Skip to main content
SpringerLink
Log in

Truth, Fiction, and Stipulation

  • Chapter
  • First Online:
Truth, Objects, Infinity

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 28))

  • 396 Accesses

Abstract

For the past few years, I have been fortunate enough to teach, annually, a third year undergraduate module in the philosophy of mathematics. It is a testimony to Paul Benacerraf’s great influence on the discipline that the module is structured very naturally in two halves, which could quite easily be subtitled “Before Benacerraf” (BB) and “After Benacerraf” (AB). The story I tell starts at the end of the 19th century, with Cantor’s development of the new infinitary set theory, and mathematicians’ and philosophers’ concerns about how (or whether) we can make sense of this new mathematics that is not grounded in Kantian intuition of space and time.

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 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
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

References

  • Azzouni, J. (1994). Metaphysical myths, mathematical practice: The ontology and epistemology of the exact sciences. Cambridge: Cambridge UP.

    Book  Google Scholar 

  • Baker, A. (2005). Are there genuine mathematical explanations of physical phenomena? Mind, 114(454), 223–238.

    Article  Google Scholar 

  • Baker, A. (2009). Mathematical explanation in science. The British Journal for the Philosophy of Science, 60(3), 611–633.

    Article  Google Scholar 

  • Batchelor, G. K. (1967). An introduction to fluid dynamics. Cambridge: Cambridge UP.

    Google Scholar 

  • Benacerraf, P. (1973). Mathematical Truth. The Journal of Philosophy, 70(19), 661–679.

    Google Scholar 

  • Colyvan, M. (2002). Mathematics and aesthetic considerations in science. Mind, 111(144), 69–74.

    Article  Google Scholar 

  • Colyvan, M. (2010). There is no easy road to nominalism. Mind, 119(474), 285–306.

    Article  Google Scholar 

  • Einstein, A. (1920). Relativity: The special and the general theory, (R. W. Lawson, Trans.). London: Methuen & Co Ldt.

    Google Scholar 

  • Field, H. H. (1989). Realism, mathematics, and modality. Oxford: Basil Blackwell.

    Google Scholar 

  • Gödel, K. [1947] (1990). What is Cantor’s continuum problem? In S. Feferman (Ed.-in-chief), Collected works: Publications 1938–1974 (Vol. II, pp. 515–525, 176–187). Oxford: Oxford UP.

    Google Scholar 

  • Gödel, K. [1964] (1990). What is Cantor’s continuum problem? (Revised and expanded version of Gödel [1947] 1990). In S. Feferman (Ed.-in-chief), Collected works: Publications 1938–1974 (Vol. II, pp. 259–273, 254–270. Oxford: Oxford UP.

    Google Scholar 

  • Hilbert, D. [1926] (1983). On the infinite. P. Benacerraf & H. Putnam, Eds. (E. Putnam & G. J. Massey, Trans., [1964] (1983), pp. 183–201.

    Google Scholar 

  • Leng, M. (2010). Mathematics and reality. Oxford: Oxford UP.

    Book  Google Scholar 

  • Leng, M. (2012). Taking it easy: A response to Colyvan. Mind, 121(484), 983–995.

    Article  Google Scholar 

  • Maddy, P. (1992). Indispensability and practice. The Journal of Philosophy, 89(6), 275–289.

    Article  Google Scholar 

  • Maddy, P. (1997). Naturalism in mathematics. Oxford: Oxford UP.

    Google Scholar 

  • Melia, J. (1998). Field’s programme: Some interference. Analysis, 58(2), 63–71.

    Article  Google Scholar 

  • Quine, W. V. O. [1951] (1953). Two dogmas of empiricism. In From a logical point of view: 9 logico-philosophical essays (pp. 20–46). Cambridge, Massachusetts: Harvard UP.

    Google Scholar 

  • Quine, W. V. O. (1960). Word and object. Cambridge: The MIT Press.

    Google Scholar 

  • Quine, W. V. O. [1935] (1976). Truth by convention. In The ways of paradox and other essays (Revised and enlarged edition, pp. 77–106). Cambridge, Massachusetts: Harvard UP.

    Google Scholar 

  • Quine, W. V. O. [1954] (1977). Carnap and logical truth. In The ways of paradox and other essays (2nd ed., pp. 107–132). Cambridge, Massachusetts: Harvard UP.

    Google Scholar 

  • Russell, B. S. (1919). Introduction to mathematical philosophy. London: George Allen and Unwin.

    Google Scholar 

  • Yablo, S. (1998). Does ontology rest on a mistake? Aristotelian Society, Supplementary, 72, 229–261.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, University of York, Heslington, YO10 5DD, UK

    Mary Leng

Authors
  1. Mary Leng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mary Leng .

Editor information

Editors and Affiliations

  1. FRE Sciences, Normes, Décision, CNRS, Paris, France

    Fabrice Pataut

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Leng, M. (2016). Truth, Fiction, and Stipulation. In: Pataut, F. (eds) Truth, Objects, Infinity. Logic, Epistemology, and the Unity of Science, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-45980-6_7

Download citation

Publish with us

Policies and ethics

Search

Navigation