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Problems of Structure and Growth: Towards an Interactive Model of the Growth of Scientific Knowledge

  • G. L. Pandit
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 73)

Abstract

Dominant traditions of internal criticism, in which are rooted radical and endless philosophical disagreements concerning the very nature and task of philosophy, have prevented many important and crucial kinds of questions from being asked. At least one such set of questions can be raised concerning epistemology. Indeed, the questions concerning the nature of a theory of knowledge are inseparably interlinked with questions that must be raised concerning the type of critical evaluation to which such a theory can be subjected. Taking epistemology broadly as the theory of the structure and growth of knowledge and given an epistemological theory in this sense, the question of the method of critically ‘testing/evaluating’ it in some effective or decisive manner must be faced sooner or later. In the event of there being two or more competitive epistemological theories, this question would assume a special kind of relevance. Indeed, in such a situation it is quite reasonable to go beyond the traditional standards of philosophical criticism, that restrict the evaluation of a philosophical theory to a species of internal criticism alone, and require some kind of external criticism that could enable us to identify the significance of each of the rival theories and to decide between them. In so far as the method of internal criticism derives all its principles from logic, a choice from among rival epistemological theories can only be made on extra-logical grounds when they are all equally good internally/logically.

Keywords

Active Element Scientific Theory Interactive System Background Theory Conceptual Innovation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.
    In an unpublished paper I draw a distinction between what I call a logical as against a methodological concept of a theoretical system, i.e., between (1) a theoretical system consisting of a newly proposed theory and a set of background theories which bear a presupposition relation of logical support to the former and (2) an axiomatic formal deductive system which is accompanied by an appropriate interpretative system of its own. The former concept captures the Duhemian insight underlying his arguments for the disconfirmation of a whole `group of theories’ in science. For the latter concept, see R. Carnap (1956a), pp. 38–42 and K. R. Popper (1972a), p. 239.Google Scholar
  2. 2.
    For a discussion of these concepts, see Section 3.3.Google Scholar
  3. 3.
    This idea is precisely what I propose to develop presently as an interactive model of the growth of knowledge, according to which this growth is a function of the inter- actions between the developmental structures of problems and theories in science.Google Scholar
  4. 4.
    This may be shocking at first, just as A. Rosenblueth, N. Wiener, and J. Bigelow (1943), pp. 18–24, are said to have shocked many psychologists by propounding the view that machines with negative-feedback control system were teleological systems. In a sense one can even speak of the `growth’ of non-living systems such as complex machines designed by man. Taking machines in general to be control hierarchies as against mere structural hierarchies like stones, crystals and even elementary particles, one can quite legitimately speak of machine-growth in the sense of replacement of one kind of machine by another more comprehensive kind which incorporates all the essential and useful structural and functional properties of the former. The process of growth in the context of non-living control hierarchies is thus identifiable in terms of the concept of systems-replacement in the above sense. It is quite significant that in this century science finds it necessary to extend its study of evolutionary phenomena to the astronomical scale in the large (ranging from stellar evolution to that of the universe as a whole). For such studies it is becoming more and more necessary to assume that the universe as a whole must be a more or less hierarchically organized, self-regulating interactive system with its sub-systems in a state of perpetual interaction. Attempts by physicists to develop alternative (e.g., `steady state’ and `big-bang’) evolutionary models of the universe on the basis of modern physical theory are significant in this context.Google Scholar
  5. At the terrestrial level, the problem of explaining developmental phenomena of the organic world has given rise to the science of developmental biology, which studies the patterns and mechanisms of growth/evolution at various structural and functional levels of complexity ranging from the individual cells to individual organisms. Ultimately it aims at discovering empirically testable explanatory theories of cellular development, differentiation, specialization and interaction and their organization into higher multi-cellular living systems with their own control hierarchies.Google Scholar
  6. 5.
    The terms `interactive system’ and `interactive model’, which were introduced in G. L. Pandit (1976), pp. 409–436, will become precise as we proceed.Google Scholar
  7. 6.
    Norbert Wiener (1968), pp. 378–79, who founded and conceived of cybernetics as a science of control and communication in machines and in living organisms, concedes that “it encompasses much wider horizons.” It seems quite reasonable to go beyond this original narrow conception so as to conceive of it as a general systems theory.Google Scholar
  8. 7.
    See Ludwig von Bertalanffy (1969), p. 60.Google Scholar
  9. 8.
