Clark, List: CG: To my eyes the main issue is the realism vs. nominalism issue both in terms of the nature of possibilities as well as the relationship of individuals to generals.
Is there a way to connect this with John Sowa's earlier comment, which I am still pondering? JFS: Every universal is a specification for some kind of diagram, and every particular is something we classify by relating it to some diagram ... Then the distinction between nominalism & realism depends on the way you interpret the specification: Is it just a verbal agreement, or is it a law of nature that is independent of anything we may say? I am still hoping that he will elaborate on it and provide examples. In the meantime, while casting about online for anything that would help me explore this notion further, I came across the following remarks by Murray G. Murphey. MGM: A diagram is not a *pure *icon, but it is *chiefly *an icon and it is this fact which accounts for its importance in mathematics ... Mr. Arthur Burks has termed the icon a "specific universal" since it is a *specific *thing which can stand for *any* member of a class ... For in constructing the icon, we do not construct *one *particular case under the hypothesis, we rather construct *any *particular case under the hypothesis. And it is only because of this fact that the mathematician can afford to neglect such *individual *characters of his constructs as the color of the ink ... The analogy to induction consists in the fact that we do deal with *the *particular case; the difference is that we deal with *any *particular case. (*The Development of Peirce's Thought*, pp. 234-235, emphases added) Interestingly, on the previous page, Murphey quotes a 1908 letter to Francis Russell in which Peirce seemed to abandon his careful 1902 distinction between images and diagrams. CSP: ... every deductive inference is performed, and can only be performed, by imagining an instance in which the premisses are true and *observing* by contemplation of the image that the conclusion is true. The image, as *singular*, must of course have determinations that the premisses as *general*, have nothing to do with. But we satisfy ourselves that the particular determinations of the image chosen, so far as they go beyond the premisses, could make no difference. (p. 233, emphases in original) In a sense, then, one can *abstract *a diagram from an image by ignoring the *singular *determinations of the latter that have no bearing on whatever *general *properties of the former are significant *for one's purposes*. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Mon, Mar 27, 2017 at 3:03 PM, Clark Goble <[email protected]> wrote: > On Mar 27, 2017, at 11:37 AM, Jerry LR Chandler < > [email protected]> wrote: > > This idea of the mathematics and forms of possibility was articulated > already by Francis Bacon 1561-1626. see the writings of Graham Rees. > (Including Marriage of Physics and Mathematics.) > > Right, it’s not that uncommon an idea. > > To my eyes the main issue is the realism vs. nominalism issue both in > terms of the nature of possibilities as well as the relationship of > individuals to generals. > > That’s why that Fraser review from 1871 is interesting as he does get > right at the nominalist/realist issues. > > Now going back to our discussion of realism a few months ago it’s worth > asking what the cash value or realism vs. nominalism is. Despite it being > such a focus for Peirce I’m not sure it entails that much difference - > particularly with possibilities. > > Where it does matter is more in Peirce’s cosmology where you have > possibilities becoming actualities along more or less neoplatonic lines. > That is the issue ultimately is one of a thoroughgoing modal realism more > like platonism than even Hegelianism. (Despite that it’s often to Hegel > that Peirce is compared and contrasted) >
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