Abstract
An objection may be raised to the solution we proposed in the preceding section to the problem of eliminating the clash between, say, classical and quantum mechanics.
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Notes
- 1.
The considerations that will be developed in the present section and in the two following sections have been outlined by the author in diverse papers, and were given a synthetic presentation in Agazzi (1985).
- 2.
It may be noted that in the textbooks of traditional logic, the theory of the terms was developed considering them as constituents of propositions, and it was usual to distinguish three kinds of term: mental, oral and written. Mental terms were concepts. Already for Aristotle, however, oral and written terms were considered signs of the mental terms, and this justifies the modern practise of considering a term only as a linguistic expression, that designates the concept. This is the convention we shall adopt in the present work. Other authors might prefer, e.g., “express” or some other equivalent terminology.
- 3.
The empirical attributes which are being considered here as tools for fixing the reference of the discourse should not be regarded as properties giving rise to a definite description of a certain Mr. Smith, but as ostensive criteria which we select in order to intersubjectively point to the referent. Their role is therefore that of offering a complex of conditions that functions as a rigid designator in Kripke’s sense. What is interesting, however, is that these predicates express at the same time some property of Mr. Smith (which his name alone would not do), so that they play a double role, that of ostensively providing the reference, and that of providing a description at the same time. The combination of these two functions, which is not really transparent in the case of this everyday example, will be apparent in the case of the operational predicates of science.
- 4.
To use our Kripkean analogy again, theoretical statements may be valid in several ‘possible worlds’ and, by means of their links with the operational predicates, they are shown to refer to the particular world in which our objects reside, being rigidly referred to it by the operational predicates, which are equipped with an ostensive role.
- 5.
The already-mentioned thesis of the theory-ladenness of all scientific terms obviously amounts to the negation of the said clear-cut distinction, but the question has a much longer history even in the empiricist philosophy of science. Indeed, this philosophy has its roots in the doctrine of the Vienna Circle, that made ‘empirical verification’ the condition of the meaningfulness of sentences, which in turn entailed that only observational terms have meaning. Since it soon became apparent that many scientific statements were doomed to be meaningless if this criterion were to apply, a progressive liberalisation began which tried to remain faithful to the verifiability principle while attributing increasing importance to the formal and syntactical features of ‘the language of science,’ which was to constitute a means for the circulation as well as the true creation of meaning. In this way, while it was originally supposed that meanings could percolate up from their genuine source (the observational terms) to the other terms (the theoretical ones), the development of the investigation led to conceiving of meaning as something global, pertaining to the theory as a whole, rather than to single terms. In this way the thesis of the theory-ladenness of all scientific concepts had already been explicitly elaborated within the logical empiricist epistemology, especially in the late 1950s and early 1960s, and was ready to be used just a few years later by those who made of it a cornerstone of the incommensurability thesis. The steps in this development may be clearly perceived in Carnap (1936, 1952, 1956), Hempel (1952, 1958), and Sellars (1961). A very good survey of this story is provided in the chapter ‘Empiricist Criteria of Cognitive Significance: Problems and Changes’ of Hempel (1965) (which is almost a reprint of two earlier papers).
- 6.
This is the most usual way of presenting this issue. Historical accuracy however leads one to recognise that this new way of conceiving of the axiomatic method had already been prepared by Pasch (see Pasch 1882), and had been completely developed by Peano and his school between 1889 and 1899 (i.e., in the decade preceding the first publication of Hilbert’s Foundations of Geometry). In particular, Mario Pieri (a disciple of Peano) explicitly defended the idea that the meaning of the primitive concepts is ‘defined’ through the postulates (see Pieri 1899, 1901). While Pieri called this a “definition through postulates,” it became customary later to call it an “implicit definition.” However, this latter expression was not considered a very satisfactory way of characterising this contextual interdependence of meanings, and nowadays it is used in a much more restricted and technical sense in mathematical logic. The reason for this dissatisfaction was that it is not really clear how the meaning of the single primitive concepts could be fixed on the basis of the simultaneous presence of the postulates.