    J. W. N. Watkins (1974), pp. 393–95. Here (p. 395) he writes: “The alleged impossibility of mind-body interaction is not God-given but only Descartes-given (or, rather Descartes-implied).”Google Scholar
  10. 9.
    The kind of unquestioned dominance that the traditional theory of interaction enjoys even to this day is indicated by Alastair Hannay’s following communication on the manuscript of my (1976): “You isolate interaction as the basic explanatory element in the growth of (scientific) knowledge and say interaction must be between things of different kinds, whereas in its ordinary root sense `interaction’ refers to a transaction between two things of the same kind, namely human beings... ”Google Scholar
  11. 10.
    I am indebted to the biologist H. H. Pattee (1972), pp. 3–4, for borrowing this distinction which he draws in the context of the subcellular control systems.Google Scholar
  12. 11.
    Ibid., p. 3.Google Scholar
  13. 12.
    Cf. W. S. Bullough (1967), p. 171.Google Scholar
  14. 13.
    Cf. H. H. Pattee (1972), pp. 4–5.Google Scholar
  15. 14.
    Cf. ibid., p. 4.Google Scholar
  16. 15.
  17. 16.
    Ibid., pp. 6–8.Google Scholar
  18. 17.
    Ibid., p. 6 Pattee (ibid.), p. 7, writes: “The integrated records, descriptions and instructions in cells are no less a language system because we know the molecular structure of some of their coding devices and symbol vehicles... In biological studies at all levels of organization we find the same implicit recognition of language-constrained behaviour, such as references to hormones, chemotactic substances, and controllers of genetic expression as message molecules.”Google Scholar
  19. 18.
    Ibid., p. 8.Google Scholar
  20. 19.
  21. 20.
    Cf. ibid., p. 21.Google Scholar
  22. 21.
    The following generalizations of Pattee (ibid.), pp. 11–17, seem to be essentially not of such restricted generality as to render them systems-specific, but of an unrestricted character and hence biologically neutral: (1) A control hierarchy constrains the behaviour of the elements of a collection so that they perform some coherent activity. (2) The coherent activity of the hierarchical control system is simpler than the detailed activities of its elements. (3) Hierarchical constraints classify degrees of freedom to achieve selective behaviour. (4) Both the selection of sensitive degrees of freedom (or the choice of relevant variables), and the mechanism which performs the selective activity appear largely arbitrary. (5) New hierarchical constraints can continue to appear at higher levels without destroying the existing constraints at the lower levels. (6) There are many physical structures that execute the same function; and there are many descriptions of the same physical structure.Google Scholar
  23. 22.
    That a natural language contains a meta-language is, in Pattee’s words (ibid.), p. 16, “also a continuable or recursive property that allows us to say whatever we wish about what we have just said — no matter on how abstract a level we may have said it — while still retaining the same fixed and finite set of grammatical rules and arbitrary symbols. In other words, natural language always permits new classification and new interpretation of its structures, even though its substructure remains fixed.” See also ibid., p. 15.Google Scholar
  24. 23.
    Cf. Davis (1958).Google Scholar
  25. 24.
    See N. Chomsky (1964), p. 9.Google Scholar
  26. 25.
    Cf. N. Ruwet (1973), p. 29.Google Scholar
  27. 26.
    Cf. N. Chomsky (1967), pp. 397–401, 434–38; (1964), pp. 8, 111; (1976), p. 83; (1977), pp. 3, 32–33, 81, 164.Google Scholar
  28. 27.
    Cf. N. Chomsky (1964), p. 22.Google Scholar
  29. 28.
    Ramôn Margalef (1968), p. 2.Google Scholar
  30. 29.
    Cf. A. Kaplan (1953), p. 406.Google Scholar
  31. 30.
    Cf. O. Mayr (1970), p. 111.Google Scholar
  32. 31.
    Norbert Wiener (1953), p. 107.Google Scholar
  33. 32.
    R. J. Goss (1964), p. 43.Google Scholar
  34. 33.
    For further discussion and examples of feedback, see W. C. Wimsatt (1971), pp. 241–56 and E. Manier (1971), pp. 225–40.Google Scholar
  35. 34.
    A characteristic of negative feedback,“ says Margalef (ibid.), p. 2, ”is that not only the entire system but also some selected states of the system show a considerable persistence through time. A cybernetic system influences the future... in the sense that the present state sets limits or patterns for future states. Thus, the present state is a bearer of information... information has to do with any aposteriori restrictions of apriori probabilities. Any cybernetic system, through the interactions of its parts, restricts the immensely large numbers of apriori possible states and, in consequence, carries information... “Google Scholar
  36. 35.
