Eugene Lashchyk, Scientific Revolutions, 1969

(C) Incommensurability and Incompatibility of Paradigm-Theories

I turn in this section to a discussion of the third thesis -- T3 -- the incompatibility and incommensurability of succeeding paradigms. Kuhn states:

The normal-scientific tradition that emerges from a scientific revolution is not only incompatible but often actually incommensurable with that which has gone before.{22}

My objective in this discussion will be first of all to explain what Kuhn means by the incompatibility and incommensurability thesis, in particular, what reasons does he give to support such a thesis. Secondly, I will try to explain the relevance of T3 to T4 and T5, in particular, I would like to examine whether commitment to T3 implies that scientific change is necessarily an unreasonable or an irrational activity.

In the following quotation Kuhn mixes together the reasons for incompatibility and incommensurability of successive paradigms. He states:

Successive paradigms tell us different things about the population of the universe and about that population's behavior. They differ, that is, about such questions as the existence of subatomic particles, the materiality of light, and the conservation of heat or of energy. These are the substantive differences between successive paradigms, and they require no further illustration. But paradigms differ in more than substance, for they are directed not only to nature but also back upon the science that produced them. They are the source of the methods, problem-field, and standards of solution accepted by any mature scientific community at any given time. As a result, the reception of a new paradigm often necessitates a redefinition of the corresponding science. Some old problems may be relegated to another science or declared entirely 'unscientific.' Others that were previously non-existent or trivial may, with a new paradigm, become the very archetypes of significant scientific achievement. And as the problems change, so, often, does the standard that distinguishes a real scientific solution from a mere metaphysical speculation, word game, or mathematical play. The normal-scientific tradition that emerges from a scientific revolution is not only incompatible but often actually incommensurable with that which has gone before.{23}

It is difficult to determine from the above quotation what Kuhn means by the two terms in question. Fortunately, Kuhn discusses the two notions separately in various parts of SSR. Even so, the problem of finding a coherent interpretation for the application of both properties, incompatibility, and incommensurability of successive paradigms, as I will try to show shortly, will prove to be extremely difficult if not an impossible task without making some modifications in Kuhn's system.

In describing incompatibility of successive paradigms Kuhn says:

From the viewpoint of this essay these two theories are fundamentally incompatible in the sense illustrated by the relation of Copernican to Ptolemaic astronomy: Einstein's theory can be accepted only with the recognition that Newton's was wrong.{24}

But what does it mean for two successive paradigm-theories in the same field to be "fundamentally incompatible"? A quick but still inconclusive answer is forthcoming, namely, two theories are incompatible if both cannot be held to be right. This answer only leads us to another obvious question: "when can a paradigm-theory be said to be right or wrong?" Since Kuhn certainly doesn't mean morally right or wrong, we must search for another interpretation more appropriate to the context of science. By saying that a paradigm-theory is wrong Kuhn seems to mean that the anticipations, predictions, and measurements which are generated by the particular paradigm are in conflict with the observations made. Such conflicts Kuhn describes as anomalies.{25} A new theory that "renders the anomaly lawlike" will thus be in conflict with the old theory under which the phenomena in question appeared anomalous (unanticipated). Some things have been brought into the open but many questions still remain. Agreed that there is some conflict between two paradigm-theories that make different predictions, the question is "what type of conflict is it?" Or, to put the original question anew: "what type of incompatibility does Kuhn attribute between successive paradigm- theories?"

There are at least two senses of the term incompatible presently in use in philosophical literature:

1. Logical incompatibility.

2. Conceptual incompatibility.

Let me first define logical incompatibility. Assume that a theory is composed of a class of sentences and call the class of sentences of theory T1 P and the class of sentences of theory T2 O then Tl will be logically incompatible with T2 just in case from the third class which contains exactly the elements of P and the elements of O, a sentence S can be derived together with its negation ~S.

