ABSTRACT: The aim of this paper is a comparative analysis of the Lvov-Warsaw School and Frege-Russell's tradition. The Comparison of these is made on the grounds of the analysis of existence. Choosing "existence" as the object of the analysis is very essential. It is so because understanding of the category of existence is strongly connected with the whole system. Thus, while analyzing the category, one can make a reconstruction of the concept scheme (in both traditions); show their functioning; and compare them to each other. It is easy to notice that in both these systems: a) analyzing is strongly connected with the way of expressing existence in a language, b) the essential problem is to which category existence belongs, c) the main question is whether existence is a predicate. Since the problem of analyzing—especially the problem of applying logic in philosophy—played an essential role both in Frege-Russell's system and Twardowski's school, the author of this paper wants to show how this was understood there (especially application of logic to some philosophical problems).

I. Introductory Remarks

G. Frege in the introduction of his "Grundlage der Aritmetik" formulates a general principle: "nach der Bedeutung der WŲrter im Zusammenhang, nicht in iherer Vereinzelung gefragt werden mu" (G. Frege, Grundlage der Arithmetik, Darmstadt 1961, p. XXII, p. 161. H. Sluga, Gottlob Frege, London 1980, p. 94.). This principle is often called a "context principle". It is stated in there that: 1) A term has a meaning when it belongs to a proposition (is one of its elements); 2) Previous analysis of a proposition is a condition for analysis of the term. Such a view presupposes that proposition is something complex and heterogeneous i.e., its elements belong to different semantic categories. The principle given above makes the following distinctions possible: 1) Division of grammatical elements from logical elements, 2) Division of subjective (psychological) elements from objective elements. Quine in his Two Dogmas of Empiricism states that applying this principle makes an important reorientation in semantics—"the reorientation whereby the primary vehicle of meaning came to be seen no longer in the term but in the statement" (W.V.O. Quine, Two Dogmas of Empiricism, in: From a logical point of view, New York 1963, p. 39). From the above it is easy to see that the meaning of a term is connected with its function in the proposition, for as we know the function depends upon it's location in the proposition. The analysis of terms at Twardowski's and his disciples’ theories is done "in abstracto." It doesn't presuppose any existence of proposition. Hence different roles which terms play in a proposition (subject, predicate) aren't important for the analysis of the terms. (K. Twardowski, Zur Lehre vom Inhalt und Gegenstand der Vorstellung, Wein (1994) p 1-15, T. Cze_owski, Logika, Toru_ 1962, p. 11-12). To reveal the proper meaning of a term, it is necessary to grasp the term as lingual equivalent of presentation. As judging presupposes the existence of at least one presentation so proposition (judgement in logical sense) presupposes the existence of at least one name. And this makes the analysis of the name (term) possible apart from the proposition.

II. Name–Predicate

Twardowski defines the name in three ways: 1) From an epistemological point of view - name is the equivalent of presentation; 2) From a semantic point of view - every name denotes an object. Any name always has its extension (denotation). (K. Twardowski, Zur Lehre, p. 10-12, F. Brenatano, Psychologie v. emp. Standpunkt, t. II, Leipzig 1925, s127); 3) From an ontological point of view—an object belonging to the denotation of the name can be: a) ens habens actualen existentiam, b) ens possibile, c) ens rationis. Such a determination of the name causes that, firstly, ordinary names, general names and fictious names are names in the same way: secondly, to be an object of the name doesn't mean to exist. Therefore Twardowski's concept of the name differs essentially from the concept of name, we can find in the predicate logic, whereas it is very close to Leˇniewski's language of "Ontology" (KŁng G., Ontologie und logistische Analyse der Sprache. Wien 1963.). What is the most important is that the same name can occur as a subject or a predicate in a statement; the parts of the complex matter may change place arbitrarily. From the above it follows that there is no essential difference between the subject and the predicate of the statement. The same name can be a subject and a predicate ( J.Jadacki,The Metaphisical Basis of K. Twardowski's Deskriptive Semiotics, in RRR Lublin 1992, p.57-70).

