The problem of abstract entities Empiricists are in general rather suspicious with respect to any kind of abstract entities like properties, classes, relations, numbers, propositions, etc. They usually feel much more in sympathy with nominalists than with realists in the medieval sense. As far as possible they try to avoid any reference to abstract entities and to restrict themselves to what is sometimes called a nominalistic language, i. However, within certain scientific contexts it seems hardly possible to avoid them.
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Empiricism, Semantics, and Ontology Rudolph Carnap [In this essay Carnap is concerned with the question of the "reality" of the sorts of what he calls "abstract entities" which are not the objects of direct observation.
Examples of such "abstract objects" include the objects of mathematics, propositions in languages, classes, and relations between objects. While earlier positivists had wanted to ban "metaphysical" questions about the "reality" of things from meaningful discourse altogether, their attempt to "reduce" all knowledge to a foundation of observation statements about "sense data" in effect was committed to the metaphysical view that such "sense data" are the real things of which reality consists, a metaphysical view known as "phenomenalism.
Such questions that take the linguistic framework as given are called by Carnap "internal" questions to that framework i. However, if one steps "outside" the framework, and asks not whether statements referring to such entities are meaningful in this language, but whether this language is the "correct" or "true" framework which "corresponds to "reality," then one is asking what Carnap calls an "external question.
In other words. The linguistic framework itself cannot be meaningfully said to "correspond" or "not correspond" to "reality"; instead Carnap now tells us it "can only be judged as being more or less expedient, fruitful, conducive to the aim for which the language is intended.
Judgments of this kind supply the motivation for the decision of accepting or rejecting the kind of entities. This is naturally problematic for the empiricist who wants to justify scientific claims to knowledge, giving the positivist a sort of "uneasy conscience": Empiricists are in general rather suspicious with respect to any kind of abstract entities like properties, classes, relations, numbers, propositions, etc.
They usually feel much more in sympathy with nominalists than with realists in the medieval sense. As far as possible they try to avoid any reference to abstract entities and to restrict themselves to what is sometimes called a nominalistic language, i.
However, within certain scientific contexts it seems hardly possible to avoid them. In the case of mathematics, some empiricists try to find a way out by treating the whole of mathematics as a mere calculus, a formal system for which no interpretation is given or can be given.
Accordingly, the mathematician is said to speak not about numbers, functions, and infinite classes, but merely about meaningless symbols and formulas manipulated according to given formal rules. In physics it is more difficult to shun the suspected entities, because the language of physics serves for the communication of reports and predictions and hence cannot be taken as a mere calculus.
A physicist who is suspicious of abstract entities may perhaps try to declare a certain part of the language of physics as uninterpreted and uninterpretable, that part which refers to real numbers as space-time coordinates or as values of physical magnitudes, to functions, limits, etc.
More probably he will just speak about all these things like anybody else but with an uneasy conscience, like a man who in his everyday life does with qualms many things which are not in accord with the high moral principles he professes on Sundays. Recently the problem of abstract entities has arisen again in connection with semantics, the theory of meaning and truth.
Some semanticists say that certain expressions designate certain entities, and among these designated entities they include not only concrete material things but also abstract entities, e.
Thus he hope to help epiricists who find it necessary to refer to such abstract entities in their scientific claims, as must all use of mathematics, to "overcome" their "nominalistic scruples": It is the purpose of this article to clarify this controversial issue. The nature and implications of the acceptance of a language referring to abstract entities will first be discussed in general; it will be shown that using such a language does not imply embracing a Platonic ontology but is perfectly compatible with empiricism and strictly scientific thinking.
Then the special question of the role of abstract entities in semantics will be discussed. It is hoped that the clarification of the issue will be useful to those who would like to accept abstract entities in their work in mathematics, physics, semantics, or any other field; it may help them to overcome nominalistic scruples. In order to understand more clearly the nature of these and related problems it is above all necessary to recognize a fundamental distinction between two kinds of questions concerning 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 linguistic 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 second, questions concerning the existence or reality of the system of entities as a whole, called external questions.
