Ladislav Tondl (Czechoslovakia)
PROBLEMS OF EMPIRICAL BASIS OF SCIENCE
1. SCHEMES OF THE ANALYSIS OF THE „UNIVERSE OF DISCOURSE”
An obvious postulate of scientific activity is th a t the results of such activity, i. e. any statem ents of science refer to something. In o th er words it is presum ed th a t statem ents made by science have not only a meaning, b u t also a denotation, i. e. th a t th ey refer to a certain orbit of objects the aggregate of w hich we shall term a universe of discourse. W hat we have here in mind is not the universe of discourse of science in its entire ty, in all the historical developm ent of science. Such a universe of discourse can n atu ra lly provide an object of philosophical meditations. In our reflections, however, we shall always speak of the universe of discourse as of a lim ited region, specified in a certain m anner, w hich is inter alia also relativised by a certain province of science, a science ta k en always at a certain stage of its evolution. This also implies th at the universe of discourse so conceived m ust be regarded as a p a rt of th e w orld at large. This also implies th a t this universe of discourse can be extended to include new objets, not reckoned w ithin the original delim itation of the universe of discourse.
From the form al point of view the universe of discourse is a certain non-em pty set of objects characterised in a certain m anner. W hat is therefore always needed is a definite criterion th a t would enable us to decide w hether any object is, or is not, an elem ent of the given uni verse of discourse, and w hether it is therefore essential to take into consideration this elem ent when analysing the universe of discourse. In science, the criteria for these decisions can assume diverse characters: For em pirical and experim ental sciences, these m ay be, above all, empi rical or experim ental criteria. We consider it a m atter of course th a t biology trea ts of phenom ena of live nature, th a t therm ics studies th er mal phenomena, accustics the acoustic phenom ena, and so forth. It m ay
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certainly be pointed out th a t the attrib u tes “live” , “th erm al”, “acoustic” can be regarded as em pirical attribu tes only in the common language, w hereas in contem porary science, we by far do not consider these or sim ilar attrib u tes as p u rely empirical or even as discernible by m an ’s sensory activities. A sim ilar objection is entirely legitimate. In the developm ent of science we frequently witness how, in the course of the specification of the universe of discourse of a discipline of science, n u m erous originally purely em pirical criteria gradually change their m ean ings, how in science theoretical criteria are taken into consideration in an ever increasing measure. The m ajority of the criteria th at origi nally operated as em pirical criteria, are thought of as theoretical criteria in contemporaneous science. Due to this development, m any of the the oretical criteria are at present very rem ote from the originally purely em pirical criteria. If, for example, we delim it the scope of our investi
gations by stating th a t we shall be concerned w ith “phenomena of non-linear oscillations”, we shall not be in the first analysis concerned w ith an answ er to the question w hether we are facing electromagnetic, mechanical or other oscillations, b u t on the contrary, we shall aim at those common theoretical characteristics which are being shared by em pirically entirely different provinces. Analogous thoughts can be form ulated w ith regard to processes of m anagem ent, inform ation processes and so on, inasm uch as here as well w h at is in th e forefront of our attention is the stru cture of these processes, their adequate expression by the corre sponding m athem atical formalism, and not the em pirically heterogeneous facets of the systems w ithin whose fram ew orks the processes of m an agem ent and communication processes come into play. The criteria for the specification of a universe of discourse can also have a conventional character. W hen studying the properties and the behaviour of systems of constructive elements, for instance, of the Turing machines (which have not been, and basically cannot be, either technically or em pirically implemented), it is expedient to lay down, in advance and on the strength of a convention, which objects shall be included into the re spective universe of discourse.
In science, in the specification of the given universe of discourse, we are basically unable to establish the p rio rity of certain criteria over others. A lthough we are witnessing a situation w here the selection of these criteria is to an ever g reater ex ten t dependent on theoretical conclusions and also on theoretical aims, pragm atical considerations are gaining ground here as well, considerations determ ined, above all, by an answ er to the question w hat the given inquiry serves or ought to serve. In th e progress of science we experience a reciprocal effect of w hat is being referred to as the “object of science” and w hat forms the complex of methods, discoveries, theoretical and experim ental means of a given science, including th e goals at the attaining of which
the use of these means is aimed. The selection of th e universe of discourse no doubt influences the choice of the methods, theoretical and experim ental means and so fo rth —on the other hand, however, the complex of these methods and means substantially influences the specification of the universe of discourse. Such reciprocal influencing and the consequent gradual changes in the specification of th e universe of discourse appear very clearly in th e developm ent of certain fields in the physics: W hen accoustics first form ed and was la te r developed, it was at first concerned w ith the study of the phenom ena th a t could be registered by the hum an ear. The first steps in the specification of the universe of discourse w ere obviously founded here on a p urely em pirical criterion. However, a fu rth e r study of acoustic phenom ena, the study of the oscillations, the discovery of the D oppler effect as w ell as fu rth e r advances in this field not only caused such phenom ena th a t could not be discerned by th e hum an ear to be included into the original universe of discourse, b u t also brought about fundam ental chan
ges in the original criteria for the specification of th e so-called acoustic phenomena.
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So far, we have been considering the universe of discourse solely by presenting an outline of certain problem s of ex tern al specification of the universe of discourse. However, of no lesser im portance to the m ethod ology of science are also the issues connected w ith an intern al analy sis of the universe of discourse. It is evident th a t such in ternal analysis depends prim arily on the n atu re of the universe of discourse itself. In our fu rth e r account we shall tu rn our attention to some of the more essential schemes of the analysis th a t can be applied p articularly to em pirical and experim ental sciences.
Basically, we m ust point out th a t certain elem entary schemes of in ter nal analysis of the universe of discourse w hich we encounter in em piri cal and experim ental sciences are due to common sense, and originate in some categories of the curren t lan g u ag e.1 This is especially the case w ith the scheme “thing—pro p erty ”, (or the extended scheme “thing— —p roperty—relation”), but after all w ith fu rth e r schemes as well: the “situations” scheme in the universe of discourse, and th e “events” scheme. Let us now inquire at some length into the individual schemes, and into certain logical and methodological links between such schemes. Their strict distinction is of course being carried out solely in view of the need for a more detailed analysis—in the common language and cu rrent thinking such schemes are intertw ined and m utually supplem ent each other.