In the system of Frege and Russell separate characteristics of predicate and name are given. Predicate can be determined in two ways: a) in a semantic way as a general name, b) in a syntactic way as a propositional form. The predicate which is determined in these ways is not a complete expression, it doesn't designate an object i.e. its meaning is not derived directly from their denotation. Whereas the name is determined as simple symbol, directly designating an individual, this individual is its meaning: if "a" is a name it must name something. Name is a term that can only occurs as a subject in a statement. We can easily see that category of predicate essentially differs from the category of name. (B. Russell, Introduction to Mathematical Philosophy, London 1919,s.174, 179). Therefore as given we have a distinction of that which presents a fact as such and of that which doesn't. Using Ajdukiewicz's terminology we can univocally state that the predicate, in Russell and Freges, understanding is of the [n,n] category.

III. Meaningful condition and truth condition

In the second section we have stated that, according to Russell and Quine, the subject of the proposition refers to something that exists. It is stated that the sine qua non condition of predication is that the subject of proposition applies to an existing object. For example, whether the sentence is true or false depends on the success or failure of the predicate but the failure of singular term appears to deprive the predicate of the chance of either success or failure. In this case, predication is made possible, i.e. meaningful when there exists an object designated by the subject of the proposition, and this means that a truth or falsity characterization of a predicate is possible. This is the first argument for connecting meaningfulness conditions with truth conditions Another argument is based on the thesis: a = a R (x (x = a), which by virtue of its meaning leads to the thesis (x (x, which says that "everything exists." It is clearly seen that the thesis: (x (x = a) is such a thesis which guarantees the truth. This shows that meaningful conditions are essentially connected with truth conditions. In adding a term to a language it is presupposed that the term or refers to an existing object or is true of something existing.

In Twardowski's and his disciples view meaningful conditions are sharply distinguished from true conditions. The possibility of analysis of some statement's elements in abstracto, i.e., out of the statement context, shows that condition laid on the elements differ from the conditions laid on the statement. In Leˇniewski's "Ontology", by allowing all kinds of names, meaning is distinguished from truth. Therefore one can define a meaningful proposition in such a way that the concept of designation wouldn't be used. Also a definition of synonymy uses the categories of meaning, not the categories of truth. So it is seen from the above that the conditions of meaningfulness differ essentially from the conditions of truth.

IV. Contradiction and Tautology: the impossibility of denying existence

We shall distinguish three kinds of requirements which account for the fact that tautology appears in the assertion of existence and contradiction in the denial thereof. These requirements also give the basis for the thesis concerning what existence is not. 1. Requirements as to the subject in logical propositions: (a) logical: proper names must fulfil the same existential condition which holds for individual terms in the predicate calculus; (b) semantic: by definition any name in the logical sense necessarily designates an existing object. 2. Logical requirements:(A) x = x R (y (y = x)(B) Pa R (x Px(C) (x Px R Pa3. The epistemological requirement: an object designated by a proper name is given directly. Russell understands "directly" as tantamount to the impossibility of denying what is given. The above three ascertainment constitute a reason why in this system a proposition of the form "a exists," where a is a name in the logical sense, is meaningless and a proposition of the form "a does not exist" is contradictory. Demonstrating that the proposition "a exists" is tautological and the proposition "a does not exist" is contradictory is sophisticated and precise way of expressing the view that existence is not a predicate. For showing the tautological character of the former proposition, consisting in the fact that whatever was to distinguish the term "exists" is already contained in the subject, serves in fact to show that existence adds nothing to the subject of that proposition (existence is not sensorially given). On the other hand the fact that contradiction arises whenever one attaches the phrase "does not exist" to the subject of a singular proposition shows that any use of a name in the logical sense either expresses cognitive contact with reality or presupposes non-emptiness of a domain. The merit of those ascertainments consists in rejecting any possibility of considering existence as a predicate independently of any context this term may appear. In Twardowski's system the problem of tautology and contradiction of the propositions "a exists" and "a does not exist" respectively does not arise. For they accept the following ontological and logical arguments: a) An ontological aspect: expressions used in a judgement, in spite of the fact that they fulfil the function of designating a certain object, do not imply and do not justify the existence of that designated object. The function of designating, like the function of presenting, is existentially neutral. A judgement presupposes the meaningfulness of its expressions but not the existence of a designated object. That is, a judgement states the existence; but it does not presuppose the existence as it presupposes the conditions of its meaningfulness. b) A logical aspect: Twardowski calls into question the classical law of subalternation (SaP RSiP). As it is immediately seen, truth of this law depends also on an existential assumption which states that for any predicate S there is such x that x is S [ (S) ((x) Sx]. Negation of that assumption should be viewed in the context of a negative interpretation of the law of identity and this immediately leads to rejection of the law x=x.R (y (y = x) traditionally grounding the principle ((x)((x) which results in the impossibility of denying existence. These conclusions, due to the negative formula for universal judgements accepted by the Twardowski and his disciples, are considered to be incorrect. However, rejection of the law of subalternation indicates also rejection of all existential assumptions which were accepted in the classical theory of judgement. The assumption concerning a domain of objects of which something is predicated is meta-theoretical. In other words, the Twardowski rejects Quine's thesis (x (x exists). It is a consequence of the above arguments that the function fulfilled by a name is essentially different from the function fulfilled by the term "exist." Another important result is that the relation of exclusion between the propositions "a exists" and "a does not exist" is not guaranteed by the fact that the proposition "a exists" says something about a certain object in the proposition "a does not exist" does not. The condition of their mutual exclusion is based on the fact that the proposition (1) treats something as existing and (2) as non-existing.

