Skip to main content
SpringerLink
Log in
Book cover

Hermeneutics and Science pp 135–155Cite as

Incommensurability as a Bound of Hermeneutics in Science

  • Chapter

Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 206))

Abstract

In my opinion, what is prejudicial to the present debate on hermeneutics in science is an inadequate notion of science, rather than an inadequate notion of hermeneutics. Present science is so complex and wide in scope that rightly philosophers look for a version of it reduced to synthetic notions. Of course, it is a hard task to characterize science in a synthetic and at the same time adequate way. The traditional, dominant attitude among scientists is to reply by presenting science according to a peculiar ideal, i.e. as a strictly deductive system which includes the most powerful mathematics possible. As a natural consequence, many artifacts, in my opinion, follow, to qui pro quo’s.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography and Notes

  1. I. Lakatos: Philosophical Papers, Cambridge, 1980, II, 1.3; G. Metadikes, A. Nerode. Lakatos: Philosophical Papers, Cambridge, 1980, II, 1.3; G. Metadikes, A. Nerode: “The introduction of non-recursive methods into Mathematics”, in A.S. Troelstra, D. van Dalen (eds.): The L.E.J. Brouwer’s Centenary Symposium, North-Holland, Amsterdam, 1982, 318–334.

    Google Scholar 

  2. It is enough to refer to A. Koyré: From the Closed World to the Infinite Universe, J. Hopkins U.P., Baltimore, 1957.

    Google Scholar 

  3. A. Robinson: Non-Standard Analysis,North-Holland, Amsterdam, 1960, ch. X.

    Google Scholar 

  4. E.G. Kogbetlianz: Foundamentals of Mathematics from an advanced Point of View, Gordon Breach, 1968, XXIII-XXVIII.

    Google Scholar 

  5. E. Bishop: Foundations of Constructive Mathematics, McGraw-Hill, New York, 1967. For an introductory reading see his “A constructivistic Manifesto”.

    Google Scholar 

  6. A. Drago: “Relevance of Constructive Mathematics to Theoretical Physics”, in E. Agazzi (eds.): Logica e Filosofia della Scienza, oggi, CLUEB, 1986, vol. II, 267–273. S. Cicenia, A. Drago: “Evidence for a scientific filiation of N.I. Lobachevsky from Lazare Carnot”, XVIII ICHS, Hamburg-Munchen, 1989; “Conoscenza matematica ponendo un problema. Evidenza di una filiazione scientifica di Lobacevskij da Lazare Carnot”, in L. Magnani (ed.): Conoscenza e Matematica, Marcos, Milano, 1991, 469–484.

    Google Scholar 

  7. C.C. Gillispie: Lazare Carnot Savant,Princeton U.P., 1971, ch.3.

    Google Scholar 

  8. A. Drago, C. Mordillo: “Perchè l’ordine logico dei principi della termodinamica inverte l’ordine di scoperta storica?”, Atti IV Congr. Naz. St. Fisica,Como, 1983, 113–121. A. Drago: “A Characterization of the Newtonian Paradigm”, in G.B. Scheurer, G. Debrock (eds.): Newton’s Philosophical and Scientific Legacy,Kluwer Acad. P., 1988, 239–252. E. Mach actively looked for an alternative to the Aristotelian organization (Z. Loparic: “Problem-solving and Theory-structure in Mach”, Stud. Hist. Phil. Sci., 15,(1984), 23–49). In recent years the same effort was done by E.W. Beth: The Foundations of Mathematics,Harper, New York, 1970, I, 2. I remark that my “problematic organization” is a broader category than a “problem solving theory” (Simon) and it is a narrower category than a “program of scientific research” (Lakatos).

    Google Scholar 

  9. L. Carnot: “Dissertation sur l’infini” in C.C. Gillispie: op. cit., p. 182, 225.

    Google Scholar 

  10. L. Carnot: Essai sur les machines en général, Defay, Dijon, 1782, p. 44.

    Google Scholar 

  11. S. Carnot: Refléxions sur la puissance motrice du feu,Bachelier, Paris, 1824, footnote p. 18.

    Google Scholar 

  12. This is the basic statement of most chemists in both 18th and 19th centuries. See H. Guerlac: “Quantification in Chemistry”, ISIS, 52, (1961),194–214.