By conceptual incompatibility I will understand the type of incompatibility that Nathan Brody and Paul Oppenheim described in a recent article in the Journal of Philosophy. They state:

Another such difficulty is often referred to as "the duality of matter and light." According to macrophysical theory, any macroobject that is corpuscular (C) and not wavelike (W) at some time will always be C and not W. ire respective of the experimental arrangement by means of which it is investigated. According to macrophysical theory, the properties C and W are incompatible; that is, C and W are incompatible (means): that is, C and W can be conceived as dispositional properties such that a macroobject can have either the property of C and not W or the property of W and not C, but not both properties.{26}

Some have suggested that Kuhn doesn't mean by "incompatibility" anything quite so "simple-minded" as logical incompatibility. But I find it difficult to substitute other interpretations of incompatibility at least for some passages in Kuhn's SSR. I have in mind the following passage:

But if new theories are called forth to resolve anomalies in the relation of an existing theory to nature, then the successful new theory must somewhere permit predictions that are different from those derived from its predecessor. That difference could not occur if the two were logically compatible.{27}

What can it mean to deny that two paradigm-theories are "logically compatible except to say that they are logically incompatible?

We have finally arrived at one clear sense of the term "incompatibility" as Kuhn seems to use it. Various problems still remain. In the first place, a historical example illustrating logical incompatibility will be helpful. Secondly, can every case of conflict between successive paradigm- theories be reduced to this strongest of conflicts namely, logical incompatibility? Thirdly, can this sense of the term "incompatible" be conjoined with the term "incommensurable"?

Since it is with the resolution of anomalies that Kuhn believes scientists develop incompatible paradigm- theories, I will discuss one such anomaly and its resolution as discovered by Lavoisier. A sketch of the phlogiston theory and some of the anomalies are discussed in section (B) of this chapter. Lavoisier reported the following anomalous observation: "About eight days ago I discovered that sulphur in burning, far from losing weight gains it. It is the same with phosphorus."{28}

This report about the gain in weight after combustion of phosphorus and sulphur was anomalous because of the following type of reasoning under the phlogiston theory.

Prediction of Phlogiston Theory

Pl
In all cases of the combustion of materials phlogiston is released into the air.

P2
Whenever an element loses some part of its composition, it loses in weight.

P3
Phlogiston has weight.

P4
When sulphur undergoes combustion, then phlogiston is released into the air.

P5
Sulphur underwent combustion.

Therefore,

Cl
Phlogiston is released into the air.

C2
It is not the case that sulphur, after combustion, gained in weight.

The anomaly was removed when Lavoisier developed the oxygen theory under which the anomalous observation report was rendered lawful by having that observation report deduced from another paradigm-theory.

Explanation of Anomalous Prediction in Lavoisier's Oxygen Theory

O1
In all cases of the combustion of materials oxygen is taken from the air and combined with the material to form an oxide.

O2
Whenever two elements that have weight x and y respectively combine, the resulting weight is greater than either of the two weights separately (x + y) > x or (x + y) > y.

O3
Oxygen has weight.

O4
Sulphur underwent combustion.

Therefore,

Cl
Some oxygen has been taken from the air.

C2
Sulphur,after combustion, gained in weight.

Using the previously defined notion of logical incompatibility it can be concluded that because a contradiction can be deduced from the conjunction of the set [P1 - P5] and the set [O1 - O5], namely, C2 and ~C2, the two paradigm-theories are logically incompatible. Kuhn doesn't explicitly affirm or deny that this type of incompatibility will result in the case of every two successive paradigms. Some passages in SSR suggest that such differences must of necessity occur always. Summarizing the section on incompatibility, Kuhn says:

Let us, therefore, now take it for granted that the differences between successive paradigms are both necessary and irreconcilable.{29}

Such differences seem to follow from Kuhn's very definition of paradigms. Since a paradigm arises only in response to crisis precipitated by anomalies, such differences are part of the very essence of a paradigm. Such reasoning suggests that such differences are a priori rather than empirical findings. The following questions remain: Is Kuhn's view of the differences between paradigms the same as in the earlier quote? Are these differences reducible to those of logical incompatibility? Since such an interpretation is not denied in this context, it remains a possible interpretation. Furthermore, the above quotation seems to imply that all successive paradigms are incompatible. But such an interpretation conflicts with another passage where Kuhn explicitly recognizes that his argument is not a priori. He is not arguing that it is logically impossible for two paradigms to be compatible.

