OBJECTS, QUANTIFICATION, AND ONTOLOGY
(from Milton Munitz, Contemporary Analytic Philosophy, pp. 363-375)


 



We have seen that for Quine ontology-as a saying of what there is-is to be understood basically as a matter of speaking of objects. Accordingly, ontologies may be identified, and the differences among them recognized, by what kinds of objects they posit or countenance. The sophisticated language of quantification, as used in logic, helps to make clear what ontological commitments are involved in some stretch of discourse. Since on this approach much hinges on the interconnections among `object', `reference to objects', `quantification', and `ontology', Quine has devoted a great deal of attention to these topics. He has done so by way of giving a deeper analysis to these themes than he had sketched in "On What There Is," under the pressure of having to respond to various critics. Our task now, in coming to closer grips with Quine's philosophy, is to follow him in some of these further details.

Despite the great stress that Quine places on the role of logic in refining and regimenting our language for purposes of giving the latter greater power as a cognitive instrument, he is not so preoccupied with the importance of logic that he fails to take into. account the wider setting in which it comes to play its role. On the contrary, he gives much attention in various directions to this wider setting, thereby making the understand ing and appreciation of the positive powers of logic deeper. He also drives home our sense of the human origins of logic and of the inescapable relativity inherent in an o our conceptual tools. Thus Quine's study of the relations of logic to language engages him, among other matters, in an examination of the psychological and social factors involved in the learning process by the individual; and of the multiple uses of language. It encourages him to take note of the social factors at work in developing many different languages, as well as the interpersonal role that language plays in communication. These questions have to do, among other things, with what he calls .the 'ontogenesis of reference'-the discrimination of the various stages in the growth of an individual, from the earliest steps taken in early childhood in learning to use language to the later mastery of the most sophisticated language-use by the mature adult. In short, Quine is aware of the numerous forces at work -in human nature and the surrounding natural and social environment that affect the use of language. He is on guard not to fall into the trap himself of taking formal logic as a heaven sent self contained tool that does not hav its earthly roots in human nature.

Quine is sensitive, in another direction, to what logic can and cannot do. He is deeply aware of the matter of the diversity of conceptual systems, and of the fact that we cannot get `outside' the use of some conceptual system, however per vasive and .taken-for granted it may be. We cannot divest ourselves of of the grid or filter of a conceptual system in order to determine what the world is like independently and absolutely-that is, .apart from.theuse of such a conceptual system and what is says the world is like. Quine thus takes serious the matter of conceptual relativity. He drives home this point by examining the intimate connection of thought and language. He upholds what we may think of as a severely modified ,form of 'Kantianism' -a type of linguistic relativism. Logic, for all its importance in regimenting language; and in improving the rigor and clarity of linguistic expressions, does not give us the means for achieving some set of unique, absolute, and eternally valid insights. Logic itself is hedged in by all our human limitations; it is relative to the encompassing contextual uses uses of multiple human languages.

Let us turn to see, in specific examples, how Quine works out his support for these general points. Let us consider, first, the whole question of how. we come to develop and use the term `object' itself. ;this is a term that is important (as we have seen) in in understanding the very enterprise of ontology, in the use of first-order quantification, and in examining what lies at the bottom of many philosophic controversies-especially those about whether, in addition to physical objects, we must acknowledge other types of object as well, for example abstract, intensional, or possible ones.

Let us consider first, as Quine recounts it, the way in which a child, at a very early stage, long before it comes to be in a position to discriminate objects as such, acquires its first items of vocabulary. Consider, in other words, the character of early, unsophisticated language-use. It occurs when a child learns to respond to or use its first few words. Out of this matrix it will come at a later stage, and with the help of adults and their tools alreadyacquired, to discriminate and identify objects.

Consider the acquisition of such terms as `mama', `water', and `red', at an early stage of the child's development.