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(a) One of the most cu rren t schemes of the in tern al analysis of the universe of discourse is the scheme “thing—pro perty”, or the m ore w id ened scheme “thing—p roperty—relation”. L et us how ever underline th e fact th a t in this connection we shall not go into the details of the traditional ontological complex of problems, which the philosophical literatu re concerned w ith these concepts has hardly succeeded in clearly ordering, b ut shall focus our attention exclusively upon those questions th a t are related to the analysis of the universe of discourse and the developm ent of the language of science.
The scheme “thing—p ro p erty ” is anchored in the common language, and is based on the m ost elem entary version of empiricism: we are in a position to distinguish various „things” about u s -b y differentiating the “properties” of these things, the sim plest version of such differen tiation being the sensory differentiation. In this m ost elem entary form the notorious dispute about the p rio rity of the thing or the p ro perty does not arise as yet. Such a dispute only arises as soon as we begin to ascribe to this scheme m ore profound philosophical and especially ontolo gical contexts. 2 If we centre our attention upon the form al aspects of the said scheme, and confine ourselves to th e most general determ ina
tion th a t the “thing” is an object (individual object) in the given universe of discourse, then it is tru e of any one thing th at it is possible to state something about it. This “stating som ething” about a thing we usually in terp ret in such a w ay th a t to an individual thing, an ordered pair, a triad, a group of n things we assign certain properties.
The most convenient logical form s for the expression of the said scheme are therefore supplied by the logic of predicates. The universe of discourse is here a (non-empty) class of (individual) objects. The predicates we then reg ard as nam es of th e properties of these objects, and also as nam es of the properties of ordered pairs, triads, groups of n objects, hence also th e nam es of relations between objects. The scheme “thing—property—relatio n ” which relies upon common sense and a most elem entary version of empiricism, can thus be explicated by those means th a t are provided by predicate logic. W ith respect to any p red icates, the universe of discourse can be partitioned into subclasses of objects, ordered pairs, triads or groups of n objects, to which the given predicates could or could not be assigned. N aturally we cannot out th a t some of these subclasses m ay be em pty. This also means th a t the said scheme, w hich we have explicated by means of predicate logic, p er m its us to develop a dual in terp retatio n of the role of predicates: an
2 Carried to ultimate consequences, the concept of the „thing” is an abstraction in a similar respect as the concept of „property”. What we are faced with is merely that in the continuum of discernable phenomena we have a tendency to regard some of these phenomena as „things”, and others as „properties”. Nor can we rule out whatever we shall term a „thing” in one context, we shall call „property” in another.
in terpretation of th e role of the predicates as nam es of the properties of objects (or ordered pairs, triads or groups of n objects), this version representing, from the sem antic viewpoint, the intensional aspect of this interpretation, and an in terp retatio n of the predicates as names of the classes of objects (ordered pairs, triads, groups of n objects), this la tte r version representing th e extensional aspect of this in terp re tation.
The concept of “predicates” can be considered as a nam e of any pro p erty of objects or their ordered pairs, triad s or groups of n objects. In this connection we m ay be confronted w ith properties discernible em pirically, or w ith properties th a t can be discerned on the basis of other criteria. It cannot be ruled out, either, th a t the class of those objects th a t w ill arise from the given universe of discourse by appli cation of a certain predicate will be an em pty class.
The explication of the traditional scheme “thing—p ro p erty —relatio n ” by means of a language founded on th e logic of predicates is able also to solve the problem of relativ ity in the relation “thing—p ro p erty ”. F rom the n a tu ra l language we have learn t th a t it is possible to “state som ething” about a class or a pro p erty as well. Also in the language of science it is m andatory to take into account a situation w here the statem ents form ulated by science do not refer to th e objects alone of a universe of discourse, bu t also to classes of these objects, th eir p ro perties, etc. From this angle it is indispensable to distinguish predicates as different types, i. e. to take into consideration w hat was brought into logical thought by the theory of types.
The predicates are fu rth erm ore presum ed to be capable of express ing all the properties of, and relations betw een objects, i. e. for exam ple em pirical and theoretical properties, qualitative and quantitative pro perties, tem poral and spatial, invariable and variable properties, etc.
(b) A nother scheme of internal analysis of a universe discourse is one th a t can be best characterised as a “situation” scheme, a scheme of “tem poral and spatial regions”, “fields”, and so forth. In the case of the scheme “thing—property—relation” the analysis of the universe of discourse can lead us as fa r as the individual objects. H ere we therefore presum e th a t either we shall have a t our disposal certain principles of individualisation, or the individual objects are the actual starting-point of the specification, of the in tern al analysis and the partition of the entire universe of discourse. In the case of the “situations” scheme, there is no need to postulate th a t through the medium of an analysis of the universe of discourse we shall reach individual objects.
In the cu rren t language, the question “w hat is the situation?” (this question being norm ally understood as “w hat is the situation in a certain assumed or delim ited space?” ) is usually answ ered by characterising the distribution of certain p arts of the universe of discourse, th e ir
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reciprocal relations, and the like. The question “w hat is the situation?” (it being understood th a t w hat is m eant here is the “meteorological situation” in a definitely assumed or defined region) will be answ ered by the meteorologist to the effect th a t in one p a rt of the contury it is raining, in another the sky is overcast, and in still another sunshine has been registered. A question aimed at the situation on the battlefield shall be answ ered by th e staff officer by offering a description of the distribution and location of the forces of his side, combined w ith the inform ation on the location of the tanks, infantry, etc. of the enemy.
It m ay seem th a t the “situations” scheme represents a certain modi fication of the scheme th a t is founded on the relationship between the categories of “a p a rt” and “th e w hole”. Such a contention is however only p artly justified, nam ely in so far as by “the w hole” we understand the entire universe of discourse. In the event of th e “situations” scheme it is typical th a t we have in m ind the relation of the given region, the given field—to the entire universe.
The “situations” scheme can be best explicated by means of the lan guage w hich is based upon the logic of the classes (or those m athem at ical m eans th at are supplied by the theory of sets). W hat is involved here are in particular diverse possibilities of operations concerning classes, the relations betw een classes, and the like.
