Jeff, List: As John Sowa already noted in his reply, a *mathematically *adequate conception of continuity is not a strict prerequisite for a *semeiotically *or *metaphysically *adequate conception of continuity. Otherwise, every logician and philosopher would also have to be a (pure) mathematician. In my view, it is sufficient to have a hypothesis about continuity that is amenable to drawing necessary conclusions--i.e., the *broad *definition of mathematics that Peirce adopted from his father--and then testing whether that hypothesis and those conclusions prove fruitful within each discipline. Again, the Cantorian pseudo-continuum has turned out to be an adequate *model *of continuity for many (most?) mathematical, scientific, and practical purposes; but it does not satisfy the criteria that Peirce established for the conception of a *true *continuum.
Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sat, Aug 3, 2019 at 9:04 PM Jeffrey Brian Downard < [email protected]> wrote: > Jon, List, > > The questions lead, I think, to a natural progression. > > 1) We seek a mathematically adequate conception of continuity for the > sake of developing a sufficiently rich conception of continuity for inquiry > in logic and semiotics. > > 2) In turn, we seek a logically adequate conception of continuity for the > sake of developing a sufficiently rich conception of continuity for inquiry > in metaphysics. > > 3) Finally, we seek a philosophical conception of continuity that is > adequate for logic and metaphysics for the sake of developing a > sufficiently rich conception of continuity for inquiries in the special > sciences. > > As such, figuring out what conception of continuity is adequate for pure > mathematics and, in turn in applied mathematics is essential. For the sake > of applying mathematics to positive questions in the sciences, a proper > understanding of different kinds of mathematical models and forms of > measurement are important for our inquiries in philosophy and the special > sciences. After all, each of these cenoscopic or idioscopic sciences can be > made rigorous only insofar as we are competent to employ the right sorts > of mathematical models and forms of measurement in those areas of inquiry. > > --Jeff > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 > >>
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