We in our maturity have come to look upon the child's mother as an integral body who, in an irregular closed orbit, revisits the child from time to time; and to look upon red in a radically different way, viz., as scattered about. Water, for us, is rather like red, but not quite; things are red, stuff alone is water. But the mother, red, and water are for the infant all of a type; each is just a history of sporadic encounter, a scattered portion of what goes on. His first learning of the three words is uniformly a matter of learning how much of what goes on about him counts as the mother, or as red, or as water. It is not for the child to say in the first case `Hello! mama again', in the second case `Hello! another red thing', and in the third case `Hello! more water'. They are all on a par: Hello! more mama, more red, more water...
In order for the child to be able to use words in such a way that it can be said to have begun to master the conceptual scheme employed by adults, it must learn to be able to refer to or talk about individual objects, recognized as such. For this purpose it needs to learn how to use individuative terms.
It is only when the child has got on to the full and proper use of individuative terms like "apple" that he can properly be said to have taken to using terms as terms, and speaking of objects. Words like "apple," and not words like "mama" or "water" or "red," are the terms whose ontological involvement runs deep. To learn "apple" it is not sufficient to learn how much of what goes on counts as apple; we must learn how much counts as an apple, and how much as another. Such terms possess built-in modes of individuation?'
A physical object such as an apple has an individual identity, marking it out from other objects, closely similar or not. Its individual identity enables one to identify it as the same object from one moment to the next, or as enduring over a stretch of time; and, if it is a movable or moving physical object, as the same object that moves from one place to another. Individual physical objects are the first and paradigmatic examples of `object'. The terms we use to refer to individual physical objects, one at a time-individuative (singular) terms-accomplish this by what Quine calls `divided reference'.

Individuative terms, however, need to be carefully distinguished from `mass (or bulk) terms' that might sometimes be confused with the individuative ones. Thus there is a difference between the use of the term `apple' to represent a kind of stuff, `apple-stuff, as distinguished from an apple' or 'these apples' or `this apple', where the latter expressions show the use of individuating (divided reference) devices of language, used to refer to individual objects.

Individuative terms are commonly made to double as bulk terms. Thus we may say "There is some apple in the salad," not meaning "some apple or other"; just as we may say "Mary had a little lamb" in either of two senses. Now we have appreciated that the child can learn the terms "mama," "red," and "water" quite well before he ever has mastered the ins and outs of our adult conceptual scheme of mobile enduring physical objects, identical from time to time and place to place; and in principle he might do the same for "apple," as a bulk term for uncut apple stuff. But he can never fully master "apple" in its individuative use, except as he gets on with the scheme of enduring and recurrent physical objects.

How can we ever tell, then, whether the child has really got the trick of individuation? Only by engaging him in sophisticated discourse of "that apple," "not that apple," "an apple," "same apple," "another apple," "these apples."

Until individuation emerges, the child can scarcely be said to have general or singular terms, there being no express talk of objects. The pre-individuative term "mama," and likewise "water" and "red" (for children who happen to learn "water" and "red" before mastering individuation), hark back to a primitive phase to which the distinction between singular and general is irrelevant. Once the child has pulled through the individuative crisis, though, he is prepared to reassess prior terms. "Mama," in particular, gets set up retroactively as the name of a broad and recurrent but withal individual object, and thus as a singular term par excellence. Occasions eliciting "mama" being just as discontinuous as those eliciting "water," the two terms had been on a par; but with the advent of individuation the mother becomes integrated into a cohesive spatiotemporal convexity, while water remains scattered even in space-time. The two terms thus part company.

The mastery of individuation seems scarcely to affect people's attitude toward "water." For "water," "sugar," and the like the category of bulk terms remains, a survivalof the pre-individuative phase, ill fitting the dichotomy into general and singular. But the philosophical mind sees its way to pressing this archaic category into thedichotomy. The bulk term "water" after the copula can usually be smoothly reconstrued as a general term true of each portion of water, while in other positions it ismore simply construed as a singular term naming that spatiotemporally diffuse object which is the totality of the world's water .

As we have just seen, in his exploration of the powers and uses of language, Quine studies some of the features of the acquisition of competency in the use of language in its first, tentative, and relatively crude stages in early childhood. At the same time, `language', as Quine and every one else realizes,covers an enormously rich, complex, and diversified aspect of human culture and behavior. In the study of that complexity

Quine is much concerned to stress the importance of using the refined tools of language that come to the fore in the development of the technical vocabularies ofscience, mathematics, and logic. In particular, as a logician working within the broad tradition of the new logic inspired by the pioneering studies of Frege, Quine hasdevoted himself to showing the contribution logic can make toward achieving economy, exactness, and rigor in our use of language for cognitive purposes. It does soby what Quine calls a process of `regimenting discourse' and by offering a `canon_ is notation' for codifying the underlying structure of language.

