Hi Jon S, List, Here is the message that was sent offlist about Francisco Vargas's presentation on Peirce's mathematical conception of continuity. I was thinking it was part of the thread I'd already brought back to the list discussion.
I don't remember the details of what Francisco said about SIA, although it is probably the most interesting system among those listed in the table for the sake of understanding what Francisco and Fernando are saying about Peirce's mathematical conception of continuity. The system is based on Alexander Grothendieck’s work on Algebraic Geometry, as developed by the likes of Bill Lawvere and John Bell. As with intuitionism, the law of excluded middle is being shelved. As with non-standard analysis, infinitesimals are the basis of all functions. If you are interested in learning about Lawvere's use of category theory in the development of SIA, I highly recommend his book: https://img.4plebs.org/boards/tg/image/1460/05/1460059215690.pdf It provides an accessible introduction to category theory, although more will be needed to see how that is being applied in SIA. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jeffrey Brian Downard Sent: Friday, September 6, 2019 11:18 PM To: Jon Alan Schmidt Subject: Re: Fw: [PEIRCE-L] Re: Vargas on Continuity Hi Jon, I don't remember the details of what Francisco said about SIA, although it is probably the most interesting system for the sake of understanding what Francisco and Fernando are saying about Peirce's mathematical conception of continuity. The system is based on Alexander Grothendieck’s work on Algebraic Geometry, as developed by the likes of Bill Lawvere and John Bell. As with intuitionism, the law of excluded middle is being shelved. As with non-standard analysis, infinitesimals are the basis of all functions. If you are interested in learning about Lawvere's use of category theory in the development of SIA, I highly recommend his book: https://img.4plebs.org/boards/tg/image/1460/05/1460059215690.pdf It provides an accessible introduction to category theory, although more will be needed to see how that is being applied in SIA. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jon Alan Schmidt <jonalanschm...@gmail.com> Sent: Friday, September 6, 2019 10:00:03 PM To: peirce-l@list.iupui.edu Subject: Re: Fw: [PEIRCE-L] Re: Vargas on Continuity 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<http://www.LinkedIn.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt>
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