Skip to main content
SpringerLink
Log in

The Mathematics of Philosophy: A Brief Review of My Work

  • Chapter
Critical Rationalism, Metaphysics and Science

Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 161))

  • 189 Accesses

Abstract

Agassi has attacked subjectivism, for example, in his paper ‘Subjectivism — from infantile disease to chronic illness,’ and at first this made me wonder why I had been invited to contribute to the Festschrift. For much of my work in the philosophy of science and in statistics has a sub–jectivistic slant. To some extent I agree with him because, for example, I believe that the aim of a subjectivistic theory is to reduce subjectivism. But I believe it is impossible to cure the “disease” entirely, and that is where Agassi and I part company. I regard my basic position as so obvious as not to be worth defending directly and I thought it would be more useful to defend it indirectly by reviewing my work on the mathematics of the philosophy of science. It has a coherence that would be difficult to explain if my basic position was without merit.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bernstein, L.H., Good, I.J., Holtzman, G.I., Deaton, M.L., and J. Babb (1989). “The diagnosis of acute myocardial infarction from two measurements of creatine kinase isoenzyme MB with use of nonparametric probability estimation,” Clinical Chemistry, Vol. 35, pp. 444–47.

    Google Scholar 

  • Einstein, A. (1905/1923), “Zur Elekrodynamik bewegter Körper,” Annalen der Physik, Vol. 17, pp. 549–560;

    Google Scholar 

  • Einstein, A. (1905/1923), “Zur Elekrodynamik bewegter Körper,” English trans, in Lorentz et al. (1923), 37–65.

    Google Scholar 

  • Good, I.J. (1950), Probability and the Weighing of Evidence. London: Charles Griffin New York: Hafners, pp. 119.

    Google Scholar 

  • Good, I.J. (1951/52), “Rational decisions,” Journal of the Royal Statistical Society B, Vol. 14, pp. 107–114.* (Conference of 1951.)

    Google Scholar 

  • Good, I.J. (1959), “Kinds of probability”, Science Vol. 129, pp. 443–447.*

    Article  Google Scholar 

  • Good, I.J. (1960), Review of K.R. Popper, “The logic of scientific discovery,” Mathematical Reviews, Vol. 21, pp. 1171–1173.

    Google Scholar 

  • Good, I.J. (1960/62a), “The mind–body problem or could an android feel pain?”, in: Jordan Scher (ed.), Theories of the Mind New York: Free Press, London, Macmillan, pp. 490–518.

    Google Scholar 

  • Good, I.J. (1960/62b), “Subjective probability as the measure of a non–measurable set,” in: E. Nagel, P. Suppes and A. Tarski (eds), Logic Methodology, and Philosophy of Science. Stanford: Stanford University Press), 319–329.* (Conference of 1960.)

    Google Scholar 

  • Good, I.J. (1961/62), “A causal calculus”, British Journal for the Philosophy of Science, Vol. 11, pp. 305–318;

    Article  Google Scholar 

  • Good, I.J. (1961/62), “A causal calculus”, British Journal for the Philosophy of Science, Vol. 12, pp. 43–51;

    Article  Google Scholar 

  • Good, I.J. (1961/62), “A causal calculus”, British Journal for the Philosophy of Science, Vol. 13, p. 88.*

    Google Scholar 

  • Good, I.J. (1963), “Maximum entropy for hypothesis formulation, especially for multidimensional contingency tables”, Annals of Mathematical Statistics, Vol. 34, pp. 911–934.

    Article  Google Scholar 

  • Good, I.J. (1965), The Estimation of Probabilities: an essay on modern Bayesian methods, Cambridge, MA: MIT Press.

    Google Scholar 

  • Good, I.J. (1966), “How to estimate probabilities”, Journal of the Institute ofMathath–ematics and its Applications, Vol. 2, pp. 364–383.

    Article  Google Scholar 

  • Good, I.J. (1968), “Corroboration, explanation, evolving probability, simplicity, and a sharpened razor”, British Journal for the Philosophy of Science, Vol. 19, pp. 123–143.

    Article  Google Scholar 

  • Good, I.J. (1970/71), “The probabilistic explication of information, evidence, surprise, causality, explanation, and utility”, in: Foundations of Statistical Inference (Proceedings of an international symposium at Waterloo, April 1970). Toronto: Holt, Reinhart and Winston of Canada, 1971; pp. 108–141 [with Appendix, discussion and replies].*

    Google Scholar 

  • Good, I.J. (1971a), ‘Twenty–seven principles of rationality”, Appendix to Good (1970/71), 124–127.*

    Google Scholar 

  • Good, I.J. (1971b), “46656 varieties of Bayesians”, letter in The American Statistician Vol. 25, pp. 62–63.

    Google Scholar 

  • Good, I.J. (1972/74), “Random thoughts about randomness”, invited lecture in the symposium on the Concept of Randomness dedicated to the memory of L.J. Savage in the Biennial Meeting of the Philosophy of Science Association, October 1972. In PSA 1972 (Boston Studies in the Philosophy of Science, Dordrecht: D. Reidel 1974), 117–135.*

    Google Scholar 

  • Good, I.J. (1974). “A correction concerning complexity”, British Journal for the Philosophy of Science Vol. 25, pp. 289.

    Article  Google Scholar 

  • Good, I.J. (1977a). “Dynamic probability, computer chess, and the measurement of knowledge”, in: E.W. Elcock & D. Michie (eds.), Machine Intelligence 8 London: Ellis Horwood Ltd. & John Wylie, 139–150.*

    Google Scholar 

  • Good, I.J. (1977b), Review of Bruno de Finetti, Theory of Probability (English tr. by A. Machi and Adrian Smith, New York: Wiley; Vol. 1, 1974; Vol. 2, 1975), Bulletin of the American Mathematical Society Vol. 83, pp. 94–97.

    Article  Google Scholar 

  • Good, I.J. (1977c), “Explicativity: a mathematical theory of explanation with statistical applications”, Proceedings of the Royal Society of London, series A, Vol. 354, pp. 303–330.*

    Article  Google Scholar 

  • Good, I.J. (1979), “Introductory remarks for the article in Biometrika 66, ‘A.M. Turing’s statistical work in World War II’.” Invited by J.L. Britton of King’s College, London, for the collection of Turing’s papers.

    Google Scholar 

  • Good, I.J. (1979/81), “Some history of the hierarchical Bayesian methodology”, in J.M. Bernardo, M.H. DeGroot, D.V. Lindley, and A.F.M. Smith, eds. Bayesian Statistics: Proceedings of the First International Meeting in Valencia (Spain), May 28 to June 1979, University of Valencia, 1981), pp. 489–510 & 512–519 (with discussion).*

    Google Scholar 

  • Good, I.J. (1981), “The philosophy of exploratory datum analysis,” invited paper for the ASA annual meetings at Houston, 1980 August. Amen Statist. Assoc. 1980 Proceedings of the Business & Econ. Statist. Section, pp. 1–7.

    Google Scholar 

  • Good, I.J. (1981/83), “The robustness of a hierarchical model for multinomials and contingency tables”, in: G.E.P. Box, Tom Leonard & Chien–Fu Wu (eds) Scientific Inference, Data Analysis, and Robustness, New York: Academic Press, Proc. Conf., Univ. of Wisconsin, 1981 November, 191–211.

    Google Scholar 

  • Good, I.J. (1983a), Good Thinking: The Foundations of Probability and its Applications. Minneapolis: Univ. of Minnesota Press.

    Google Scholar 

  • Good, I.J. (1983b), “The philosophy of exploratory data analysis”, Philosophy of Science, vol. 50, pp. 283–295. (A rewritten form of Good, 1981.)

    Article  Google Scholar 

  • Good, I.J. (1983c), “Weight of evidence: a brief survey,” for the Second Valencia International Meeting on Bayesian Statistics, Valencia, Spain, 1983 September 6–10, 249–269 (including discussion).

    Google Scholar 

  • Good, I.J. (1984a), “Weights of evidence in medical diagnosis”, C190 in Journal of Statistical Computation and Simulation, vol. 19, pp. 171–173.

    Article  Google Scholar 

  • Good, I.J. (1984b). “The best explicatum for weight of evidence”, CI97 in Journal of Statistical Computation and Simulation, vol. 19, pp. 294–299.

    Article  Google Scholar 

  • Good, I.J. (1985/88a). “Causal tendency: a review”, in: William Harper & Brian Skyrms (eds), Causation, Chance, and Credence, I Dordrecht: Reidel, pp. 23–50. Proceedings of a conference in Irvine, California, in 1985.

    Google Scholar 

  • Good, I.J. (1985/88b), Response to Wesley Salmon’s critique in William Harper and Brian Skyrms, eds. Causation, Chance, and Credence, I Dordrecht: Reidel) pp. 73–78.

    Google Scholar 

  • Good, I.J. (1986a), Some statistical applications of Poisson’s work. Statistical Science, vol. 1, pp. 157–180 (with discussion).

    Article  Google Scholar 

  • Good, I.J. (1986b). “A pragmatic theory of truth of theories or hypotheses”, C251 in Journal of Statistical Computation and Simulation, vol. 24, pp. 319–320.

    Article  Google Scholar 

  • Good, I.J. (1986c). “The whole truth”, The Institute of Mathematical Statistics Bulletin, vol. 15, pp. 366–373. (An editor’s invited column.)

    Google Scholar 

  • Good, I.J. (1987), “Some checks on the consistency of probability judgments and a conjectured method for improving those judgments”, C277 in Journal of Statistical Computation and Simulation vol. 28, pp. 63–71.

    Article  Google Scholar 

  • Good, I.J. (1987/90), “Speculations concerning the future of statistics”, Journal of Statistical Planning and Inference: Special Issue on Foundations of Statistics and Probability (proceedings of a conference in 1987 in honor of I.J. Good) vol. 25, pp. 441–466.

    Google Scholar 

  • Good, I.J. (1988a), “Statistical evidence”, Encyclopedia of Statistical Sciences, Vol. 8. New York: Wiley, pp. 651–656.

    Google Scholar 

  • Good, I.J. (1988b), “The interface between statistics and philosophy of science,” Statistical Science, vol. 3, pp. 386–112 (with discussion).

    Article  Google Scholar 

  • Good, I.J. (1988/89), “The interface between statistics and the philosophy of science,” for the Logic, Methodology, and Philosophy of Science VIII (Fenstad, J.E., Frolov, I.T., and Hilpinen, R., (eds.,) Amsterdam: North Holland and Elsevier pp. 393–411. Proc. Conf. in Moscow in 1987.

    Google Scholar 

  • Good, I.J. (1989a), “Yet another argument for the explication of weight of evidence”, C312 in Journal of Statistical Computation and Simulation vol. 31, pp. 58–59.

    Article  Google Scholar 

  • Good, I.J. (1989b), “A suspicious feature of the Popper/Miller argument”, C315 in Journal of Statistical Computation and Simulation vol. 31, pp. 62–63. Reproduced in Philosophy of Science, vol. 57, 1990 pp. 535–536

    Article  Google Scholar 

  • Good. I.J. (1989c), “The theorem of corroboration and undermining, and Popper’s demarcation rule”, C317 in Journal of Statistical Computation and Simulation, vol. 31, pp. 119–120

    Article  Google Scholar 

  • Good, I.J. (1990a), Review of E.T. Jaynes, “The relation of Bayesian and maximum entropy methods,” Maximum–entropy and Bayesian methods in science and engineering, Vol. 1 (Laramie, WY, 1985 and Seattle, WA, 1986/87), pp. 25–29, Fund. Theories Phys., Dordrecht: Kluwer Acad. Publ., 1988;

    Google Scholar 

  • Good, I.J. (1990a), Review of E.T. Jaynes, “The relation of Bayesian and maximum entropy methods,” Mathematical Reviews vol. 90e. p. 2874, Rev. 62007.

    Google Scholar 

  • Good, I.J. (1990b), List of publications to No. 1850 mostly available for distribution; with a very rough subject index. Statistics Department, Virginia Polytechnic Institute and State University, Technical Report 90–4.

    Google Scholar 

  • Good, I.J. (1991a), “The kinematics of special relativity, and Dingle’s fallacies”, Physics Essays, vol. 4, pp. 591–595.

    Article  Google Scholar 

  • Good, I.J. (1991b), “Weight of evidence and the (Bayesian) likelihood ratio”, Chapter 3 of The Use of Statistics in Forensic Science (C.G.G. Aitken & D.A. Stoney, eds.; Ellis Horwood), pp. 85–106. Also as a Tech. Rep. 89–16. [In the book the parentheses around Bayesian are omitted.]

    Google Scholar 

  • Good, I.J. (1992/91), “The Bayes/non–Bayes compromise: a brief review”, Journal of the American Statistical Association. In Press. Also to be published in the first issue of the ASA Presidential Invited Paper Series. For a longer version see Technical Report 91–16B, Statistics Department, Virginia Tech, Blacksburg, Virginia 24061 (1991).

    Google Scholar 

  • Good, I.J. & W.I. Card (1971), “The diagnostic process with special reference to errors”, Methods of Information in Medicine, vol. 10, pp. 176–188.

    Google Scholar 

  • Good, I.J. and A.F. McMichael (1984), “A pragmatic modification of explicativity for the acceptance of hypotheses”, Philosophy of Science, vol. 51, pp. 120–127.

    Article  Google Scholar 

  • Good, I.J., G.I. Holtzman, M.L. Deaton, and L.H. Bernstein (1989), “Diagnosis of heart attack from two enzyme measurements by means of bivariate probability density estimation: statistical details”, C328 in Journal of Statistical Computation and Simulation, vol. 32, pp. 68–76.

    Article  Google Scholar 

  • Jaynes, E.T. (1957), “Information theory and statistical mechanics”, Physical Review, vol. 106, pp. 620–630;

    Article  Google Scholar 

  • Jaynes, E.T. (1957), “Information theory and statistical mechanics”, Physical Review, vol. 108, 171–190.

    Article  Google Scholar 

  • Keynes, J.M. (1921), A Treatise on Probability. London: Macmillan.

    Google Scholar 

  • Kolmogorov, A.N. (1933), Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin: Springer.

    Google Scholar 

  • Larousse (1959/68), The New Larousse Encyclopedia of Mythology, London: Hamlyn.

    Google Scholar 

  • Lindley, D.V. & Smith, A.F.M. (1972), “Bayesian estimates for the linear model”, J. Roy. Statist. Soc. B, vol. 34, pp. 1–41 (with discussion).

    Google Scholar 

  • Littlewood, J.E. (1953), A Mathematicians Misellany. London: Methuen.

    Google Scholar 

  • Lorentz, H.A., Einstein, A., Minkowski, H., and Weyl, H. (1923), The Principle of Relativity. English translations (by Nathan Morrison) of eleven articles. New York: Dover Publications.

    Google Scholar 

  • Michie, D. (1977), “A theory of advice”, in: E.W. Elcock & D. Michie (eds), Machine Intelligence 8, Chichester: Ellis Horwood, Ltd., New York: Wiley, pp. 151–168.

    Google Scholar 

  • Minkowski, H. (1908/1923), An address on Space and Time at the 80th assembly of German Natural Scientists and Physicians. English translation in Lorentz et al. (1923), pp. 75–91.

    Google Scholar 

  • Ogden, C.K. (1932), Bentham’s Theory of Fictions. London: Routledge and Kegan Paul.

    Google Scholar 

  • Poisson, S.F. (1837), Recherches sur la Probability des Jugements, Paris: Bachelier.

    Google Scholar 

  • Popper, K. (1959), The Logic of Scientific Discovery. London: Hutchinson.

    Google Scholar 

  • Ramsey, F.P. (1931), Foundations of Mathematics. London: Kegan Paul.

    Google Scholar 

  • Salmon, W. (1985/88), “Intuitions — good and not so good”, in: B. Skyrms & W.L.

    Google Scholar 

  • Harper (eds), Causation, Chance and Credence Vol. 1, pp. 51–71.

    Google Scholar 

  • Suppes, P. (1970), A Probabilistic Theory of Causality. Amsterdam: North–Holland Publishing Company.

    Google Scholar 

  • Terletskii, Ya P. (1968), Paradoxes in the Theory of Relativity. New York: Plenum Press.

    Google Scholar 

  • Walley, P. (1991), Statistical Reasoning with Imprecise Probabilities. London: Chapman and Hall.

    Google Scholar 

  • Wrinch, D. & Jeffreys, H. (1921), “On certain fundamental principles of scientific discovery”, Philosophical Magazine, ser 6, Vol. 42, pp. 369–390.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistic, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0439, USA

    I. J. Good

Authors
  1. I. J. Good
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. York University, Toronto, Canada

    I. C. Jarvie

  2. Tel-Aviv University, Israel

    Nathaniel Laor

  3. Child Study Center, Yale University, USA

    Nathaniel Laor

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Good, I.J. (1995). The Mathematics of Philosophy: A Brief Review of My Work. In: Jarvie, I.C., Laor, N. (eds) Critical Rationalism, Metaphysics and Science. Boston Studies in the Philosophy of Science, vol 161. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0471-5_13

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-0471-5_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4211-6

  • Online ISBN: 978-94-011-0471-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation