List:
Jeff replied off-List that he does not remember the details of what Vargas
said about SIA, and offered a few reading suggestions for learning more
about it. I have already studied some of the basics, and as with the
Spanish language, I probably know just enough to be dangerous. :-)
My best guess right now is that Vargas deems SIA's reflexivity to be
questionable because infinitesimals are not "parts of the same kind" as
others, since they are (potentially) non-zero while having squares that are
zero. On the other hand, my understanding is that what SIA fundamentally
defines is not the set of real *numbers*, but a real *line*, such that
infinitesimals ("linelets" or "microsegments") may be understood as its *only
*(indefinite) parts, unless and until numbers are artificially "marked off"
on it.
As for supermultitudeness, Zalamea's definition is that a continuum "cannot
possess any determinate multitude since then it could be surpassed by the
power of that multitude" (p. 8 n. 6). He later adds that "its size must be
fully generic, and cannot be bounded by any other actually determined size"
(p. 14). I think that this notion of "size" is misleading, because it
treats the parts as prior to the whole, rather than derived from it. I
suggest *inexhaustibility *as a more appropriate property, because it
corresponds to how "a Continuum has, IN ITSELF, no definite parts, although
to endow it with definite parts of no matter what multitude, and even parts
of lesser dimensionality down to absolute simplicity, it is only necessary
that these should be marked off, and although even the operation of thought
suffices to impart an approach to definiteness of parts of any multitude we
please" (R S-30 [Copy T:6]; c. 1906).
Regards,
Jon S.
On Sat, Sep 7, 2019 at 12:00 AM Jon Alan Schmidt <[email protected]>
wrote:
> Jeff, List:
>
> I have a few follow-up questions specifically about Smooth Infinitesimal
> Analysis (SIA). Vargas's table indicates that SIA satisfies the conditions
> of inextensibility, potentiality, and infinitesimals, but has question
> marks for reflexivity and supermultitudeness. Do you recall whether he
> discussed this particular assessment during his presentation, or perhaps
> have some ideas of your own about it? In what sense is it doubtful, or at
> least uncertain, whether SIA adequately captures those two properties? How
> exactly is Vargas's new model an improvement over SIA relative to Peirce's
> conception of a true continuum?
>
> Thanks,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
>>
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