John, Kirsti, List ... The relationship between being and representing a universe of discourse arose in a very interesting way in discussions on the Laws Of Form List, stemming from a question about boundaries of regions in Venn diagrams.
Cf: Differential Logic • Comment 2 https://inquiryintoinquiry.com/2017/12/28/differential-logic-%e2%80%a2-comment-2/ Re: Laws Of Form Discussion https://groups.yahoo.com/neo/groups/lawsofform/conversations/topics/3570 <QUOTE> As always, we have to distinguish between the diagram itself, the representation or sign inscribed in some medium, and the formal object it represents under a given interpretation. A venn diagram is an iconic sign we use to represent a formal object, namely, a universe of discourse, by virtue of properties the sign shares with the object. But it is only the relevant properties that do the job — the icon has many properties the object lacks and the object has many properties the icon lacks. As far as the universe of discourse goes, its regions do not necessarily have any boundaries defined. In order to define boundaries for the regions we would need to impose a particular topology on the object space. However, even at the level of abstract logical properties, such as described by a propositional calculus, we can construct a differential extension of the calculus by attaching names to the qualitative changes involved in crossing from regions to their complements, and that is what leads to the simplest order of differential logic. See the following article for the basic intuitions: Differential Propositional Calculus http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus </QUOTE> On 12/12/2017 3:36 PM, Jon Awbrey wrote:
Kirsti, List, I have been occupied with other work and not had the opportunity to keep up with all the list discussions. I appreciate the work Gary and Jeff and the other SPINners are doing to reconstruct the text of Peirce's lectures and I understand all the reasons why people encountering this material for the first time would want to keep their noses close to the text as it's writ. Still, my first encounter with this material was fifty years ago and the edges of my work on the graphical formal systems for logic it inspired have advanced a ways beyond these first inklings, at least, in certain directions. At any rate, I think I left off responding about here. I'll stick a pin in it and try to get back off and on. Regards, Jon
> On 11/28/2017 10:47 AM, kirst...@saunalahti.fi wrote: >> John, Jon, list, >> >> Thank you for a most interesting discussion. >> >> Not being so keen on set theory, or the utterly simple assertions >> formal logic has so far dealt with, I would like to draw your >> attention to these assertion of mine: >> >> If there exists a sheet of assertion, for example a blackboard >> or a piece of paper, there has to have been some co-operative >> human beings to make even the empty ones. >> >> If there exists any assertion stated on it, there has to have been >> a human individual to draw/write (etc) it. >> >> As you can see, I have taken time into the timelessly considered >> issue of empty sets. >> >> Thus, empty sheets may exist, but they can only become real >> (have any effect) if and only if some community (of whatever >> kind) not only exists, but has become real. >> >> How about these? Comments? >> >> These present some outcomes from taking BOTH formulations of >> the Pragmatic Maxim simultaneously seriously. Which they >> usually are not. People tend to take sides at the outset. >> >> I have made wonders with modulations of Aristotelian syllogisms >> on this basis. With the help of two new concepts, experiential time >> and experiential meaning. Which have been exploited, but not funded. >> >> Which kind of reminds me of someone else ... Who on earth could it be ... >> >> With kind regards, >> >> Kirsti >> > -- inquiry into inquiry: https://inquiryintoinquiry.com/ academia: https://independent.academia.edu/JonAwbrey oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey isw: http://intersci.ss.uci.edu/wiki/index.php/JLA facebook page: https://www.facebook.com/JonnyCache
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