Omyla, Mieczyslaw. 1976. "Translatability in Non-Fregean Theories." Studia Logica no. 35:127-138.
———. 1978. "Boolean Theories with Quantifiers." Bulletin of the Section of Logic no. 7:76-83.
———. 1982. "The Logic of Situations." In Language and Ontology. Proceedings of the 6th International Wittgenstein Symposium. 23rd to 30th
August 1981 Kirchber Am Wechsel (Austria), edited by Leinfellner, Werner, Kraemer, Eric and Schamk, Jeffrey, 195-198. Wien: Hölder-Pichler-Tempsky.
"Professor Roman Suszko introduced a broad class of languages into the literature of logic. In honour of Wittgenstein Suszko named these
languages W-languages. Syntax, semantics and consequence operations in these languages are based on the famous ontological principle: whatever exists is either
a situation, or an object, or a function. The distinguishing property of W-languages is that they contain sentential and nominal variables, identity
connectives and identity predicates. The intended interpretation of W-languages is such that sentential variables range over the universum of situations,
nominal variables range over the universum of objects. All other symbols in these languages except sentential and nominal variables are interpreted as symbols
of some functions both defined over the universum of situations and the universum of objects. Identity connectives correspond to identity relations between
situations, and identity predicates correspond to identity relations between objects. It is obvious that the ordinary predicate calculus with identity is a
part W-language excluding sentential variables, but the most often used sentential languages are the part of W-languages without nominal variables and identity
predicates. In this paper, I will discuss only W-languages containing sentential variables, connectives and possibly quantifiers binding sentential variables."
———. 1982. "Basic Intuitions of Non-Fregean Logic." Bulletin of the Section of Logic no. 11:40-47.
———. 1989. "Non-Fregean Logic and Ontology of Situations." Ruch Filozoficzny no. 47:27-30.
———. 1990. "The Principles of Non-Fregean Semantics for Sentences." Journal of Symbolic Logic no. 55:422-423.
———. 1994. "Non-Fregean Semantics for Sentences." In Philosophical Logic in Poland, edited by Wolenski, Jan, 153-165. Dordrecht:
Kluwer Academic Publishers.
"In this paper I intend to present the general and formal principles of non-Fregean semantics for sentences and to derive the simplest
consequences of these principles. The semantic principles constitue foundation of non-Fregean sentential calculus and its formal semantics and the
philosophical interpretations of it. Non-Fregean sentential calculus is the basic part of non-Fregean logic. Non-Fregean logic is a generalization of classical
logic. It was conceived by Roman Suszko under the influence of Wittgensteinian's Tractatus Logico-Philosophicus. The term "non-Fregean" indicates that
the set of semantic correlate of sentences need not contain of just two elements, as it assumed by Frege in Über Sinn und Bedeuting (1892). Frege
accepted the following semantic principle:
(A.F.) all true sentences have the same common referent, and similarly all false sentences also have the one common referent.
J. Łukasiewicz interpreted the common referent of true sentences as "Being" and analogically the common referent of all false sentences as
"Unbeing". Suszko called the principle (A.F) the "semantical version of the Frege an axiom".
In Abolition of the Frgean Axiom (1975) Suszko wrote: "If one accepts the Fregean Axiom then one is compelled to be an absolute
monist in the sense that there exists only one and necessary fact".
According to Suszko (A. F.) has a counterpart in the language of classical logic which is a formula asserting that the universe of sentential
variables is a two-element set. This formula is not expressed that fact in the language of non-Fregean logic.
In SCI and modal systems (1972) Suszko presents the properties of his logic as follows: "... nonFregean logic is the realization of
the Fregean program in pure logic, logically bi-valent and extensional with two modifications: (1) keep formulas (sentences) and termes (names) as disjoint
syntactic categories, having sense and denotations,as well, and (2) drop the desperate assumption that all true or false senetences have the same denotation
(not sense that is proposition)"." pp. 153-154.
———. 1996. "A Formal Ontology of Situations." In Formal Ontology, edited by Poli, Roberto and Simons, Peter M., 173-187. Dordrecht:
Kluwer Academic Publishers.
"The theoretical foundation for this paper is the system of a non-Fregean logic created by Roman Suszko under the influence of Wittgenstein's
Tractatus Logico-Philosophicus. In fact, we use just a fragment of it called here a non-Fregean sentential logic.
Our basic term is that of a 'situation'. We do not answer the question what situations are. We simply assume that sentences present
situations, and we provide a criterion determining when two sentences of some fixed language present the same situation.
