Elementary proposition

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The term elementary sentence is mainly associated with Ludwig Wittgenstein's philosophy of language , and sometimes with a slightly different meaning, also used by other representatives of logical empiricism or atomism, especially Rudolf Carnap . These are the smallest linguistic units that take on truth values, that is, they can be true or false. Furthermore, in the wake of Walter Burkert, the axioms of the Euclidean elements of geometry (Στοιχεῖα) are called “elementary propositions of mathematics”.

Bertrand Russell's atomic propositions

George Edward Moore's theory had postulated exactly one corresponding fact that made it true for every true sentence. In contrast to this, Bertrand Russell's logical atomism argues that truth makers are only required for atomic sentences, that is, only for sentences which contain a relation of n “names” and no truth-functional operators (such as “and”, “or”, “not”) ") And no quantifiers (like" all "). Truth-functional sentence structures formed from these atomic sentences are made true by those truth-makers who make the atomic sentences that go into them true. This enables a greater ontological economy.

Wittgenstein's early semantics in the Tractatus

Wittgenstein's Tractatus logico-philosophicus (TLP for short) developed, based primarily on ideas by Gottlob Frege and Bertrand Russell , a theory of meaning according to which sentences are composed of atomic semantic units. This ties in with Russell's atomism. Wittgenstein speaks of elementary proposition for the smallest units capable of truth values, that is, sentences that can express a state of affairs, that is, can be true or false. As with Russell, conjuncts must not be included. Since the sentence represents the state of affairs, "depicts" in Wittgenstein's words, this has been called an image theory of meaning. Wittgenstein represents in the Tractatus:

"One thing may or may not be the case and everything else remains the same"

- TLP 1.21

The TLP is based on the fact that both facts and elementary sentences representing them are independent of one another as far as their meaning is concerned. This independence guarantees that the truth values ​​of elementary sentences can be offset according to the truth tables specified in the TLP , so that every syntactically permissible combination of elementary sentences describes a logically possible situation. Wittgenstein later considers this demand for independence to be wrong. While Russell and Carnap certainly give examples of elementary sentences, Wittgenstein sees such an explication as an analytical goal that has not yet been achieved and later emphasizes the unpredictability of the structure of elementary sentences.

Elementary propositions in logical atomism and logical empiricism

The research program to be taken from the Tractatus consists of

"That when analyzing the sentences [colloquial language] we have to come up with elementary sentences that are directly related."

- TLP 4,221

As a result , attempts were made , especially by the Vienna Circle , to arrive at such elementary sentences by analyzing linguistic modes of expression. A verificationist epistemology should be based on this foundation . The Vienna Circle later also speaks of protocol sentences , which breaks away from the condition of logical atomicity. Wittgenstein also adopted such a conception of elementary sentences and opposed his conception represented in the TLP. He observes that sentences such as “Here is a red rose” or “This place is now red” are only permissible in an extended definition of “elementary proposition”, namely when one defines: “It contains no truth function and is not through one Defines an expression that contains a "or" that it is neither a truth function of other propositions nor is defined as such "; but:

“From 'a is now red' it follows, however, 'a is not green now' and the elementary sentences in this sense are therefore not independent of one another, like the elementary sentences in my calculus described at the time, from which I assumed that the whole use of the sentences must be mutually exclusive to be traced back to him; - misled by a wrong concept of this return. "

Wittgenstein also opposed the verificationist approaches, some of which were formulated with reference to his writings and ideas.

Problems of elementary sentences

The problem of elementary sentences is a lively debate in Wittgenstein's environment. As an example, Friedrich Waismann's defense, noted in his theses around 1930 :

“It is not a hypothesis that there are elementary propositions. The requirement of the existence of elementary sentences is the requirement that our statements have meaning. The fact that we understand the sentences of our ordinary language guarantees that there are elementary sentences. The elementary propositions are what gives meaning to all other propositions. We can understand the sentences of our colloquial language without knowing what the elementary sentences look like. Just as we understand most expressions without knowing their definition, or how we move without knowing how each individual movement comes about. One could ask: How is it possible that we understand the sentences of our colloquial language if we do not know the elementary sentences? The answer is: applying a rule does not mean knowing about the rule. For example, we can introduce new characters by definition and we can break down the characters we already know by definition. In this last case, only the definition clarifies the meaning of the sentences. But we can understand these themselves without knowing the wording of the definition. "

The core argumentation can be reconstructed as follows: If we understand sentences in everyday language, then on the logical foundation of elementary sentences. But we understand language. So there are elementary propositions. Obviously, the argument stands and falls, among other things, with specifying alternatives to the first premise, i.e. more plausible semantic theories.

