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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 3/4/2008 12:18 AM (GMT -6) |   | |
Tom (from Alan’s thread): “Perhaps the Hex will help. Greg and I still burn candles in front of large posters of it we love its elegance so much!”
Hey Tom,
I saw this a while back. Never posted it. But since we’re talking about indeterminancy logic again …
Did you know that the “Hand Book of the First World Congress on the Square of Opposition” has hexagons galore (with diagrams)?
Check it out: http://www.square-of-opposition.org/images/handbook.pdf
Some quotes:
Page 4: Robert Blanch has shown that it makes sense to consider also a dual triangle of subcontrariety and that these two triangles form a star-of-david within a hexagon where the traditional square takes place.
Page 7: To speak more simply (more intuitively), the logical square has given place in 1953 (thanks to Robert Blanch´e) to a “logical hexagon”,
Page 25: After generalizing the classical theory of opposition of propositions, and extending it to the structure of opposition of concepts, and after restructuring Apuleius’ square by transforming it into a hexagon, and after noticing that his oppositional hexagonal structure has fruitful applications in different fields (which we shall illustrate with the application of the hexagon to the logic of norms by G. Kalinowski), Robert Blanch´e has claimed that his logical hexagon can be considered as the objective basis of the structure of the organization of concepts and as the formal structure of thought in general. | | Back to Top | | |
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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 3/4/2008 12:20 AM (GMT -6) | | | Another one:
Check out the “Hexagon of Modalities” on p. 4:
Teaser quote:
P. 1: It is true also in the modal version of the square, we have necessary, possible and impossible, but no primitive name for not necessary. . . .
... We get a better understanding of these relations of opposition in the perspective of Blanché’s hexagon ... | | Back to Top | | |
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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 3/4/2008 12:22 AM (GMT -6) | | |
One more:
ftp://ftp.cle.unicamp.br/pub/e-prints/vol.4,n.1,2004.pdf
Page 10:
"I had read some years ago something interesting on the square of opposition by Robert Blanch´e and I decided to look back at Blanch´e. The analysis of the square of opposition by Blanch´e is something very nice and profound. He suggests to replace the square of the quantifiers by a hexagon made of two triangles, one of contrariety, one of subcontrariety. The six vertices of the hexagon represents six quantifiers. If we made a similar construction for modalities, we have an hexagon with six modalities, and we see clearly where stands contingency, it is the vertice _^¬_ of the triangle of subcontrariety." | | Back to Top | | |
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 3/4/2008 2:55 AM (GMT -6) | | | Thanks JET! Awesome.
I think Alan told me about the confernece on the Square (held in Switzerland a few years ago?). But I didn't know about Blanch. Dang.
Guess we won't get to be famous now. But at least we know we're not crazy. Tom
Post Edited (HumanHypostasis) : 3/4/2008 8:03:26 AM (GMT-6) | | Back to Top | | |
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 3/4/2008 3:16 AM (GMT -6) | | | | |
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One Love
Registered Member
Date Joined Jan 2003
Total Posts : 13888
| Posted 3/4/2008 7:38 AM (GMT -6) | | Wonderful. Independent confirmation. 
Whoever knows and recognizes how near God’s Kingdom is to him may say with Jacob, “God is in this place, and I knew it not.”
Meister Eckhart, "The Nearness of the Kingdom"
Once, having been asked by the Pharisees when the kingdom of God would come, Jesus replied, "The coming of the kingdom of God is not something that can be observed, nor will people say, 'Here it is,' or 'There it is,' because the Kingdom of God is within you.
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Alan Rhoda
Registered Member
Date Joined May 2002
Total Posts : 680
| Posted 3/5/2008 1:16 AM (GMT -6) | | Tom,
Let me know if you get any further response on the conference thing. I'd be interested in helping you work up a good presentation.
Alan | | Back to Top | | |
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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 12/1/2008 8:41 AM (GMT -6) | | From Greg's blog on Nov. 28, 2008 at www.gregboyd.org/blog/:
Greg: But I asked [Bill] Craig why an omniscient being wouldn’t also know the truth value of propositions asserting what might and might not take place, where “might” is considered the contradictory of “will not” and “might not” is considered the contradictory of “will”? In this view, if God knows it is true that “x might and might not do y at a certain point in time,” then God knows it is false both that “x (certainly) will” and “x (certainly) will not do y at a certain point in time.”
Bill Craig: Craig responded by pointing out that this is not how “might” and “might not” usually function in philosophical semantics ...
Earl: If anything, among the world's top philosophers in regards to the square of opposition, it seems like the trend is towards the hexagon (or, at least, the hexagon enjoys a prominent place in the recent literature as shown in this thread).
Doesn't this mean that Craig has to give up his argument about how 'might' and 'might not' "usually function in philosophical semantics"?
Btw, here's another interesting link: "But despite this importance of the concept of opposition, it is still rather unknown that, nowadays, “opposition theory” (for short: the square) has definitively given place, in 2004, to “n-opposition theory” (an infinity of logical-geometrical, highly symmetrical, n-dimensional solids), a new rich and growing field (or zoo…) of modal logic at the intersection between abstract logic and solid n-dimensional geometry. To speak more simply (more intuitively), the logical square has given place in 1953 (thanks to Robert Blanché) to a “logical hexagon”, and in 2004, after some works of Béziau (2003) on the relations of instances of this last figure to negation, it has been proven (Moretti, Pellissier) that both the square and the hexagon, followed by a new “logical cube”, belong to a regular series of n-dimensional objects called “logical bi-simplexes of dimension n” (and the zoo goes even beyond this!)." www.square-of-opposition.org/alessio%20moretti.htmlPost Edited (JET) : 12/1/2008 8:25:11 AM (GMT-6) | | Back to Top | | |
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 12/1/2008 6:12 PM (GMT -6) | | Hey JET-
I saw that post of Greg's too. He and Craig have talked about this several times. I don't think Craig quite gets it. My guess is Craig is ignorant of Blanche's work and of the explosion of logical studies surrounding the Square & Hex. So it just isn't true today that in philosophical jargon "might" and "might not" have Craig's single established meaning. Time is a movin' on.
The Conference is in Corsica in either April or May of '09, but I can't get Jean-Yves to give me a sure date. I was gonna go, but now it looks like I'll be stuck here in Iraq! Ha.
Looking through the literature on those sites (and I told Beziau this too), NOBODY has applied the Hexagon to theology (omniscience, foreknowledge, etc.). So though the Hex has been around for sometime, our use of it is something new. That's what we wanted to present at the Conference. But it looks like Greg or Alan will have to do it!
T | | Back to Top | | |
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