Although, as we have already pointed out, in th e case of the “situ ations” scheme th ere is no need to postulate th a t the analysis of the universe of discourse shall be carried through down to individual ob jects, on the other hand it is not necessary either to rule this out entirely. We m ust bear in mind th a t individual regions or fields also consist of individual objects, and th a t we are obviously not always capable of achieving a complete differentiation of these individual objects. The essential feature consists in th a t these individual objets can be consid ered as elements of th e given class.
In this connection it is expedient to discern two degrees of indivi dualisation:
(1) The elem entary degree of individualisation consists in w hether we are able to prove th a t the object being considered does or does not belong to a certain class.
(2) A higher degree of individualisation consists in w hether we are able to prove th a t the object being considered does or does not belong to all these classes th a t we are able to distinguish by means of a p a rti tion of the universe of discourse.
These two degrees of individualisation can also be expressed by those m eans th a t are offered by the scheme “thing—p roperty—relation”. In the form er event we are able to prove only one property of the object. In the la tte r event we are able to prove all (known, accessible) properties of the object.
From the methodological point of view the differentiation of the two degrees of individualisation is most im portant. In medical diag nostics, an exam ple of the first-degree individualisation is a statem ent th a t the p atien t th a t is being exam ined has influenza. A sim ilar sta tem ent has already a practical im portance and can affect the m easures
to be taken, such as the choice of therapy. However, for a m ore thorough exam ination of the p atien t and a m ore perfect decision-making about an adequate and effective th erapy such a statem ent is insufficient. W hat is needed is to pass to a higher degree of individualisation, i. e. an investigation as to w hat fu rth e r properties the object under exam i nation exhibits, or—w hich is ju st another w ay of expressing the same postulate—to w hich of the other classes th e object u nder investigation could or could not be assigned. In our instance we may, for example, be faced w ith the task of ascertaining other diseases the p atien t is suffering from, w ith the problem of w idening the orbit of symptom s which we shall reckon w ith w hen establishing a m ore exact diagnosis, and so on.
As is clear from the above account, the “situations” scheme can be well converted to the “thing—pro p erty—relation” scheme. This is also apparent from the m utual relationship betw een th e two m ethods w hich are linked w ith the “situations” scheme, i.e. the m ethod of the stru ctu re description and the method of the state descriptio n .3 W hen describing a stru ctu re we presum e th a t the given universe of discourse has been partitioned into a (finite) num ber of classes. The description of the structu re then consists in the determ ination of the num bers of individual objects, ordered pairs, triads or groups of n-objects belonging to indi vidual classes. When describing a state, we presum e, in addition, th a t we are in a position to discern all the individual objects. The descrip tion of the state then consists in determ ining w hich definite individual objects, ordered pairs, triads or groups of n objects can be assigned to individual classes. If we give a description of th e stru ctu re or, in addition of the state of the given universe of discourse, we provide a certain picture of the situation of the given universe of discourse.
(c) W ith regard to both above-said schemes of intern al analysis of the universe of discourse we norm ally presum e th a t we are capable of overlooking or clearly specifying the entire universe of discourse.4 Con
3 The elementary ideas of the method of state description were developed by L. Wittgenstein [WITTGENSTEIN]. As to the formal aspect, the method of state description (as a starting point of semantic analysis), as w ell as the descrip tion of the structure were detailed especially by R. Carnap [CARNAP],
4 This also applies to the scheme „thing—property—relation”. If for instance we are in a position to apply to the given universe of discourse three properties expressed by one-place predicates Px, P2 and P3, we can in that manner partition the universe of discourse into a total of eight classes according to which of these properties have or have not objects of individual classes. Some of these classes may of course be empty.
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tra ry to this, w ith another scheme th a t we encounter frequently both in cu rren t life and in science this postulate is not fulfilled. If we state th a t “it is raining here now ”, we do not establish the meteorological situation in the whole of our geographical region, bu t m erely make a statem ent in respect of a certain event, at a certain tim e and in a certain place. The scheme of such statem ents concerning the universe discourse can be refferred to as “events” scheme (or “facts” scheme).
The m ost suitable explication of th e “events” scheme can be supplied by the language of the propositional calculus. If we consider as a state m ent any correctly form ed expression about w hich we can decide w hether it is tru e or not, then th a t w hich from the semantic angle corre sponds to the statem ent can be term ed an event. In th a t case the uni verse of discourse is form ed by all the possible events, i. e. by all th a t about w hich statem ents can be made. If we have two statem ents, say a statem ent r (it is raining), and a statem ent m (there is m ud) than the tru th fu ln ess or un truthfulness of these statem ents, or any state m ents arising from a combination of the form er statem ents will refer solely and exclusively to the given events, regardless of any considera tion for the entire universe of discourse.
The “events” scheme is often made use of to express the results of observations, m easurem ents or experim ents, especially if the statem ent has the character of protocol-statem ent, or a definite statem ent of facts. As an elem entary form of protocol-statem ent we m ay regard the sen tence: “In a given place and a t a given tim e the observer (experim enter) has established such and such a thing.” It is evident th a t this statem ent does not give any inform ation on the events th a t took place in other places a t another time, nor does it give any inform ation as to w hat the observer had established in the same place previously, or at the same tim e in another place. F u rth e r protocol-statem ents would be needed to establish such fu rth e r events.
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The three schemes set out above of the analysis of the universe of discourse evidently do not exhaust all the possible schemes th a t we can encounter in cu rren t language and in the language of science. How
ever, th ey represent the m ost freq u en t and it seems also the most im portant modes of handling w hat we regard as objects of the cognitive processes in empirical and experim ental sciences. The results of these cognitive processes can be expressed in diverse schemes, not ruling out the possibility to express the same result by means of various schemes, or the possibility of reducing one scheme to another scheme.
It is also n atu ral if w ith respect to each of the said schemes we meet w ith some problems, complications and difficulties of semantic and ontological nature. Seeing, however, th a t this w ork is not aimed at
a more detailed analysis of the questions of this kind, we shall confine ourselves to some selected exam ples of such problems.
