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rossfadeinout
Registered Member
Date Joined Oct 2002
Total Posts : 428
| Posted 2/10/2004 11:35 AM (GMT -6) |   | | | |
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Alan Rhoda
Registered Member
Date Joined May 2002
Total Posts : 680
| Posted 2/10/2004 11:58 AM (GMT -6) | | Hey thanks, Ross! I've just glanced over the article, but it does seem relevant to our "indeterminacy logic". De Rose seems to be primarily interested in epistemic indeterminacy, whereas we are interested primarily in ontological indeterminacy. He does, however, endorse the view that with respect to future contingents both "will" and "will not" are neither true nor false, which is one way to make room for an open future.
Anyway, thanks again. If you find any more relevant articles, please let us know.
God bless,
Alan | | Back to Top | | |
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 2/10/2004 9:35 PM (GMT -6) | | Yeah, Ross. Thanks. I skimmed it. Will read it more carefully in a couple days. DeRose is an open theist who (like many) denies bivalence. So regarding an event p which is "open," DeRose would say "p will happen" and "p will not happen" are both neither true nor false, whereas we will argue that these are false. DeRose argues that their truth value is "indeterminate." We'll argue that abandoning bivalence isn't necessary to argue the open view logically.
Another thing about this article. Using some simple notation would have helped him, 'cause spelling it all out in long sentences makes it difficult to follow. And DeRose seemed to be trying to make sense of the different every day uses of "might" and "possible" from (like Alan said) an epistemic point of view. But if epistemic indeterminacy is what he's arguing, he'd have to do that (except he ends up arguing the future is open). Maybe it'll make more sense after I read it more carefully.
Tom | | Back to Top | | |
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Diogenes Perhaps
Registered Member
Date Joined Nov 2003
Total Posts : 10
| Posted 3/11/2004 4:03 AM (GMT -6) | | quote:
Originally posted by kingsaint
I'm not sure if it has already been posted, but here is my prediction of the Hexagon of indeterminacy logic given certain clues:
http://gregboyd.officehiway.com/2004/2004-03-07_Boyd_A-Little-Bitty-Minnow-in-a-Big-Flash-Flood.pdf
go down fifth slide, grasshoppa....
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Diogenes Perhaps
Registered Member
Date Joined Nov 2003
Total Posts : 10
| Posted 3/11/2004 8:31 AM (GMT -6) | | quote:
Originally posted by kingsaint
I think a mapping would go like this:
(A) = Zp = x would do y (A in square of opposition)
(B) = ~Qp = either x would do y or x would not do y
(C) = Z~p = x would not do y (E in square of opposition)
(D) = ~Zp = x might not do y (O in square of opposition)
(E) = Qp = x might and might not do y
(F) = ~Z~p = x might do y (I in square of opposition)
No woulds.
I think Z are wills (determinate), Q are mights (indeterminate).
Woulds are from the world of possible worlds.
Which is a member of itself, a conundrum wrapped in an enigma. With a side order of mystery.
But perhaps Godot will show up and explain it all someday. | | Back to Top | | |
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Alan Rhoda
Registered Member
Date Joined May 2002
Total Posts : 680
| Posted 3/11/2004 12:02 PM (GMT -6) | | quote:
Originally posted by Diogenes Perhaps
quote:
Originally posted by kingsaint
I think a mapping would go like this:
(A) = Zp = x would do y (A in square of opposition)
(B) = ~Qp = either x would do y or x would not do y
(C) = Z~p = x would not do y (E in square of opposition)
(D) = ~Zp = x might not do y (O in square of opposition)
(E) = Qp = x might and might not do y
(F) = ~Z~p = x might do y (I in square of opposition)
No woulds.
I think Z are wills (determinate), Q are mights (indeterminate).
Doc, Tom, and I have been collaborating on a paper that develops the hexagon and relates it to the open theism debate. I would say, kingsaint, that the mapping you propose is almost, but not entirely correct. First, as Diogenes points out, 'would' should be 'will'. 'Would' only comes into play with counterfactual conditionals like "If someone were to pay me a million dollars, then I would buy a new car." Second, there is no simple parallel to ~Zp and ~Z~p on the square. ~Zp is not equivalent to O in the square of opposition, but rather
~Zp = Qp or Z~p
In terms of the square, ~Zp = E or (I and O).