    Chomsky (1964), p. 22, speaks of “rule-governed creativity” and “rule-changing creativity” in the systems-specific contexts respectively of (a) linguistic performance conforming to an underlying system of rules with recursive power, that represents linguistic competence and (b) linguistic performance that involves considerable deviations from rules and that ultimately triggers changes in the relevant underlying system of rules. Rule-governed creativity is, according to him, “the kind of ”creativity“ that leaves the language entirely unchanged (as in the production — and understanding — of new sentences, an activity in which the adult is constantly engaged)”; while the rule-changing creativity is “the kind that actually changes the set of grammatical rules (e.g., analogic change).” See also N. Ruwet (1973), pp. 26–28.Google Scholar
  37. 36.
    Taken as an input-output system — Cf. W. F. Hill, (1963), p. 199 — such a system may be alternatively defined, after J. Rothstein (1958), p. 37, “as an organization with a function”, where “a function” means “a mapping of one set of alternatives which we call the input into another set called the output.” A measuring system that “maps a set of states of an object of interest into the set of possible indications of the apparatus” or a communication system which “maps a set of messages from a source into a set of messages at a destination” illustrates this functional aspect of an interactive C-H. system.Google Scholar
  38. 37.
    J. Rothstein, ibid., p. 35.Google Scholar
  39. 38.
    Consider, e.g., a multicellular organism that develops from a single cell dividing itself into two major functional organizations, “the nucleus, in which the coded information for all of the cell’s metabolic mechanism resides, and the cytoplasm, where the business of metabolism is transacted.” See F. J. Gottlieb (1966), p. 92. In the words of Gottlieb (ibid.), p. 97, “Although the total potential capacity of the cell rests in the nucleus, the realization of this potential is dependent upon the chemical and spatial constitution of the cytoplasm which, in turn, depends on the proper genetic information for its functioning. In addition, the make-up of the cytoplasm is, in part, a function of the environment.” At the level of developmental biology, the cytoplasm and the nucleus may thus be regarded as the multipotent elements of the cell as an interactive system, where the environmental elements with their own associated sets of alternatives play a role in determining their total potential for development into a multi-cellular organism.Google Scholar
  40. 39.
    See Oskar Lange (1965), p. 17.Google Scholar
  41. 40.
    Ibid., p. 4.Google Scholar
  42. 41.
    This example is also cited by Lange. Cf. ibid., p. 5.Google Scholar
  43. 42.
    Ibid. The unique relation between the input and output states of an active element, the former determining the latter in the sense of the assumption (4) above, is called by Lange the mode of action of that element.Google Scholar
  44. 43.
    See. J. Rothstein (1958), p. 35.Google Scholar
  45. 44.
    Ibid.; cf. Ramon Margalef (1968), p. 2. Indeed, it would not be unreasonable to define an active element as one which, together with other active elements, is capable of forming a C-H system and a non-active element as one which, together with other such elements, can form only a S-H system.Google Scholar
  46. 45.
    Ramon Margalef, (1968), p. 16, writes: “Everywhere in nature we can draw arbitrary surfaces and arbitrarily declare them boundaries separating two sub-systems. More often than not it turns out that such boundaries are asymmetric; they separate two sub-systems that, although arbitrarily limited, are different in their degrees of organization. There is some energy exchange between the two sub-systems in the sense that the less-organized sub-system gives energy to the more organized, and, in the process of exchange, some information in the less-organized is destroyed and some information is gained by the already more-organized,” according to this principle the boundaries separating two subsystems’ in an interactive system of cytoplasm-nucleus or prey-predator type are asymmetric’ in the sense that they separate two sub-systems that differ in their degrees of organization. It is far from trivial and quite significant to speak of prey-predator interaction in population biology or ecological theory, social interaction between human individuals in social psychology or sociology, therapeutic interaction in psychology, weaker and stronger interactions in physics and so on precisely because in each case elements of different orders of organization are involved.Google Scholar
  47. 46.
    The fundamental concept of organization of a primordial kind may alternatively be defined as involving energy concentration of some kind’. C. A. Muses, Comment by C. A. Muses’ in J. Rothstein (1958), lxxix e.g., writes: “... some form of energy concentration must be the basis for any kind of order; just as energy scattering is the basis of disorder.”Google Scholar
  48. 47.
