p Quine started out from the fact that there are alternative, i.e., logically incompatible, interpretations of a formal system.

p For example, to define what kind of objects are numbers, we must give an interpretation of the formal system of arithmetic that would satisfy the arithmetical operations and laws; in particular, the primitive term O must be defined and the operation S the application of which to any element of the given system generates the next element Sn. Two versions of number are known. Ernst Zermelo chose the empty class X as O and the singular class {*} for every x as S_x. The numbers 0, 1, 2, 3,... become respectively X, { \] , {{ \}\, {{{ \}}j , etc.

p In Neumann’s version, the empty class X is chosen as O and the natural number is defined as the class of all preceding numbers, that is, S_x appears as x V{x} .In this case, the number 1 will be { X j , the number 2- { 0,1] , i.e., (X{X]} , the number 3- (0,1, 2,) or (x,{Xj, UMH etc.^^66^^

p Both versions satisfy arithmetical laws and operations. But they are alternative. To demonstrate that, let us ask this question: does the number 3 belong to the number 5? According to Zermelo, the answer must be negative, and according to Neumann, positive. "Indeed, according to Neumann’s theory, for any two numbers x and y, the number x is smaller than the number y, if and only if x belongs to y and * is a proper subset of y. Symbolically: x <y = x e y. Since the number 3 is smaller than the number 5, the number 3 belongs to the number 5. According to Zermelo, this argumentation leads to an incorrect conclusion, inasmuch, as one number, x, belongs to another, y, if, and only if, y is the number following the number x. Symbolically: x e y = y = S_x. Since the number 5 is not the number following the number 3, the number 3 does not belong to the number 5. Thus we come to contradictory assertions.”^^67^^ This contradiction is explained by the fact that the concept of the number following some x differs in the two theories.

p In considering objects to which a theory relates, we must give an interpretation of the corresponding formal system, that is, we must translate the terms and propositions of the given system into the terms and propositions of another. At the same time, we have seen that a given formal system admits of different translations characterised by alternative ontologies. "We may accept that translation of a theory entails a change in ontology: e.g., one may go on from a universe of numbers to a universe of sets. The new objects must satisfy the laws of the old theory, and it becomes necessary to explain in what way translation of the theory can yield incompatible systems with different ontologies. It might be asserted that the new object is an explanation of the old in the sense that the ontological status of the former is clearer than the status of the latter, so that the latter is reducible to the former. But how is one to understand that the old object is also reducible to another, new object included in an alternative theory?”^^68^^

p Quine attempts to explain these facts in a philosophicallogical conception touching on a wider range of problems than the logical foundations of mathematics only.

p He asks: what is, in general, translation from one language into another? Imagine that a researcher in anthropology has discovered a tribe absolutely unknown to science and is trying to learn its language. To do that, the researcher must translate the terms and other 4inguistic constructions of a foreign language into his native one. Each language, as Quine sees it, is an ensemble of terms and 182 grammatical forms that are not only connected with one another by definite dependence relations but also “ attached” at some points to the objects and phenomena of extralinguistic reality. It is exactly this latter circumstance that permits us to use the language as an instrument for the description of what occurs in the world. It is important to understand the manner in which the language constructions are “attached” to what happens in the real world, Quine continues. Man can know something about reality first of all because he gets certain information about it through his sense organs. But sensory information by itself does not yet carry a definite division of the world into a system of objects of a certain type. This dissection, Quine believes, is given by language, by the entire totality of its lexical and grammatical means. Different languages can apparently solve this task in different ways. For example, in order that different objects might be discovered in the world, standing in definite spatio-temporal relations to one another and subject to definite processes, there must be more in the language than the division of words into nouns and verbs. Subjects and predicates must also be differentiated in the utterance, and there must be linguistic methods of distinguishing between and identifying objects: “this”, "that which”, "the same”, expressions of the singular and plural number, etc. A language is possible in which all these linguistic means are absent. For carriers of such a language, external objects do not exist in the same manner as those to which speakers of European languages are accustomed (the character of these languages is doubtless connected with a definite type of culture). Each language is characterised by its own system of dissecting the world and by the type of meanings which are ascribed to these objects-(Quine believes that meanings are the dependences in a given linguistic system). For this reason, not only meanings but also objects or referents of linguistic expressions cannot be given extralinguistically.