In th e scheme “thing—prop erty —relatio n ” we m ake statem ents on individual objects, either definite objects, or some objects, o r all the objects having the given property, and th e like. We therefore presum e “the existence” of these objects. Is it, however, legitim ate to presum e, in the same sense, also th e existence of classes of these objects, the existence of properties of, and relations betw een these objects? While the concept of “existence” is m ultivalent and can be in terp reted in diverse fashions, such a question or sim ilar questions can be the object of disputes and discussions. 5 Analogous problem s also arise in th e “si tuations” scheme, especially if we explicate this scheme by means of a language based on the logic of classes.
Also in th e case of th e “events” scheme some problem s arise, and become the object of discussions and disputes. If we issue from the said explication of the “events” scheme by m eans of the language of the propositional calculus, and assuming th a t we respect th e postulate th a t a statem ent is any correctly form ed expression about w hich we can decide w hether it is tru th fu l or u n tru th fu l, th en we most often m eet w ith the problem s expressed by th e following questions:
Which are th e criteria of a “correct form ation” of linguistic expres sions? (In p articu lar are these criteria predom inantly syntactic or also semantic, or in addition pragm atic as well?) If w h at corresponds to tru e statem ents is w hat we re fer to as “events” or “facts”, then w hat is it th a t corresponds to false statem ents? It is clear th a t this la tte r question can only be posed if we accept w h at has been stated in the antecedence, i. e. a “fact” or an “event” corresponds to a tru e statem ent. Can we take the circum stance th a t w h at the statem ent expresses did not occur or is not occurring also to be an “event” or a “fact”? Also in the investigation of these problem s th e corresponding specialised literatu re offers a v ariety of conceptions.
A lthough the problem s of this kind can by no means be underesti m ated, th e investigation and solution of substantive methodological disputes can on no account be reduced to disputes over th e p rio rity of one o r another ontological approach. For this reason, in our fru th e r ac count we shall devote to these problem s b u t the strictly necessary in terest, w hile focusing most of our attention upon problem s of typically methodological character. In order to sim plify the analysis of these problem s we shall depart p rim arily from th a t analysis of th e universe of discourse w hich is based on the first of th e three schemes.
5 Although this or similar questions form a certain complex, there is still a difference in the formulation and interpretation of these questions between nomi nalism, platonism and conceptualism, or between what corresponds to these concep tions in oontemporary mathematics and logic. These mutually differing conceptions naturally submit substantially differing answers to questions of this kind.
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2. COMMUNICATION MODEL AND THE PROBLEM OF SCIENTIFIC EMPIRICISM Any results of the cognitive activity in science can be communicated only through the medium of language. Therefore, they assume the form of statem ents of language; at the same time we alw ays presum e th a t these statem ents refer to something, or, in other words, th a t they have a m ean ing, th a t they can be sem antically analysed. This sem antical analysis is supported either by the results of certain procedures (for example observation, m easurem ent, experim ent and the like), or by other state m ents (for exam ple statem ents indicating the results of the said proce dures, statem ents of theoretical character, axioms, theorems, and so forth). In any case, statem ents expressing the results of a cognitive activity have a m ediated character. This m ediation consists in th a t the objects of the universe of discourse, be th ey objects discernible by our senses or constructive objects to w hich we refer the statem ents, can
only be reached by means of certain procedures.
For an elucidation of the above-m entioned m ediation we can use to advantage th e communication model, w hich presupposes communication connections of a m inim um of three blocks: (A) the block of the “source of inform ation” ; (B) the block of “the observer’s channel”, of the “chan
nel of the experim enter or the m easuring equipm ent” or still more generally “the channel of science” ; (C) the block of “statem ents”. Sche m atically the connection b e tw e e n 'th e three blocks can be sketched as follows:
A
B
C
Block A can be visualised as a (finite or infinite) set of events in tim e and space, objects of most diverse nature, and the like. In this connection we assume th a t at least some of these events or objects can be discerned by means of block B. In other words, block A is made up of a set objects of most varied nature, but such objets as can be taken as distinguishable stim uli for block B. We m ay for instance be faced w ith a set of sensorially discernible objects w hich can be observed pro vided block B is a hum an observer. We m ay also be facing a set of objects th a t can be reconstructed as (hypothetical) causes of certain reactions of block B, for instance, a set of diseases calling fo rth certain discernible symptoms, movements of m icroparticles which call forth certain discernible traces in the m easuring or experim ental equipment, and the like.
Block B m ay be represented by a hum an observer, or possibly an observer fitted w ith equipm ent augm enting th e pow er of the senses to discern (e. g.: a microscope, telescope, a m easuring equipm ent, etc.) or finally any m easuring or experim ental equipm ent able to register th e stim uli coming from block A. If we say th a t block B is able to discern the stim uli coming from block A, it does not alw ays im ply th a t block B is able to discern all the stim uli coming from block A, or to discern them absolutely adequately. Between block A and block B we presum e the existence of an inform ational link in which n atu rally also noise m ay appear. This noise m ay influence the extent of inaccuracies, m istakes or errors which characterise the reactions on the p a rt of block B to stim uli coming from block A.
The properties of block A and those of block B m u tually differ in im portant respects: While block A m ay consist of an infinite set of objects or events, and therefore can generate an infinite m ultitude of stim uli, block B is able, in a definite tim e and w ithin a definite space, always to register only a finite am ount of stimuli. The problem of methodological finitism is therefore anchored in block B, and n ot neces sarily in block A. For block B, in addition, certain thresholds are always characteristic betw een which th e la tte r is able to discern the stim uli coming from block A. A finite and lim ited degree of attainable discerni- bility is also characteristic of block B. Thus definite lim its are always set to the activity of block B.
A part from the lim its of this kind, o ther lim its m ay be presumed, the lim its related to the possibility of an (uncontrollable) retroaction of block B upon block A (in the block scheme the possibility of such retroaction is indicated by a tw o-directional connection betw een A and B). In the developm ent of scientific discovery the lim its of this kind w ere encountered in the quantum theory, w here they w ere form ulated in the from of the un certainty relation: If the m easurem ent of the po sition of a m icroparticle can be accomplished w ith accuracy Ax, and if a sim ultaneous m easurem ent of its im pulse can be accomplished w ith accuracy zip, then the w ell-know n relation applies:
Ax • zip ^ c,
w here c is a quantity of an order corresponding to P lanck’s constant. Analogous relations w ere also form ulated for oth er pairs of physical quantities. It is obvious th a t w ith the aid of th e means of block B, the state of block A can only be represented up to certain limits, these lim its being also given by a retroaction of block B upon block A. (In the interpretation of the un certain ty relation it is for exam ple assumed th a t block B is represented by an electron microscope. Then the mea surem ents of tem poral and spatial and im pulse-energy param eters of the
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object to be m easured can be-if we come close to a certain lim it—af fected by the beams employed in the electron microscope.)
