Peirce on the role of poietic creation in mathematical reasoning

: C.S. Peirce defines mathematics in two ways: first as "the science which draws necessary conclusions," and second as "the study of what is true of hypothetical states of things" (CP 4.227–244). Given the dual definition, Peirce notes, a question arises: Should we exclude the work of poietic hypothesis-making from the domain of pure mathematical reasoning? (CP 4.238). This paper examines Peirce's answer to the question. Some commentators hold that for Peirce the framing of mathematical hypotheses requires poietic genius but is not scientific work. I propose, to the contrary, that although Peirce occasionally seems to exclude the poietic creation of hypotheses altogether from pure mathematical reasoning, Peirce's position is rather that the creation of mathematical hypotheses is poietic, but it is not merely poietic, and accordingly, that hypothesis-framing is part of mathematical reasoning that involves an element of poiesis but is not merely poietic either. Scientific considerations also inhere in the process of hypothesis-making, without excluding the poietic element. In the end, I propose that hypothesis-making in mathematics stands between artistic and scientific poietic creativity with respect to imaginative freedom from logical and actual constraints upon reasoning
Keywords C.S. Peirce  mathematics
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,357
External links
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA
    David W. Agler (2010). Peirce's Direct, Non-Reductive Contextual Theory of Names. Transactions of the Charles S. Peirce Society 46 (4):611-640.
    Similar books and articles

    Monthly downloads

    Added to index


    Total downloads

    18 ( #78,273 of 1,088,427 )

    Recent downloads (6 months)

    1 ( #69,601 of 1,088,427 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature

    Start a new thread
    There  are no threads in this forum
    Nothing in this forum yet.