Empiricism, Semantics, And Ontology

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<p>12/29/11 Empiricism, Semantics, and Ontolog1/15 .ditet.com/carnap/carnap.htmlEMPIRICISM, SEMANTICS, AND ONTOLOG*RUDOLF CARNAPRevue Internationale de Philosophie 4 (1950): 20-40. Reprinted in theSupplement to Meaning and Necessit: A Stud in Semantics and ModalLogic, enlarged edition (University oI Chicago Press, 1956).1. THE PROBLEM OF ABSTRACT ENTITIESEmpiricists are in general rather suspicious with respect to any kind oIabstract entities like properties, classes, relations, numbers, propositions, etc.They usually Ieel much more in sympathy with nominalists than with realists (inthe medieval sense). As Iar as possible they try to avoid any reIerence toabstract entities and to restrict themselves to what is sometimes called anominalistic language, i.e., one not containing such reIerences. However, withincertain scientiIic contexts it seems hardly possible to avoid them. In the case oImathematics some empiricists try to Iind a way out by treating the whole oImathematics as a mere calculus, a Iormal system Ior which no interpretation isgiven, or can be given. Accordingly, the mathematician is said to speak notabout numbers, Iunctions and inIinite classes but merely about meaninglesssymbols and Iormulas manipulated according to given Iormal rules. In physics itis more diIIicult to shun the suspected entities because the language oI physicsserves Ior the communication oI reports and predictions and hence cannot betaken as a mere calculus. A physicist who is suspicious oI abstract entities mayperhaps try to declare a certain part oI the language oI physics as uninterpretedand uninterpretable, that part which reIers to real numbers as space-timecoordinates or as values oI physical magnitudes, to Iunctions, limits, etc. Moreprobably he will just speak about all these things like anybody else but with anuneasy conscience, like a man who in his everyday liIe does with qualms manythings which are not in accord with the high moral principles he proIesses onSundays. Recently the problem oI abstract entities has arisen again in connectionwith semantics, the theory oI meaning and truth. Some semanticists say thatcertain expressions designate certain entities, and among these designatedentities they include not only concrete material things but also abstract entitiese.g., properties as designated by predicates and propositions as designated bysentences.1 Others object strongly to this procedure as violating the basicprinciples oI empiricism and leading back to a metaphysical ontology oI thePlatonic kind.It is the purpose oI this article to clariIy this controversial issue. The natureand implications oI the acceptance oI a language reIerring to abstract entities will12/29/11 Empiricism, Semantics, and Ontolog2/15 .ditet.com/carnap/carnap.htmlIirst be discussed in general; it will be shown that using such a language does notimply embracing a Platonic ontology but is perIectly compatible with empiricismand strictly scientiIic thinking. Then the special question oI the role oI abstractentities in semantics will be discussed. It is hoped that the clariIication oI theissue will be useIul to those who would like to accept abstract entities in theirwork in mathematics, physics, semantics, or any other Iield; it may help them toovercome nominalistic scruples.2. LINGUISTIC FRAMEORKSAre there properties classes, numbers, propositions? In order tounderstand more clearly the nature oI these and related problems, it is above allnecessary to recognize a Iundamental distinction between two kinds oI questionsconcerning the existence or reality oI entities. II someone wishes to speak in hislanguage about a new kind oI entities, he has to introduce a system oI new waysoI speaking, subject to new rules; we shall call this procedure the constructionoI a linguistic frameork Ior the new entities in question. And now we mustdistinguish two kinds oI questions oI existence: Iirst, questions oI the existence oIcertain entities oI the new kind ithin the frameork; we call them internalquestions; and second, questions concerning the existence or reality of thesstem of entities as a hole, called eternal questions. Internal questionsand possible answers to them are Iormulated with the help oI the new Iorms oIexpressions. The answers may be Iound either by purely logical methods or byempirical methods, depending upon whether the Iramework is a logical or aIactual one. An external question is oI a problematic character which is in needoI closer examination.The orld of things. Let us consider as an example the simplest kind oIentities dealt with in the everyday language: the spatio-temporally orderedsystem oI observable things and events. Once we have accepted the thinglanguage with its Iramework Ior things, we can raise and answer internalquestions, e.g., "Is there a white piece oI paper on my desk?" "Did King Arthuractually live?", "Are unicorns and centaurs real or merely imaginary?" and thelike. These