In several papers devoted to Hilbert’s Foundations of Geometry which appeared in the Jahresbericht der deutschen Math.-Vereinigug in the years 1903 and 1906, as well as in a couple of letters to Hilbert (see Frege 1969, vol. 2), Frege correctly pointed out that the totality of the postulates may at most define a ‘second order’ concept (of which the primitive concepts occurring in the postulates are so to speak the ingredients), but cannot establish the meaning of these concepts themselves. Frege’s criticism remained uninfluential (owing to the growing favour of the formalist trend in mathematics), and at most led later to a ‘readjustment’ of the issue. As was suggested by Bernays in a review of the then newly discovered correspondence between Frege and Hilbert (published in the Journal of Symbolic Logic 7, 1942: 92–93), the postulates of elementary geometry, for example, represent an explicit definition not of the single concepts occurring in them, but of the concept of Euclidean three-dimensional space.
Even so, Frege’s correct criticism has not been met; and if we give it the attention it deserves, we must at least refrain from saying that the axiomatic context (or any linguistic context) entirely determines the meaning of the concepts. We are certainly entitled to say (as we have said) that this meaning depends also on the context on an intensional level; but this dependence cannot mean the dissolution of the meaning in the context, otherwise no meaning at all could emerge. This is why the thesis of total ‘meaning variance’ is already untenable for semantic reasons.
We are not particularly interested in discussing the semantic ‘stability’ which must exist to some extent even if context is given its fullest role. On the other hand, we shall later present specific arguments in favour of the existence of a ‘stable core’ in the meanings of the operational concepts, based on referential reasons. What we may say here is that every concept enters into a scientific theory equipped with a meaning whose structure is well articulated and depends on many factors. It is therefore wrong to say that terms receive their meanings totally and only through the theoretical context. This is actually an authentic formalistic fallacy which goes back to Carnap’s proposal to consider physical theories as interpreted logical formal calculi (see Carnap 1934). In fact empirical theories do not begin to exist as formal systems, but may at most be ‘formalised’ after they have attained a certain stage of development. At this stage it may also be possible to detect the ‘variance’ of meaning which occurs as a consequence of a term’s being located in a different context, but this ‘variance’ is always partial. Therefore, when a term is used in a particular sentence, it is normally used only according to a part of its meaning, and it may well happen that the part concerned is not affected by ‘meaning variance’.
- 7.
This is actually a particular way of conceiving of incommensurability that is strictly bound to a linguistic view of scientific theories. Other ways of conceiving of incommensurability, however, relate it to a ‘gestaltic’ switch and are presented, e.g., in Dilworth (2008). They are also more in keeping with the general conception of science proposed in the present work, as will be seen later.
- 8.
This has nothing to do with essentialism, as we do not claim that the ground intension is more important than other parts of the meaning, as will be better explained in the sequel.
- 9.
This diagram will be taken up again literally in Sect. 7.2.8 in a wider discussion concerning theory comparison.
- 10.
Certain authors, such as Dilworth, lay stress on the difference between reference and referent, and maintain that reference is not, properly speaking, a property of terms or concepts, but rather an attitude of the speaker, who uses the terms with the intention of referring his listener to certain objects. We shall briefly discuss this issue in Sect. 4.1 and shall indicate why we prefer to stick to the more traditional view according to which reference is a property of terms and concepts. We should like, however, to lay stress on the intrinsic pragmatic side of science, which is the root of its unavoidable operational dimension. We have very schematically underscored this dimension by attributing a specific role and position to operational concepts, but we are aware of having left unexplored the complex nature of operations themselves and, in particular, their fundamental difference from observations. Nor are we going to go deeper into this issue in the remaining parts of this work. An accurate exploration in this direction, however, can be found in Chap. 2, of Stepin (2005), especially pp. 68–89, where a presentation of different ‘layers’ is made necessary for relating theoretical schemes with experience, via ‘instrumental situations’ and ‘empirical schemes’.