    See Chomsky (1964), p. 9. The underlying idea of different levels of organization in language may be expressed more generally and schematically as follows: OT A OCr • OC2 • 0C3,. OCn OS A OWr • Ow2 • Ow3,... Own OW 0 OLt • 0 L OL3,... OLn Here;, O’, C’, S’, W’, L’, and 0’ abbreviate theory’, organization’, concept’, statement/sentence’, word’, letter’, and the sign of non-identity respectively.Google Scholar
  49. 48.
    In the words of I. Lakatos (1971a), p. 92: “According to inductivism only those propositions can be accepted into the body of science which either describe hard facts or are infallible inductive generalizations from them.” The latest attempts to develop theories of the structure and growth of scientific knowledge on the pattern of the inductivist UMS and CMG are found in the Russellian and Wittgensteinian versions of logical atomism on the one hand and logical empiricism on the other. Consider, e.g., the Tractarian model of one of the sub-structures of language as consisting of elementary propositions and truth-functional compounds thereof. This formalizes excellently the basic idea of the traditional versions of UMS.Google Scholar
  50. 49.
    That the concept of organization-variance is, in our view, central to the concept of significant interaction is of considerable philosophical significance in the present context.Google Scholar
  51. 50.
    For the view that scientific explanation and prediction are essentially structurally identical, see C. G. Hempel (1965), pp. 278–79.Google Scholar
  52. 51.
    This is particularly true of the inductivist philosophy of science which, in its traditional formulations, confuses questions relating to the context of discovery with questions that relate to the context of justification or rational reconstruction.Google Scholar
  53. 52.
    Popper’s analysis of scientific knowledge and its growth is, strictly speaking, the only exception that I know of.Google Scholar
  54. 53.
    This point will be developed further subsequently in connection with my criticism of Lakatosian methodology of scientific research programmes.Google Scholar
  55. 54.
    If we take Carnap’s partial interpretation model of a scientific theory’s structure and meaningfulness as a model of epistemic structure, growth of scientific knowledge can then be described as “a succession of interpreted deductive systems (or sets of deductive systems).” Cf. W. D. Siemens (1971), pp. 526, 529.Google Scholar
  56. 55.
    For details relating to the explanation-theorist’s levels-conception of explanation see E. Nagel’s (1961), pp. 29–46, 79–90. And for its criticism, see W. Sellars (1961), pp. 57–77.Google Scholar
  57. 56.
    Cf. C. G. Hempel (1965), pp. 278–79.Google Scholar
  58. 57.
    See R. Carnap (1956a), pp. 38–42 and C. G. Hempel (1965), p. 249.Google Scholar
  59. 58.
    For these see Karl Popper (1968), pp. 27–30; Karl Popper (1972b), pp. 1–30; I. Lakatos (1970); P. K. Feyerabend (1965); T. S. Kuhn (1970a).Google Scholar
  60. 59.
    See K. Popper (1968).Google Scholar
  61. 60.
    But the theory-problem relationship is not as simple as is implied by the usual one-sided picture of the inductivist or the explanation-theorist. It is, on the contrary, complex and indeed so complex as to defy any methodology of epistemic appraisal that is based on a doctrine of unilateral relationship between theories and problems.Google Scholar
  62. 61.
    L. Tondl (1973), pp. 131–148.Google Scholar
  63. 62.
    L. J. Beck’s translation (1952), p. 208. Rule 13 of Descartes’ posthumously published Regulae ad directionem ingenii (1701) begins by making three points, in the words of Beck (1952), p. 208: First “there must be something which we do not know in every problem, otherwise there would be no point in asking the question.” Secondly, this something must be “designated in some way or other, for otherwise nothing would push us to investigate it rather than anything else.” And, thirdly, it can only be `designated’ or determined’ “by the aid of something which is already known. ” Cf. Regulae Rules 12, 14 and N. K. Smith (1952), pp. 76, 81.Google Scholar
  64. 63.
    This is, e.g., illustrated by what we often call the commonsense view of the physical world’, if considered as a kind of rudimentary physical science. At this level it seems almost impossible to distinguish our physical descriptions as a sort of theoretical talk from the broader framework of our language in which that talk is embedded. For a more lucid and elaborate statement to this effect see H. Feigl et al. (1971), p. 149.Google Scholar
  65. 64.
    Following P. Duhem, W. O. Quine (1951) also argues to this effect in his attack on the analytic-synthetic dichotomy taken as a dichotomy between our language (as a matter of meaning-relations) and our empirical theories about the world of facts. See Quine (1951), p. 41.Google Scholar
  66. 65.