Wittgenstein's later criticism of the meaning theory of the Tractatus

In Wittgenstein's notes, selected and sorted into the TLP, there are already statements of problems for the project being pursued. For example, he wrote on June 1, 1915:

“The elementary sentence consists of names. But since we cannot show the number of names of different meanings, neither can we show the composition of the elementary proposition. Russell said that there are simple relations between different numbers of things (individuals). But between what numbers? And how should that be decided? - Through experience? "

Wittgenstein regards the logical structure of elementary sentences as still completely unexplained and unpredictable:

“The form of the elementary sentences cannot be foreseen. It is just ridiculous to think that you can get by with the usual form of colloquial language, with subject-predicate, with dual relations and so on. Already the one thing that the real number or something similar to the real number can appear in the elementary proposition shows how completely different the elementary proposition can be from all other propositions. And it is impossible for us to foresee today what can still occur there. Only when we logically analyze the phenomena do we know what form the elementary propositions have. Here is an area where there is no hypothesis. The logical structure of elementary sentences need not have the slightest resemblance to the logical structure of sentences. Just think of the physical equations: how enormously complex are they built. The elementary sentences will also be of this complexity. "

- 22.12.1929 in conversation with Moritz Schlick

Later he considers the project goal initially striven for as fundamentally unattainable:

“I thought that one day one would be able to state the elementary sentences. Only in the last few years have I given up on this error. "

Wittgenstein moves away from his demand for logical independence:

“What was wrong with my view was that I believed that the syntax of the logical constants could be set up without paying attention to the inner context of the sentences. It is not like that. For example, I cannot say: At one and the same point there is red and blue at the same time. Here the logical product is incomprehensible. Rather, the rules for the logical constants are only part of a comprehensive syntax that I didn't know about at the time. "

Wittgenstein tried to take such logical structures into account in such a way that sentences have a place within a "sentence system", so that

"That from the existence of a state of affairs one can infer the non-existence of all the others that are described by the sentence system."

Wittgenstein's later theoretical approaches are more strongly influenced by pragmatic elements. Thus, among other things, the orientation towards objects, as assumed in the TLP as "ideal" prerequisites, falls in favor of an orientation towards concrete, in particular linguistic behavior, even in the narrow case of logical calculations:

“It is of the greatest importance that we always think of an example for a calculus of logic to which the calculus applies, and that we do not give examples and say that they are actually not ideal, but that we still have them Not. That is the sign of a wrong view. (Russell and I have labored with it in various ways. Compare what I say in the "Logical-Philosophical Treatise" about elementary propositions and objects.) "

At the same time as Rudolf Carnap , Wittgenstein criticized his own earlier view:

“The idea of ​​constructing elementary sentences (as Carnap tried to do, for example) is based on a wrong conception of logical analysis. She regards the problem of this analysis as that of finding a theory of elementary propositions. It is based on what happens in mechanics when a number of basic laws are found from which the whole system emerges. My own view was wrong: partly because I was not clear about the meaning of the words "a logical product is hidden in a sentence" (and similar), and secondly because I too thought the logical analysis had to bring hidden things to light. "

- Note dated November 28, 1931

Elementary sentence in methodical constructivism

An elementary statement is one of the prime statements that can be introduced by a predication ( Kuno Lorenz ). Elementary sentences are sentences which usually consist of a nominator , a copula and a predicator (example: Napoleon is a Corsican ) and which are not linked by logical signs.

Around 1970 Paul Lorenzen introduced appredicators. Instead of "Fido ε dog and Fido ε brown" the elementary statement "Fido ε a brown dog" is provided. Lorenzen, however, aims to speak of a dog-like brown. "Fido" is a self-predication, "brown" is an appredication. The database expert and computer science pioneer Hartmut Wedekind sees Lorenzen's use of several predicators in an elementary sentence as a parallel to Edgar F. Codd's introduction of relational databases . This would overcome logical atomism .

Lorenzen provides a Tatcopula (tut) and an event copula κ in addition to the usual actual copula ε. The sentence: "Tilman carries ( carries) water into the house with buckets." is therefore an elementary proposition.

This Lorenzsche revision of the procedure of the logical propaedeutic is controversial in the methodical constructivism . It can be interpreted as a departure from the linguistic-philosophical approach in Wittgenstein 's late philosophy .

