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Share full text access. Please review our Terms and Conditions of Use and check box below to share full-text version of article. Abstract The development of communication Infrastructures and the rapid growth of networking facilities in information technologies increase information mobility and the decentralization of work processes in industry and services. Citing Literature. Related Information.
Close Figure Viewer. Browse All Figures Return to Figure. Previous Figure Next Figure. Email or Customer ID. Forgot password? Old Password. If I am not mistaken,the anomalous position of mathematicshad its basis in the fact that the concept of a theory of Objects had not yet been formed. Mathematics is, in its essentialfeatures,a part of the theory of Objects. I say "in its essentialfeatures" in order to explicitly leave open the possibility of a specificdifferentiationof mathematicalinterests which I believe is one of the unexplainedmatters mentioned above.
Thh claim cannot be elevatedto the level of an accomplishedfact, but, on the contrary, is scarcely beginning to be fulfilled, for the theory as a whqle is somethingto be developed, and not somethingready to'be exhibited.
The high stageof development of one of its parts constlutes an external obstacleto the -J-t. E- tl" beginningsof relevant work, see E. Mally, in No. A mathematicianmight well be disturbed by the suggestionthat he is "really" a theorist of Objects Gegerutandstheoretiker. This is so becausea sciencewhich already exists cannot be either charactenzedor even named in terms of a sciencewhich is still merely an object of aspiration. Moreover, a relatively general science as such can and must set itself goals which are foreign to the relatively specializedsciences.
This secondpoint is somewhatobscured,in the case of the relation of mathematicsto the theory of Objects, by the fact that in the domain of the theory of Objects mathematics represents not one of several but, at least for the time being, the only special science of its type which is known and recognized. A twofold task, perhaps quite dissimilar in its two aspecls, is, accordingly, to be ascribedto the theory of Objects. On the one hand, the theory of Objectshas the problems of a scienceof the highest degreeof generality and comprehensiveness.
On the other, it has, as if standing in the place of a whole group of specializedsciences,those problemswhich so far have not received any special consideration. Becauseof the necessityfor descendinginto relatively specialized domains which arises from this situation, its nature as a general scienceis unavoidably again obscured. Consequently,the subsumption of mathematicsunder the theory of Objects can easily appear to threatenthe distinctive characterand specialclaim of the former.
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However, such external and accidental matters ought not to hamper insight into the essentialconnection between mathematics and the theory of Objects tg the extent that that connectionexists. This not entirely simple situation can, perhaps, best be given its due by saying: Mathematicsis certainly not the theory of Objects, but is now as before a sciencein its own right. However, its Objects are includedin the domain which the Theory of Objects,also having its own justification, must deal with as a whole.
The severalsciencesrnust first be given. T'hen the necessityfor examining more closely their nature and mutual relationship may become justified. However, science is also, at least partially, the result of premeditatedactivity. In employingsuch foresightedness,the theory of sciencecan also deal with scienceswhich do not yet exist but should exist. It can find itself directed toward renderingthe idea and the tasks of such sciencesas preciseas possible in anticipation of them.
In the preceding discussionwe found ourselvescompelled by our interest in Objects to. In this connettion, it is incumben? The theory of Objects, which we must claim to be a proper science,is, in the main, a sciencethat for the time'beinghardly exists at altr-especially as a separatediibipline explicitly recognizedin its own right.
But, although no investigationshave been carried out in the name of the theory of Objects, we must not suPposethat this sciencehas been wholly neglected. This is not the proper time to trace theseconnections;nevertheless,in introducing this new science it is appropriateto make somemention of them, Thus, some notice can be taken of necessitieswhich have been felt for a long time and which have already found expressionin the r,nostdiverseways, necessitieswhich have arisen in consciouslyworking out interests that are very widespread,but which have often been unconscious of their real goal.
In fact, I believethht no specialhistorical investigationis actually required to establishthat, although the theory of Objects may not have been pursued "explicitly" heretofore, it has all the rnore frequently been pqrsued "implicitly. We can in this sense,even if it be only for momentary undqetdnding, separatea specializedand a generaltheory of Objects. The Theory of Obiects [ ] We have referred above to the faat that speciatrized in a certain sensethe most specialized ttreory of Objec'r. This luster has long led to efforts to make the procedure, more mathematico,accessibleto other sciences-I might say, other domains of Objects.
