Peirce on Abstraction

ion in connection with some topics from recent linguistic theory and from Gestalt theory. Peirce mentions abstraction at least as early as the 1867 "On a New List of Categories" (see 1.549); another early reference (1868) is given in 2.422. In these locations, he apparently fails to make an important distinction which he is clear about in his later writings, as for example, about 1901: A decrease in supposed information may have the effect of diminishing the depth of a term without increasing its information. This is often called abstraction; but it is far better to call it prescission; for the word abstraction is wanted as the designation of an even far more important procedure, whereby a transitive ele ment of thought is made substantive, as in the grammatical change of an adjec tive into an abstract noun. This may be called the chief engine of mathematical thought. (2.364) Prescission is the process in which blue, green, and red balls are all recognized as spherical, and German Shepherds and Chihuahuas are both recognized as dogs. We prescind from the color, say, and, considering only the shapes, recognize the sameness of all balls in this regard. Peirce suggests in this pas sage that we not think of this process as abstraction, but reserve that term for the process which enables us to speak of the "dormitive virtue" of opium. The 1867 and 1868 locations (1.549, 2.422) appear to ignore the abstrac tion/prescission distinction. It might be tempting to see this as evidence of an This content downloaded from 157.55.39.35 on Mon, 29 Aug 2016 05:02:13 UTC All use subject to http://about.jstor.org/terms PEIRCE ON ABSTRACTION 213 essential difference in treatment of this topic from the early to the late Peirce. The early Peirce recognized the distinction, however, at least so far as the products of the two processes are concerned; in an 1868 letter to the editor of the Journal of Speculative Philosophy he writes: You have apparently understood me as applying the term "abstract" to any con cept the result of abstraction. But as I intimated [see 6.620], I adopt that accepta tion in which "whiteness" is said to be abstract and "white" concrete. (6.627) It would seem that Peirce here is following the historical and ambiguous tradition of calling both prescission and the transformation from "white" to "whiteness" abstraction, while being clear about the difference between the results of the processes, and so between the equivocally named processes themselves. Peirce was later to become very clear about naming the processes; I note one other passage, from a 1904 letter to E. H. Moore: There are two entirely different things that are often confused from no cause that I can see except that the words abstract and abstraction are applied to both. One is a a e a leaving something out of account in order to attend to something else. That is precisive abstraction. The other consists in making a subject out of a predicate. Instead of saying, Opium puts people to sleep, you say it has dormitive virtue. This is an important proceeding in mathematics. For example, take all "symbolic" methods, in which operations are operated upon. This may be called subjectal abstraction.3 Peirce also (and more frequently) calls that process "hypostatic abstraction." It is hypostatic or subjectal abstraction that Peirce is interested in; a hint as to why he is interested in it is given in his allusions in these passages to mathematical reasoning; we shall develop this aspect of abstraction at length. Jaakko Hintikka has done us the great service of bringing to our atten tion4 and tying to contemporary experience one of Pierce's central observa tions about necessary?which is to say mathematical?reasoning: this is that nontrivial deductive reasoning, even in areas where explicit postulates are employed, always considers something not implied in the conceptions so far gained [in the par ticular course of reasoning in question], which neither the definition of the object of research nor anything yet known about could of themselves suggest, although they give room for it.5 Such "theorematic reasoning," to use Peirce's term, introduces its novel ele ments into the reasoning process in the form of icons, which are then "ex perimented upon in imagination." That "all necessary reasoning is diagram matic"6 is a refrain of which the later Peirce seems not to tire; "theorematic reasoning," with its introduction of novelty in diagram, or icon, he contrasts This content downloaded from 157.55.39.35 on Mon, 29 Aug 2016 05:02:13 UTC All use subject to http://about.jstor.org/terms