p Quine tries to assert a behaviourist, naturalist view of the psyche and language. He believes consciousness to be a kind of fiction. All psychical phenomena may and must be described, in principle, in terms of the physiology of higher nervous activity. Meanings as phenomena of the world of consciousness or of a supra-individual ideal world do not exist. There are only rules for “attaching” definite language expressions to stimuli of the given sort and methods for transforming some language expressions into others. It would be inaccurate, however, to draw the conclusion that Quine interprets language as a purely formal system. Quine believes it to be fundamentally erroneous 183 to divide language expressions into those which describe experience (meaningful or synthetic propositions) and those which record purely linguistic relations (analytical propositions, that is, propositions empty of meaning). All elements of a language system are mutually connected, he believes, and this system as a whole serves as an instrument of describing experience. It is this “attachment” of the language system to experience that makes it impossible to single out those relations within the language that would be purely formal and have no definite semantic meaning. In actual fact, any relation between the elements of a given language system may be regarded both as a relation between meanings (it is important to bear in mind that meaning, according to Quine, is not an extralinguistic entity but belongs to the given language and expresses the mutual relations between its elements) and a fixation of a definite extralinguistic content, that is, knowledge of the world. The meanings of language elements do not exist outside knowledge of the world. In its turn, knowledge of the world can only exist through internal relations of the elements of the linguistic system, that is, through their meanings. Choosing the angle from which to consider the relations of language expressions to the knowledge of the world which they carry is purely conventional: the choice is determined by the goals of analysis. (True, taking into account that meanings are neither extralinguistic nor intralinguistic entities—we shall touch on this point below—^Quine thinks it best to stop all discussion of meanings and discuss only the relations within the language and the relations of the language to the world of objects or referents). Thus any language system is at the same time a definite system of knowledge about the world, a definite theory with an inherent ontology. In particular, a natural language is also a kind of theory.

p The need is sometimes asserted for distinguishing between language and theory in view of the following facts: first, different theories may be formulated with the aid of identical language means, and even at the pre-thepretical level the carriers of the given language may hold different views on a number of questions; second, it is well known that one and the same theory may be expressed in different languages, the term “language” being applied not only to the natural languages (English, French, etc.) but also to artificial ones, as the language of mathematics.

p In his reply to these arguments Quine deems it necessary to stress the conventional nature of the division into language and theory: every language is a kind of theory, and any theory may be presented as a language. One must 184 only remember that the theories themselves (and, correspondingly, the languages) may belong to different levels, they may possess a different degree of generality, etc. An everyday natural language expresses the broadest theory possible, embodying certain general orientations of " common sense”. One may agree with these general orientations and at the same time differ in the understanding of relatively more special problems. It is therefore possible to formulate in terms of one and the same natural language different systems of views, among other things, different scientific theories. As for the translation of the given theory from one language into another, it may be regarded as practically realisable only in some cases, but theoretically, that is, in the proper sense of the term, it is unattainable, Quine believes, for theoretical content unrelated to the language means of its expression does not exist. Any translation changes the content of a theory to some extent or other, and in some cases the change may be rather significant, affecting its ontology. Quine’s proposition concerning the impossibility of "radical translation" will be considered in detail somewhat later.

p The question of the types of objects presupposed by the given language is not a purely formal one for Quine, it is not merely a question of conventionally adopting a certain mode of expression, as in Rudolf Carnap’s theory. (The latter assumed that ontological questions, being “external” relative to the language system, do not admit of theoretical solution and are merely identical with accepting or rejecting the given modes of expression.) Quine insists that accepting a given theory (viz. language) signifies adopting not only certain modes of expression but also a conception of the world, or an ontology. He therefore regards ontological problems as extremely important and belonging to the content of a theory (or language). If a theory is logically formalised, the objects permitted by it are the values of its variables. (For theories of this kind, Quine formulates his famous thesis: "The ontology to which one’s use of language commits him comprises simply the objects that he treats as falling within the subject matter of his quantifiers—within the range of values of his variables.”^^69^^ In this case "to exist" means "to be a value of a bound variable".)

p Let us go back to the above example with an anthropologist. If this researcher observing the life of an unknown tribe speaking an entirely unfamiliar language attempts at the very beginning to translate into his tongue expressions unrelated directly with what is given in experience, he will hardly succeed: that much is obvious. Indeed, he 185 has no instruments for establishing the meaning of these expressions. He should obviously first of all try to establish the meanings of those words and expressions which are closest to experience, recording what is given directly. In doing so, he will apparently assume that he observes the same objects of the environment as the natives whom he studies. Further, the anthropologist will bear in mind that the neurophysiological apparatus responsible for receiving information from the external world is common to all men. He will thus conclude that stimulus meanings of words and expressions and, consequently, those meanings which directly characterise the “attachment” of the language to the objects of the external world (the referents) and which differ from meanings as a system of intralinguistic relations, can be relatively easily singled out and must be common to different languages. (True, they will pertain only to those expressions which are more or less directly correlated with experience.)

p The anthropologist will here start from the premise that referents are extralinguistic entities, namely, the objects of the external world.

p Our researcher will endeavour to apply his theoretical orientation in practice. Supposing that he observes that each time a rabbit scurries by, the native emits the sound sequence “Gavagai”. The anthropologist surmises that “Gavagai” denotes, in the language of that tribe, the same thing that is denoted by the word “rabbit” (or rather the expression "Lo, a rabbit”) in his native language. Our researcher is not fully confident that the surmise is correct. Could it be that “Gavagai” relates not to rabbits at all but to all rapidly moving objects? Or it may be that “Gavagai” is a rabbit but not any kind of rabbit—only a fast-running rabbit. To test his conjecture, the anthropologist continues his studies. On the one hand, he extends the range of observation, and on the other, establishes contact with the natives: pointing to a rabbit sitting still and pronouncing the sounds “Gavagai”, the researcher observes the reaction of the members of the tribe and tries to establish whether they regard the pronunciation of this sound combination appropriate to the given situation. Observing for some time the behaviour of the natives and communicating with them through gestures, the researcher will settle on “rabbit” (or, to be more precise, the short phrase "Lo, a rabbit”) as a translation of “Gavagai”. In this way the anthropologist, Quine states, can translate a series of words and expressions of an unfamiliar language directly correlated with the experientially perceived events.

p Translation of language constructions correlated with 186 experience in a more mediated fashion is a more complicated matter. In translating these constructions, says Quine, the anthropologist will take into account, first, the connection between them and those expressions that he can translate already, second, their inclusion in "verbal behaviour" which stands, in its turn, in definite relations with objective, experientially fixed situations, and third, certain fundamental features of such a specific object as “language” with which he is familiar from his mastery of his own language. In this way the anthropologist will finally solve the task of formulating the instruments of translation from the natives’ language into his own.

p The model for formulating a scheme of translation described here is, of course, extremely general and idealised. Still, Quine believes it to be a sufficiently precise expression of the main traits of the current practice of ethnolinguistic studies and, more broadly, the practice of translation from any language to any other in general. Quine has no intention at all of criticising this practice, for in his view it is impossible in any other form. However, he tries to show the theoretical untenability of those precepts which are usually associated with it and without which this practice can and must do, in Quine’s opinion.

