Gary F., List: GF: Maybe he [Vehkavaara] just invented it ["negative science"] to distinguish it from “positive science.”
That is what I suspect, as well, and it is not a very apt choice. Peirce defines a "positive science" in one place as "an investigating theoretical science which inquires what is the fact, in contradistinction to pure mathematics which merely seeks to know what follows from certain hypotheses" (CP 5.13n, c. 1902); and in another as "an inquiry which seeks for *positive *knowledge; that is, for such knowledge as may conveniently be expressed in a *categorical proposition*," whereas mathematics is a "Conditional or Hypothetical Science" (CP 5.39-40, EP 2:144, 1903). 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. I agree, thanks for the clarification. GF: What we usually call the “empirical” sciences generally observe objects that are not imaginary in the sense that mathematical constructions are. Indeed, and what Peirce calls "empirics" in c. 1896 seems to go well beyond what he calls "phaneroscopy" several years later--also encompassing logic, metaphysics, and the special sciences, but presumably not the normative science of ethics, which seems to fall under "pragmatics" instead. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Tue, Jul 13, 2021 at 12:59 PM <g...@gnusystems.ca> wrote: > 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. >
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