Let L be any language. According to Tractatus Logico-Philosophicus by L. Wittgenstein sentences of any language present situations. Thus, for every language L there is associated set of situations UL given by the sentences of the language. The situattions are assigned according to non-Fregean semantics of sentences, the principles of which were described in [4] and [5]. Recently many authors discuss the problems: What are situations?, What is formal representation of situation? What is the role of the notion of situation in the theory of meaning? These problems shall not be discussed in my paper. What I would like to do is just to introduce the notion of ontology ofsituations understood as a set of formulas having three properties:

1. The ontology of situations is a theory in a so called first order language, i. e. language containing only one kind of variables.

2. The ontology is formulated in a language containing only logical symbols, i. e. variables and logical constants.

3. The theory describes only necessary facts from a universe of situations earlier presupposed. I borrowed the term ontology of situations from the title of [8], but this term is understood in a little different way here. If the alphabet of given language L does contain variables which run over the universe of situations UL , then no explicit theorems can be stated in it in a formalized way referring to the universe of situations associated with the language. To make it possible the alphabet of this language should contain, among others, the following symbols: the identity connective, variables running over a given universe of situations and quantifiers binding these variables. According to Suszko - the author of non-Fregean logic - the variables running over the universe of situations are fundamentally different from other kinds of variables, because the former are sentential formulas and only sentential variables can be substituted for them. Nominal variables cannot run over the universe of situations. They run over the set of their reification equivalents. These remarks lead to the following notion of a language of sentential logic: L is a language of sentential logic iff L is a set of formulas built, in the usual way, of three kinds symbols: statement letters, connectives, and formator binding statement letters (for example quantifiers, description operator and so on). To a language of sentential logic two interpretations usually apply:

(i) referential, when statement letters are variables running over a certain universe,

(ii) substitutional, when statement letters are schematic letters representing sentences of some languages or are abbreviations of sentences. Here are some examples of referential interpretations of a language of sentential logic:

1. The Fregean interpretation of the classical sentential logic. Sentential variables run over a two-elements universe: Truth, and Falsehood.

2. Lukasiewicz's and Post's interpretation with sentential variables run over a set of logical values.

3. Wittgenstein's and Suszko's interpretation with sentential variables running over a universe of situations.

4. Kripke's and Kit Fine's interpretation with sentential variables running over a set of possible worlds. An important example of a language of sentential logic is the language of non-Fregean sentential logic. The formulas of the language are built, in the usual way, by means of the following symbols: sentential variables: p, q, r,..., truth-functional connectives: Ø (negation), Ù (conjunction), Ú (alternative), Þ (implication), Û (equivalence), identity connective: º and quantifiers: ", $ binding sentential variables. Non - Fregean logic was created by Suszko under the influence of Wittgenstein's Tractatus Logico-Philosophicus in 1968. In honour of Wittgenstein Suszko named languages in which the logic is defined , W- languages. In the alphabet of these languages there are, among other symbols, two kinds of variables: one running over a universum of situations and the other one running over a unversum of objects. Thus, the language of non-Fregean sentential logic is such a fragment of W-languages which does not contain any nominl formulas. If to the axioms of non-Fregean logic the axiom:

(p º q) º(p Û q) is added (called by Suszko the ontological version of the Fregean axiom) then the truth-functional logic is obtained with two equivalence connectives, which are only graphically different but interchangeable in any context without altering the theorems of any theory containing Fregean axiom.. The logical bivalence of non-Fregean logic is expressedby theorems: Ø( p Û Ø p) p ÚØ p

From them and the Fregean axiom it follows that in classical logic variables run over two-elements sets which may be identified with the set of logical values. In the language of non-Fregean sentential logic it is possible to formulate theorems related to any universe situations but in the language of the classical sentential logic only theorems releted to two-elements Boolean algebra can be formulated. Semantics for non-Fregean logic was created by S. L. Bloom and R. Suszko in their papers [1],[2] and [7]. According to the semantics the models for the language of non-Fregean sentential logic are structures: M =(U, F) where: U is a generalization of SCI- algebra on the given set U, and F is suitable subset of U. In any model M the logical constants have the intended interpretation, therefore any model for the language of sentential logic will be treated as a formal representation of a certain universe of situations with a distinguished set of of facts in it. In order to simplify the formulations a generalized algebra of any model M for non-Fregean sentential will be called the algebra of situations, and the set F will be called the set of all facts occuring in this model. Algebra of situations is the same as what Suszko named semimodels. Let M be

(U, F) any model for the language of non-Fregean sentential logic, and K = {(U, Fi): i Î I}

be the family of all models for the language of non-Fregean sentential logic L determined by the algebra of situations U. Models of the class K are determined by the same set of situations. Moreover they are articulated in the same way in the language L, and differ at most the set of facts realized in them. We denote: Tr(M) - the set of all formulas true in M of the language of non-Fregean sentential logic, Val(U) =Ç {TR(M): M Î K}

Definition. T is an ontology of situations in the language of non-Fregean sentential logic L iff T is a theory in L and there exists an algebra of situations U such that T Ì Val( U). Symbolically: T is OSL Û T ÎTH(L) and T Ì Val(U) where: OSL - denotes the set of all ontology of situations in the language of non-Fregean sentential logic L, TH(L) - the set of all theories in the language L. Three direct corollaries of the definition:

1. Cn (Æ) is the smallest ontology of situations, i. e. Cn (Æ) is an ontology situations and moreover every ontology of situations includes Cn (Æ).

2. If X is a set of equalities i. e. X = { aºb: a, b ÎL} such that Gn(X) is consistent then Cn(Gn(X)) is a certain ontology of situations,(where Gn(X) is the set of all generalizations of all formulas from the set X).

3. In the language of classical sentential logic there is only one ontology of situations, i. e. the set of all formulas true in two-elements Boolean algebra, i. e. the set of all tautologies of the classical sentential logic.

References

[1] Bloom S. L., A completness for"Theories of kind W", Studia Logica 27, (1971), p. 43-55.

[2] Bloom S. L., Suszko R., Investigations into the the sentential calculus with identity, Notre Dame Journal, (1972), 13/3, p. 289-308.

[3] Omyla M., The logic of situations, Language and Ontology, Wien, 1982 , p. 195-198.

[4] Omyla M., Die-Suszko Semantik für Satz-Sprachen, Termini, Existenz, Modalitäten, Philosophische Beiträge, Humboldt Uniwersität zu Berlin, 1986, p. 72-80.

[5] Omyla M., Zarys logiki niefregowskiej, (An Outline non-Fregean logic), in Polish, Warsaw 1986.

[6] Suszko R., Ontology in the Tractatus of L. Wittgenstein, Notre Dame Journal of Formal Logic 9, (1968), p. 7-33.

(7) Suszko R., Quasi-completeness in non-Fregean Logic, Studia Logica 29, (1971), p. 7-14.

[8] Wolniewicz B., Ontologia sytuacji (Ontology ofsituations), in Polish, Warsaw 1985.

Ruch Filozoficzny, XLVI, no. 1, 1989, 27-30.