The lay-out of this paper is the following. First we set out certain philosophical consequences of the assumption adopted in classical logic
that the only connectives of the language in question are the truth-functional ones. Then we sketch out briefly the axiomatics of non-Fregean sentential logic,
and of a formal semantics of the algebraic type for it.
Next, for an arbitrary model for a non-Fregean sentential logic, we pick out from the formulae true in that model a theory to be called the
'ontology of situations determined by the model in question' - in contradistinction to all sentences holding contingently in that model, i.e. not determined by
its algebra. In the ontology of situations determined by a model we point out those propositions which pertain to possible worlds." p. 173
Philosophical Interpretations of non-Fregean Sentential Logic
According to the principles of non-Fregean semantics as presented in Omyla 1975, all sentences of an interpreted language have their
references. However, not in every such language are we in a position to put forward universal and existential theorems with regard to the structure of the
universe of those references. To be in such position the language in question must contain as its sublanguage the language of non-Fregean sentential logic, or
at least a significant part of it. As we are not interested here in the universe of any particular language, but only in that of a quite arbitrary one, let us
consider now some philosophical aspects of arbitrary models of that kind. Let M = (U, F) be such a model. The elements of the universe of U do not generally
answer to the intuitions we have about the reference of sentences, and about situations in particular. However, the algebraic structure imposed on U by the
theory TR(M) is the same as that of a possible universe of situations, with regard to the operations corresponding to logical constants. Moreover, the set F
has the formal properties of a possible (or 'admissible') set of situations obtaining in that universe. This is so because sentential variables are at the same
time sentential formulae, and because the logical constants get in the model M their intended interpretation. Thus for any model M = (U, F) its algebra U is a
formal representation of some universe of situations, and the set F is a formal representation of some admissible set of facts obtaining in some universe of
situations. Not all the generalized SCI-algebras represent some algebra of situations; for not all of them contain a set F representing the facts, i.e. such
that the couple (U, F) is a model. This depends on how the operations in the algebra U are defined. For the sake of simplicity the algebra of any model M = (U,
F) for the language of a non-Fregean sentential logic will be called the algebra of situations occurring in the model M, and the designated set F will
be called the set of facts obtaining in M. Such a terminology is appropriate here for we are interested only in the formal properties of those
universe of situations which in view of our semantic principles find expression in the logical syntax of the language in question, and in consequence operation
holding in it. By the completeness theorem for non-Fregean logic it follows that for any consistent theory T in L there is a model M such that T e TR(M). Hence
any theory in the language of non-Fregean sentential logic will be called a theory of situations.
The term 'ontology of situations' we take over from the title of Wolniewicz 1985 [Ontologia sytuacji: Ontology of situations in
Polish], but we understand it a bit differently. By an ontology of situations we mean a theory describing the necessary facts of universe of
situations fixed beforehand. I.e. an ontology of situations is a set of formulae holding in some fixed universe of situations, independently of which
situations there are facts. To be more accurate, by an ontology of situations we mean a set of formulae with the following three properties:
( 1) An ontology of situations is a theory having in its vocabulary just one kind of variable - e. the sentential one. Under the intended
interpretation they range over a universe of situations. (Like in modem set theory there are variables of just one kind, i.e. those ranging over sets.)
(2) An ontology of situations is formulated in a language containing logical symbols only, i. e. logical constants and variables. To justify
that postulate let us note that such a basic theory should not presuppose any other terminology except the logical one. At most it might adopt some specific
ontological terms as primitive, characterizing them axiomatically. However, we shall deal here only with such ontologies of situations which are expressed
exclusively in logical terms." pp. 180-181.
———. 2003. "Possible Worlds in the Language of Non-Fregean Logic." Studies in Logic, Grammar and Rhetoric no. 6:7-15.
"The term "possible world" is used usually in the metalanguage of modal logic, and it is applied to the interpretation of modal connectives.
Surprisingly, as it has been shown in Suszko Ontology in the Tractatus L. Wittgenstein (1968) certain versions of that notion can be defined in the
language of non-Fregean logic exclusively, by means of sentential variables and logical constants. This is so, because some of the non-Fregean theories contain
theories of modality, as shown in Suszko Identity Connective and Modality (1971).
Intuitively, possible worlds are maximal (with respect to an order of situations) and consistent situations, while the real world may be
understand as a situation, which is a possible world and the fact.
Non-Fregean theories are theories based on the non-Fregean logic. Non-Fregean logic is the logical calculus created by Polish logician Roman
Suszko in the sixties. The idea of that calculus was conceived under the influence of Wittgenstein's Tractatus. According to Wittgenstein, declarative
sentences of any language describe situations."