Among these logician's tools there is the powerful and important use of the predicate calculus, along with the use in the calculus, of the techniques of quantifyingvariables. The understanding of what is involved in the use of this calculus leads directly to raising various questions about the nature and extent of the domains to beranged over in quantification, the meaning of such terms as `existence' and `identity', the matter of thedecidability or undecidability of the truth-value of quantified sentences, and many other related topics. These questions have obvious connections with certaintraditional concerns of philosophy, particularly in metaphysics (ontology). In our summary of Quine's papers, "On What There Is" and "Two Dogmas of Empiricism," we have had a glimpse of his approach to these kinds of questions. Let us now fill in some of the details by taking advantage of his later writings, among them hismajor work Word and Object.
 
According to Quine, the advantages of using the formal devices of the predicate calculus become wholly clear if we restrict our attention to the use of first order quantifications. In such quantifications we make use of the universal quantifier, `(x)', which is read `everything x is such that ', and the particular (sometimes called the `existential') quantifier, `($x)', read as `something x is such that-'. In first-order quantifications these quantifiers are attached to individual variables, i.e., to variables that range over individual objects. Although there are just these two quantifiers, the universal and the particular, each can be defined in terms of the other, so that for purposes of economy we can get along with one quantifier only. Thus `($x)( ___x)' can be rewritten as 'not (x) not (___ x)', and in turn `(x)(___ x)' can be rewritten as `not ($x) not (___ x).

For purposes of determining the ontological commitments of language that makes use of quantifiers, such- commitments are clearly revealed by the use of either type of quantifier, universal or particular. Each type of quantifier, as attached to a variable, ranges over a domain of'-objects (values of the variable) as bound by the quantifier in question. Thus the so-called `existential' quantifier (the particular quantifier) has no greater role in revealing ontological commitments than does the universal quantifier. However, in his earlier writings, and in his later writings as well, Quine sometimes features the use of the `existential' quantifier in discussing the criterion of ontological commitment, as well as in connection with the meaning of the term `existence'. While his stress on the use of the existential quantifier could lead to some misunderstanding, it should be emphasized that the use of the universal quantifier is just as involved in expressing ontological commitments as is the particular one, for it is the kind of objects represented by the domain over which the quantified variables range that determines the ontological commitments of a given theory. The question of general ontological commitments has to do with the semantics of the language. For this purpose, the use of quantifiers, whether universal or particular, will serve equally well to indicate the domain of objects over which the quantifiers range. On the other hand, the use of some one of the quantifiers or some array of them to translate the logical structure of a specific sentence has to do with the truth-conditions for that specific sentence. It is more pointed in its concerns than the broader `semantic' question of the ontological commitments presupposed in using the quantifiers as ranging over some posited type or kind of objects.

We come now to a further point. For Quine there is an important distinction to be made between variables and schematic letters. Thus quantifiers are only to be used in connection with variables, not with schematic letters. Variables are those expressions which, in first-order quantifications, range over the domain of values that are the individual objects making up that domain. In first-order quantification the quantified variables are always individual variables. None of the other expressions used, e.g. predicate expressions, can be quantified, since predicates do not stand for objects.

When we schematize a sentence in the predicative way "Fa," or "a is an F," our recognition of an "a" part and an "F" part turns strictly on our use of variables of quantification; the "a" represents a part of the sentence that stands where a quantified variable could stand, and the "F" represents the rest.  Thus, where predicates or other nonquantifiable expressions are used, these are represented by schematic letters, not by variables. Accordingly, while certain appropriate linguistic expressions may be substituted both for individual variables and for schematic letters, those expressions that can be substituted for individual variables would typically be names or other singular terms and would represent individual objects in the domain of values of the variable. However, linguistic expressions that could be used as substitutions for schematic letters do not oblige us to consider them as designating some object or as representing some kind of nonlinguistic entity. Whereas variables range over values (a domain of objects), schematic letters are linguistic expressions for which other linguistic expressions may be substituted. It is therefore the variables, as quantified, that carry ontological commitments, not schematic letters.

The importance of making the foregoing distinction comes out in connection with Quine's discussion of the topic of `existence'. It is here, according to him, that the role of quantifying variables makes clear what claims to existence amount to.
 

What we have to get clear on is when to consider that a sentence mentions certain things and thereby assumes their existence. Looking for names is no help, since anyone can disclaim assumption of the object by declaring that the alleged name is not a name. What counts, rather, are the variables. The objects assumed in a given discourse are the values of the variables. They are the things in the ,miverse over which the variables are interpreted as ranging. If a man's assertions are such that protons,- unicorns, or universals have to be among the values of the variables in order for the assertions to be true, then he has no business denying the assumption of protons or unicorns or universals.