- 11.
The notion of the position of a single particle is an operational concept, for example, in the classical mechanics of material points, while it is a theoretical concept in the kinetic theory of gases.
- 12.
We have said that we do not accept the ‘traditional’ partition of observational and theoretical terms. However, a much more complex use of the notion of observation is very much in keeping with our way of characterising the operational concepts in which complex instruments enable us to ‘observe’ entities that are unobservable in the everyday meaning of this term, which strictly relates it to perception. This is in keeping with the well known claim that our instruments can be seen as ‘amplified human senses,’ so that it is correct to say that we can ‘observe’ thanks to them much more than we could observe without them.
This extension of the notion of observability (that, e.g., plays a significant role in Harré 1986) becomes even more important if we consider that the ability to ‘observe’—in this much richer and more interesting sense—increases with the development not only of sophisticated technology, but of scientific knowledge as such. An excellent presentation of this enlarged sense of observation is to be found in. Shapere (1982) and, in a sense directly related to the operational approach offered in the present work, in Buzzoni (1987). However, since in the great majority of the literature the dichotomy ‘observational-theoretical’ is still understood in its old empiricist form, we shall avoid using “observational” and use “operational” instead, except for some special and explicitly declared purposes. Let us note, however, that we are not doing this in order to stay faithful to an alleged ‘genuine’ sense of the notion of observation, simply because we do not share the ‘radical empiricist’ tenet that endorses such a view. This tenet, for example, permeates van Fraassen (2008) and is expressed through such sharp declarations as “in the sense in which I use that term: observation is perception, and perception is something possible for us, if at all, without instruments” (p. 93); and in the subtitle “Observation by instruments’: our bewitching metaphors” (p. 96). Modern natural sciences have been characterised by being empirical and not purely speculative, precisely because they adopted instrumental observation (with the decisive advantages of intersubjectivity and precision that everyone recognises); therefore it sounds surprising that such a fundamental fact is declassed to the status of a metaphor within an approach that intends to offer a good interpretation of the nature of modern science. This, however, might be precisely a significant symptom of the intrinsic fragility of the radical empiricist tenet itself.
- 13.
Having distinguished between theories and laws, we may even say that the ‘available knowledge’ is represented by the accumulation of the expressions of known laws rather than of laws and theories (the latter concerning the understanding and explanation of laws). However, this issue is not particularly important here, and we can safely admit that even theories belong to the said ‘available knowledge,’ according to the broad sense of knowledge we have already accepted, and according to which understanding and explanation are constituents of knowledge despite their being hypothetical.
- 14.
We have made much use of intensional ways of speaking, but this should not be seen as peculiar, since all discussions related to ‘theory-ladenness’ are in fact of an intensional nature, since the context-dependence of meanings cannot help but be primarily related to their intensions. Therefore, we do not criticise the structuralist view of theories for having resorted to intention in order to give a sense to the notion of “intended applications” or of “target system.” We simply note that the structuralist approach is essentially constituted by a sophisticated use of set theoretical formalisms – instead of the traditional formal-logical tools—in the metatheoretical analysis of empirical theories; and there is no way of characterising intentionality by means of such instruments. Therefore, in the last analysis, the fact that a certain model M represents or applies to a certain target system T only depends on the “intention” of some scientist to consider it to be able to do this. This obviously entails subjectivity, and this does not disappear even if we concede that such an intention is that of a certain scientific community, because what still fails is the indication of how the scientist or the scientific community can evaluate whether the model M represents the target system T or not. The operational criteria we have insisted upon play precisely this decisive role. For a more developed presentation of the structuralist view one can consider, besides Sneed (1971), also the classical works Stegmüller (1979) and Balzer-Moulines-Sneed (1987) and the survey by Diez-Lorenzano (2002).
- 15.