And ~Z~p is not equivalent to I in the square, but rather
~Z~p = Qp or Zp
In terms of the square, ~Z~p = A or (I and O).
God bless,
Alan | | Back to Top | | |
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kingsaint
Registered Member
Date Joined Oct 2003
Total Posts : 80
| Posted 3/12/2004 10:41 AM (GMT -6) | | Alan, please critique,
I use possible worlds talk to make sense of this stuff. Given our world W at t1, let S be the set of possible worlds which branch out of W at t1. If we are interested in whether x does y, then there are three ways to characterize S in regard to x doing y: (1) all worlds in S are worlds in which x does y, (2) no worlds in S are such that x does y, and (3) in some worlds in S x does y and in some worlds in S x does not do y. These three situations correspond to the three "primitives" in Alan/Tom/Doc system:
(1) x will do y = all worlds in S are such that x does y
(2) x will not do y = no worlds in S are such that x does y
(3) x might and might not do y = some worlds in S are such that x does y and some worlds in S are such that x does not do y.
The other points of the hexagon are defined similarly:
(4) x might do y = there is at least one world in S such that x does y. This says nothing about the existence of worlds where x does not do y, so "might" does not entail "might not".
(5) x might not do y = there is at least one world in S such that x does not do y.
(6) x will do y or x will not do y = all worlds in S are such that x does y or all worlds in S are such that x does not do y.
Random thoughts:
A. It seems that open theism is committed to the existence of S's which are "mixed bags", there are alternative possibilities. This seems to true, I'm not an expert in such matters, but I find it interesting that quantum theory (superpositions [alternatives] seem to exist in our world) plays a role in many physical theories of consciousness (Roger Penrose et al). Could it be that consciousness (human free will choice) is intimately related to the alternatives built into quantum theory?
B. "Hillary Clinton will be president in 2008 or Hillary Clinton will not be president in 2008" is false (contrary to law of excluded middle) if it is true that there are worlds in S such that Hillary Clinton is president in 2008 and there are worlds in S such that Hillary Clinton is not president in 2008.
C. Bivalence can be affirmed. "There will be a sea battle tomorrow" has a truth value depending on the nature of the worlds in S.
"Nobody who omits doing good works nowadays does so in order not to be tempted to become self-righteous; he omits it because it is easier."
--Philip Merlan, "Toward the Understanding of Kierkegaard" | | Back to Top | | |
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 3/12/2004 7:20 PM (GMT -6) | | Alan: …there is no simple parallel to ~Zp and ~Z~p on the square. ~Zp is not equivalent to O in the square of opposition, but rather
~Zp = Qp or Z~p
In terms of the square, ~Zp = E or (I and O).
And ~Z~p is not equivalent to I in the square, but rather
~Z~p = Qp or Zp
In terms of the square, ~Z~p = A or (I and O).
Tom: Hi all-
Alan and I haven’t talked on some of the details in a while, but for what it’s worth, in my view there IS a simple parallel between ~Zp (hexagon) and O on the square on the one hand and ~Z~p (hexagon) and I on the other hand. If all you know is that O is true on the Square then you also know that either E is true or ‘I and O’ are conjointly true. That is, there are only two cases in which O on the Square can be true, as the subaltern of E or as conjointly true with I. This exactly parallels the Hexagon, where if all you know is that ~Z~p is true then you also know that either Zp is true or ‘~Z~p and ~Zp’ are conjointly true. Same parallel holds for I and ~Z~p.
I = ~Z~p and O = ~Zp. In fact the Square is fully present on the hexagon (along with two other Squares of Opposition).
