[FOM] Formalisation vs Foundation

[Jon Awbrey]

Re: Gergely Buday
At: http://www.cs.nyu.edu/pipermail/fom/2012-July/016545.html

Gergely,

C.S. Peirce took an interesting stand on the foundational status of mathematics,
taking it together with phenomenology as the most basic sciences, and making logic,
as a normative science, depend on them.

| Normative science rests largely on phenomenology and on mathematics;
| metaphysics on phenomenology and on normative science.
|
| Charles Sanders Peirce, ''Collected Papers'', CP 1.186 (1903)

The dependency relations among the sciences can be graphed as follows:

  o---------------------------------------------------------------------o
  |                                                                     |
  |                  Metaphysics o                                      |
  |                              |\                                     |
  |                              | \                                    |
  |                              |  \                                   |
  |                              |   o Normative Science                |
  |                              |  / \                                 |
  |                              | /   \                                |
  |                              |/     \                               |
  |                Phenomenology o       o Mathematics                  |
  |                                                                     |
  o---------------------------------------------------------------------o

NB.  If this ascii figure doesn't work in your browser, here is a recent
blog post where I refer to it:

http://inquiryintoinquiry.com/2012/05/31/definition-and-determination-4/

Regards,

Jon