The Limits of Knowledge; Mathematics and Methodological Principles

  • Joseph C. Pitt
Part of the The University of Western Ontario Series in Philosophy of Science book series (WONS, volume 50)


The limits of knowledge are determined by the world, by the apparatus the investigator brings to bear on problems, and the cognitive values and methods that govern the objectives of the process of inquiry. There is little we can say about the world per se Kant was right to emphasize. The position I start from here is that what is of epistemological interest is not the way the world is, but (a) the character of the inquiry as determined by the goals, values and methods of the inquirers,32 and (b) the way the world is believed to be.


Human Knowledge Scientific Realist Methodological Principle Deductive Proof Abstracted Principle 
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  1. 32.
    See Pitt [1981, Chapter 5].Google Scholar
  2. 33.
    This passage echoes the famous and generally misunderstood quote from The Assayer quoted at the beginning of Chapter 1. It differs in two crucial reports. Here Galileo does not equate “this grand book” with the universe. Second, while in The Assayer he leaves open the possibility that anyone can learn the language of mathematics, here he explicitly denies that possibility.Google Scholar
  3. 34.
    Recall Plato’s divided line and the allegory of the cave in the Republic.Google Scholar
  4. 35.
    See Plato’s Meno.Google Scholar
  5. 36.
    The case might be made that Galileo thought all final “causes” were “occult.”Google Scholar
  6. 37.
    If it turns out my efforts fail, we might want to admit that the old arguments over Galileo’s use of experiments, his empiricism versus his Aristotelianism (in the methodological form Wallace [ 1989 ] sees him retaining), his cheating, etc. may have had something to them. But I doubt it. If my attempt to characterize Galileo’s epistemology in relatively neutral terms fails, it only means I have failed, not that this proves Galileo is the last Aristotelian or the first Newtonian.Google Scholar
  7. 38.
    An excellent contemporary source for the realism debate is Leplin [1984].Google Scholar
  8. 39.
    See Laudan [1984].Google Scholar
  9. 40.
    It is also complicated by the manner in which determination of the truth of many theoretical Claims is dependent on the technological infrastructure which makes a mature science possible.Google Scholar
  10. 41.
    See Sellars [1963, Chapter 5].Google Scholar
  11. 42.
    For a delightful presentation of this position see Rescher [1985].Google Scholar
  12. 43.
    See Rorty [1967, pp. 1–2].Google Scholar
  13. 44.
    cf. Laudan [1984].Google Scholar
  14. 45.
    It is also worth mentioning in passing that the “ideals” that cannot be known by man might be interpreted to be a reference to Piatonic Ideals by Galileo, thereby being a further rejection of classic Platonism, firming up the position discussed in Section 2 above.Google Scholar
  15. 46.
    In his Introduction to his translation of Two New Sciences Stillman Drake discusses Galileo’s use of proportionality and explains how it derives from an earlier medieval tradition. Drake also correctly stresses the difference between Galileo’s formulation of those ratios based on principles articulated in Euclid’s book V and in Archimedes from modern algebraic accounts of the same problems. Donald Mertz, in two important papers ([1980] and [1982]) provides an analysis of Galileo’s theory of the tides from the point of view of the theory of proportions. Once awakened to Galileo’s use of this technique, it is difficult to follow his reasoning without an appreciation for the extent to which it permeated his thought.Google Scholar
  16. As we have seen, the use of the language of proportionality also seems to enter Galileo’s public language rather late, primarily in the Dialogue. This leads one to suspect this means that Galileo came late to this knowledge. If so, one might see this as partial grounds to challenge William Wallace’s claim [1984] that Aristotelian principles of logic and science guided Galileo throughout his career, culminating in his production of Two New Sciences. A more bal-anced view might be that Galileo retained an appreciation of Aristotelian logic and principles throughout his career, one that allowed him to reformulate some Aristotelian ideas and reject others, but that it was the Euclidean theory of proportionality which provided him with the tool that made his major scientific contributions possible.Google Scholar
  17. 47.
    This should also be read as an anti-scientific realist view as well.Google Scholar
  18. 48.
    See Rossi [1975] on the general topic of the recognition of the limits of human knowledge in the scientific revolution.Google Scholar
  19. 49.
    It is interesting to note that only recently have we seen strong voices raised against the consequences of abstraction in science. See especially Cartwright [1983] and Van Fraassen [1989].Google Scholar
  20. 50.
    This can also be read as a firm rejection of a form of scientific realism known today as essentialism.Google Scholar
  21. 51.
    This is a reference to the tides - a problem which haunted Galileo from 1595 until he finished his Dialogue. See chapter 4.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • Joseph C. Pitt
    • 1
  1. 1.Virginia Polytechnic Institute and State UniversityUSA

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