Internal questions and possible answers to them are formulated with the help of the new forms of expressions. The answers may be found either by purely logical methods or 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. One linguistic framework one might adopt, the one which is in fact the one ordinarily adopted both by Carnap and everyone who uses "everyday language," is what Carnap calls the "thing language" which refers to "observable things and events.
Once we have accepted the thing language with its framework for things, we can raise and answer internal questions, e.
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. This evaluation is usually carried out, of course, as a matter of habit rather than a deliberate, rational procedure.
But it is possible, in a rational reconstruction, to lay down explicit rules for the evaluation. This is one of the main tasks of a pure, as distinguished from a psychological, epistemology. The concept of reality occurring in these internal questions is an empirical, scientific, non-metaphysical concept.
To recognize something as a real thing or event means to succeed in incorporating it into the system of things at a particular space-time position so that it fits together with the other things recognized as real, according to the rules of the framework. However, if we attempt to ask "external questions" about the "reality" of the thing world itself, the sort of question the metaphysician as opposed to the ordinary language user asks, we generate an insoluble metaphysical puzzle, which realists and idealists try to answer in their opposing ways.
The position that Carnap defends now is not that such disputes are meaningless, but are to recongized as practical questions about the choice of a linguistic framework: From these questions we must distinguish the external question of the reality of the thing world itself. In contrast to the former question, 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 ever 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 system; hence this concept cannot be meaningfully applied to the system itself. Those who raise the question of the reality of the thing world itself have perhaps in mind not a theoretical question as their formulation seems to suggest, but rather a practical question, a matter of a practical decision concerning the structure of our language.
We have to make the choice whether or not to accept and use the forms of expression in the framework in question. Our "choice" to "accept" the thing language is not made deliberately, but is something we have grown up with; it is because of our mutual acceptance for the most part of this thing language that we are able to communicate succesfully.
To be committed to a choice of a particular linguistic framework is equivalent to accepting certain linguistic rules for how to talk about the world: In the case of this particular example, there is usually no deliberate choice because we all have accepted the thing language early in our lives as a matter of course.
Nevertheless, we may regard it as a matter of decision in this sense: we are free to choose to continue using the thing language or not; in the latter case we could restrict ourselves to a language of sense-data and other "phenomenal" entities, or construct an alternative to the customary thing language with another structure or, finally, we could refrain from speaking. If someone decides to accept the thing language, there is no objection against saying that he has accepted the world of things.
But this must not be interpreted as if it meant his acceptance of a belief in the reality of the thing world; there is no such belief or assertion or assumption, because it is not a theoretical question. 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.
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.
The purposes for which the language is intended to be used, for instance, the purpose of communicating factual knowledge, will determine which factors are relevant for the decision. The efficiency, fruitfulness, and simplicity of the use of the thing language may be among the decisive factors.
And the questions concerning these qualities are indeed of a theoretical nature. But these questions cannot be identified with the question of realism. They are not yes-no questions but questions of degree.
The thing language in the customary form works indeed with a high degree of efficiency for most purposes of everyday life. This is a matter of fact, based upon the content of our experiences. However, it would be wrong to describe this situation by saying: "The fact of the efficiency of the thing language is confirming evidence for the reality of the thing world"; we should rather say instead: "This fact makes it advisable to accept the thing language.
The framework for this system is constructed by introducing into the language new expressions with suitable rules: 1 numerals like "five" and sentence forms like "there are five books on the table"; 2 the general term "number" for the new entities, and sentence forms like "five is a number"; 3 expressions for properties of numbers e.
In contrast to the thing language, from within the system of numbers, the internal question of whether a number satisfying certain conditions exists or not, is established by logical, rather than empirical means: Here again there are internal questions. Therefore the answers are here analytic, i.