Another form of such limits, analogous to H eisenberg’s uncertainty relation has been pointed out by D. Gabor [Gabor, p. 429], in the analysis of acoustic m easurem ent. If the signals are being m easured by means of an equipm ent w ith a band w idth AF, then the shortest signal th at can be m easured is AT, the product of AF and AT being greater th an or equal to the constant of the order unit.
It is n atu ra l th a t th e feedback betw een block B and block A may have a greatly diversified character. It can, for example, m anifest itself as an energetic action by the m easuring equipm ent upon the object being m easured, it m ay change the states of the object to be m easured in such a m anner th a t on the output of block B we shall not receive inform ation w hich would perm it us reliably to estim ate state A, b u t shall receive inform ation about a modified state A, this la tter state differing from the original state, in which the feedback between A and B has not occurred as yet.
The said analysis of mediation, which relies upon the communication model, m ay have a v ery general meaning, w hich does not have to be confined to m easurem ents in n atu ra l history or technical m easurements. The following thought shall bear out the above postulate. L et us assume th a t we organise a sociological research of attitudes, of public opinion, of a prestige scale, and so on. When w orking on the questionnaire or the corresponding inquiry we m ay of course form ulate some of the questions so suggestively as to influence the attitudes of the respon dents to some degree. It will, for instance, suffice to resort to certain term s of emotional meaning, it is possible to select certain questions in such a w ay th a t they can influence a certain kind of answers, and so forth. Also in such a case block B shall influence the original state of block A in such a m anner th a t the inform ation th a t we shall receive on the output of B shall not be adequate to block A as such, b u t will be the result of interaction between block A and block B.
Both block A and block B are presum ed to have stru ctu res of their own: this means, for instance, th a t the m easuring equipm ent through th e interm ediary of w hich we obtain the required data concerning the object under investigation does not have to exhibit the same character as the object to be investigated, th a t it m ay have its own independent structure, and the like. Evidently in this connection block A is presum ed to exist, or is given as objective for the purposes of the respective investigation, i. e. block A is independent of block B. On the other hand, it is equally uncontroversial th a t any statem ents in respect of anything concerning A can be form ulated only and exclusively on the strength of the data th a t are available on the o utput of B. This also implies th a t to scientific empiricism are inacceptable any reflections founded
on some kind of non-m ediated “penetration into the essence of things”, “visualising the essence”, “intuitive com prehension of the essence”, and th e like.
Of block C it is tru e as w ell th a t it has an independent stru ctu re of its own: It is a system of statem ents based on the one hand on inform a tion supplied on the output from block B, on the other on fu rth e r state m ents th a t have been included into the given system from other sources. In principle we are faced w ith a twofold mediation, w hich w as already pointed out by B. Russell, who made a distinction between “knowledge by acquaintance” and “knowledge by description”. Knowledge based on di rect experience is therefore understood here as a m ediated knowledge as well, a knowledge m ediated through block B, regardless of w h eth er this block comprises the hum an observer alone provided w ith the norm al sensory outfit, or, in addition, also w ith m easuring or experim ental equipm ent. Knowledge on the basis of descriptions can of course be like wise founded on observation, m easurem ents, experim ents and th e like, b u t he who disposes of block C, gains this inform ation (in R ussell’s te r minology: these descriptions) from com munication processes w ith other people; scientists, experim enters and others.
Schem atically we m ay represent this dual m ediation by a crossing of two communication processes:
The relations betw een Ci lt Cu Ci+1) etc. can be in terp reted as cu rren t communication processes between two or more communicants. These m ay comprise, for example, a dialogue, the relationship between au th o r and reader of a scientific study, th e relations betw een lectu rer and student, and the like.
If we say of block C (and evidently also of any of th e fu rth e r blocks, i. e. of Cj_1( C4, Ci+1, etc.) th a t these consist of statem ents, it m eans th a t in the form ulation of these statem ents we m ust observe th e respective syntactic, semantic and other rules, w hich are binding for th e language
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in which the statem ents are form ulated. The above-m entioned character istic, i. e. the stress on the relatively independent stru ctu re of block C, applies also in this respect.
*
The said communication model which underlines the twofold mediation perm its a new, m ore fru itfu l interpretation of certain traditional con cepts of w hich we avail ourselves in the analysis of the statem ents of science. These are, in particular, the concepts of “assignm ent” (in the se m antic sense), th e concept of “level”, and the concept of “experience”.
L et us first pay attention to the concept of “assignm ent”. Normally we encounter the term in a plain, and to some extent naïve question “w hat corresponds to?” This question actually postulates th a t the ele m ents of block C be simply assigned to elem ents of block A. The naïveté of this question follows clearly from a m ore detailed analysis of the vo cabulary employed for th e statem ents: Some elem ents of the vocabulary obviously have th e character of logical term s (in Russell’s term inology of “logical w ords”), in w hich the question “w h at corresponds to”, especially a question th a t w ould call for an im mediate assignment of all the ele m ents of block C to elements of block A, can never lead to a satisfactory answer, for the question has sim ply been w rongly form ulated. Disregar ding th e logical term s and confining ourselves to extra-logical term s, we are actually confronted w ith the traditional problem of denotation. This problem, w hich n atu ra lly presupposes a certain assignm ent of the ele m ents of block A and block C, cannot how ever be solved in all instances by a one-one assignment, as w ould be required by the naïve question “w hat corresponds to?” This applies in p articu lar to those elem ents of the statem ent th a t have a character of theoretical concepts having the form of tw o- or m any-placed predicates, etc. I t is for exam ple possible to in terp ret some of th e theoretical concepts as expressions stating certain links betw een em pirical concepts: The concept of specific gravity ex presses a relationship between th e w eight characteristic and the volume characteristic of a given substance. Hence, although in respect of those elem ents of block C w hich have the character of extra-logical term s it is legitim ate to ask the question aimed a t denotation, it is nevertheless naïve to in terp ret this question always as a question “w h at corresponds to?” We m ust take into consideration the fact th a t in th e case of a de notation we are not alw ays facing a one-one assignment, and in addition we m ust respect the fact th a t in this assignm ent the m ediating role of block B is often brought into play.
The semantic properties of any expressions th a t we take as elements of block C cannot of course be reduced to denotation alone. Besides de notation, this being of p articu la r im portance in the communication pro
cesses betw een Ct u Cu C4+1> etc., i. e. in w hat corresponds to R ussell’s conception of knowledge based on description—the m eaning of th e ex pressions asserts itself. The fact th a t expressions have meanings perm its us to com prehend them. From the standpoint of the com munication pro cesses betw een Ct_ lf Ct, C4+1, etc. th e m eaning is w h at is preserved in any reliable com munication between C4_ 1( Cu Cj+1, and so on.
An im p o rtan t problem upon w hich atten tio n m u st be focused w hen conducting a sem antic analysis of th e language of science is the problem of the so-called level, and selection of th e appropriate level for assign m ent. If we assume th a t block A is form ed by certain elements, we m ust take into account the possibility th a t these elem ents can be categorised, hierarchically ordered in a certain m anner, etc. Here w ill also be brought into play w h at we have characterised earlier as various schemes of an analysis of the universe of discourse. A pplying for exam ple the scheme “thing—p roperty—relation”, then we can (but this w ill be a reconstruction ex post of its kind) reckon w ith such a conception of assignm ent th a t assigns “things” to individuals, “properties” and “relations” to predi cates, etc. Sim ilar to o th er schemes, here, too, the legitim ate question a- rises in how far we actually do not attrib u te w hatever is specific to block C also to block A: in other words, we m ight be apprehensive lest th e stru cture th a t is specific to the language and the statem ents of language be not im puted to the universe of discourse itself. In any reconstruction of block A, and generally in any reconstruction of the universe of dis course we m ust therefore also take into consideration th a t betw een blocks A, B and C feedbacks begin to operate, w hich m ay how ever also take the form of a direct influencing of block A by block C. This m eans th a t in this reconstruction we m ust advance m ost judiciously, control every one of the steps we take and cofront the results of each of th e steps). In particular, it is m andatory to avoid naively realistic illusions usually reflected in the efforts to assing “som ething” in block A to any elem ent in block C.
The emphasis on the fact th a t block C possesses a relatively inde pendent stru ctu re of its own can also be taken in the sense of a h i erarchically ordered structu re. If we have said th a t block C is form ed by statem ents, we m ust take into account th a t in form ulating any state m ents we m ust use extralogical term s of th e language, or a combination of extralogical and logical term s of this language. These statem ents, in the form ulation of which the respective rules of the given language shall be observed, m ay form certain complexes, and so forth. In this w ay we shall attain a question th a t could be form ulated as follows: W ith respect to w hich category, on w hich the form ulation of the statem ents or a com plex of the statem ents is founded, are we entitled to consider an assign ment? If, as we have m entioned we are norm ally inclined to assign to in dividuals and predicates certain things, properties and relations, are we
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entitled to consider, in a sim ilar fashion, the assignm ent of other, especial ly th e “higher” categories? The trad itio n al logico-semantic investigation of the problem of denotation, according to which individual objects are assign
ed to the nam es of individuals, w hile classes of individual objects or classes of ordered pairs, triads or groups of n objects are assigned to predicates, actually considers the relations between blocks A and C only a t this level. If for th e denotation of th e sentence we take the tru th val ue, i. e. th e en tity of constructive nature, we have already exceeded the fram ew ork of the relations between blocks A and C. (This also applies to other attem pts to solve the denotation of sentences operating concepts such as “belief”, “assertion”, “conviction”, and the like.) Basically there is no need to raise objections to th e conception of the tru th value as a denotation of the sentence. I t should how ever be borne in m ind th at this conception cannot be placed at the same level w ith th e conception of the denotation of individuals and predicates, and th a t this conception exceeds the fram ew ork of the relations betw een blocks A and C. This practically implies th a t we are actually moving w ithin this fram ew ork at only one of these levels, w hereas at other levels, i. e. a t the level of statem ents or sentences, at the level of sentential complexes and th e like, we have already exceeded the said fram ew ork. It is n atu ra l th a t if we select other schemes of analysis of the universe of discourse, such as the events scheme, we shall witness a change also in th e form of th a t level w hich rem ains w ithin th e fram ew ork of the relations betw een blocks A and C.
«
So far, we have been considering th e concept of “level” from the point of view of block C, i. e. from the point of view of th e sphere of state ments. The concept of level can, however, also be considered from the angle of block A. In this respect, taking into consideration physical and chemical phenomena, we m eet w ith a differentiation of th e macrolevel and the microlevel, th e macroscopic, quantum and subquantum levels, taking into account economic phenom ena, we m eet w ith a differentiation of various economic levels (national level, level involving a branch, an enterprise, etc.). We also witness the differentiation of diverse levels of biological, social and other phenomena. In all these and sim ilar cases the concept of “level” refers to block A or generally to the universe of dis course of cognitive activity. I t is also evident th a t th e differentiation of the various levels is based here upon objective differences and m ore or less objective criteria.
While we emphasise th a t th e differentiation of diverse levels rests on objective differences — such differences exist, e. g., betw een the quantum processes and th e macroprocesses in physics and n atu ra lly also between the corresponding descriptions of the two processes—this does not mean
th a t the concept of “level” has or ought to have an absolute m eaning and th a t it is possible to construct some uniform scale of levels, applicable absolutely to all situations. A ttem pts to establish such an absolute scale w ere being made, especially in nineteenth-century science. Such attem pts usually aimed a t an objective substantiation of the classification of sci ences, at a lasting differentiation of the so-called form s of the motion of m atter, and so on. (Sometimes we w ere liable to lose sight of th e fact th a t diverse form s of the motion w ere term ed in keeping w ith the then existing sciences and the previously know n types of th eir competence. The selection of the nam es of th e sciences was then the starting point for the differentiation of diverse form s of motion, and this differentiation became in tu rn the startin g point for the classification of sciences. It is not difficult to realise th a t this w hole reasoning progresses in a circle, and is actually contingent upon the fund of knowledge w ithin our mo m entary reach.)