questions are to be answered by empirical investigations. Results oIobservations are evaluated according to certain rules as conIirming ordisconIirming evidence Ior possible answers. (This evaluation is usually carriedout, oI course, as a matter oI habit rather than a deliberate, rational procedure.But it is possible, in a rational reconstruction, to lay down explicit rules Ior theevaluation. This is one oI the main tasks oI a pure, as distinguished Irom apsychological, epistemology.) The concept oI reality occurring in these internalquestions is an empirical scientiIic non-metaphysical concept. To recognizesomething as a real thing or event means to succeed in incorporating it into thesystem oI things at a particular space-time position so that it Iits together withthe other things as real, according to the rules oI the Iramework.From these questions we must distinguish the external question oI thereality oI the thing world itselI. In contrast to the Iormer questions, this questionis raised neither by the man in the street nor by scientists, but only byphilosophers. Realists give an aIIirmative answer, subjective idealists a negative12/29/11 Empiricism, Semantics, and Ontolog3/15 .ditet.com/carnap/carnap.htmlone, and the controversy goes on Ior centuries without ever being solved. And itcannot be solved because it is Iramed in a wrong way. To be real in thescientiIic sense means to be an element oI the system; hence this concept cannotbe meaningIully applied to the system itselI. Those who raise the question oI thereality oI the thing world itselI have perhaps in mind not a theoretical question astheir Iormulation seems to suggest, but rather a practical question, a matter oI apractical decision concerning the structure oI our language. We have to makethe choice whether or not to accept and use the Iorms oI expression in theIramework in question.In the case oI this particular example, there is usually no deliberate choicebecause we all have accepted the thing language early in our lives as a matter oIcourse. Nevertheless, we may regard it as a matter oI decision in this sense: weare Iree to choose to continue using the thing language or not; in the latter casewe could restrict ourselves to a language oI sense data and other "phenomenal"entities, or construct an alternative to the customary thing language with anotherstructure, or, Iinally, we could reIrain Irom speaking. II someone decides toaccept the thing language, there is no objection against saying that he hasaccepted the world oI things. But this must not be interpreted as iI it meant hisacceptance oI a belief in the reality oI the thing world; there is no such belieI orassertion or assumption, because it is not a theoretical question. To accept thething world means nothing more than to accept a certain Iorm oI language, inother words, to accept rules Ior Iorming statements and Ior testing accepting orrejecting them. The acceptance oI the thing language leads on the basis oIobservations made, also to the acceptance, belieI, and assertion oI certainstatements. But the thesis oI the reality oI the thing world cannot be among thesestatements, because it cannot be Iormulated in the thing language or, it seems, inany other theoretical language.The decision oI accepting the thing language, although itselI not oI acognitive nature, will nevertheless usually be inIluenced by theoreticalknowledge, just like any other deliberate decision concerning the acceptance oIlinguistic or other rules. The purposes Ior which the language is intended to beused, Ior instance, the purpose oI communicating Iactual knowledge, willdetermine which Iactors are relevant Ior the decision. The eIIiciency, IruitIulness,and simplicity oI the use oI the thing language may be among the decisiveIactors. And the questions concerning these qualities are indeed oI a theoreticalnature. But these questions cannot be identiIied with the question oI realism.They are not yes-no questions but questions oI degree. The thing language in thecustomary Iorm works indeed with a high degree oI eIIiciency Ior mostpurposes oI everyday liIe. This is a matter oI Iact, based upon the content oI ourexperiences. However, it would be wrong to describe this situation by saying:"The Iact oI the eIIiciency oI the thing language is conIirming evidence Ior thereality oI the thing world; we should rather say instead: "This Iact makes itadvisable to accept the thing language."The sstem of members. As an example oI a system which is oI a logicalrather than a Iactual nature let us take the system oI natural numbers. TheIramework Ior this system is constructed by introducing into the language new12/29/11 Empiricism, Semantics, and Ontolog4/15 .ditet.com/carnap/carnap.htmlexpressions with suitable rules: (1) numerals like "Iive" and sentence Iorms like"there are Iive books on the table"; (2) the general term "number" Ior the newentities, and sentence Iorms like "Iive is a number"; (3) expressions Iorproperties oI numbers (e.g. "odd," "prime"), relations (e.g., "greater