In contrast to the internal question, the extenal question asking about the reality of numbers apart from the linguistic framework is "metaphysical" in pejorative sense of positivists in that there are no empirical conditions by which such a question could be answered or in other words it is "unverifiable" , such questions are therefore "without cognitive content" i. To begin with, there is the internal question which, together with the affirmative answer, can be formulated in the new terms, say, by "There are numbers" or, more explicitly, "There is an n such that n is a number.
Moreover, it is rather trivial in contradistinction to a statement like "There is a prime number greater than a million," which is likewise analytic but far from trivial , because it does not say more than that the new system is not empty; but this is immediately seen from the rule which states that words like "five" are substitutable for the new variables.
Therefore nobody who meant the question "Are there numbers? This makes it plausible to assume that 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 framework of numbers, if we were to accept it, would be found to he empty or not? Therefore our judgment must be that they have not succeeded in giving to the external questions and to the possible answers any cognitive content.
Now Carnap turns his attention to a third linguistic framework employed by logic, the "propositional framework". In what sense can we say there are "propositions"? Again we need to distinguish the internal question from the external: The system of propositions New variables, "p", "q", etc. Further, the general term "proposition" is introduced. Therefore, every sentence of the form ".
This holds, for example, for the sentence: a "Chicago is large is a proposition. With the help of the new variables, general sentences may be formed, e. The statement "There are propositions" may be meant in the sense of d ; in this case it is analytic, since it follows from a and even trivial. If, however, the statement is meant in an external sense, then it is non-cognitive. It is important to notice that the system of rules for the linguistic expressions of the propositional framework of which only a few rules have here been briefly indicated is sufficient for the introduction of the framework.
Any further explanations as to the nature of the propositions i. A took at the rules shows us that they are not, because otherwise existential statements would be of the form: "if the mental state of the person in question fulfills such and such conditions, then there is a p such that.
The fact that no references to mental conditions occur in existential statements like c , d , etc. Further, a statement of the existence of linguistic entities e. The fact that no such reference occurs in the existential statements here, shows that propositions are not linguistic entities.
The fact that in these statements no reference to a subject an observer or knower occurs nothing like: "There is a p which is necessary for Mr. X" , shows that the propositions and their properties, like necessity, etc.
Although characterizations of these or similar kinds are, strictly speaking, unnecessary, they may nevertheless be practically useful. If they are given, they should be understood, not as ingredient parts of the system, but merely as marginal notes with the purpose of supplying to the reader helpful hints or convenient pictorial associations which may make his learning of the use of the expressions easier than the bare system of the rules would do.
Such a characterization is analogous to an extrasystematic explanation which a physicist sometimes gives to the beginner. He might, for example, tell him to imagine the atoms of a gas as small balls rushing around with great speed, or the electromagnetic field and its oscillations as quasi-elastic tensions and vibrations in an ether. In fact, however, all that can accurately be said about atoms or the field is implicitly contained in the physical laws of the theories in question.
Carnap now uses his distinction between "internal" and "external" questions to address the traditional philosophical "problem of universals," which originated with Plato and led him to his theory of forms. Philosophers have worried over the "reality" of "universals," such as "red. Carnap shows how from his point of view these questions are solved by distinguishing internal from external questions.
The system of thing properties The thing language contains words like "red," "hard," "stone," "house," etc. Now we may introduce new variables, say "f ," "g, " etc.
How can I get involved? To decree dogmatic prohibitions of certain linguistic forms instead of testing them by their success or failure in practical use, is worse than futile; it is positively harmful because it may obstruct scientific progress. Let us grant to those who work in any special field of investigation the freedom to use any form of expression which seems useful to them; the work in the field will sooner or later lead to the elimination of those forms which have no useful function. Let us be cautious in making assertions and critical in examining them, but tolerant in permitting linguistic forms. It lets you quickly and straightforwardly define languages, construct logics for those languages, and stipulate their semantics.
Empiricism , Semantics , and Ontology