The point of view according to w hich the distinction of the levels is not absolute also implies th a t it is not possible to prove the existence of some fundam ental, elem entary or initial level th a t w ould represent a re duction basis for the other levels, i. e. such a level to w hich all the for m ations of higher levels could be reduced. This n atu ra lly does not mean a negation of the im portance of any reduction, and p articu larly not the negation of any explanatory value of th e reduction. Taking for instance such a system of levels as are the molecular, atomic and quantum levels, then it is sufficiently w ell-know n th a t modern physics operates w ith explanations of num erous phenom ena th a t appear at a “higher” level, w ith the aid of those elements and means th a t can be proved a t a “low er” level. The situation is analogous in the relations of biological, biochemi cal, chemical and physical levels, and the like. At th e same tim e it is how ever notorious th a t at a higher level appear some phenom ena, pro perties or processes w hich cannot be explained by all th a t is accessible to us from the “low er” level. It is evident th a t this m ay be due either to insufficient knowledge of th e “low er” level or to the occurrence of some new, qualitatively different phenom ena at the higher le v e l6. In other words, besides quantitative differences betw een diverse levels we cannot rule out qualitative differences between them.
From w h at has been said of the m utual relations of various levels it can be gathered th a t we postulate a plu rality of scales of such levels as w ell as a relativity of w hat can — under the given circum stances — be
6 In this connection, the followers of emergent philosophy speak of the „emer gence” of new properties and processes, and hence also of „emergent” properties. They of course not infrequently overlook that such „emergent” properties can stem from our insufficient acquaintance with the „lower” levels, or — as it was custo mary to express in the physics — from the existence of so-called hidden parameters. This naturally does not imply that we should at all cost and under any circum stances postulate the existence of the so-called hidden parameters, as was the aspira tion of a certain school of interpretation of the phenomena of quantum mechanics.
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considered as an initial level. Moreover, w hen defining such a relative initial level we cannot ignore a substantial p art played by block B, i.e. by the observer’s channel, the m easuring equipm ent, or generally speak ing the channel of science. It should be noted th a t any system, however superior, w hich in the cognitive process has th e role of block B, i.e. th e observer’s channel, has always b u t lim ited possibilities of discerning objects in block A, i.e. is restricted w ithin certain thresholds, has but a lim ited degree of discerning ability, etc. The concept of “level” in the sense set out above is therefore always relativised also w ith respect to the properties and possibilities of block B. From th a t angle, every level th a t we are in a position to distinguish from another, no m atter w hether “higher” or “low er” level, is linked to a possibility of discerning only a finite num ber of classes or a finite num ber of properties attrib u ted to the objects of block A. This is w here, too, the very foundations of me thodological finitism are anchored.
It should y et be elucidated w hat is m eant by a “higher” and a “low er” level. Also this distinction m ust be relativised w ith regard to the pro perties and possibilities of block B. W hat m atters is the orbit of the data coming from block A w hich block B is capable of discerning. Let us for instance assume th a t block B is able to discern inform ation alt a2, a3 ... an. If we im prove the degree of attainable discerning pow er of block B (this actually implies th a t we shall pass from block B to block B'), so th a t in a region (e.g. tem poral o r spatial region) w here only ax and a2 had for m erly been discerned, henceforth also allt a12, a13 ... aln and a21, a23 ... a2m w ill be discerned as well, then we shall have passed from a “higher” to a “low er” level. It is obvious th a t the elements of th e higher level will not always coincide w ith the sets of elements of the lower level.
From this standpoint any refinem ent of the discerning ability actu ally represents a transition from the higher to the lower level, and, con versely, any coarsening of such ability, ordinarily accompanied by an extension of the viewing field, represents a transition from the lower to a higher level. However, in practical thinking of n a tu ra l historians a dif feren t approach to these levels has established itself. It is the approach which does not see the prerequisites for the transition from one level to another in ju st any change in the properties of capabilities of block B, but solely in changes th a t modify qualitatively the natu re as w ell as the function of block B. Of th e transition from one level to another the fol lowing circum stances are, in particular, characteristic:
(a) On transition from one level to another we usually come up against the lim its of the possibilities of th e equipm ent of one type. Such limits set to the possibilities of a macroscopic m easuring equipm ent w ith re gard to microprocesses is expressed, for exam ple by th e Heisenberg relation.
laws governing the phenom ena being investigated changes as well. Abid ing by the problem s of physics, it is clear th a t th e character of the laws of quantum physics differs from the laws of classical mechanics.
(c) Upon transition from one level to another the changes also com prise the m easuring units or the system of fundam ental param eters w hich characterise the phenom ena being investigated.
W hile the said facts can probably be best dem onstrated on the tra n sitions betw een physical levels, analogous facts are likely to occur in other fields as well. However, not always are these facts so thoroughly respect ed, as is the case in physics. It is for instance absolutely essential th a t in the analysis of the economic problem s we should have at our disposal different systems of basic param eters if we are concerned w ith the be haviour of an individual, or th e economic problem s occurring w ithin the fram ew ork of an enterprise, or finally the economic problem s w ithin the context of the national economy as a whole.
The communication model of cognitive activity described above also perm its us to enhance the accuracy of the interpretatio n of th e concept of “experience”. On the basis of the traditional approach, as experience we norm ally understood th e complex of sensorial data, i.e. the data th a t could be discerned and registered by the hum an observer. S tartin g from the communication model described above, operating blocks A, B and C we m ay point out the following rud im en tary deficiencies of the tradition al concept of experience:
(a) The traditional concept of experience is as a rule considerably static: it confines experience to a complex of ready data. At any rate, also the term of “d ata”, w hich today we usually understand in the in form ational sense, i.e. as inform ation, originally im plied som ething ready, something th a t was “given”.
In m odern science, however, experience cannot be confined to a cer tain integrated complex of data qualified in a certain m anner, ready in any situation. Experience, as we intuitively com prehend it in present-day science, is rath e r a process, a succession of certain operations, certain qualified m easures, and the like.