We shall scarcelybe tripped unr by any significant error if we add: wheneversuch atternptshave been undertaken, then to that extent an effort has been naadealso to do the task of specializedtheory of Objects in areas outside of rnathernatics. When the merchant or the engineercatrculates,he has as little to do with the theory of Objects as with any other theory.
Flowever, certain presuppositionshaving to do with Objects lie naturally at the base of such practicanapplications; it is not otherwisewhen the application results in a theoretical interest. In contrast with the technique of calculation which dernands complete attention, the nature of these presuppositionscan rernain fully in the background"This is ilinrstratedmost clearly by the theory of probability and the theory of probable error, which even now are still not recognizedby everyone as naturatrlybelonging to Logicand psychology.
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The nature of these assulroptionscan possibly put the calculationsin question at the serviceof the theory of Objects as we can see in the case of the theory of combinations. Meanwhile, geometry seernsbetter prepared than arithrnetic to extend a hand beyond its narrow borders to discoveriesin the theory of Objects.
It pertains to the theory of Objects becauseit is in no way tied up with the so-calledreality, or more precisely,real existenceof tirne. It is obvious that the analogy is valid for phoronorrnyto a rnuoh greaterrneasure;if-what seemsto me to need no proof-,A. Fliifler is correct in contending that tension is the "third fundamental phenomenonof rnechanics" along with space and time,82then an additional direction is indicated in which this science,without prejudice to its naturaXlyernpirical character,engagesthe iraterestsof the Eltjfler, "Zur gegenwiirtigen Naturphilosophie," p.
In any case, "the theory of dimensions" mentioned on p. I trust that it is not excessively personal for me to report at this time that much of the essential nature of the way in which the theory of Objects frames its questions originally occurred to me while I was engagedin supposedly exclusivelypsychologicallabors toward clarification of thesematters. What I have called the encroachmentof the mathematicalapproach beyond its strictest limits has an instinctive and unconscious iharacter in comparison with the completely explicit attempts to expand that domain and to generalizeto the fullest extent possible that way of framing a problem.
Thesehaveprobably alreadyachieved someimportanceunder the name of the generaltheory of functions; one cannot fail to see this in such designationsas "the theory of extension" and "the theory of manifolds," and even under the frequently misunderstoodcatchword, "meta-mathematics. A similar statusmay be ascribedto the endeavors and results customarily grouped under the generalname of "mathematical logic," even though those endeavorsare in many respects intended for an'entirely different purpose.
Cf' his Gr. The Theory of Obiects [ tences. As this quick survey showsdespiteits somewhatcursory nature, the theory of Objects is by no means completely dependentupon work which is yet to be performed. Indeed, one might ask whether the attempt to introduce a "theory of Objects" lneans any more than a new name for an old concern. One could easily go on to find that it is indifferent to the investigationitself whether it is undertaken by a mathematician,physicist, logician, ot a student of the theory of Objects.
Nevertheless,a misunderstandingwould lurk in this last move-a misunderstandingwhich was countered explicitly at the beginning of this exposition. It is certainly immaterial who solvestheoretical problems and under which name he solvesthem.sourliamalsubt.gq
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If recognitionas a special discipline should be successfullyobtained for the theory of Objects, one would, now as before, always have physicists,linguists, and the repreto be thankful to nnathematicians, sentativesof other sciencesfor their energeticfurthering of the interestsof the theory of Objects, even when they do not mean to havedepartedfrom the legitimateterritory of their own science. But, for many, recognition of this science would clarify the nature of the problems to be solved-especially where as is commonly the case the most relevant works are not of the greatestimportance.
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A natural consequence of this is that old problemsare renderedprecise and new ones introduced. From the point of view of the theory of Objects, the problems and concernswhich we have just grouped together-and which at first glancewould seemso diverse-present themselvesas belonging together; the value of such a point of view is thus confirmed.
Ct, Uber Annahmen,esp, pp. Therefore, if someofleshould claim that these studiei are properly existencetherefore can be inferred from the fact of the appearance. I would certainly not deny that the things that thus appear are of interestto the physicist.