V. Existential Proposition

We shall move now to propositions with descriptions, i.e., propositions where not a name in the logical sense but a description plays the role of a subject.

Descriptions are such language expressions which do not possess independent meaning. They are incomplete symbols. A definition of a description is tantamount to a definition of a propositional form in which that description appears. Description is not a value of name variable. Identity of two descriptions is recognized not on logical but on empirical grounds. Any description fulfils its functions regardless of whether a described object exists or not. The above characteristic indicates an essential difference between descriptions and proper names from a syntactic and semantic point of view. It shows that descriptions, in contrast to proper names, are not that parts of propositions which correspond to appropriate parts of the reality. This is the reason why a description may be a subject of a sentence only in the grammatical sense, but not in the logical. In the latter sense it is either a predicate or a conjunction of predicates. Hence, in a logical analysis the predicative function of description should be revealed. That is, one should create a situation in which the localisation of a given expression in a proposition would conform to functions fulfilled by that expression. The most important things is, however, that giving descriptions an ontologico-syntactical status different from that given to names should allow us to introduce the propositions "a exists" and "a does not exist" to language. A logical form of propositions containing descriptions is given in the following formulas: (x (Fx ( Gx) for indefinite descriptions and (x {Fx ( Gx ( (x [ ( Fy ( Gy) R ( y = x) ] } definite ones. Then, as Frege says, a proposition "some people are German" is as good an existential judgement as a proposition "some people exist" for a proposition "Leo Sachse exists" is tantamount to a proposition (x (x=Leo Sachse), which states that "there is at least one things which is Leo Sachse." Quine on the other hand, following the intention hidden in the theory of description, would say, that each case of predication including names, let as say F(a) would be explained as a shortening for quantification ((x) (Ax ( Bx). Such a proposition includes neither logical constants nor free variables and the formula "there exists at least one" or "there exists at most" is followed by a predication or a conjunction of predications.

Propositions with a description as their subject have a different logical form than those with a logical name, although the form of a subject, taken in abstracto, does not need to reveal differences: a) it is a general, not an atomic, proposition; (b) it is composed, not simple. Such a proposition is an existential proposition and is not a contradiction and not a tautology. Thus, if propositions with descriptions are de facto propositions containing characterization, then it is a logical consequence that the existential proposition in Russell's view is a proposition with description. That is, one is allowed to talk about existence if that object existence of which will be asserted is given through description. Thus, the question about existence, the question which, as we saw, was a question of whether or not existence is a predicate, should be expressed as follows: is existence, in the sense of the existential quantifier, a predicate or is it not? The conceptual formula first elaborated by Frege and Russell and later developed by Quine leads initially to a reformulation of this question and then it dictates a precise answer.

According to Brentanists the principle form of judgement is "A exists" or "AB exists". In a judgement one affirms or rejects something, and therefore the judgement quality is a condition of distinguishing various categories of judgements. Twardowski claims that the main reason for this solution is the fact that relations were usually objects of judgements and so in a natural way one looked for members or terms of that relations. The argument for a two-element structure of judgement looks as follows: (1) The motive for passing a judgement is not an attempt of unifying presentations into one whole but that of referring to a whole given in presentation and apprehended in a name. (2) Two distinct presentations are not necessary for passing a judgement; one is sufficient in order for judgement to appear. (3) Twardowski rejects the classical division of judgements into general and singular. These two latter concepts acquire then a new meaning and place in proposition. The concept of "general" is derivative with respect to negation and "singular" is derivative with respect to affirmation. (4) Matter of a judgement (AB) is the same as that of (BA). (5) For Twardowski the difference between a judgement (a) "Socrates is bold" and (b) "a man is bold" is not a difference in existential commitment but lies in the fact that in the case of (a) the ground of that judgement is a complete presentation and in the case of (b)—an incomplete presentation. This is the reason why the procedure of reducing (a) and (b) to an existential form in both cases is the same.

