Selection from C.S. Peirce, “A Syllabus of Certain Topics of Logic” (1903)
An Outline Classification of the Sciences
180. This classification, which aims to base itself on the principal affinities of the objects classified, is concerned not with all possible sciences, nor with so many branches of knowledge, but with sciences in their present condition, as so many businesses of groups of living men. It borrows its idea from Comte’s classification; namely, the idea that one science depends upon another for fundamental principles, but does not furnish such principles to that other. It turns out that in most cases the divisions are trichotomic; the First of the three members relating to universal elements or laws, the Second arranging classes of forms and seeking to bring them under universal laws, the Third going into the utmost detail, describing individual phenomena and endeavoring to explain them. But not all the divisions are of this character.
The classification has been carried into great detail; but only its broader divisions are here given.
181. All science is either,
- A. Science of Discovery;
- B. Science of Review; or
- C. Practical Science.
182. By “science of review” is meant the business of those who occupy themselves with arranging the results of discovery, beginning with digests, and going on to endeavor to form a philosophy of science. Such is the nature of Humboldt’s Cosmos, of Comte’s Philosophie positive, and of Spencer’s Synthetic Philosophy. The classification of the sciences belongs to this department.
183. Science of Discovery is either,
- I. Mathematics;
- II. Philosophy; or
- III. Idioscopy.
184. Mathematics studies what is and what is not logically possible, without making itself responsible for its actual existence. Philosophy is positive science, in the sense of discovering what really is true; but it limits itself to so much of truth as can be inferred from common experience. Idioscopy embraces all of the special sciences, which are principally occupied with the accumulation of new facts.
185. Mathematics may be divided into
- a. the Mathematics of Logic;
- b. the Mathematics of Discrete Series;
- c. the Mathematics of Continua and Pseudo-continua.
I shall not carry this division further. Branch b has recourse to branch a, and branch c to branch b.
186. Philosophy is divided into
- a. Phenomenology;
- b. Normative Science;
- c. Metaphysics.
Phenomenology ascertains and studies the kinds of elements universally present in the phenomenon; meaning by the phenomenon, whatever is present at any time to the mind in any way.
Normative science distinguishes what ought to be from what ought not to be, and makes many other divisions and arrangements subservient to its primary dualistic distinction.
Metaphysics seeks to give an account of the universe of mind and matter.
Normative science rests largely on phenomenology and on mathematics; metaphysics on phenomenology and on normative science.
(Peirce, CP 1.180–186, EP 2.258–259, Online)
Inquiry Into Inquiry 
Thanks for this, Jon. What a great mind Peirce had! It’s remarkable how well this taxonomy holds up after all the work on foundations and all the critique of that work done over the past century!
This is just the tip of the iceberg, of course. I personally don’t put much stock in taxonomies outside natural realms like biology. I even have a mild aversion to them. But the line that ends this excerpt has always grabbed my attention and keeps coming back to me whenever I puzzle over the marriage of logic and mathematics, so I have at long last decided to go back and examine its context a little further.
But if people didn’t make taxonomies, Jon, we wouldn’t have so much fun demolishing them! That what Peirce calls normative science rests on phenomenology and mathematics, I heartily accept, though few would, I think. I don’t know what to make of his saying that metaphysics is dependent upon normative science, except de facto (which is why metaphysics had such a bad reputation for most of the twentieth century, except among you crazy mathematicians). 🙂
BTW, I have a notion about why mathematicians are often given to metaphysics, and it’s not entirely a matter of inclinations toward Platonism. Mathematicians are used to stumbling upon ideas that open up new realms. My notion is that they aren’t as enthralled by current conceptions as others are–that they are more inclined than most to expect the discovery of keys to new understandings that subsume and comprehend and transform the previous ones. Does this accord with your and experience? Just curious.
Yes, field guides can be useful, when written by people who spend a fair share of time in the field. The problem that often arises in philosophical discussions, though, is when birdwatcher books are written by people who don’t actually like watching birds. The animadversions that follow in that train tend to become as interminable as they are inconsequential.
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