    Google Scholar 

  13. N.I. Lobachevsky: “Géométrie Imaginaire”, Crelle’s J., 17 (1837), p. 302.

    Google Scholar 

  14. G.Birkhoff, J. von Neumann: “The logic of quantum mechanics”, Ann. Math., 37, (1936), 23–43.

    Google Scholar 

  15. S. Haack: Deviant Logics, Oxford U.P., 1960.

    Google Scholar 

  16. M. Dummett: Elements of Intuitionism,Oxford, 1975. D. Prawitz: “Meaning and Proof: The Conflict between Classical and Intuitionistic Logic”, Theoria,43, (1977), 6–39. “Incommensurable scientific theories: the rejection of the double negation logical law”, in D. Costantini and M.G. Galavotti (eds.): Nuovi problemi della logica e della filosofia della scienza,CLUEB, Bologna, 1991, vol. 1, 195–202. It is a surprising fact that very little attention has been devoted to this logical law by logicians, linguists and philosophers; perhaps the reason is that almost all natural languages attribute several roles to double negations, say as rhetorical sentences (-A=A), or even as one strong negation (Italian: “non c’è nessuno”) beyond as a proper double negation.

    Google Scholar 

  17. For instance, A. Drago: “The alternative content of Thermodynamics: Constructive Mathematics and Problematic Organization of the Theory”, in K. Martinas (eds.); Thermodynamics History and Philosophy: Facts, Trends, Debates, World Scientific, Singapore, 1991, 329–345; “Is Gödel’s Incompleteness Theorem a consequence of the two kinds of organization of a scientific theory?” in Z.W. Wolkowsky (ed.): First International Symposium on Gödel’s Incompleteness Theorems, World Scientific, Singapore, 1993, 107–135; “Sulla negazione di S. Freud e i fondamenti della scienza”, in G. Sala, M. Cesa-Bianchi (eds.): La presenza di Gustavo Iacono nella psicologia italiana, La Milanesa, Rho, 1992, 137–150.

    Google Scholar 

  18. A. Drago: “Una definizione precisa di incommensurabilità”, in F. Bevilacqua (ed.): Atti VII Congr. Naz. Storia Fisica, Padova, 1986, 124–129; “An effective definition of incommensurability”, VIII Congress on Logic, Methodology and Phil. Sci., Moscow, 1987, 4, pt.1, 159–162 and in C. Cellucci (eds): Temi e prospettive della logica e della filosofia della scienza contemporanee, CLUEB, Bologna, 1988, vol. II, 117–120.

    Google Scholar 

  19. In my opinion an enlightening study on Heidegger’s thinking is that by P.A. Heelan: “Hermeneutical Realism and Scientific Observation”, in P.D. Asquith, T. Nickles (eds.): PSA 1982,vol. 1, Michingan U.P. 1982, 77–87; in particular, see p. 78–79.

    Google Scholar 

  20. T.S. Kuhn: The Structure of Scientific Revolutions,Chicago U.P., Chicago, 2° ed. 1969, Ch. 12.

    Google Scholar 

  21. M. Masterman: “The Nature of Paradigm”, in I. Lakatos and A. Musgrave (eds.): Criticism and the Growth of Knowledge,Cambridge U. Press, Cambridge, 1970, 59–89; T.S. Kuhn: “Considerations on my critics”, ibid., 313–364.

    Google Scholar 

  22. K. Lorenz: “Rules vs. Theorems”, J. Phil. Logic, 2 (1973) 352–369.

    Article  Google Scholar 

  23. A. Coppola, A. Drago: “Galilei ha inventato il principio d’inerzia?”, in S. D’Agostino, S. Petruccioli (eds.): Atti V Cony. Naz. Storia Fisica, Rend. Acc. XL, 12,(1984) Roma, 319–327.

    Google Scholar 

  24. G. Galilei: Discorsi su due nuove scienze, Leida, 1638.

    Google Scholar 

  25. G. Galilei: Tractatio de Praecognitionibus et Praecognitis, Antenore, Padova, 1988.

    Google Scholar 

  26. A. Drago: “A characterization of the Newtonian paradigm”, op. cit.; A.E. Shapiro: “Experiment and Mathematics in Newton’s theory of Color” Phys. Tod.,37, sept. 1984, 34–35, stresses that Newton was unsuccessful in achieving an optical theory owing to his commitment to an AO.

