C.S. Peirce on Cenoscopy and Ideoscopy; Maritain's Three Degrees of Abstraction

§4. The Divisions of Science 

238. [...] All knowledge whatever comes from observation; but different sciences are observational in such radically different ways that the kind of information derived from the observation of one department of science (say natural history) could not possibly afford the information required of observation by another branch (say mathematics). [...]

239. I recognize two branches of science: Theoretical, whose purpose is simply and solely knowledge of God's truth; and Practical, for the uses of life. In Branch I, I recognize two subbranches, of which, at present, I consider only the first, [the sciences of discovery]. Among the theoretical sciences [of discovery], I distinguish three classes, all resting upon observation, but being observational in very different senses.^†P1

240. The first is mathematics, which does not undertake to ascertain any matter of fact whatever, but merely posits hypotheses, and traces out their consequences. It is observational, in so far as it makes constructions in the imagination according to abstract precepts,[1] and then observes these imaginary objects, finding in them relations of parts not specified in the precept of construction. This is truly observation, yet certainly in a very peculiar sense; and no other kind of observation would at all answer the purpose of mathematics.^†P2

241. Class II is philosophy, which deals with positive truth, indeed, yet contents itself with observations such as come within the range of every man's normal experience, and for the most part in every waking hour of his life. Hence Bentham calls this class, coenoscopic.^†1 These observations escape the untrained eye precisely because they permeate our whole lives, just as a man who never takes off his blue spectacles soon ceases to see the blue tinge. Evidently, therefore, no microscope or sensitive film would be of the least use in this class. The observation is observation in a peculiar, yet perfectly legitimate, sense. If philosophy glances now and then at the results of special sciences, it is only as a sort of condiment to excite its own proper observation.

242. Class III is Bentham's idioscopic^†2; that is, the special sciences, depending upon special observation, which travel or other exploration, or some assistance to the senses, either instrumental or given by training, together with unusual diligence, has put within the power of its students. This class manifestly divides itself into two subclasses, the physical and the psychical sciences; [...]

NOTES

†P1 Some catholic writers recognize sciences resting upon authority. No doubt, everybody of good sense believes some things substantially because he has been brought up to do so; but according to my conception of what science is, that is not science. Indeed, belief proper has nothing to do with science. [Baldassare] Lablanca [Dialettica, vol. II, lib. IV, c. 1, 1875] admits a class of documentary sciences. This is more plausible; although, as that author admits, documentary evidence enters into every science, while nothing can have rested wholly on documentary evidence to the original authors of the documents. He reckons as documentary sciences, history, linguistics, political economy, statistics, and geography. But it is quite plain that these do not form a natural group; especially since this geography must include physical geography.

†P2 Many writers of France (as Comte and Ribot), and of Germany (as Schopenhauer and Wundt), and a few in England (as Cave), have given mathematics the first place among the sciences, contrary to the doctrine of Plato and Aristotle, which has caused so many to place it below philosophy in point of abstractness. I mention this to show that I am taking no revolutionary position here: I am open to charges enough of heresy to answer to, to make me desire to avoid those that can be avoided.

†1 "Coenoscopic . . . from two Greek words, one of which signifies common — things belonging to others in common; the other looking to. By coenoscopic ontology, then, is designated that part of the science which takes for its subject those properties which are considered as possessed in common by all the individuals belonging to the class which the name ontology is employed to designate, i.e. by all individuals." The Works of Jeremy Bentham, Edinburgh, 1843, viii, 83, footnote.

†2 "Idioscopic . . . from two Greek words, the first of which signifies peculiar. In Idioscopic ontology, then, we have that branch of art and science which takes for its subject such properties as are considered as peculiar to different classes of beings, some to one such class, some to another." Ibid.

 Source: C.S. Peirce, The Collected Papers of Charles Sanders Peirce, 1.238–242; http://sententiaedeo.blogspot.com/2012/01/cenoscopy-versus-ideoscopy.html

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Notes:

1. Peirce's division of theoretical sciences into three classes--special sciences (ideoscopic), mathematics, and philosophy (cenoscopic)--fits with Jacques Maritain's three degrees of abstractions. They are as follows: the first,

“the mind can consider objects abstracted from, and purified of, matter but only to the extent that matter is the basis of diversity amongst individuals within a species [….] The mind thus considers bodies in their mobile and sensible reality [….] Such an object can neither exist without matter […] nor can it be conceived without matter. It is this great realm that the ancients called Physica.” [Equivalent of Peirce's special sciences.]

[Second,] “the mind can consider objects abstracted from, and purified of, matter insofar as matter is the general basis for the active and passive sensible properties of bodies. In this case, it considers nothing more than a certain property which it isolates within bodies [namely] quantity [….] This is an object of thought which cannot exist without sensible matter, but which can be conceived without it [….] This is the great field of Mathematica.”[Equivalent of Peirce's mathematics.]

[Third,] “the mind can consider objects abstracted from, and purified of, all matter. In this case it considers […] being as such and its laws. These are objects of thought which not only can be conceived without matter, but which can even exist without it, whether they never exist in matter, as in the case of God and pure spirits, or whether they exist in material as well as in immaterial things [e.g. substance, quality, act and potency, beauty, goodness, etc.] This is the wide domain of Metaphysica” (Jacques Maritain, The Degrees of Knowledge, trans. Gerald B. Phelan (Notre Dame, IN: University of Notre Dame Press, 2009), 38). [Equivalent of Peirce's philosophy.]