than") andIunctions (e.g. "plus"), and sentence Iorms like "two plus three is Iive"; (4)numerical variables ("m," "n," etc.) and quantiIiers Ior universal sentences ("Iorevery n . . . ) and existential sentences ("there is an n such that . . .") with thecustomary deductive rules.Here again there are internal questions, e.g., "Is there a prime numbergreater than a hundred?" Here however the answers are Iound not by empiricalinvestigation based on observations but by logical analysis based on the rules Iorthe new expressions. ThereIore the answers are here analytic, i.e., logically true.What is now the nature oI the philosophical question concerning theexistence or reality oI numbers? To begin with, there is the internal questionwhich together with the aIIirmative answer, can be Iormulated in the new terms,say by "There are numbers" or, more explicitly, "There is an n such that n is anumber." This statement Iollows Irom the analytic statement "Iive is a number"and is thereIore itselI analytic. Moreover, it is rather trivial (in contradistinctionto a statement like "There is a prime number greater than a million which islikewise analytic but Iar Irom trivial), because it does not say more than that thenew system is not empty; but this is immediately seen Irom the rule which statesthat words like "Iive" are substitutable Ior the new variables. ThereIore nobodywho meant the question "Are there numbers?" in the internal sense would eitherassert or even seriously consider a negative answer. This makes it plausible toassume that those philosophers who treat the question oI the existence oInumbers as a serious philosophical problem and oIIer lengthy arguments oneither side, do not have in mind the internal question. And indeed, iI we were toask them: "Do you mean the question as to whether the Iramework oI numbers,if we were to accept it, would be Iound to be empty or not?" they wouldprobably reply: "Not at all; we mean a question prior to the acceptance oI thenew Iramework." They might try to explain what they mean by saying that it is aquestion oI the ontological status oI numbers; the question whether or notnumbers have a certain metaphysical characteristic called reality (but a kind oIideal reality, diIIerent Irom the material reality oI the thing world) or subsistenceor status oI "independent entities." UnIortunately, these philosophers have so Iarnot given a Iormulation oI their question in terms oI the common scientiIiclanguage. ThereIore our judgment must be that they have not succeeded ingiving to the external question and to the possible answers any cognitive content.Unless and until they supply a clear cognitive interpretation, we are justiIied inour suspicion that their question is a pseudo-question, that is, one disguised inthe Iorm oI a theoretical question while in Iact it is a non-theoretical; in thepresent case it is the practical problem whether or not to incorporate into thelanguage the new linguistic Iorms which constitute the Iramework oI numbers.The sstem of propositions. New variables, "p," "q," etc., are introducedwith a role to the eIIect that any (declarative) sentence may be substituted Ior avariable oI this kind; this includes, in addition to the sentences oI the original12/29/11 Empiricism, Semantics, and Ontolog5/15 .ditet.com/carnap/carnap.htmlthing language, also all general sentences with variables oI any kind which mayhave been introduced into the language. Further, the general term "proposition"is introduced. "p is a proposition" may be deIined by "p or not p" (or by anyother sentence Iorm yielding only analytic sentences) . ThereIore every sentenceoI the Iorm ". . . is a proposition" (where any sentence may stand in the place oIthe dots) is analytic. This holds, Ior example, Ior the sentence:(a) Chicago is large is a proposition.(We disregard here the Iact that the rules oI English grammar require not asentence but a that-clause as the subject oI another sentence; accordinglyinstead oI (a) we should have to say "That Chicago is large is a proposition.")Predicates may be admitted whose argument expressions are sentences; thesepredicates may be either extensional (e.g. the customary truth-Iunctionalconnectives) or not (e.g. modal predicates like "possible," "necessary," etc.).With the help oI the new variables, general sentences may be Iormed, e.g.,(b) "For every , either or not-."(c) "There is a such that is not necessary and not- is notnecessary."(d) "There is a such that is a proposition."(c) and (d) are internal assertions oI existence. The statement "There arepropositions" may be meant in the sense oI (d); in this case it is analytic (since itIollows Irom (a)) and even trivial. II, however, the statement is meant in anexternal sense, then it is non-cognitive.It is important to notice that the system oI rules Ior the linguisticexpressions oI the propositional Iramework (oI which only a Iew rules have herebeen brieIly indicated) is suIIicient Ior the introduction o...</p>

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