p Indeed, Quine argues, what proves that the referents, the objects to which linguistic expressions refer, are extralinguistic entities? It is true, of course, that stimulus meanings are common to all men. But objects are by no means identical to stimulus meanings (whereas the anthropological researcher discussed above identifies the two). Different objective dissections may correspond to one and the same stimulus meaning, these dissections being determined by the properties of the language. When the anthropologist establishes that the sound sequence “Gavagai” refers to the same stimulus meaning as the word “rabbit”, that does not mean that both these linguistic units have identical referents. Pointing to a rabbit and pronouncing “Gavagai”, a native may mean a rabbit in a sense different from ours, e.g., those aspects of the rabbit which are at the given moment within his field of vision rather than a separate integral object characterised also by aspects that are not perceived at the given moment. “Gavagai” may be used in the natives’ language to denote something different from a kind of objects that are similar to each other in their "general rabbity" characteristics, each of them being at the same time unique; it may rather denote the phenomenon of some general “rabbitness” in the given area of space and at the given moment (in this case, the language will not possess any means of expressing 187 the grammatical form of number or a division of nouns into abstract and concrete).^^70^^ Generally speaking, there are many modes of objective interpretation of the stimulus meaning corresponding to our word “rabbit”, and enumerating them all is not the main thing. The main thing is, according to Quine, that it is impossible to establish from observation of the natives’ behaviour what types of objects are the referents of a given unknown language. (Let us recall once again that Quine strictly distinguishes between objects and stimulus meanings. It is not too difficult to establish the latter.) One and the same group of stimulus meanings, one and the same external behaviour may be reflected in different language systems characterised by different dissections of the world of objects. But if that is so, it is in general impossible to establish unambiguously the system of objects to which the foreign language refers. It also means that there is no unambiguously correct (Quine calls it “radical”) translation from one language to another. In practice the anthropologist studying a foreign language will take into account the coincidence of objects as referents of language expressions. As for the translation of those expressions which have no direct stimulus meanings, it will be attained, first, only by taking into account the connections between these expressions and those that have stimulus meaning, and second, on the analogy with grammatical and lexical constructions of the translator’s native language. Quine believes that even if one assumes that the ontology of the translator’s language is common to both languages (though this assumption cannot be substantiated at all, in his view), different analytical schemes are possible of the correlation of separate language expressions in the two languages, that is to say, different variants of translation exist. In other words, radical translation is indeterminate. As a rule, the translator does not fully realise this fact, considering the analytical scheme of translation of his choosing the only possible one. As for the mutual relations of those languages that have a sufficiently firmly established tradition of translation (e.g., translation from German into French or from English into Russian), the existence of an analytical scheme of translation may not be realised at all, for there is no question of searching for such a scheme: it was found a long time ago in the work of previous generations of translators, and the possibility of a fundamentally different scheme does not even occur to translators.

p In this connection, Quine asks this question: how can we determine the ontology of a given language or theory, that is, the system of objects to which this language or 188 theory refers? For the carriers of the given system, the language modes of expression and the ontological content are inseparable from each other: the world is given them through a system of meanings, and meanings embody knowledge of the world. To separate that which belongs to language from that which pertains to the world itself, we must go beyond the framework of the given language system and compare it with the world. Quine believes, however, that we have no way of penetrating the world as such, for the world as an ensemble of objects is always given to us only through some language system or other. (Quine does not negate the objective and real existence of the world, that is, its being independent of man and language, but he insists that the world is given to man only through some linguistic or theoretical system.) We cannot therefore speak of absolute ontology of the given language system but only of its relative ontology. When we ask what are in reality the objects of the given language or theoretical system, the role of the "world of objects" with which the system under study is compared is played by another language or theoretical system and not the world as such. The ontology of such a system is not discussed here: the system itself and the world of its objects are given as something undifferentiated. In other words, in defining the ontology of the given linguistic or theoretical system, we perform in actual fact translation from one language into another. The language into which we translate defines the world of objects of the language from which we translate (that is to say, the object to which the word “Gavagai” refers, to recur to the above example, is a rabbit, i.e. that which is denoted by the appropriate word of our language). We should not forget, however, that depending on the language into which a text in the given language will be translated, the latter will be ascribed different ontologies, in Quine’s opinion. But even if we refer to two given languages only, here again one may accept different analytical schemes of translation (let us recall Quine’s thesis about the indeterminate character of radical translation).^^71^^ In this case, when the question arises about the ontology of the language into which we translate, here again we run into the same problem: we can say something about this ontology only in relation to some other language. Quine concludes that there can be no answer of absolute value to the question of what the objects of a given theory are. The ontology of a given theory can only be established in relation to some other theory. If we want to know, for instance, what kind of objects are in fact numbers, we must translate the system of 189 arithmetic into some other mathematical system, e.g., set theory, and one of the theories (Zermelo’s) will provide one answer to this question, while Neumann’s will give another. As a matter of fact, the reverse procedure is also possible. To answer the question about the kind of objects sets really are, we may try to translate the propositions of set theory into the language of arithmetic. On the analogy with the relativist theory of space and time, Quine believes it possible to speak of a relativist theory of the objects of theory, or of ontological relativity.^^72^^

