‘Beobachtungssprache und theoretische Sprache’, Dialectica 12(1958).
R. Carnap, Meaning and Necessity, Univ. of Chicago Press, 1947.
G. Frege, The Foundation of Arithmetic, Oxford 1950.
H. P. Grice and P. F. Strawson, ‘In Defence of Dogma’, in: Classics of Analytic Philosophy (ed. by R. R. Ammerman), McGraw-Hill 1965.
A. Grzegorczyk, ‘Próba ugruntowania semantyki jezyka opisowego’ (‘An Attempt to Establish the Semantics of Descriptive Language’), Przeglad Filozoficzny XLTV (1948).
T. Hobbes, ‘Elementa Philosophiae’, in: Latin Works (ed. by M. Molesworth), vols. 1-5 (1893-45).
I. Kant, Kritik der reinen Vernunft, Philosophische Bibliothek Bd. 73a, Meiner, Leipzig 1926.
W. Kneale, ‘Are Necessary Truths True by Convention?’, Aristotelian Society Proceedings (1947) (supplement).
W. Kneale and M. Kneale, The Development of Logic, Oxford 1962.
M. Kokoszyńska, ‘O dwojakim rozumieniu uzasadnienia dedukcyjnego’ (‘On the Double Meaning of Deductive Justification’), Studia Logica XIII (1962).
M. Kokoszynska, ‘O dyrektywach inferencji’ (‘On the Rules of Inference’), Rozprawy logiczne, PWN 1964.
C. I. Lewis, An Analysis of Knowledge and Valuation, La Salle, Illinois, 1946.
H. Mehlberg, The Reach of Science, Toronto 1958.
O. Ore, An Introduction to the Theory of Graphs.
A. Pap, ‘Necessary Propositions and Linguistic Rules’, Archivio di Filosofia, Roma 1955.
A. Pap, Semantics and Necessary Truth, Yale Univ. Press, 1958.
M. Przelecki, ‘Z semantyki pojec otwartych’ (‘From Semantics of Open Concepts’), Studia Logica XV (1964).
M. Przelecki, ‘W sprawie istnienia przedmiotów teoretycznych’ (‘On the Existence of Theoretical Objects’), Teoria i do[wiadczenie, PWN, 1966.
M. Przeiecki, ‘O pojeciu zdania analitycznego’ (‘On the Concept of Analytic Sentence’), Studia Logica XIV (1963).
W. V. O. Quine, ‘Two Dogmas of Empiricism’, in: From a Logical Point of View, Harvard Univ. Press, 1953.
B. Stanosz, ‘Formalne teorie zakresu i treŜci wyrazeń’ (‘Formal Theories of the Scope and Content of Expressions’), Studia Logica XV (1964).
R. Suszko, ‘Logika formalna a niektóre zagadnienia teorii poznania’, (Formal Logic and some Problems of Epistemology’), Myśl Filozoficzna (1956).
M. G. White, ‘The Analytic and the Synthetic: An Untenable Dualism’, in: Semantics and the Philosophy of Language (ed. by W. L. Linsky), Univ. of Illinois Press, 1952.
R. Wójcicki, Analityczne komponenty definicji arbitralnych’ (‘Analytic Components of Arbitrary Definitions’), Studia Logica XIV (1963).
R. Wójcicki, ‘Analityczność, syntetyczność, empiryczna sensowność zdań’, Studia Filozoficzne 3 (1966); appeared as: ‘Analyticity, Syntheticity, Empirical Meaningfulness of Sentences’, Studia Filozoficzne 4 (1970), supplementary volume in English.
R. Wójcicki, ‘O warunkach empirycznej sensownosci terminów’ (‘On the Conditions of Empirical Meaningfulness of Terms’), Teoria i doświadczenie, PWN, 1966.
R. Wójcicki, ‘Semantical Criteria of Empirical Meaningfulness’, Studia Logica XIX (1966).
References
This principle may be considered to be the result of stating more precisely the condition of adequacy for the definition of logical truth adopted by Carnap. In the original this condition runs as follows: “A sentence is L-true in a semantic system S if and only if is true in S in such a way that its truth can be established on the basis of the semantical rules of the system S alone, without any reference to (extra-linguistic) facts.” Carnap [8], p. 10.
We find this approach in the work by Stanosz [27].
We have in mind here mainly the works by Przelecki [23] and [24] as well ag Wójcicki [32] and [33].
For simplicity’s sake we have disregarded the phenomenon of vagueness of observational terms here.
The symbol Cn denotes here the classical logical consequence. The relation Cn may in certain languages be different from C J (consequence in language J), and it is certainly different from C o (immediate consequence), which canot be a transitive relation, since in that case the fulfilment of the condition (ii) of the definition (Dl) by a person X would surpass human abilities.
The symbol x i§Δ denotes the relation x i restricted to the set Δ.
The concept of prolongation of models was introduced into discussions in the field of semantics of languages of empirical theories by M. Przelecki [23], who used the term ‘enrichment’. R. Suszko suggested the use of the term ‘prolongation’.
In the situation under discussion there is no such prolongation of model in which sentences would be true. There would exist such a model—against the assumption-and it would be,if Since and hence then
This theorem is the immediate consequence of the known theorems on logical consequence: If then Cn Cn(CnX)).
We would obtain the simplest criterion of strict analyticity by presenting the set of strictly analytical sentences, i.e. the set of sentences as the set of consequences of some definite set of sentences Z. Though the set of strictly analytical sentences is-as we have demonstrated—a system, we do not know whether it is always finitely axiomatizable. It is known, on the other hand, that it is not always axiomatizable in terms of a certain set of postulates. In particular, the equation given below does not always hold
To be precise, the models of the formalized language L R possess several universes. One of them corresponds to the range of variability of the individual variables, the others—occurring in the number equal to the number of types of predicate variables—correspond to the sets of values of these variables. Since the latter ones can be determined with the help of U (e.g.: 2U, 2U×U, 2U×U×, etc.) there is no need to mention them.
The intuitive sense of this definition becomes clear when we assume that The symbol (Z, i) then denotes the set of those postulates with indices smaller than i, which do not belong to although they fulfil condition (i) of the definition (D15) formulated below.
The terminology concerning the graphs has been taken from Ore’s book [20].
This follows from the known theorem of Gödei on the incompleteness of richer logical systems.
Editor information
Rights and permissions
Copyright information
© 1977 PWN - Polish Scientific Publishers - Warszawa
About this chapter
Cite this chapter
Nowaczyk, A. (1977). Analytic Sentences in the Semantic System. In: Przełęcki, M., Wójcicki, R. (eds) Twenty-Five Years of Logical Methodology in Poland. Synthese Library, vol 87. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1126-6_22
Download citation
DOI: https://doi.org/10.1007/978-94-010-1126-6_22
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-1128-0
Online ISBN: 978-94-010-1126-6
eBook Packages: Springer Book Archive