First notice that if there are such reasons, they do not derive from the logical structure of scientific know ledge. In principle, a new phenomenon might emerge with out reflecting destructively upon any part of past scientific practice. Though discovering life on the moon would today be destructive of existing paradigms (these tell us things about the moon that seem incompatible with life's existence there), discovering life in some less well-known part of the galaxy would not. By the same token, a new theory does not have to conflict with any of its predecessors. It might deal exclusively with phenomena not previously known, as the quantum theory deals (but, significantly, not exclusively) with subatomic phenomena unknown before the twentieth century. Or again, the new theory might be simply a higher level theory than those known before, one that linked together a whole group of lower level theories without substantially changing any. Today, the theory of energy conservation provides just such links between dynamics, chemistry, electricity, optics, thermal theory, and so on. Still other compatible relationships between old and new theories can be conceived. Any and all of them might be exemplified by the historical process through which science has developed. If they were scientific development would be genuinely cumulative.{30}

It is hard to see how new theories could arise without these destructive changes in beliefs about nature. Though logical inclusiveness remains a permissible view of the relation between successive scientific theories, it is a historical implausibility.{31}

Kuhn's argument is therefore historical and empirical.

Before I discuss the second type of incompatibility, namely conceptual incompatibility, let me turn to a discussion of the incommensurability aspect of Thesis 3. By so doing, I will try to bring out the reasons why we need to extend Kuhn's claims about incompatibility beyond the logical type.

In the case of the incommensurability thesis, Kuhn's argument seems to depend on the following set of presuppositions: l. Since paradigms define the realm of significant scientific problems that need to be solved, and since this class of significant problems varies from paradigm to paradigm, there is disagreement about the list of significant problems that any paradigm must solve.{32} 2. ". . . Proponents of competing paradigms practice their trades in different worlds. . . . Practicing in different worlds, the two groups of scientists see different things when they look from the same point in the same direction."{33} 3. In the transition from the old paradigm-theory to the new paradigm theory, the terms, even though they might be the same, change in meaning. "Within the new paradigm, old terms, concepts, and experiments fall into new relationships one with the other." Such terms as "space", "earth", "motion", "mass" change in meaning from one paradigm to another.{34}

For the above reasons, successive paradigm-theories are incommensurable.

In the first place, let me point out, that in the argument for incommensurability given above, Kuhn presupposes at least four of the six clusters of paradigms which I identified previously. The first and the third premises basically summarize the sense of paradigm in the scientific cluster. The first premise also extends the meaning to the metascientific cluster and the third premise presupposes both the meta physical and the gestalt clusters of paradigm. As was pointed out previously, such transition from one sense of paradigm to another does not help to make the conclusion more plausible, once the various shifts in meaning are identified.

The particular brand of incommensurability thesis that Kuhn propounds includes not only radical change of meaning from one paradigm to another but also change in observation and observation language, change in important problems deemed scientific rather than metaphysical, and change in the conception of what science is. It can be truly said that nothing remains the same in the transition from one paradigm to another. If this is a correct description of Kuhn's position, and in one sense it is, for everything in the argument is either a direct quotation or a close paraphrase, then how are we to interpret the original quotation where Kuhn attributes both incommensurability and incompatibility to subsequent paradigms?

Logical incompatibility will be a very rare occurrence between successive paradigms if change in meaning occurs as regularly as Kuhn seems to suggest. In any case, partly because Kuhn, I think, has too strict a criterion for change in meaning,{35} and partly because some terms that enter a scientific theory keep their pre-scientific meaning the same, there are occurrences of the logical incompatibility of theories. In other words, I would be inclined to modify Kuhn's conception about change in meaning rather than give up Kuhn's earlier claims about logical incompatibility. But even though the above considerations will allow for some cases of logical incompatibility, many candidates for conflict between paradigms will not be adequately explicated by using just the logical type of conflict. It is necessary to extend the notion of incompatibility to what I earlier called conceptual incompatibility. Under such incompatibilities, for example, it appears inconceivable to apply to the same macroobject both the property of being corpuscular -- C -- and that of being a wave -- W. To apply C and W to the same macroobject is to involve ourselves in conceptual incompatibilities. Analogously, I think that when Kuhn states that successive paradigms are incompatible, at times, such incompatibility has to be analyzed not as logical but conceptual incompatibility. For Ptolemaic astronomy to view the earth as moving was conceptually incompatible with its theoretical framework. It was "inconceivable" that such a description could be applied to the planet earth. It should be pointed out that what is conceptually inconceivable to one generation of scientists and philosophers might not be so for others. It was "inconceivable" for Kant that our space could be any other except Euclidean space. Such is no longer the case. It should be pointed out that for conceptual incompatibility things could be as incommensurable as Kuhn has made them out to be. But can scientific change be made into a reasonable activity under such an under standing of incommensurability? I think that Kuhn himself modifies the various aspects of incommensurability mentioned above.

