Well, I guess I underestimated how eager we are to focus on the classification of sciences! A couple of brief questions before I post the slides on that:
Robert, thanks for attaching the Tommi Vehkavaara diagram. In it mathematics is labelled “negative science.” This is a new term for me, and I haven’t found it in any of Peirce’s texts, so it would be helpful if you explain what it means, or else point us to the paper where Tommi does so. (Maybe he just invented it to distinguish it from “positive science.”) Jon, you wrote that “what mainly distinguishes it [phaneroscopy] from mathematics is observation vs. imagination; or rather, observation as including but not limited to products of the imagination” — but for the very reason you give after the semicolon, I wouldn’t want to frame the distinction as “observation vs. imagination.” Peirce says that even mathematics is observational, in a quote that Robert posted earlier: CSP: The first [ science ] 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, 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. (CP 1.239) GF: So the “very peculiar” kind of observation in mathematics is observation of imaginary objects, while phaneroscopic observation is of any objects that can be “before the mind” regardless of whether they are imaginary or not. (What we usually call the “empirical” sciences generally observe objects that are not imaginary in the sense that mathematical constructions are.) Gary f. From: peirce-l-requ...@list.iupui.edu <peirce-l-requ...@list.iupui.edu> On Behalf Of Jon Alan Schmidt Sent: 13-Jul-21 12:33 Gary F., List: At the risk of jumping the gun ... GF: For example, Peirce says that the practice of phanerocopy consists of “observation and generalization.” As Daniel Campos discusses in a 2009 paper (https://www.researchgate.net/publication/236711950_Imagination_Concentration_and_Generalization_Peirce_on_the_Reasoning_Abilities_of_the_Mathematician), Peirce also says that mathematical reasoning requires the "intellectual abilities" of imagination, concentration, and generalization. It seems to me that concentration likewise plays an important role in phaneroscopy--"the power of concentration of attention, so as to hold before the mind a highly complex image, and keep it steady enough to be observed” (CP 2.81, 1902)--so what mainly distinguishes it from mathematics is observation vs. imagination; or rather, observation as including but not limited to products of the imagination, such that phaneroscopy is indeed a positive science (in the sense described below) while mathematics is a strictly hypothetical science. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt <http://www.LinkedIn.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt <http://twitter.com/JonAlanSchmidt> On Tue, Jul 13, 2021 at 10:20 AM <g...@gnusystems.ca <mailto:g...@gnusystems.ca> > wrote: List, Slide 14 is the last in Part 2 of the slideshow, and I’m sure many of us are eager to start on Part 3, which is about “the place of phaneroscopy in Peirce’s mature classification of the sciences.” So unless questions arise today about the specific content of this slide, I’d like to post the next slide tomorrow, along with slides 16 and 17 (as a sort of triptych). They outline the two principles which guide Peirce’s classification of sciences, which I think need to be considered together. Here’s why: Peirce’s classification is mostly inherited from Auguste Comte, including the hierarchical order which places the most abstract sciences at the top, with the idea that they supply principles to the lower sciences. Comte also introduced the concept of positive science, which (for Peirce at least) means experiential science. (This usage of “positive” has nothing to do with “positive logic” (as opposed to “negative logic.”) Where Peirce differs from today’s common usage is that he considered the normative sciences (esthetics, ethics and critical logic) to be positive sciences. He also argued, from 1902 on, that the normative sciences — and especially logic — depend for their principles on mathematics and phenomenology/phaneroscopy. We can’t hope to understand the relationship in practice between mathematics and phaneroscopy by reducing either one to the other. That is Peirce’s point in asserting that phaneroscopy is a positive science while mathematics is not. The classification hierarchy in which order is determined by dependence for principles of the lower upon the higher does not reflect the procedural order in the practice of heuristic sciences. For example, Peirce says that the practice of phanerocopy consists of “observation and generalization.” Naturally we tend to assume that observation comes first and generalization later. But if we are practicing this science for the purpose of discovering the categories as elements of a phaneron which includes possibilities and actualities, we are quite likely to start with possibilities and then do a ‘reality check’ to see whether our hypothetical schema applies as well to actualities; and the reality check must be a kind of observation, experiential like the surprising events that prompt us to come up with a hypothesis in the first place. Indeed all theoretical sciences, to the extent that their theories are testable, go through cycles of observation and generalization and testing and modification, or conjecture and refutation (Popper). In practice, then, sciences can precede each other so that there is no pragmatic significance in debates over which comes first. This is all a sort of prolegomena to André’s outline of the two principles which, he says, guide the classification of sciences. I suppose those who consider themselves experts in that department (which I don’t!) might want to skip Part 3 of the slideshow and jump ahead to Part 4, which is entitled “From mathematics to phaneroscopy”; but I think that would violate a cardinal principle which I just invented: Thou shalt not rush a slow read. Gary f.
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