Re: Peirce List • Jeffrey Brian Downard • Gary Richmond • John Collier
According to Peirce, it is logic that draws on both mathematics and phenomenology.
At any rate, Peirce takes the distinctive position that normative science, which includes logic, “rests largely on” phenomenology and mathematics. Unless there is a case to be made for a practical difference between drawing on and resting on, as those phrases are intended in the present setting, I would have to say they mean the same thing.
I discussed the relationship among these sciences in a previous post and drew the following figure to illustrate it.
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)
Syllabus : Classification of Sciences (CP 1.180–202, G-1903-2b)
The following post contains a longer excerpt from Peirce’s Classification of the Sciences.
Inquiry Into Inquiry 
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Check out Bunge, Method, Model, and Matter (1973). He defines systems science as ‘an exact and scientific metaphysics’. Exact, being mathematically precise. Scientific as applying to the sciences (e.g. Biology, Economics, etc.). Metaphysics as above the sciences as a method. In terms of a bubble diagram it would be:
[Mathematics (exact)] [Metaphysics (method)] \ / [Systems Science] / \ [Biology] [Economics] … [other sciences]Pingback: Peirce’s Categories • 4 | Inquiry Into Inquiry
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