In a certain interpretation one could say that existence can be stated in propositions consisting of a proposition-forming functor and its argument being an affirmative or a negative proposition. For existence this functor has a form "it is true that" and is joined to a proposition p or not-p as its argument. All propositions of the form "it is good that" and "it is true that" consist of modus and dictum. From a logical point of view modus differs from dictum for the former is a functor and the latter is its argument. From an epistemological point of view, on the other hand, that what is expressed in a dictum is presentable, i.e. the content contained in a dictum is given in a presentation and the content of a modus is not; it is only stated in a judgement. Thus, between modus and dictum there appear the same categorical difference as it does between presentation and judgement. Structurally, this difference consists in the fact, that a modus jointed with a proposition of the form (s/n) and (s/n, n), which becomes its argument, constitutes a category which is one level higher than the category of its arguments: s // s / n. This is the reason why propositions in which existences is asserted cannot be understood as functions of a variable x, that is of an argument "n" but should be interpreted as propositions which are specification of a function of a variable functor "f", i.e., "s".

VI. Existence

Our analyses in the previous sections gave us the context in which it is possible to introduce the term "to exist" into language without creating contradiction. It is know that when something is said to "exist", it is always described given. In the phrase: (x (x = Leo Sachse) there is at least one thing that is identical with Leo Sachse. We maintained also that predicates, in contrast to proper names, is characterised through an expression "is true of." A predicate does not refer to something but "is true of." Saying that a predicate truly describes a certain object says something about a predicate itself (about a concept) and not about an object described by that predicate. According to Frege, in this aspect existence has a similarity to numbers (G. Frege, Die Grundlage der Arithmetik. Eine logish mathematische Untersuchung uber Begriff der Zahl, Darmastadt 1961, p.64 ). To say "something exists" is to say that "Px is true or one argument satisfies a function Px". It is then evident that existence is a predicate, but a predicate which describes a predicate, i.e. a propositional function (B. Russell, The Philosophy of Logical Atomism, in Logic and Knowledge, ed. Ch. Marsh, New York 1971, p. 232-234). If the fundamental difference between singular terms on the one hand and predicate on the other, existence must be a predicate. It cannot be a first-level predicate for this would create contradiction; so it must be a second-level predicate. Twardowski, similarly to Frege and Russell, admits that existence is not a quality of things and that truth of a proposition is connected to assertion of existence. However, existence does not appear as a meta-language presupposition and is not identical with non-emptiness of denotation or with fulfilment of a certain function. It is a specific functor, which appears when anything is something. In Leˇniewski we read: ex (a) = E (b) - b is a: a exists if and only if when for a certain b, b is a ( Cz. Lejewski, On Leˇniewski's Ontology, in Ratio, I ( 1958) n.2,p. 150-176). That is, when something is a. Thus, a functor of existence does not appear as a result of the existential commitment of a name which plays the role of a subject. This is so, for in the Lvov-Warsaw School "being an object', as it is evident in Leˇniewski's system, is a distinct thesis [(a is b) then a is an object], logically and epistemologically independent of a functor of existence. "To exist" acquires its meaning only from that it is connected to. This verb describes nothing. Twardowski's thesis that existence is not a predicate is absolute, and any relativization which takes existence to be a second-level predicate is totally foreign to their approach. Even more, both in Brentano's and in Twardowski's systems there is no possibility of reformulating a question of whether existence is a predicate into a question of whether it is not the case that existence is a second-level predicate and of connecting the category of existence either with the existential quantifier or with the variable bound by a quantifier or at least with a propositional function itself


Our analysis has shown that there are many differences between the two schools. All the sections show not only these differences but also their particular foundations. In the light of this paper we can see not only that the thesis i.e. "existence is a second level predicate" is different from the thesis: "existence is not a predicate at all" but also we can see what reasons for them are. It has been shown that applying logical tools to analysis of some philosophical problems presuppose a previous philosophical analysis of these tools. Because of that, the differences shown here have dealt not only with the analysed object (i.e., existence) but they also show different analytical tools have been used.