p An impcJrtant point of Quine’s conception is that each language has its own mode of dissecting the objective world. This assertion, however, does not entail, in Quine’s view, that each language has its own ontology, into which we cannot penentrate from the outside, being therefore compelled to interpret it on the analogy of the ontology of our own language. Quine believes that one cannot discuss the ontology of the given language as long as it is considered by itself: although a language carries a definite world picture in itself, the interrelation between language and the world of objects is not singled out in it. To find out in what way language expressions are correlated with objects, i.e., to single out the ontology of the given language, we have to speak about it in some other language, the ontology of which is not discussed in the context of this discourse. The problem of ontology is one of mutual relation or mutual translatability of different languages or theories. We therefore do not know the ontology of our own language, says Quine.

p The ontology of the latter can only be discussed in some other language (and the ontology itself will look differently depending on the language into which the texts in our own tongue are translated). True, one may attempt to reveal the ontology of our language while remaining within its boundaries, and such attempts are made both in everyday life and especially in logic and philosophy. In this case, however, our language must figure twice, in different capacities: once as an object language (that is, the language whose ontology is elucidated), and another time as the language in which we discuss the ontology of the object language. Here we translate the sentences of our language into sentences of the same language. The sentences we translate need not be equivalent to those that result from translation. Generally speaking, even in this case, according to Quine, we can choose different analytical schemes of translation. And that means that the ontologies ascribed to our language will differ depending on the scheme of translation.

p When we communicate with another person speaking the same language as we do, we are convinced that we refer to one and the same world of objects. We believe that in this case, at any rate, our own object dissection of the world and that of our partner must coincide.

p But why are we so confident about it? Quine asks. Is it solely because our interlocutor pronounces approximately the same sounds as we do in similar situations? How can we make judgements about the meaningful world picture which our partner associates with these sounds? We ascribe to his words a relation to definite objective referents only because we translate his speech into the language which we use ourselves. From Quine’s standpoint, our language as a system of predispositions to definite verbal behaviour appears to us in quite a different light than any other language which we always treat as an object language: that is true not only of the language of a foreign people but also of that of our countrymen.

p Quine believes that the conception of ontological relativity is applicable to all language systems or theories: not only to natural, ordinary (national) languages but also to theories in mathematics and other sciences. True, we should bear in mind the following important factor. In mathematics, we can do more than translate the theory of arithmetic into the language of set theory: we can also perform retranslation. Each of these theories may appear as an object one (the theory whose ontology is established) or the one that functions as the premise (the theory specifying the ontology of the object theory). The reason for this freedom of action is equal mastery of both theories. The situation with natural languages is different. Only one of them is our native or mother tongue. We therefore usually judge of the ontology of other languages on the basis of translating them into our own: it is the latter that specifies the object dissection of the world in ternis of which we understand and interpret other languages.