In the first place, observation reports, even though they are not theoretically neutral, nevertheless they can impose limitations on our concept and theory formation. Furthermore, even though our theories do condition us to see things we might not have seen without them, it doesn't follow that scientists can see whatever they like. Should this be true, anomalies would never be reported. But the observation of anomalies is an indispensable cog in Kuhn's account of scientific change. We can conclude therefore that the second reason given above for the incommensurability thesis does not undermine reasonableness in paradigm debates. Kuhn himself has disarmed the threat.

That paradigms determine what problems and solutions to problems are scientific can be granted without undermining the possibility of rationality in scientific change. What is important in this respect is that some criteria remain independent of paradigm change. As I have stated in Thesis 5, Kuhn himself seems to argue for such independent criteria. I will argue for T5 in the next section of this chapter.

Furthermore, if everything changes (I have shown already some cases where this is not so) how are we going to specify when two theories are competing theories? If any two theories are incommensurable in Kuhn's sense or even Feyerabend's sense, how can they be competing or alternative theories? I think that Kuhn has a way of explicating the notion of a competing or alternative theory. What gives rise to the development of an alternative theory is the crisis that exists within the dominant paradigm-theory. Furthermore, it is the proliferation of anomalies, (i. e., puzzles which the problem-solving tools of the dominant paradigm theory are unable to resolve), which has resulted in the crisis stage. An alternative theory will be any theory which attempts to resolve or remove the anomalies which led to the downfall of the old theory. The alternative theory which does this best is a good candidate for a new paradigm-theory.

The whole problem of meaning of terms in scientific theories is much more complicated than either Kuhn or the logical positivists have made it out to be.

On the one hand, the logical positivists oversimplified the problem by dividing scientific terms into observational and theoretical and ultimately the theoretical terms have meaning only if they can be somehow reduced to the observational terms. The demarcation line between observational terms and theoretical terms is somewhat arbitrary. This was pointed out by many philosophers, among them the late N. Hanson,{36} P. Achinstein,{37} as well as Kuhn and Feyerabend. Furthermore, to argue that only statements containing observational terms are strictly speaking meaningful, is much too narrow a view to take of the problem of meaning.

On the other hand, Kuhn and Feyerabend go to the other extreme by arguing that the meaning of a term is completely theory-laden. Only by looking at the interlocking relationships of the term to the other terms in the theory can one get at the meaning of a term. Thus, when a term goes from one theory to another it necessarily changes in meaning. Such a criterion for change of meaning is much too rigid.{38}

Furthermore, as I have already pointed out, referential or denotative meaning probably changes more slowly than sense meaning or intentional meaning.

The best way to spell out the meaning of scientific terms of a theory is to supply an exact definition of the term giving the necessary and sufficient characteristics that must be satisfied if the term is to apply. Certainly, this is one method that Kuhn doesn't mention specifically and which is one of the best methods for specifying the meaning of a term. Not every term can or is thus introduced. Suffice it to say, that when an exact definition of a term is the same in two different theories we have one case in which terms from different theories can have the same meaning, naturally provided that the "same" terms in the two definitions have the same meaning. Take the case of classical mechanics and of Bohr's theory of the atom, in both theories velocity and acceleration are given the same necessary and sufficient characteristics or the same exact definition is given (i. e., "velocity" is defined as "time rate of change of position" and "acceleration" as "time rate of change of velocity."){39}

Concepts for which exact definitions are not supplied can nevertheless be used in two theories with at least the core meaning being the same or, as P. Achinstein puts it, the semantically relevant criteria are the same. Thus, "position" and "time" have the same semantically relevant properties{40} (i. e., properties which in and of themselves tend to count for classifying an item as an x in the Bohr theory and in classical mechanics. Putting the matter in the terminology developed in Chapter III, the paradigm examples of certain terms can be the same with change in theories. Thus, the paradigm example for "electroscope", insect", "atom", "telescope" can be and actually have been the same with change in theories.