We have the modern logic of quantification to thank for making evident the existential force of the variable. The existential quantifier "($x)" is the distilled essence of existential talk. All imputations of existence can be put as existential quantifications. Moreover, all the other uses of variables-in universal quantification, in singular description, in class abstraction, in algebra-can be paraphrased in familiar ways so that the variables end up as variables of existential quantification.

This existential role belongs to variables only in the strict sense of the word; not to schematic letters. Schematic letters, such as the sentence letters of truth function logic and the predicate- letters of quantification theory, occur only in schemata and not in sentences, and they take only substitutions and not values.

By variables I mean bound or bindable variables. These, if we construct our discourse along the lines of neoclassical logic, are the primary instrument of reference to objects. The objects are the values of the variables .

We have been examining Quine's views of the scope and character of ontology. In the judgment of some philosophers, Quine's efforts to restore the legitimacy, meaningfulness, and importance of this branch of philosophical injury are of no avail. According to these critics, those who engage in ontologicaldiscussions and disputes are not able to bring their discussions to a successful resolution; the questions they raise and a fortiori the proposed answers they would give are pseudoquestions and seudoanswers. One of these critics is Rudolf Carnap. This type of charge was made by him in a well-known paper entitled "Empiricism, Semantics, and Ontology."  To this Quine responded, for instance in his paper "On Carnap's Views on Ontology."2' In the course of this response heseeks to show his grounds for divergence from Carnap, and thereby-to uphold what he takes to be the genuine, legitimate cognitive status of ontology. It will be of interest for us to explore this dispute as a way of obtaining a further clarification of Quine's views on the nature of ontology. As we explore answer, we shall find that in some respects he shows himself to share with Carnap certain -views about the nature of cognitive inquiry. It is a position we might characterize (roughly) as a type of `conventionalism', `pragmatism', `linguistic relativism', or (severely modifed) `Kantiamsm'. In any case;-as we explore these points we-shall at the- same time be laying the groundwork for our examination, later in this chapter, o f certain other aspects of Quine's philosophy, in particular his stance on modality and the indeterminacy of translation.

Let us turn first to Carnap's strictures on `ontology' and the way he would characterize its status. Ca rnap begins his discussion by pointing out that when philosophers engage in a dispute about, for example, whether-there are certain abstract entities such as properties, classes, nu mbers, and propositions -with philosophers called `realists' (in the Platonic sense) giving an affirmative answer and those called `nominalists' giving- a negative answer-this dispute cannot be - resolved as long as it is conducted in the traditional manner.-For, Carnap maintains, the dispute so conducted fails to take into account an important distinctionthat between `internal' and `external' questions. The failure to draw and acknowledge-this distinction is common to all sides in the dispute. It is only by making this distinction that one is in a position to settle the dis pute. One will then realize that insofar as the dispute concerns an `external' question it is a pseudoquestion and there is no possible meaningful or correct (true) answer that could be given. The question has no genuine cognitive validity, and hence cannot be answered by a `yes' or `no' on the basis of some kind of relevant objective evidence. This type of `external' question underlies the- dispute between the realists and nominalists regarding whether there are or are not abstract entities of one kind or another. It is also characteristic of other types of disputes in ontology. They are all equally `metaphysical', i.e. `meaningless', hence cognitively irresolvable. On the other hand, if the question were seen as simply an `internal' question, then it is not only meaningful but in many cases relatively trivial because easily solvable, or at any rate, if not already solved, one for which the procedure for obtaining a solution is readily available. In order to understand this fundamental distinction between `external' and `internal' questions, we first have to follow Carnap as he introduces the notion of a framework.

Are there properties, classes, numbers, propositions? In order to under
stand more clearly the nature of these and related problems, it is above all
necessary to recognize a fundamental distinction between two kinds of questions con
cerning the existence or reality of entities. If someone wishes to speak in his
language about a new kind of entities, he has to introduce a system of new ways of
speaking, subject to new rules; we shall call this procedure the construction of
a framework for the new entities in question. And now we must distinguish two
kinds of questions of existence: first, questions of the existence of certain
entities of the new kind within the framework; we call them internal questions; and sec
ond, questions concerning the existence or reality of the framework itself,
called external questions. Internal questions and-possible answers to them are formu
lated with the help of the new forms of expressions. The answers may be found
either by purely logical methodsor by empirical methods, depending upon
whether the framework is a logical or a factual one. An external question is of a
problematic character which is in need of closer examination.


To bring out the force of these distinctions Carnap considers a number of examples. Consider first the use of the linguistic framework in daily use in which we talk about and describe ordinary observable physical objects and events=tables, chairs, walking, raining, and so on. Carnap calls the use of this framework the use of the `thing-language'.

Once we have accepted this thing-language and thereby the framework of things, we can raise and answer internal questions, e.g., "Is there a white piece of paper on my desk?", "Did King Arthur actually live?", "Are unicorns and centaurs real or merely imaginary?", and the like. These questions are to be answered by empirical investigations. Results of observations are evaluated according to certain rules as confirming or disconfirming evidence for possible answers .
Suppose that instead of asking specific questions about things of the kind just illustrated (internal questions that can be answered by empirical investigation), one -were-to ask--"Are there really things in the world?" Carnap says- that this kind of question is no longer answerable by appropriate empirical methods. It is an `external' question.

In contrast to the former questions, this question is raised neither by the man in the street nor by scientists, but only by philosophers. Realists give an affirmative answer, subjective idealists a negative one, and the controversy goes on for centuries without being solved. And it cannot be solved because it is framed in a wrong way. To be real in the scientific sense means to be an element of the framework; -hence this concept cannot be meaningfully- applied to the framework itself.

To accept the thing world means nothing more than to accept a certain form of language, in other words, to accept rules for forming statements and for testing, accepting, or rejecting them. Thus the acceptance of the thing language leads, on the basis of observations made, also to the acceptance, belief, and assertion of certain statements. But the thesis of the reality of the thing world cannot be among these statements, because it cannot be formulated in the thing language or, it seems, in any other theoretical language.


Consider, as another example, the language concerning the natural numbers, in which use is made of such expressions as 'five', 'one million', 'odd', `prime', 'plus', and so on.

Here again there are internal questions, e.g., "Is there a prime number greater than hundred?" Here, however, the answers are found, not by empirical investigation based on observations, but by logical analysis based on the rules for the new expressions. Therefore the answers are here analytic, i.e. logically true.
Suppose, once more, that the external, 'ontological' question were raised concerning the existence or reality of numbers as such. To this Carnap replies:
Those philosophers who treat the question of the existence of numbers as a serious philosophical problem and offer lengthy arguments on either side, do not have in mind the internal question. And, indeed, if we were to ask them: "Do you mean the question as to whether the system of numbers, if we were to accept it, would be found to be empty or not?", they would probably reply: "Not at all; we mean a question prior to the acceptance of the new framework". They might try to explain what they mean by saying that it is a question of the ontological status of numbers; the question whether or not numbers have a certain metaphysical characteristic called reality (but a kind of ideal reality, different from the material reality of the thing world) or subsistence or status of "independent entities". Unfortunately, these philosophers have so far not given a formulation of their question in terms of the common scientific language. Therefore our judgment must be that they have not succeeded in giving to the external question and to the possible answers any cognitive content. Unless and until they supply a clear cognitive interpretation, we are justified in our suspicion that their question is a pseudoquestion, that is, one disguised in the form of a theoretical question while in fact it is non-theoretical; in the present case it is the practical problem whether or not to incorporate into the language the new linguistic forms which represent the framework of numbers .
To summarize the main point that Carnap makes: We need to distinguish genuine q lions that have a possible answer by the use of suitable scientific, lo- gical, or mathematical procedures. These are `internal' to a framework, to the use of an adopted language. On the- other hand, questions raised in ontology about the 'reality' or `existence' of certain entities (things,, numbers, abstract entities such as classes, propositions, properties, and so on) are =external-questions. They have no genuine merit as theoretical, cognitive questions,-because there is no acceptable way of answering them. There is, in short, an important division between science and ontology; the former, raises 'intemal' questions, the later "external' questions:

In his response to Carnap, Quine disagrees with the distinction Carnap draws between science and ontology, insofar as Carnap would limit the first to the raising of internal questions and criticize the latter for raising external ones. Quine agrees with Carnap about the relevance and importance of considering what is involved in the adoption of a `framework' (a language or conceptual scheme). And he agrees with Carnap that we cannot 'step outside' the use of some language to ask about what there is in reality, apart from our using some language or other to say what there is. He agrees, furthermore, with Carnap that the choice among different available languages, old or newly proposed, is a matter that ultimately calls for decision on grounds of 'practical', i.e. pragmatic, considerations-that is, how well, in comparisons with others, a language or conceptual scheme works, as judged in terms of considerations of simplicity,-economy, and the like. Quine's main-point. of divergence from Carnap has to do with Carnap's insisting on making a sharp distinction between science and ontology. For Quine, both science and ontology require the use of some language or other, and what holds true for the one holds for the other. When properly construed, ontology is not mired down in raising pseudoquestions; it has as sound a status in cognitive inquiry as does any branch of science, and is bound by the same typical conditions or constraints that apply to any legitimate inquiry. Any inquiry must make use of some language. All 'saying' is relative to the resources of the language used for doing the saying. Since we can never dispense with the use of some language, this holds as much for science and mathematics as it does for ontology. The only relevant considerations have to do with judgments of a comparative sort, in which one language or conceptual system is compared with another, but.never with something 'outside', i.e., with 'reality' as it exists independently and apart from the use of a language system.

In supporting these general points of disagreement (and also agreement) with Carnap, Quine chooses to call attention to what he considers a more fruitful distinction than the one Carnap makes between 'internal' and `external' questions. Instead of saying that ontology raises the latter kind of questions and science the former kind, Quine says that if we properly understand what ontology is about we will say that ontology is interested in working with certain broad category expressions, whereas science is preoccupied with what may be called expressions for subclasses. This is a question of a breadth or range of interest; it is a question of degree, not of kind. It is not that category-expressions as used by ontology are on 'the other side' of the framework, and subclasses on 'this side'. Both are on 'this side'. Both ontology and science must employ language, and cannot raise `external' questions. But instead of condemning ontology for working with 'category' expressions, as distinguished from the more limited domains of one or another science, one should recognize that it is every bit as legitimate an inquiry as that of science.

Carnap's dichotomy of questions of existence is a dichotomy between questions of the form "Are there so-and-so's?" where the so-and-so's purport to exhaust the range of a particular style of bound variables, and questions of the form "Are there so-and-so's?" where the so-and-so's do not purport to exhaust the range of a particular style of bound variables. Let me call the former questions category questions, and the latter ones subclass questions. I need this new terminology because Carnap's terms `external' and `internal' draw a somewhat different distinction which is derivative from the distinction between category questions and subclass questions. The external questions are the category questions conceived as propounded before the adoption of a given language; and they are, Carnap holds, properly to be construed as questions of the desirability of a given language form. The internal questions comprise the subclass questions and, in addition, the category questions when these are construed as treated within an adopted language as questions having trivially analytic or contradictory answers.

But now I want to examine the dichotomy which, as we see, underlies Carnap's distinction of external and internal, and which I am phrasing as the distinction between category questions and subclass questions. It is evident that the questio whether there are numbers will be a category question only with respectto lan ages which appropriate a separate style of variables for the exclusive purpose of referring to numbers. If our language refers to numbers through variables which take classes other than numbers as values, then the question whether there-are numbers becomes a subclass question, on a par with the question whether there are primes over a hundred.

According to Quine, then, the basic distinction between ontology and science is not where Carnap draws it, but has to do with the kinds of bound variables that a discipline chooses to deal with. If the bound variables are of the type and scope that belong to category words one may say this marks an ontological statement, whereas if it is of the subclass variety it may be part of a statement belonging to one or another of the sciences. This distinction is not an absolute one, and will vary with the kind of language in use. Since both ontology and science have to adopt some language__or other, and quantify over some range of variables, there is no essential difference in cognitive status, or with- respect to `meaningfulness', that divides ontology from science. At best, the difference between ontology and science is a question of degree of scope, of range of subject matter,. of role- within a total system of beliefs.

Within natural science there is a continuum of gradations, from the statements which report observations to those which reflect basic features say of quantum theory or the theory of relativity. The view which I end up with . . . . is that statements of ontology or even of mathematics and logic form a continuation of this continuum, a continuation which is perhaps yet more remote from observation than are the central principles of quantum theory or relativity. The differences here are in my view differences only in degree and not in kind. Science is a unified structure, and in principle it is the structure as a whole, and not its component statements, one by one, that experience confirms or shows to be imperfect.

Carnap maintains that ontological questions, and likewise questions of logical or mathemacal principle, are questions not of fact but of choosing a convenient scheme or framework for science; and with this I agree only if the same be conceded for every scientific hypothesis.