p In natural scientific knowledge the problems of ontology are settled, in Quine’s view, in the same way, i.e., through translation of the terms and propositions of one theory into the language of another. For instance, if we ask ourselves the question what really is the object referred to in physical theory as the atom, we must translate this theory into the language of another, e.g., that which operates with the "sense datum" terms, or uses the terminology of laboratory operations, or else applies terms referring to non-observable objects: it will be shown in the last case that such and such substantive processes of 191 objective reality correspond to the word “atom”. The process of translation may reveal that some language expression of the object theory does not correspond to any real entity from the standpoint of the premise theory: that is the position, e.g., with the term “ether” if we try to translate the theory of classical physics into the language of modern science. It may also happen that we shall be unable to find any modes of translating one theory into another. In this case, Quine thinks, we cannot make judgments about the ontology of the given theory. Yet, Quine believes, the attempts to reduce the content of natural scientific knowledge to the content of "sense data" and protocol statements (something that was intensely practiced by logical positivists) are untenable. At the same time he regards conceptual theoretical gaps, the emergence of fundamentally new systems of knowledge, and scientific revolutions as a rare and undesirable phenomenon in the development of natural science. Here he differs strongly with Kuhn, as we see. In Quine’s view, natural sciences develop through gradual changes and restructuring of theoretical constructions, so that questions of ontology arise here fairly rarely. (Quine believes that even metamathematical studies, dealing with problems of interpretation of formal systems, can in some cases do without solution of ontological problems.)

p According to Quine, the experiences of each group of subjects that are carriers of a given language or theory are more or less continuous, and the experiences of each individual subject are even more so. Everything that appears in the field of his experience, including other languages or theories, is interpreted in terms of the world picture embodied in this experience. The question of how other subjects that are carriers of other languages or theories see and understand the world is meaningless, according to Quine: one ascribes a certain ontology to other languages proceeding from the properties of one’s own. At the same time, this conception starts put from the premise that different language or theoretical systems implement different object dissections of reality. And that means that, although experience is continuous within the group of carriers of the given language, it is discrete in the relations between different groups using different languages (or theories).^^73^^ Groups of carriers of different languages or theories live in different worlds. Accepting this thesis, Quine concurs with Sapir and Whorf as well as Kuhn. A substantive addition Quine makes to this thesis is his assertion that the subjects themselves that are carriers of different languages or theories usually do not notice that 192 they live in different worlds, as they interpret other worlds on the analogy of their own. They can learn another language (translating it into their own) and even communicate with the carriers of another language and yet remain outside this other world. Different worlds exist in different dimensions and do not therefore come into contact or interact. The carriers of different languages or theories in Quine’s interpretation remind one of Leibnitz’s monads which reflect the whole world, yet "have no windows" and do not actually interact with other monads, although they have the impression that they do participate in such interactions.

p That does not, of course, mean that a person cannot master another language so that it will become his second native language (that is only possible when a person is included in a different cultural system). The subject will in this case master the mode of object dissection of the world which is characteristic of the new language. However, for Quine the main point is that one cannot simultaneously use two languages. When the given subject speaks the new language and thinks in it, his native language functions as an object one, and vice versa. Two languages (and correspondingly two world pictures) cannot come into contact in one experience field. The transition from one language to another as the basis of conversation and thinking may in this case be viewed in the same light as transposition into a different dimension.

p Kuhn and Feyerabend, as we recall, insist that different paradigms and major scientific theories carrying different visions of the world come into conflict with one another; it even happens in the consciousness of an individual subject, as a result of which one of the paradigms replaces others. According to Quine, however, different language or theoretical conceptions characterised by different object dissections of the world cannot come into this kind of conflict, lying as they do in different dimensions: whenever the interrelation of two theoretical systems is elucidated and their ontologies are established, one of them acts as an object theory and the other, as a premise theory.

Quine does not specially consider the problems of scientific revolutions. His assertion, however, that conceptual changes in the development of science can only be gradual shows that he does not accept the existence of such revolutions. Reasoning in abstracto, we can, of course, imagine an attempt at describing successive replacement of paradigms in the language of Quine’s conception of ontological relativity. In this case, however, we would, first, have to reject the assertion of the gradual 193 character of conceptual changes in science and, second, give an interpretation of the paradigms themselves and the process of their successive replacement that would be essentially different from Kuhn’s.