In this connection it is important to point out that even if some terms of a scientific theory are new, one can come to comprehend the meaning of such terms by studying the theory. In particular one needs to study the use of these terms in problem-solving situations as well as in experimental situations. Communication between scientists committed to different paradigms can only be postponed but never completely stopped. Discussions over the merits of two or more paradigm-theories are possible.

Except for a few overzealous statements concerning the incommensurability thesis, due in part to his loose use of the term "paradigm", Kuhn has brought to our attention many important points that either have been forgotten or have never been made.

l. The meaning of some terms is completely determined in some theories. This is an extremely important insight which philosophers of science have forgotten for a time in part due to the preoccupation with attempts at setting up a neutral observation language.{41}

2. Each normal scientific tradition determines the problems that are significant.

3. Acceptable solutions to scientific problems are also determined by a particular scientific tradition.


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Notes

{22} SSR, p. 102. [Back]

{23} SSR, p. 102. [Back]

{24} SSR, p. 97 [Back]

{25} "Unanticipated novelty, the new discovery, can emerge only to the extent that his anticipations about nature and his instruments prove wrong. Often the importance of the resulting discovery will itself be proportional to the extent and stubbornness of the anomaly that foreshadowed it. Obviously, then, there must be a conflict between the paradigm that discloses anomaly and the one that later renders the anomaly lawlike." SSR, p. 96. [Back]

{26} Nathan Brody and Paul Oppenheim, "Application of Bohr's Principle of Complementarity to the Mind-Body Problem," Journal of Philosophy, LXVI, 4 (1969),, p. 98. [Back]

{27} SSR, p. 96. [Back]

{28} Harvard Case Histories in Experimental Science, Vol. I, p. 72. [Back]

{29} SSR, p. 102. [Back]

{30} SSR, p. 94. [Back]

{31} SSR, p. 97. [Back]

{32} "In the first place, the proponents of competing paradigms will often disagree about the list of problems that any candidate for paradigm must resolve. Their standards or their definitions of science are not the same. . . . Lavoisier's chemical theory inhibited chemists from asking why the metals were so much alike, a question that phlogistic chemistry had both asked and answered." SSR, p. 147. [Back]

{33} SSR, p. 149 [Back]

{34} "What had previously been meant by space was necessarily flat, homogeneous, isotropic, and unaffected by the presence of matter. If it had not been, Newtonian physics would not have worked. To make the transition to Einstein's universe, the whole conceptual web whose strands are space, time, matter, force, and so on, had to be shifted and laid down again on nature whole. Only men who had together undergone or failed to undergo that transformation would be able to discover precisely what they agreed or disagreed about. Communication across the revolutionary divide is inevitably partial." SSR, p. 148. [Back]

{35} See Israel Scheffler's Science and Subjectivity, Chapter 3, "Meaning and Objectivity." [Back]

{36} Norwood Hanson, Patterns of Discovery (Oxford: Oxford Univ. Press), Chapters I and II. [Back]

{37} Peter Achinstein, Concepts of Science, Chapter V, "Observational Terms," pp. 157-178. [Back]

{38} Dudley Shapere, "Meaning and Scientific Change" in Mind and Cosmos, ed. by R. G. Colodny (Pittsburgh: Univ. of Pittsburgh Press, 1966), see particularly pp. 55-56. [Back]

{39} Peter Achinstein, Concepts of Science, p. 102. [Back]

{40} Ibid., pp. 102-103. [Back]

{41} Peter Achinstein gives the example of the term "entropy" which he thinks is completely theory-laden in classical thermodynamics. With change in the theory the term "entropy" no longer meant the same thing. Concepts of Science, p. 104. [Back]


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