literature

  • Erich Ammereller: The mapping relationship. On the problem of intentionality in the Tractatus. In: Ludwig Wittgenstein: Tractatus logico-philosophicus . Published by Wilhelm Vossenkuhl . Akademie-Verlag, Berlin 2001, ISBN 3-05-002694-4 , ( interpreting classics 10), p. 112ff, here 128ff.
  • James Bogen: Wittgenstein's Tractatus . In: Stuart G. Shanker (Ed.): Philosophy of science, logic, and mathematics in the 20th century . Routledge, London 1996, ( Routledge history of philosophy 9), ISBN 0-415-05776-0 , pp. 157ff.
  • Hans-Johann Glock : Wittgenstein Lexicon . Wissenschaftliche Buchgesellschaft, Darmstadt 2000, ISBN 3-534-14543-7 , pp. 93-98 et passim (see index sv).
  • Ernst Michael Lange : Ludwig Wittgenstein. "Logical-philosophical treatise". An introductory commentary in the “Tractatus” . Schöningh, Paderborn et al. 1996, ISBN 3-8252-1922-4 , ( UTB for science, Uni-Taschenbücher 1922), p. 93ff. et passim (see index sv).
  • Kuno Lorenz : Elements of Language Criticism An Alternative to Dogmatism and Skepticism in the Analytical Philosophy Suhrkamp, ​​Frankfurt 1970
  • Wilhelm Kamlah , Paul Lorenzen : Logical propaedeutics or preschool of reasonable speech. Bibliographisches Institut, Mannheim ( BI-HTB 227 / 227a ) 1967; 2., verb. u. exp. Edition 1973 ISBN 3411052279 Reprint 1990, 1992; since 1996 Metzler, Stuttgart; engl .: Logical Propaedeutic. Pre-School of Reasonable Discourse. (Trans. H. Robinson) University Press of America, Lanham 1984
  • Rainer Hegselmann: Classical and constructive theory of the elementary proposition: Journal for philosophical research 33 (1979) 89-107
  • Paul Lorenzen: Textbook of the constructive philosophy of science. Bibliographisches Institut, Mannheim 1987; Metzler, Stuttgart ²2000 ISBN 3-476-01784-2 .

Individual evidence

  1. ↑ See for example Wolfgang Künne : Truth , in: Ekkehard Martens / Herbert Schnädelbach (ed.): Philosophy. A basic course, Volume 1, Reinbek bei Hamburg 1991, 116ff, here 139ff
  2. ↑ For example, Wittgenstein himself explicitly in a note from September 1, 1937: "If you want to use the term" elementary proposition "as I did in the logical-philosophical treatise, like" atomic proposition "in Russell ..." , Bergen Electronic Edition (BEE for short) Item 116, 80.
  3. ↑ "a direct connection of objects ... without the aid of logical constants", BF McGuinness (Ed.): Ludwig Wittgenstein Werkausgabe Vol. 3 (short: Works 3), Frankfurt / M. 1984, 73
  4. ↑ In the note of September 1, 1937, already quoted. There he continues with a stricter definition: “But if it should be said that the proposition is an elementary proposition [...] only if its complete logical analysis shows that it is not composed of other propositions by means of truth functions, this presupposes that one has an idea of ​​such an "analysis". In earlier times I myself spoke of the "complete analysis", thinking that philosophy must finally dissect all propositions in order to clarify all connections and to eliminate any possibility of misunderstanding. As if there was a calculus in which this dissection was possible. I had in mind something of the kind of definition Russell used for the specific article [...] It was based on a false idealistic picture of language and its use. [...] "
  5. ↑ BEE # 211, 540f and # 212,344f and included in the “Big Typescript”, # 213, No. 28, p. 77 in Vol. 11 of the “Wiener Ausgabe”, ed. M. Nedo, Springer, Vienna 2000 and two thousand and one, Frankfurt / M.
  6. ↑ Werke 3, 233ff, here 247f.
  7. ↑ Works 3 38ff, here 42
  8. ↑ Works 3, 73
  9. ↑ Works 3, 64
  10. ^ BEE # 115, 55
  11. ↑ BEE # 112, 133, Big Typescript, p. 77
  12. ↑ Kuno Lorenz, Elementaraussage , in: Jürgen Mittelstraß (ed.) Encyclopedia Philosophy and Philosophy of Science. Vol. 2 of the 2nd edition Stuttgart Metzler 2005, ISBN 978-3-476-02102-1
  13. ↑ cf. also: Rainer Hegselmann: Classical and constructive theory of the elementary proposition: Journal for philosophical research 33 (1979) 89-107
  14. ↑ see this interview ( Memento from November 11, 2007 in the Internet Archive )
  15. ^ Textbook of constructive philosophy of science, 2000² pp. 26–52
  16. ↑ For connection to Wittgenstein's late philosophy, see W. Kamlah, P. Lorenzen: Logische Propädeutik , p. 44. - With "Der Vogel singt" "singen" is obtained as a self-predicator. The direct connection between an elementary statement and its introduction to the prediction is lost. ( Kuno Lorenz : Elementaraussage in: Jürgen Mittelstraß (ed.): Encyclopedia Philosophy and Philosophy of Science. Second edition. Stuttgart Metzler. ISBN 978-3-476-02101-4 (Volume 2) 2005.)