The above considerations explain how we can satisfy a very reasonable requirement concerning the relative stability of reference expressed by Harré: “Our theory of reference must not make the achievement of a referential relation between a person and thing so fragile a link that every change in the meaning of the vocabulary with which we describe the things we believe to exist requires us to revise our ontology. Nor must we make that link, once achieved, so robust, that we are obliged to hold on to it no matter how much the meanings of our descriptive vocabulary has changed” (Harré 1986, p. 99). We have seen that the indispensable ‘stability of the semantic logos’ is granted by the permanence of the referential core of the intension of concepts that is compatible with significant changes in the linguistic-contextual part of this intension. That this stability also entails a stability of ontology will become clear in the sequel, when the decisive ontological role of reference is discussed. A more detailed discussion of this issue will be presented in Sect. 5.3.5.
- 16.
Feyerabend in particular has insisted on this point, already in his (1963), pp. 16ff.
- 17.
To be fair, one should recognise that neither Kuhn nor Feyerabend suggest that incommensurability should imply incomparability. Kuhn allows that theory comparison may take place, but on grounds other than those suggested by the logical-deductive scheme accepted by empiricists and Popperians. We are not interested here in examining these other grounds, such as accuracy, scope, simplicity, fruitfulness, and the like, most of which Dilworth has incorporated into the Perspectivist conception of science (see Dilworth 2008, Ch. 9, pp. 66–88), but simply want to show how the incommensurability thesis is in itself untenable, and therefore how it makes some sense also to compare theories according to the logical-deductive scheme. In parts of this book to come, on the other hand, we shall also clearly indicate the limits of this scheme, and propose a more comprehensive approach. Let us therefore quote a passage of Kuhn in which all the above considerations are present:
The point-by-point comparison of two successive theories demands a language into which at least the empirical consequences of both can be translated without loss or change. That such a language lies ready to hand has been widely assumed since at least the seventeenth century when philosophers took the neutrality of pure sensation-reports for granted and sought a ‘universal character’ which would display all languages for expressing them as one. Ideally the primitive vocabulary of such a language would consist of pure sense-datum terms plus syntactic connectives. Philosophers have now abandoned hope of achieving any such ideal, but many of them continue to assume that theories can be compared by recourse to a basic vocabulary consisting entirely of words which are attached to nature in ways that are unproblematic and, to the extent necessary, independent of theory. That is the vocabulary in which Sir Karl’s basic statements are framed. He requires it in order to compare the verisimilitude of alternate theories or to show that one is ‘roomier’ than (or includes) its predecessor. Feyerabend and I have argued at length that no such vocabulary is available. In the transition from one theory to the next words change their meanings or conditions of applicability in subtle ways. Though most of the same signs are used before and after a revolution—e.g. force, mass, element, compound, cell—the ways in which some of them attach to nature has somehow changed. Successive theories are thus, we say, incommensurable.
Our choice of the term “incommensurable” has bothered a number of readers. Though it does not mean ‘incomparable’ in the field from which it was borrowed, critics have regularly insisted that we cannot mean it literally since men who hold different theories do communicate and sometimes change each others’ views. More important, critics often slide from the observed existence of such communication, which I have underscored myself, to the conclusion that it can present no essential problems (Kuhn 1970, pp. 266–267).
- 18.
This claim has often been made, especially by Feyerabend, who has consequently denied that two different theories may “refer to the same objective situation.” See, e.g., Feyerabend (1978), p. 70. This stance, however, is incompatible with his acceptance in his (1975) of gestalt-switch phenomena as constituting instances of incommensurability (as has been pointed out in Dilworth 2008).
- 19.
Just to give a brief example, the notion of velocity retains its most intuitive intensional features in quantum mechanics, being understood as the rate of change of the position of a particle in its trajectory with respect to time. However it is precisely because the assimilability of a particle to a material point localised in space and time, or the notion of trajectory, are problematic, that the concept of velocity also undergoes modifications. Heisenberg’s uncertainty relations may be seen as the new ‘contextual’ situation which modifies the composition of the traditional intensional pattern of concepts imported from classical to quantum mechanics.