(b) A nother draw back of the traditional approach to the concept of science is in th a t this approach basically postulates data th a t could be characterised in a uniform fashion as being valid for all the situations. This practically implies th a t this traditional approach operates w ith a single type of block B, a block B binding for all situations. Hence the attem pts to develop an entirely uniform characteristic of experience. It is of course generally known th a t such attem pts a t a uniform characteris tic of experience, as was e.g. assumed by pragm atism , operationalism or some version of logical empiricism (for exam ple the conception of the so-called protocol-sentences, basis-sentences, Konstatierungen and the like), could not be considered adequate in all situations.
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(c) The traditional approach to experience identifies experience w ith a complex of ready data, and this actually means th a t any data are ta k en on the output of block B. This also means th a t the m easure of re levance of these data is being left out of account. The concept of the re levance of data is of course not given in an abstract way, b u t is always dependent on a given task or a class of tasks and goals th a t are connected w ith the investigation of the tasks. This practically means th a t it is not ju st any data th a t can be registered w hich are essential to the solution of the task. In medical diagnosing the physician m ay ascertain a m ulti tude of symptoms in th e patient. However, for the purposes of the diagnosis only some of th e symptoms are relevant, and the m easure of relevance of th e various symptoms m ay differ. The concept of the rele vance of data cannot therefore be confined to a semantic concept linked w ith th e given universe of discourse, b u t also be understood as a prag m atical concept, linked to the goals, demands, requirem ents or expecta tions th a t we relate to th e investigation of the task in question.
Scientific knowledge, especially in n atu ra l sciences, actually operates w ith another, m uch w ider and more dynam ical concept of “experience”. While the in terpretation of the traditional approach to experience is being prim arily developed in philosophy, a greater accuracy in the mod ern approach to experience can be ra th e r encountered in the theory of statistical decision-making or in the theory of games. Assuming th a t we operate the said blocks A, B and C, then w hat we are confronted w ith in the last block is a decision-making process th a t is to evaluate the state prevailing in block A. Taken generally, as experience we understand all those steps th a t lead to im parting greater accuracy to the evaluation and to enhancing the quality of the decision-making. It is beyond doubt th a t this conception of experience does not th in k of experience as of a static act, b u t as of a dynamic process, a succession of certain steps.
This approach to experience can be dem onstrated on a simple exam ple of statistic decision-making: L et block A be represented by an u rn con taining a great m ultitude of black balls and w hite balls. We are however unable to gain an insight into the urn, and only a lim ited sample of ju st a few balls can always be taken out of th e urn. Indubitably, every fu r th e r draw ing can only improve the estim ate of the originally unknow n a priori distribution, or render more exact the hypothesis of the source of inform ation. The system in which we can include into the calculation the results of the steps taken in the past (i.e. th e previous drawings), m ay be characterised as an experience system. Such a system presup poses the im plem entation of individual steps on the strength of th e eval uation of the results of the previous steps. Evidently such an approach does not take data as isolated pieces of inform ation, regardless of the tasks in w hich these data can be p u t to use, regardless of the aims th a t are being followed precisely in this investigation. In the traditional con
ception, experience data therefore represent experience only in so fa r as they can im part g reater accuracy to our evaluations, rend er more exact the hypotheses serving as grounds for th e decision-making, and thus raising the quality of th e decisions.
The said exam ple of the experience system can be modified fu rth er. It should be noted th a t in em pirical sciences we as a ru le do not study only the respective fields th a t rem ain invariable, b u t also processes of the changes. From this viewpoint it is possible to modify the original exam ple of th e source of inform ation: Let block A be once m ore represented by an u rn w ith a large m ultitude of black balls and w hite balls, the m u tu al proportion of w hich we are to estim ate. L et us fu rth e r presum e th a t we cannot gain an insight into the urn, and th a t we cannot draw b u t a lim ited sam ple comprising ju st a few balls. However, besides the operation perform ed by the hum an observer or experim enter, th ere is a demon, who can—also in certain intervals and in certain lim ited num bers— add to the u rn or w ithdraw from it black or w hite balls, thus som ew hat altering the original a priori distribution. In such a situation two cases may occur: In the first case it is the demon th a t “w orks” faster th an the hum an observer or experim enter, who in such a case has no chance to improve his estim ates of the a priori distribution. I t is know n th a t the fam iliar Bergson scepticism takes this view of th e problem of expe rience. The developm ent of knowledge in n a tu ra l history, however, ra th e r bears out the second alternative, in w hich the hum an experim enter is faster, prom pter and also cleverer th an any demon of nature. From this standpoint the experience process is a game against a p artn e r whose strategy we are not fam iliar w ith, or w hich we know only partly, and who is capable of somewhat changing these strategies. However, step by step we are capable of overcoming him. This la tte r alternative instance corresponds to th a t approach to scientific discovery w hich w as devised by A. Einstein and N. Wiener.
From the two schematical forms of f .AUrience systems it is obvious th a t experience cannot be confined m „iy to th e data on the o u tp ut of block B, i.e. to the results of the observation, m easurem ents or experi m ents th a t have not been evaluated, b u t m ust also include the evaluation of the form er results of this kind as well as of previous decisions w hich were selected in view of th e results hitherto registered. Consequently, also the concept of experience is n ot restricted to d ata on the output of block B, b u t includes any measures leading to an im provem ent in the quality of the decision-making, for exam ple im provem ents in the function of block B, im provem ents in the hypotheses on the basis of w hich deci sions are taken, increasing the accuracy of the evaluation of the state or of the changes in block A, as well as a m ore exact form ulation of the expectations of possible consequences of the chosen decisions, etc. The factors to which are due the extension and perfection of experience
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therefore comprise not only progress in the sense of a quantitative w iden ing of em pirical data, b u t also any advances of theoretical n atu re or advances achieved in m easuring and experim ental techniques, which are liable to improve the quality of our decision-making and lend greater accuracy to our knowledge of the universe of discourse under our scrutiny.
REFERENCES
CARNAP Rudolf, Introduction to Semantics, Studies in Semantics, Cambridge (Mass.), 1942.
GABOR Dennis, „Theory of Communication”, Journal of the Inst. Elec. Engrs., Lon don, S3, 1946, p. 429.
KORNER Stephan, Experience and Theory, London, Routledge and Kegan Paul, 1966. WITTGENSTEIN Ludwig, Tractatus logico philosophicus, New York 1922.