Tom | | Back to Top | | |
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 3/12/2004 7:33 PM (GMT -6) | | quote:
kingsaint: I use possible worlds talk to make sense of this stuff. Given our world W at t1, let S be the set of possible worlds which branch out of W at t1. If we are interested in whether x does y, then there are three ways to characterize S in regard to x doing y: (1) all worlds in S are worlds in which x does y, (2) no worlds in S are such that x does y, and (3) in some worlds in S x does y and in some worlds in S x does not do y. These three situations correspond to the three "primitives" in Alan/Tom/Doc system:
(1) x will do y = all worlds in S are such that x does y
(2) x will not do y = no worlds in S are such that x does y
(3) x might and might not do y = some worlds in S are such that x does y and some worlds in S are such that x does not do y.
The other points of the hexagon are defined similarly:
(4) x might do y = there is at least one world in S such that x does y. This says nothing about the existence of worlds where x does not do y, so "might" does not entail "might not".
(5) x might not do y = there is at least one world in S such that x does not do y.
(6) x will do y or x will not do y = all worlds in S are such that x does y or all worlds in S are such that x does not do y.
Nothing there I disagree with. Sounds good.
kingsaint: Random thoughts: B. "Hillary Clinton will be president in 2008 or Hillary Clinton will not be president in 2008" is false (contrary to law of excluded middle) if it is true that there are worlds in S such that Hillary Clinton is president in 2008 and there are worlds in S such that Hillary Clinton is not president in 2008.
Tom: True.
kingsaint: C. “There will be a sea battle tomorrow" has a truth value depending on the nature of the worlds in S.
Tom: Right. But it has a truth value AT THE TIME the proposition is spoken, for it either corresponds to or does not correspond to S AT THAT TIME. But possible worlds in S are constantly changing. So assuming that “There will be a sea battle tomorrow" is false at T1 doesn’t mean it won’t be true at T2. It might BECOME true at T2. But once this proposition is TRUE, it must by definition remain true. It cannot become false. A true Q can change its true value and become false. A true Z cannot.
Tom  | | Back to Top | | |
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Alan Rhoda
Registered Member
Date Joined May 2002
Total Posts : 680
| Posted 3/15/2004 3:33 PM (GMT -6) | | quote:
Originally posted by kingsaint
I use possible worlds talk to make sense of this stuff. Given our world W at t1, let S be the set of possible worlds which branch out of W at t1. If we are interested in whether x does y, then there are three ways to characterize S in regard to x doing y: (1) all worlds in S are worlds in which x does y, (2) no worlds in S are such that x does y, and (3) in some worlds in S x does y and in some worlds in S x does not do y. These three situations correspond to the three "primitives" in Alan/Tom/Doc system:
(1) x will do y = all worlds in S are such that x does y
(2) x will not do y = no worlds in S are such that x does y
(3) x might and might not do y = some worlds in S are such that x does y and some worlds in S are such that x does not do y
The other points of the hexagon are defined similarly:
(4) x might do y = there is at least one world in S such that x does y. This says nothing about the existence of worlds where x does not do y, so "might" does not entail "might not".
(5) x might not do y = there is at least one world in S such that x does not do y.
(6) x will do y or x will not do y = all worlds in S are such that x does y or all worlds in S are such that x does not do y.
I'm tracking with you, kingsaint. I like your definitions. You've persuaded me that I was overhasty in my previous post in concluding that (4) and (5) do not correspond to I and O propositions, respectively. My misgivings stemmed from the fact that 'might' on the square is ambiguous between Qp and Zp, and 'might not' is ambiguous between Qp and Z~p. The hexagon makes these distinctions explicit. The square does not. Thus, (4) and (5) do correspond to I and O propositions, but in doing so they trade on the ambiguities inherent in the square. That's what I was trying to point out, but I apparently confused myself in the process.
kingsaint: It seems that open theism is committed to the existence of S's which are "mixed bags", there are alternative possibilities. This seems to true, I'm not an expert in such matters, but I find it interesting that quantum theory (superpositions [alternatives] seem to exist in our world) plays a role in many physical theories of consciousness (Roger Penrose et al). Could it be that consciousness (human free will choice) is intimately related to the alternatives built into quantum theory?