    Google Scholar 

  27. J. Le Ronde D’Alembert: “Élémens” in J. Le Ronde D’Alembert, D. Diderot: Encyclopédie Française,17,Paris, 1753, p. 411. In fact, D’Alembert (Traité de Dynamique,Paris, 1743) stated his mechanics as centered upon a main problem, the ill-called “d’Alembert Principle”.

    Google Scholar 

  28. L. Carnot: Essai sur les machines en général, Dijon, 1782; Principes fondamentaux de l’équilibre et du mouvement, Crapelet, Paris, 1803. On p. 104 of the first work and in the Preface, p.XI-XVII of the second work he stressed and illustrated “two methods for building a theory”. Géométrie de Position, Duprat, 1803.

    Google Scholar 

  29. P. Williams: “Faraday” in C.C. Gillispie (ed.): Dictionary of Scientific Biography, Scribner, New York, 1971, 4.

    Google Scholar 

  30. S. Carnot: Refléxions sur la puissance motrice du feu,Bachelier, Paris, 1824; see also A. Drago: “The alternative content of Thermodynamics…”, op. cit.

    Google Scholar 

  31. It is enough to read C. Maxwell: Matter and Motion,1877, ch. I and ch. III for obtaining a vivid idea of his basic choices.

    Google Scholar 

  32. However, see Z. Loparic: op. cit. for a possible correction of this view on Mach.

    Google Scholar 

  33. M. Planck: Wege zur Physikalische Erkenntnis,Hirzel, Leipzig (It. transi. Boringhieri, 1955, o. 86 e 94).

    Google Scholar 

  34. The former choice is apparent in all naive mathematical formulae Marx wrote, even more in: Matematitcheskie rukopisi,Moscow, 1968. See also A. Drago: “Le implicazioni teoriche dei manoscritti matematici di K. Marx”, Testi e Contesti,n. 8 (1982) 107–116. The latter choice is apparent in his lack of principles of any kind — as a rejection of AO — and in the very great problem illustrated by his main work: Das Kapital.

    Google Scholar 

  35. B. Pour-El and J.I. Richards: Constructivity in Analysis and Physics, Springer, Berlin, 1988; N. da Costa, D. Doria. Richards: Constructivity in Analysis and Physics, Springer, Berlin, 1988; N. da Costa, D. Doria: “Undecidability and Incompleteness in Classical Mechanics, Int. J. Theor. Phys.,30,(1991) 1041–1073; G. Hellmann: ”Constructive Mathematics and Quantum Mechanics“ J. Phil. Logic, 22 (1993) 221–248; A. Drago: ”Storia del dibattito sull’introduzione della matematica costruttiva nella fisica teorica“, in F. Bevilacqua (ed.): Atti XI Congr. Naz, St. Fisica, Trento, 1990, 141–150 (abstract in J. Symb. Logic, 58 (1993) 1039–1040 ).

    Google Scholar 

  36. A. Drago: “Alle origini della meccanica quantistica: le sue opzioni fondamentali” in G. Cattaneo and A. Rossi (eds.): I fondamenti della meccanica quantistica,Editel, Cosenza, 1991, 59–79; “Incommensurable scientific theories…” op. cit.

    Google Scholar 

  37. See for ex. E. Nagel: “Logic without ontology”, in H. Feigl, W. Sellars (eds.): Readings in Philosophical Analysis, Appleton: Century-Croft, New York, 4–49. I. Lakatos (ed.): The problem of inductive logic, North-Holland, 1968.

    Google Scholar 

  38. M.G.M. Ferguson-Hessler, T. de Jongh: “On the quality of knowledge in the field of electricity and magnetism” Am. J. Phys., 55 (1987) 492–497.

    Article  Google Scholar 

  39. E. Beth: op. cit..

    Google Scholar 

  40. J. Lukasiewicz: Selected Works, North-Holland, Amsterdam, 1970, p. 84.

    Google Scholar 

  41. P. Cerreta, A. Drago: “Matematica e conoscenza storica”, in L. Magnani (ed.): Conoscenza e Matematica, Marcos y Marcos, Milano, 1991, 353–364.

    Google Scholar 

  42. H.W. Gennard, W.Y Reedy: “Planck, Kuhn and Scientific Revolutions” J. Hist. Ideas, 87 (1986) 484. P. Cerreta and A. Drago: “La Weltbild di Planck reinterpretata col paradigma di T.S. Kuhn” in F. Bevilacqua (ed.): Atti dell’VIII Congr. Naz. St. Fisica, Napoli, 1987, 65–80.

    Google Scholar 

  43. A. Koyré: “Galilei and Plato”, J. Hist. Ideas,(1943) 400–428 (French transi. in A. Koyré: Etudes d’Histoire de la Pensée Scientifique,Gallimard, 1966, 166–195,3.170–171: “Ce qu’est en 94uestion ici…[est]…la structure de la science, et donc la structure de l’Etre”.

    Google Scholar 

  44. A. Drago: “The reconciliation between the internalist and the extemalist historiographies”, VIII LMPS, Moscow, 1987, 3, 85–89; “Interpretazione delle frasi caratteristiche di Koyré e loro estensione alla storia della scienza dell’800”, in C. Vinti (ed.): Alexandre Koyré. L’avventura intellettuale, ESI, Napoli, 1994, 657–691.

    Google Scholar 

  45. A. Thackray: Atoms and Powers,Cambridge U.P., 1970 (Ital. transi. Il Mulino, 1983, p. 305); P. Williams; “Faraday”, op.cit..

    Google Scholar 

  46. T.S. Kuhn: op.cit., “Preface”.

    Google Scholar 

  47. A. Drago: “La tesi di Mach: la riformulazione della meccanica attraverso la termodinamica”, in F. Bevilacqua (ed.): Atti del X Congr. Naz. Storia Fisica, Cagliari, 1989, 153–162.

    Google Scholar 

  48. A. Drago: “The alternative content of thermodynamics”, op. cit.

    Google Scholar 

  49. P. Feyerabend: “Explanation, Reduction and Empiricism”, in H. Feigl, G. Maxwell (eds.): Scientific Explanation, Space and Time,vol. III, U. Minnesota P., Minneapolis, 1962, 28–97; “Changing Patterns of Reconstructions”, Brit. J. Phil. Sci., 28,(1977), p. 366.

    Google Scholar 

  50. T.S Kuhn: “Postscript — 1969”, in The Structure of Scientific Revolutions, U. Chicago P., Chicago, 1969, 174–210; “Theory-change as Structure-change: Comments on the Sneed formalism”, Erkenntnis, 10 (1976) 179–199, p. 191.

    Google Scholar 

  51. See the Gauss’ letter to Schumacher (28–11–1846) about N.I. Lobachevsky: Geometrische Untersuchungen der Theorie der Parallellinien, Berlin, 1840 (both translated in French by J. Houel, 1866 ).

    Google Scholar 

  52. A. Drago: “Leibniz’ Scientia Generalis reinterpretetd and accomplished by means of modern scientific theories”, in C. Cellucci (eds.): Logica e filosofia della scienza. Problemi e prospettive, ETS, Pisa, 1994, 35–54.

    Google Scholar 

  53. For a first introduction, see A. Rapoport: Strategy and Conscience, Harper, New York, 1959.

    Google Scholar 

  54. M. Gibuti: Tassonomie dei giochi 2x2 a somma non zero,Tesi di laurea in Matematica, Univ. Napoli. a.y. 1982–83. H. Moulin: “Deterence and Cooperation”, Eur. Econ. Rev., 15 (1984) 179183.

    Google Scholar 

  55. A. Drago, G. Minervini: “Una tassonomia dei giochi a tre valori”, Riv. Mat. Pura e Appl. (in Press).

    Google Scholar 

  56. To my knowledge, the best analysis of his method is the book: J. Bondurant: Conquest of Violence, California U.P., Berkeley, 1965.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Group of History of Physics, Department of Physical Sciences, University “Federico II”, Naples, Italy

    Antonino Drago

Authors
  1. Antonino Drago
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Philosophy, Technical University of Budapest, Műegyetem rkp. 3., H-1111, Budapest, Hungary

    Márta Fehér

  2. Department of Philosophy, Budapest University of Economic Sciences, Fővám tér 8., H-1093, Budapest, Hungary

    Olga Kiss

  3. Department of History and Philosophy of Science, Eötvös University, Pf. 32., H-1518, Budapest, Hungary

    László Ropolyi

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Drago, A. (1999). Incommensurability as a Bound of Hermeneutics in Science. In: Fehér, M., Kiss, O., Ropolyi, L. (eds) Hermeneutics and Science. Boston Studies in the Philosophy of Science, vol 206. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9293-2_12

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-9293-2_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5257-5

  • Online ISBN: 978-94-015-9293-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation