The Influence of Heraclitus on Modern Mathematics

  • J. Lambek
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 67)


Among the pre-Socratic philosophers we know that Thales, Pythagoras, Zeno and Democritus were involved in mathematics in one way or another. In fact, Pythagoras coined the very word “mathematics.” Heraclitus does not appear to have occupied himself with mathematical questions; so how can he be said to have influenced modern mathematics? The answer to this question will take us on a small detour.


Abelian Group Topological Space Compact Abelian Group Abelian Category Open Element 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Crapo, H.: 1977, ‘Unities and Negation: On the Representation of Finite Lattices’, preprintGoogle Scholar
  2. Eilenberg, S. and S. MacLane: 1945, ‘General Theory of Natural Equivalences’, Trans. Amer. Math Soc. 58, 231–294.Google Scholar
  3. Freyd, P.: 1964, Abelian Categories, Harper and Row, New York.Google Scholar
  4. Kan, D.N.: 1958, ‘Adjoint Functors’, Trans. Amer. Math. Soc. 87, 294–329.CrossRefGoogle Scholar
  5. Kessidi, T.: 1973, Les origines de la dialectique matérialiste (Héraclite), Les éditions du progrès, Moscow.Google Scholar
  6. Lambek, J. and B. A. Rattray: 1979, ‘A General Stone-Gelfand Duality’, Trans. Amer. Math. Soc. 248, 1–35.Google Scholar
  7. Lawvere, F.W.: 1969, ‘Adjointness in Foundations’, Dialectica 23, 281–296.CrossRefGoogle Scholar
  8. Lawvere, F.W.: 1971, ‘Quantifiers and Sheaves’, in Actes du Congrès International des Mathématiciens, Nice 1970, vol. 1, Gauthier-Villars, Paris, pp. 329–334.Google Scholar
  9. Lawvere, F.W.: 1975, ‘Continuously Variable Sets, Algebraic Geometry = Geometric Logic’, Logic Colloquium’73. Proceedings of the Logic Colloquium, Bristol, July 1973,Google Scholar
  10. H.E. Rose and J.C. Shepherdson (eds.) [Studies in Logic and the Foundations of Mathematics 80], North-Holland, Amsterdam, pp. 135–156.Google Scholar
  11. Mao Tse-tung: 1962, ‘On Contradiction’, in An Anthology of His Writings, Mouton, New York.Google Scholar
  12. Russell, B.: 1965, History of Western Philosophy, George Allen and Unwin, London.Google Scholar
  13. Tierney, M.: 1972, ‘Review of A. Kock, “Strong Functors and Monoidal Monads,”’ Math. Reviews 43, 6282.Google Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • J. Lambek
    • 1
  1. 1.McGill UniversityMontrealCanada

Personalised recommendations