Jeff, List: JD (below): What is the general trend: an increase in dimensions from 1 to 4, or a decrease in dimensions from infinity to four? How might the rival metaphysical hypotheses be tested?
JD (to Gary F.): We have to ask, if real space has 3 dimensions, then why is it a whole number and not an answer involving a decimal or fractional expression? Those are interesting questions, but I suggest that we first explore a more fundamental one--what is a *dimension *in this context? According to Wikipedia <https://en.wikipedia.org/wiki/Dimension>, "the *dimension *of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it." Of course, discrete coordinates--as well as the discrete positions and instants that they are intended to mark--are arbitrary and artificial creations of thought for the purpose of describing motion through space-time, which in itself is continuous. Does this perhaps entail that discrete dimensions of *any *whole number are likewise arbitrary and artificial creations of thought--hypothetical *representations *of space-time, rather than *real *characters of it? The definition of a dimension given in the second video linked in the post addressed to Gary F.--the one about fractals--is even more obviously arbitrary and artificial as a measure of "roughness." What *meaning *could we assign to a decimal or fractional value somehow assigned to *real *space-time as a continuous whole? Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Tue, Aug 27, 2019 at 6:35 PM Jeffrey Brian Downard < [email protected]> wrote: > Gary R., Jon S, Edwina, John S, List, > > Keeping in mind the distinction that Peirce makes between metaphysical > cosmology and physical cosmology, let me again stress a point made earlier. > Instead of assuming that, at any point in his inquiries, Peirce typically > affirmed one answer to each of the main questions in metaphysical > cosmology, I tend to think that he explored a fairly wide range of possible > answers. > > In any given text, he often does spend more effort on one set > of hypotheses and less on others. And, over the course of his career, he > often does reassess the options he has considered up to that point. As a > result of the inquiries, he does give greater weight to the plausibility of > some metaphysical hypotheses as compared to others. In many cases where he > might seem to be "taking a position", I find that he is merely pointing to > defects in some of the hypotheses. Most of the hypotheses offered in > the cosmological metaphysics of his time failed in some degree to explain > phenomena that clearly called out for explanation (e.g., why does our > common experience of time involve 1 ordered dimension and our experience > of space involve 3 dimensions?) In some cases, the problematic hypotheses > might have been amended to remedy such defects. > > I tend to think that Peirce was remarkably sanguine about the fact that > the big questions in metaphysics like "What is the origin of all things?" > and "How did the universe evolve from such beginnings?" are the kinds of > questions that get answered over the course of millennia by whole > communities of inquirers and not by any individual during the course of a > lifetime. As such, I am cautious about proclaiming that Peirce's position > on these types of questions was, at some particular point in his career, > "X" or that his final mature position was "Y". Rather, I think that he took > his own advice on questions of metaphysics and tended to hold some > metaphysical hypotheses as more plausible than others because they offered > better explanations of the phenomena at hand or as worthy of our attention > because they were easier to test. > > I find it more interesting to articulate the *reasons *he offers for > holding that one hypothetical explanation is better than other than to > insist, on textual grounds, that some answer to a question was his > considered and mature view. Clarity about the conceptions employed in the > rival hypotheses comes from understanding those reasons and especially from > seeing what we might do to put the rival explanations to the test. > > So, here is a question. Consider two hypotheses: (a) the four dimensions > of space and time that are characteristic of the world in which we > live evolved by a process of an *increase* from a one-dimensional > continuum and (b) the four dimensions of space and time that are > characteristic of the world in which we lived are the result of a process > of decrease from an objectively vague state having an infinite number of > dimensions. What is the general trend: an increase in dimensions from 1 to > 4, or a decrease in dimensions from infinity to four? How might the rival > metaphysical hypotheses be tested? > > Yours, > > Jeff > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 > >>
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