Skip to main content

Chunk and Permeate, a Paraconsistent Inference Strategy. Part I: The Infinitesimal Calculus

Abstract

In this paper we introduce a paraconsistent reasoning strategy, Chunk and Permeate. In this, information is broken up into chunks, and a limited amount of information is allowed to flow between chunks. We start by giving an abstract characterisation of the strategy. It is then applied to model the reasoning employed in the original infinitesimal calculus. The paper next establishes some results concerning the legitimacy of reasoning of this kind – specifically concerning the preservation of the consistency of each chunk – and concludes with some other possible applications and technical questions.

This is a preview of subscription content, access via your institution.

REFERENCES

  1. Boyer, C. B. (1959) The History of the Calculus and its Conceptual Development, Dover Publications, New York.

    Google Scholar 

  2. Cajori, F. (1991) A History of Mathematics, 5th edn, Chelsea Publishing Co., New York.

    Google Scholar 

  3. Feyerabend, P. (1975) Against Method, Verso, London.

    Google Scholar 

  4. Hacking, I. (1983) Representing and Intervening, Cambridge University Press, Cambridge.

    Google Scholar 

  5. Priest, G. and Routley, R. (1989) Applications of paraconsistent logic, Ch. 13 of Priest, Routley and Norman (1989).

  6. Priest, G., Routley, R. and Norman, J. (eds.) (1989) Paraconsistent Logic: Essays on the Inconsistent, Philosophia Verlag, München.

    Google Scholar 

  7. Scotch, P. K. and Jennings, R. (1980) Inference and necessity, J. Philos. Logic 9, 327–40.

    Google Scholar 

  8. Scotch, P. K. and Jennings, R. (1989) On detonating, Ch. 11 of Priest, Routley and Norman (1989).

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Brown, B., Priest, G. Chunk and Permeate, a Paraconsistent Inference Strategy. Part I: The Infinitesimal Calculus. Journal of Philosophical Logic 33, 379–388 (2004). https://doi.org/10.1023/B:LOGI.0000036831.48866.12

Download citation

  • chunking
  • infinitesimal calculus
  • paraconsistent logic