    Duhemian (logical-epistemological) conception of a theoretical system comes almost close to this view of theories as continuous with our language or vice versa. See the English translation of the 2nd (1914) edition of P. Duhem’s (1906), p. 187.Google Scholar
  67. 66.
    According to Ernst Cassirer (1953), p. 28, “All theoretical cognition takes its depar- ture from a world already pre-formed by language; the scientist, the historian, even the philosopher, lives with his objects only as language presents them to him.” At another place he argues (ibid.), p. 37, that “... one cannot grasp the true nature and function of linguistic concepts if one regards them as copies, as representations of a definite world of facts, whose components are given to the human mind ab initio in stark and separate outlines. Again, the limits of things must first be posited, the outlines drawn, by the agency of language; and this is accomplished as man’s activity becomes internally organized and his conception of Being acquires a correspondingly clear and definite pattern.”Google Scholar
  68. 67.
    For a discussion of such experiments, see B. N. Taylor, D. N. Langenberg, and W. H. Parker (1970), pp. 63–66, 77–78.Google Scholar
  69. 68.
    It is precisely in this sense that we may understand Descartes’ idea of problems as invariably involving something unknown, “the quaesitum, which is determined by reference to something already known, the datum or cognitum.”Google Scholar
  70. 69.
    Since the idea of TRp is essentially the idea of the pattern of the growth of knowledge as a pattern of theory-change leading to problem-change, TRp may be conceived as the problem-content (Tp-content) of a scientific theory: TRP = Df Tp-content. Tpcontent is, as a rule, formulated by why-questions in science, as has been shown above. Thus, e.g., the Tp-content of All metal objects increase in volume with an increase in temperature’ may be formulated or stated by means of the why-question: why do metal objects increase in volume with an increase in temperature?’ Similarly, the Tp-content of the electron theory with its assumption of electrons as carriers of an elementary charge is partly formulated by the whether-question: Whether the magnitude of the charge can be ascertained by experiment?’ It is interesting to note here that without the kind of questions such as this the famous oil-drop experiment of Millikan would not have been possible. Definition of TRp as Tp-content warrants a corresponding definition of TEp as the informative content (TI-content) of a scientific theory.Google Scholar
  71. 70.
    The idea of alternative, non-equivalent formulation of problems relative to different systems of background theory is perhaps best illustrated by the non-equivalent formulations of the problem of the nature of celestial motion relative to the alternative frameworks of Aristotelian science and the Copernican revolution respectively. More precisely, the pre-Copernican as well as the pre-Keplerian formulations of this problem as one of explaining the circular and uniform orbits of celestial bodies depend crucially upon the antecedently given Aristotelian assumption of the circular and uniform celestial motion as the most perfect and hence appropriate kind of motion. In the Copernican and Keplerian system, the problem is reformulated in new terms. More accurately, it is Kepler’s laws of planetary motion that entail a radical reformulation of the old problem, since these laws eliminate the Greek assumption of the circular and uniform character of planetary motion in favour of the alternative assumption of elliptical and non-uniform character of their motion. Thus it is partly to the Copernican and partly to the Keplerian systems of theoretical assumptions that we owe the problems of explaining the elliptical nature of planetary motion in its present formulation. Again, in modern physics, the problem concerning the phenomena of electricity, magnetism and gravitation was for a long time formulated and answered in terms of a set of classical ideas including the erstwhile physical idea of action-at-a-distance. However, it became necessary to reformulate the underlying physical problems in terms of newer concepts of different types of action-by-contact’ fields, electrical, magnetic and gravitational, respectively. The two types of formulations are essentially non-equivalent, each presupposing as well as leading to different sets of propositions.Google Scholar
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    See K. R. Popper (1972b), pp. 119, 144.72 See K. R. Popper (1972a), pp. 221–222.Google Scholar
  73. 73.
    The modification has to be along the lines of our schema II as follows:Google Scholar
  74. 74.
    See Max Weber (1949), pp. 90–91. In the field of the natural sciences, the method, if not a full-fledged methodology, of ideal-types is clearly traceable to the systems of Newtonian physics. Newton’s law of inertia serves as a classical example of an explicitly formulated ideal-type generalization.Google Scholar
  75. 75.
    Doctrines of ideal-types, understanding’ and value-relevance’ are central to these discussions. Cf. ibid. and also P. Q. Hirst (1976), pp. 58–60.Google Scholar
  76. 76.
    Cf. W. G. Runciman (1972), pp. 32–36.Google Scholar
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    David Papineau (1976), p. 145.Google Scholar
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    Ibid., p. 146.Google Scholar
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    For such a view, see E. Nagel (1973), pp. 131–32.Google Scholar
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    Cf. David Papineau (1976), pp. 142–43.Google Scholar
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    The law of inertia, as stated by Newton in the mathematical, and not the physical, portion (Book One) of the Principia (1687), says: Every body continues in its state of rest, or of uniform motion in a right [straight] line, unless it is compelled to change that state by forces impressed upon it. A. inertial frame of reference is, accordingly, one in which this law is valid. It is thus a non-accelerated coordinate system in which a body, on which no external forces are acting, moves with a uniform velocity. In A. Einstein’s (1968), p. 259, words: “Special relativity has this in common with Newtonian mechanics: The laws of both theories are supposed to hold only with respect to certain coordinate systems: those known as `inertial systems’. An inertial system is a system in a state of motion such that `force-free’ material points within it are not accelerated with respect to the coordinate system.” See also A. Einstein and L. Infeld (1961), pp. 209–212, 244.Google Scholar
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    The resolving power of Newtonian mechanics is such that the planets are seen as being “held in their complex paths by the counter-balancing forces of their tangential velocity, and the gravitational attraction of the sun.” Cf. Robin Briggs (1969), p. 77.Google Scholar
  83. 83.
    These are the constraints of Newton’s three laws of motion taken together: the law of inertia, the law of the magnitude of the force being proportional to the acceleration of the body in question, and the law of equality of action and reaction. To these, however, we must add the further constraints in the form of the unifying assumption that the forces to be invoked must be the same at the terrestrial and celestial (or planetary) level. For details, see Isaac Newton, Mathematical Principles of Natural Philosophy, Andrew Motte’s 1729 translation revised by F. Cajori, University of California Press, 1934.Google Scholar
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    Known as the inverse-square law of gravitation, it [F=G(mm’/D2) where the constant of universal gravitation G is the constant of proportionality] says: Between any two bodies whatever, of masses m and m’, wherever they may be in the universe, separated by a distance D, there is a force of attraction which is mutual, and each body attracts the other with a force of identical magnitude, which is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. For further details, see I. B. Cohen (1960), p. 171.Google Scholar
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    Cf. James W. Felt (1962), p. 384. For Mach’s criticism of Newton’s definition of mass and his own alternative definition, see his (1960), pp. 300–303. Critical discussion of Mach’s principle and his definition are to be found respectively in H. Goenner (1970), pp. 200–12 and D. A. Gillies (1972), pp. 1–24.Google Scholar
  86. 86.
    In the words of Scott A. Kleiner (1971), pp. 511–12: “... if special relativity is so axiomatized, its axioms will include the claim that mass is a function of velocity, and velocity in turn is a function of the material reference frame chosen for a given problem. On the other hand, a similar axiom for classical particle mechanics claims without qualification that each material particle has a unique positive real value for its mass. These axioms can be used to generate problems and hence as guides to research. The latter axiom informs the researcher working within classical particle mechanics that a material object’s mass is relevant to its mechanical behaviour and that its values are restricted to positive real numbers. The former axiom informs an investigator under the special theory that he must specify a material reference frame and determine an object’s velocity in that frame before he can ask for its mass.”Google Scholar
  87. 87.
    Cf. Arthur Pap (1946), p. 41.Google Scholar
  88. 88.
  89. 89.
    Cf. ibid. According to Einstein (1968), p. 259, the definition of an inertial system as one in a state of motion “such that `force-free’ material points within it are not accelerated with respect to the coordinate system... is empty if there is no independent means for recognizing the absence of forces. But such a means of recognition does not exist if gravitation is considered as a field’.” In the words of Jeremy Bernstein (1973), p. 99: The inertial mass of which Newton’s first law talks “is that property of an object which measures its response to a given force according to Newton’s law F=ma: force equals the product of the inertial mass’ times the acceleration produced.” Thus the relationship between his first and second law is quite intimate. The two laws are conceptually so inseparably related that the first law is best understood as a special case of the second law in the sense that under the condition E F=0 (i.e., under the action of no kinetic, unbalanced forces) the variable a also assumes the value 0 (the velocity of the given mass remaining unchanged): 2nd law: F = ma F = m.0 = 0.Google Scholar
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    For discussion of its original status as an auxiliary concept with its application restricted to physical description of states in the inside of a ponderable mass/body (e.g., descriptions of heat conduction or the motion of a liquid), see A. Einstein (1960), pp. 144–45. For attempts at mechanical interpretation of this concept, cf. ibid., p. 146.Google Scholar
  91. 91.
    From the point of view of both TEp and TRp, the classical Newtonian paradigm of mechanical explanation of all physical phenomena by reference to the action of forces `depending only upon distance and acting between unchangeable particles’ failed in the face of optical and electrical phenomena. Attempts to extend the paradigm to these phenomena led physicists to construct pictorial models in terms of so-called electric and magnetic fluids, light corpuscles and the ether’ frame as the absolute or preferred inertial coordinate system. Cf. G. L. Pandit (1975); Robert Resnick (1972), pp. 18–33; and A. Einstein (1960), p. 146.Google Scholar
  92. 92.
    The Newtonian paradigm is essentially the paradigm of physical description by means of non-structure, mechanical, force-laws of action-at-a-distance, such as Newton’s law of universal gravitation. Quite in contradiction with Einstein’s special theory of relativity requirement that ‘the limiting speed of a signal is C, the velocity of light’, Newtonian mechanics assumes, among other things, that the gravitational force of interaction between material bodies is transmitted “instantaneously, that is, with infinite speed.” Cf. Robert Resnick (1972), pp. 110, 210. However, what renders this paradigm highly suspect from the physical point of view is this fact together with the fact that it is doubtful whether a force-law of action-at-a-distance can have any measurable consequences in its concrete applications to physical situations. It is perhaps some such consideration as the measurability requirement of physical significance that must have made the introduction of the field concept imperative. In Einstein’s words (1960), pp. 63–64, “As a result of the more careful study of electromagnetic phenomena, we have come to regard actionat-a-distance as a process impossible without the intervention of some intermediary medium. If, for instance, a magnet attracts a piece of iron, we cannot be content to regard this as meaning that the magnet acts directly on the iron through the intermediate empty space, but we are constrained to imagine — after the manner of Faraday — that the magnet always calls into being something physically real in the space around it, that something being what we call a `magnetic field’... The effects of gravitation also are regarded in an analogous manner.” From this it is clear that the introduction of the field concept into physical theory generally was historically necessitated by a growing recognition that all descriptions of physical phenomena (such as gravitational and magnetic attraction between any two material bodies, optical phenomena and the like) in terms of action-at-a-distance forces must be without any physical content whatever.Google Scholar
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    As a result of its remarkable TRp to lead from older to newer problems, not only did it trigger radical reformulation of physical laws generally in terms of the field concept, but it also transformed some of the fundamental classical physical concepts beyond recognition. One of the several directions in which the process of reformulation proceeded is best described by Einstein (1960), p. 146: “During the second half of the nineteenth century, in connection with the researches of Faraday and Maxwell, it became more and more clear that the description of electromagnetic processes in terms of field was vastly superior to a treatment on the basis of the mechanical concepts of material points. By the introduction of the field concept in electrodynamics, Maxwell succeeded in predicting the existence of electromagnetic waves, the essential identity of which with light waves could not be doubted, because of the equality of their velocity of propagation. As a result of this, optics was, in principle, absorbed by electrodynamics...” Concept of mass serves as an example of those fundamental classical physical concepts that have undergone such a radical transformation as to trigger off problem-proliferation and development of newer theories. One aspect of this transformation is best captured by Einstein’s formula — E=cm2 — of mass-energy equation that unites what in classical physics were considered to be two fundamental laws of conservation of mass and energy. According to this equation, the inertial mass of a body is no longer a constant, but a variable that assumes different values as a function of the changes in the energy/velocity of the body. Mass concept in this sense is of special physical significance on the level of great velocities that are comparable to the limiting velocity of light. Under the general theory of relativity, however, the principle of equivalence of inertial and gravitational mass of a body captures yet another transformation that this concept has undergone. That the idea of this equivalence would not have been possible without a field-interpretation of gravitation is amply clear from Mach’s principle and the criticism of Newtonian mechanics that it entails. And without this idea, as Einstein admits, the development of the general theory of relativity would have been essentially inconceivable. For only once it became possible, with the help of the field concept, to look at the inertia of a body as a possible manifestation of some or all of the interactions coupling that body to other bodies, could the concept of mass be reduced to a problem in field theory. See E. Mach (1960), pp. 300–303.Google Scholar
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    In the words of Lincoln Barnet (1957), p. 80: “Just as Maxwell and Faraday assumed that a magnet creates certain properties in surrounding space, so Einstein concluded that stars, moons and other celestial objects individually determine the properties of the space around them. And just as the movement of a piece of iron in a magnetic field is guided by the structure of the field, so the path of any body in a gravitational field is determined by the geometry of that field.” Cf. A. Einstein (1960), pp. 64–65.Google Scholar
