John, Edwina, List: JFS: JAS highlighted Peirce's distinction, which applies to both mathematics and phenomenology:
JAS: It is incontrovertible that according to Peirce in CP 3.559 (and elsewhere), the mathematician frames a pure hypothesis without inquiring or caring whether it agrees with the actual facts or not. JFS: Yes, of course. I am glad that we agree about this. I will only add that unlike the mathematician, the phenomenologist *does *inquire and care whether a given hypothesis agrees with the actual facts or not. That is why, unlike mathematics, Peirce considers phenomenology to be a *positive *science; but what distinguishes phenomenology from the *other* positive sciences in his classification, especially metaphysics and the special sciences, is the *kind *of facts that are of interest. The phenomenologist frames a hypothesis without inquiring or caring whether it agrees with *reality *or not, only whether it agrees with the "seemings" that are or could be present to the mind in any way. ET: BUT, my point is that such an imaginary realm is not self-sustaining and must, at some time, connect to reality, where it will examine whether or not its Forms have any functionality. I am happy to say that we agree about this, as well. In fact, I see it as consistent with André's remark on slide 26 that many of the possibilities explored by mathematicians "are not merely artificial fictions of the imagination but the direct suggestions of evocative forms encountered in experience" (https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00181.html). Here I will only add that phenomenology is not limited to experience in the *strict* sense of that in cognition which is forced upon us by the *outer *world of existence, it also encompasses the *inner *world of imagination and the *logical *world of mathematics. Again, ascertaining which idealized forms "connect to reality" and thus "have any functionality" is a task for metaphysics and the special sciences, which--as John rightly observes--depend on the normative science of logic as semeiotic for the requisite principles, including methodeutic as its third branch. ET: And I'd also like to add that Gary F's very nice post on the relationship between mathematics and phenomenology is exactly what I have been arguing about for several weeks on this List ... Likewise, I agree with Gary F.'s post today ( https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00382.html), including "the one point where I think John’s description below needs to be modified." JFS: The special sciences depend on phenomenology for the raw data and on mathematics for forming hypotheses. The basis for Peirce's classification is such that instead, the special sciences depend on phenomenology for *principles*, while phenomenology depends on the special sciences for *data*. Even so, since the *purpose *of phenomenology is very different from the *purpose *of the special sciences, as Gary F. said, each involves a different kind of attention to that same data. Moreover, *all *the positive sciences depend on mathematics for principles, but someone is engaged in *pure *mathematics only when framing hypotheses and drawing necessary conclusions from them *without *inquiring or caring whether they agree with the actual facts or not. Someone who *does *inquire and care about this is engaged in *applied *mathematics within one of the positive sciences. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sun, Aug 29, 2021 at 8:40 AM Edwina Taborsky <tabor...@primus.ca> wrote: > John, List > > I'm not convinced of the isolationist purity of mathematics. I acknowledge > that 'pure' mathematics focuses on a hypothesis without acknowledgment of > whether or not it corresponds to reality or not. That can be said > about many hypothetical formations. As John said - this gives our > system the full freedom of imagination...aka..Firstness. > > BUT, my point is that such an imaginary realm is not self-sustaining and > must, at some time, connect to reality, where it will examine whether or > not its Forms have any functionality. This step might not be immediate; it > might even take years. > > But - without it, the imaginary realm would actually be hollow...Firstness > is fleeting.. > > And I'd also like to add that Gary F's very nice post on the relationship > between mathematics and phenomenology is exactly what I have been arguing > about for several weeks on this List - and have been continuously chastised > for doing so - I have rejected De Tienne's 'Move On' exhortations to us, to > Move On from Mathematics and have instead opted for the synechistic > interrelationship of these two realms-of-science. > > Edwina > > On Sat 28/08/21 8:27 PM , "John F. Sowa" s...@bestweb.net sent: > > Ediwina, Jon AS, Jeff JBD, List > > I changed the subject line to clarify and emphasize the distinction. > > ET: the distinction between pure and applied mathematics is very fuzzy. > I'd suspect it's the same in phenomenology. But I do support and agree > with [Jeff's] agenda of using both mathematics and phenomenology to > function within a pragmatic interaction with the world. > > For both subjects, the distinction is precise. JAS highlighted Peirce's > distinction, which applies to both mathematics and phenomenology: > > JAS: It is incontrovertible that according to Peirce in CP 3.559 (and > elsewhere), the mathematician frames a pure hypothesis without inquiring or > caring whether it agrees with the actual facts or not. > > Yes, of course. That distinction is the greatest power of mathematics: > it is independent of whatever may exist in our universe or any other. It > gives us the freedom to create new things that never existed before. The > only constraints are physical, not mental. > > That point is also true of phenomenology. For both fields, there is no > limitation on what anyone may imagine -- or on what anyone may invent. > > As an example, consider the game of chess. Before anyone carved the > wooden pieces, the rules of chess were the axioms of a pure mathematical > theory, for which there were no applicable facts. > > But then, somebody (or perhaps a group of people) imagined a kind of game > that did not yet exist. They discussed the possibilities, debated various > options, and finally agreed to the axioms (rules) and the designs for > physical boards and pieces. Before they played the game, there were no > facts that corresponded to the mathematical theory or to anybody's > perceptions. > > The tests of existence and accuracy are determined by the normative > sciences, especially methodeutic. For inventions, the only limitations are > the available physical resources to construct them. > > JBD: For my part, I'd like to get clearer on how the pure > phenomenological theory is supposed to support and guide the applied > activities--such as the activities of identifying possible sources of > observational error, correcting for those errors, framing productive > questions, exploring informal diagrammatic representations of the problems, > measuring the phenomena, formulating plausible hypotheses, and generating > formal mathematical models of the hypothetical explanations. > > Those issues depend on the normative sciences, especially methodeutic. The > special sciences depend on phenomenology for the raw data and on > mathematics for forming hypotheses. Then they require the normative > sciences for testing and evaluating the hypotheses. In pure math, the > variables do not refer to anything in actuality. In applied math, one or > more of the variables are linked (via indexes) to something that exists or > may exist in actuality. Those indexes are derived and tested by > methodeutic. > > John > >
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