Alan: I'm skeptical about this. It is my understanding that the thesis of real quantum indeterminacy has been and is being seriously challenged by supporters of the de Broglie-Bohm pilot wave model (I'm no expert on quantum mechanics, so don't ask me to explain what that is). You are right, of course, that open theism is committed to the existence of multiple future possibilities, but I don't see that much is to be gained by thinking of these as superpositions a la the Copenhagen interpretation of quantum mechanics. It seems to me that we would then face the sort of counterintuitive consequences that Schrodinger pointed out with his famous cat example. Is the cat whose fate hinges on a quantum event dead or alive? Well, if we allow superpositions it seems that the answer is both and neither at the same time. It is not clear how that is coherent, which was precisely Schrodinger's point. I think we can avoid superpositions altogether by simply ascribing to each of the several possible worlds in S a non-zero probability, where the total probability for S equals one.
kingsaint: "Hillary Clinton will be president in 2008 or Hillary Clinton will not be president in 2008" is false (contrary to law of excluded middle) if it is true that there are worlds in S such that Hillary Clinton is president in 2008 and there are worlds in S such that Hillary Clinton is not president in 2008.
Alan: I agree that "HC will be pres. in 2008 or HC will not be pres. in 2008" is NOW false, but I do not think that runs counter to either the law of excluded middle or bivalence. The reason why we don't have to deny those principles is because the alternatives in the disjunction are not jointly exhaustive--there is a third possibility, viz., it is NOW true that "HC might and might not become pres. in 2008". But what if instead of confining ourselves to what is NOW true we ask what is true as of election day 2008? Clearly, when election day has come and gone, either HC will have been elected, or she will not have been elected. So it seems that it is true as of election day 2008 either that HC has been elected pres. or it is not. But this poses no problem for the open theist, for all that is true NOW and at any time prior to election day when the outcome of the election is not yet settled is the disjunction: "EITHER HC is elected pres. in 2008 OR HC is not elected pres. in 2008". This disjunction is NOW true, but it is NOT true because one of its disjunctions is NOW true; rather, it is true because when election day 2008 arrives one of the disjunctions will be true.
kingsaint: Bivalence can be affirmed. "There will be a sea battle tomorrow" has a truth value depending on the nature of the worlds in S.
Alan: I agree.
God bless,
Alan | | Back to Top | | |
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Alan Rhoda
Registered Member
Date Joined May 2002
Total Posts : 680
| Posted 3/15/2004 3:47 PM (GMT -6) | | quote:
Originally posted by TGB
kingsaint: C. “There will be a sea battle tomorrow" has a truth value depending on the nature of the worlds in S.
Tom: Right. But it has a truth value AT THE TIME the proposition is spoken, for it either corresponds to or does not correspond to S AT THAT TIME. But possible worlds in S are constantly changing. So assuming that “There will be a sea battle tomorrow" is false at T1 doesn’t mean it won’t be true at T2. It might BECOME true at T2. But once this proposition is TRUE, it must by definition remain true. It cannot become false. A true Q can change its true value and become false. A true Z cannot.
Good point, Tom.
You touch on one of the distinctives of indeterminacy logic as we have developed it, namely, that the truth of any statement about the future has to be relativized to a particular time, one from the perspective of which the event in question is still in the future. In contrast, nearly every other logician wants to say that truth is either timeless or omnitemporal. The arguments for that stance simply beg the question against indeterminacy logic, so they don't prove anything, but they do have sufficient intuitive appeal that relatively few scholars have ever thought to question the timelessness or omnitemporality of truth.
BTW, Tom, I'm going to send the revised article your way. Sent it to Greg a couple weeks back with the idea that he would simply forward it on to you, but I just found out that he's been having major computer problems and hasn't had the chance to forward it. I look forward to any feedback you may have.
God bless you, bro.
Alan | | Back to Top | | |
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Sisters of Cain
Registered Member
Date Joined Mar 2004
Total Posts : 431
| Posted 3/16/2004 4:06 AM (GMT -6) | | quote:
Originally posted by might-be-don
quote:
Originally posted by Alan Rhoda..., but I just found out that he's been having major computer problems and hasn't had the chance to forward it.
Could someone just go over to his computer and show him where the 'on' button is located.
peace, don
WHERE'S THE "ANY" KEY?????? 
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