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    Cf. Lincoln Barnet (1957), p. 81; and A. Einstein and L. Infeld (1961), pp. 240–45.Google Scholar
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    To speak of the law of equality of inertial and gravitational mass is the same as speaking of the gravitational field, in contrast to electric and magnetic fields, as having the following fundamental property: All bodies that move under the sole influence of a gravitational field receive the same acceleration, “which does not in the least depend either on the material or on the physical state of the body.” See A. Einstein (1960), pp. 64–65, 68.Google Scholar
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    An inertial co-ordinate system can be understood in the sense of the Newtonian law of inertia according to which a body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line. Thus it is a system of reference-bodies or coordinates which only classical mechanics and the special theory of relativity permit for use in mechanical description. An inertial co-ordinate system may thus be defined as a system of frames of reference-bodies which have a uniform relative motion with respect to each other. Cf. A. Einstein (1960), p. 11.Google Scholar
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    Of the special theory of relativity Einstein (1960), p. 49, says that it has “crystalized out from the Maxwell-Lorentz theory of electromagnetic phenomena” and that “all facts of experience” that support the latter also support the former. While of the general theory of relativity he says (1960), p. 151, that it “arose primarily from an endeavour to understand the equality of inertial and gravitational mass.” It must be admitted that it was Ernst Mach who, through his criticism of Newtonian mechanics, initiated a lot in this direction. See E. Mach (1960), pp. 300–303.Google Scholar
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    Indeed, the Aristotelian `law’ of perfect circularity parallels the Newtonian law of inertia/perfect rectilinearity as far as the unique resolving power of an ideal-type generalization is concerned. For in Aristotelian physics, it is the material bodies moving with non-accelerated, uniform speed in a straight line that require physical explanation. In Newtonian physics, on the other hand, it is the material bodies moving with accelerated, non-uniform velocity, i.e., the departures from non-accelerated, uniform motion — that call for physical explanation.Google Scholar
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    For details concerning Tychonian circles, see I. B. Cohen (1960), p. 139.Google Scholar
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    The rudiments of the kind of analysis of motion that Newton’s first law of motion, the law of inertia, makes possible are traceable, though on a much restricted scale of terrestrial motion, in Galileo’s resolution of the complex motion of a projectile into two simultaneous, though separate and independent, components at right angles to each other, with neither one in any way affecting the other: (a) a non-accelerated, uniform horizontal component of velocity and (b) an accelerated, non-uniform vertical component. For details, see I. B. Cohen (1960), pp. 112–13, 119.Google Scholar
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    Cf. A. Einstein and L. Infeld (1961), pp. 136–37.Google Scholar
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    For example, in the field of electrical phenomena it was experimentally found, quite contrary to the Newtonian paradigm of action-at-a-distance force laws, that “a moving charge acts upon a magnetic needle.” But the force, instead of depending only upon distance, i.e., position of the charge, “depends also upon the velocity of the charge. The force neither repels nor attracts but acts perpendicular to the line connecting the needle and the charge.” See A. Einstein and L. Infeld (1961), p. 122. In the field of optical phenomena, on the other hand, the corresponding problem of “what is the medium through which light spreads and what are its mechanical properties” was similarly without any prospect of a solution within the Newtonian mechanical paradigm.Google Scholar
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    Cf. A. Einstein and L. Infeld (1961), p. 137.Google Scholar
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    Just as Newtonian dynamics clarifies and radicalizes the theoretical resolving power of the Galilean mechanics and Kepler’s laws of planetary motion, so may Einstein’s special theory of relativity be said to radicalize the theoretical resolving power of the Maxwell-Lorentz electromagnetic theory. For details concerning this theory, see A. Einstein and L. Infeld, (1961), pp. 136–152.Google Scholar
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    Cf. A. Einstein (1960), p. 149.Google Scholar
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    Cf. A. Einstein (1960), p. 150.Google Scholar
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    A. Einstein (1960), `Note to the fifteenth edition’, vi; see also pp. 136–56.Google Scholar
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    C. H. Waddington (1966), p. 108. For details, see ibid., pp. 105–123.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1983

Authors and Affiliations

  • G. L. Pandit
    • 1
  1. 1.Department of PhilosophyUniversity of DelhiIndia

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