- 20.
The tools of relativisation for the operationally definable concepts of optics in the first decades of the nineteenth century were the same both in the context of the corpuscular and of the wave theories of light, and it was thanks to them that empirical laws and experiments could be accepted with the same (operationally determinable) meaning and with the same reference, in spite of the fact that these laws were differently interpreted and explained by the two theories. However, it was precisely because of this ‘common relativisation’ of the operational concepts that the theories could be compared, and that one superseded the other at that moment. (At least in this case we believe that the result of the comparison was more decisively determined by this ‘deductive-empirical’ procedure than by anything else).
- 21.
Hence we could say that the positions of Kuhn and Feyerabend represented a progressive step in that they revealed the need to transcend the syntactical narrowness of the Deductive Model, and open the door to semantical considerations (see especially Kuhn 1974, p. 504). However, they failed to take the other step, that of proceeding to praxis, which would have shown them that theory comparison is made on the basis of ‘practically’ (we say operationally) determined referents.
- 22.
This notion of ‘conceptual space’ has some affinity with the notion of ‘paradigm,’ but differs from it inasmuch as it is prescientific. For the same reason it also differs from the ‘logical network’ of which we have spoken in previous sections, since it is not yet articulated into explicitly defined concepts and explicitly formulated sentences. When this happens, we have a transition to the construction of a theory proper, which may be considered a linguistic presentation of the Gestalt (and as such is always only partially successful); and one of the most typical features of a theory is indeed the establishment of the ‘logical network’ just mentioned.
- 23.
For example, the ‘conceptual space’ of classical mechanics was taking shape when Galileo first proposed characterising nature in terms of its quantitative features (primary qualities), which should provide knowledge of the nature of the motion of material bodies in space through the discovery of laws. To this Newton explicitly added the notion of force, that is, a very particular form of cause (or, if one prefers, a particular manifestation of efficient causality) which was not meant to ‘produce’ things, but only to modify motion by acting upon material things from the outside. This general framework or Gestalt had to be refined and analysed into a set of concepts which were really of use (e.g., some of the Galilean primary qualities, such as ‘shape’ were not retained), such as those of position, duration, mass, velocity, acceleration and force; and these concepts had to be equipped with certain operational procedures of measurement. Some work in this sense was already done by Galileo, and the rest was done by Newton with whom the actual discipline of particle mechanics was inaugurated, by means of the introduction of such theoretical concepts as that of material point, absolute space, absolute time, and so on, and the explicit formulation of theoretical laws (such as the laws of force and of gravitation).
- 24.
We shall return to this question, and analyse it with the necessary detail in Sect. 4.3.
- 25.
See the appendix: ‘The Semantics of Empirical Theories’.
- 26.
No uniformity of use exists in the literature regarding the term “denotation,” though it is most frequently employed to indicate a word-world relation, and is considered synonymous with “reference.” For reasons which have already been explained, at least in part, we speak of denotation also to indicate the relation between a linguistic expression and an abstract object, or intensional object (which does not belong to ‘world’ in the everyday meaning of this expression), while we prefer to speak of reference when the relation is established with an object for which we have ‘referential procedures’ at our disposal. This terminological convention will be further clarified in the next section.
- 27.
There is a difference between intention and intension (and between the related adjectives), but at the same time these two notions are both historically and conceptually related. We shall examine this issue in the next section.
- 28.
A synonym of “whole” in the sense we are using it here could be the more usual term “scope.” We have preferred the more exotic terminology, however, in order to underline the global and ‘transcendental’ purport of those conditions that actually envisage ‘the whole of reality’ from a ‘partial’ point of view.
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Agazzi, E. (2014). First Corollaries in the Philosophy of Science. In: Scientific Objectivity and Its Contexts. Springer, Cham. https://doi.org/10.1007/978-3-319-04660-0_3
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