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Tom
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Date Joined Jul 2001
Total Posts : 10353
| Posted 11/16/2003 8:11 AM (GMT -6) |   | This thread is for non-anal-retentive people to discuss the logic of indeterminacy in normal-human-being terms. I’ve been going wacko on this lately and haven’t been very sensitive to those who aren’t into the notation and technicality of it all. So I’d like to post here the basic ideas we’ve had so far and then in a second post include the theorems spelled out in jive talk. 
If this doesn’t go anywhere, no problem. We going to have to find a way to argue this in everyday talk ANYWAY, aren’t we Doc? We can’t argue our point to as many people as possible in technical logic-lingo. We have to find a way to spell this out.
Laika mentioned that instead of reinventing the wheel we simply define what is fundamental to expressing indeterminacy and insert it into already existing logic. This makes great sense, and I actually thought that's what we were doing. The “revolution” we’re talking about is simply giving indeterminacy a place at the table alongside determinacy. It’s that simple. But when this is done, some of the traditional ways of doing logic, illustrating logic, etc., will have to change (like dumping the square and using a triangle). And all of this relates ONLY to the future. It’s won’t touch anything about the past or present. So the square will work fine for “All grass is green” and other present realities.
Laika has also reminded us of three-valued, four-valued (and even others!) logic, in which the truth values are more than just two, namely, “true” and “false.” I don’t think we need to find a third truth value in addition to “true” and “false” to express indeterminacy though, and I think denying bivalence (i.e., that a proposition is either true or false) will make arguing our case even harder to the agents of the Matrix when we go in to work our revolution. We can stick to traditional propositional logic, insist on bivalence along with the rest of ‘em, and argue that “indeterminacy” (“Tom might-might not stop obsessing with this subject by this Christmas”) is just as independently real and consequential as “determinacy.”
OK. Here we go.
1) The revolution is a revolution in UNDERSTANDING reality, future reality to be specific. It’s already transformed theology (open theism) and science (quantum mechanics). The time has come for LOGIC to welcome the revolution. We’re saying that there are three possible states of affairs (“ways things are”) regarding the future. Alan expressed them as:
(A) It is determinately the case that x does y
(B) It is determinately the case that x does not do y
(C) It is indeterminately the case that x does y
Now, everybody actually TALKS as if this was the case. We express our beliefs about the future in three ways:
(A1) x will do y
(B1) x will not do y
(C1) x might do y
The way we talk OUGHT to reflect the truth about what is the case regarding things, in this case the future.
Now watch…
2) But the agents of the Matrix tell us that for everything that ever occurs God knew it was true BEFORE it occurred that “x will occur” (state of affairs (A)) and for everything that does not occur it was true BEFORE it didn’t occur that “x will not occur” (state of affairs (B)). Yes, there’s “x would do y” as our Middle Knowledge friends argue, but let’s introduce that a little later, because what I’ve said so far about “will” and “will not” is also believed by them, they just get there a different way. They’re agents of the Matrix as well, but they’re the upgrades of the original agents in Matrix Reloaded!
OK. If it’s true that for all that occurs that it was true before it occurred that it “will occur” and true for all that does not occur that it was true before it did not occurred that it “will not occur” then it follows that for all that occurs it was FALSE before it occurred that it “might and might not occur,” and for all that does not occur it was FALSE before it did not occur that it “might and might not occur.” What the architects and agents of the Matrix essentially tell us is that the future is made up, or consists, of only states of affairs (A) and (B). There is not state of affairs (C).
What does this do to (C1), that is, to the way we normal folks talk about the future when we say, “Oh, x ‘might’ do y,” “Sally, might say yes to coming to church,” “Fred ‘might’ decided to go to college or he ‘might’ decide to work a year first”? What TRUTH, what state of affairs, does our “might” (or our “might and might not” to be more precise) point to if REALITY (ontologically speaking) contains NO “might’s”? If it's all true or false ONLY that things “will” or “will not” occur, how are we to understand OUR USE of “might” and “might not”? Simple: It’s epistemological! All that means is, we only use “might” and “might not” because we’re NOT omniscient like God. We DON’T know the TRUTH about Fred’s deciding whether to go to college or work a year first. If we were omniscient like God, then we would know whether Fred “will” or “will not” go to college or work a year first. See? We USE might to express our IGNORANCE about the truth of the future. Such language isn’t rooted in what is actually the case about the future, it’s rooted in our NOT KNOWING what is actually the case about the future.
So, those who maintain the Matrix insist that the future is entirely a matter of states of affairs (A) and (B). Everything is either “determinately x will occur” or “determinately x will not occur.” State of affairs (C) is not ONTOLOGICALLY the case at all. It only exists in our minds and language as a way of expressing our ignorance (thus, EPISTEMOLOGY) about the future. Doc and Alan seem not to be so convinced of my distinction here. But I think it’s crucial to note as the revolution gets rolling.
This way of looking at the world, the future in particular, and expressing it is as entrenched as the Matrix itself. Only a revolution will do.
3) Now, let’s talk about our use of “might” and “might not” (and conjoined “might and might not”). The agents of the Matrix are partly correct when they say “might’ and “might not” only express our ignorance about what the truth of the matter is. For it CAN be the case that, say, “x will do y” is true (in which case “x will not do y” is false). Let's suppose too that we know it's either determinately the case that x does y or determinately the case that x does not do y. But not being omniscient, we don't know which is which. So how are WE non-anal-retentive non-logicians out on the street supposed to describe x’s doing y in this case? We use "might." That's all we can do. This "might" doesn't even exist on the square! We don’t know if x’s doing y is a “will” or a “will not,” but supposing we know it's one or the other, all we can say is, “Well, x might do y, or x might not do y.” In fact, regardless of our knowing whether state of affaris A, B, or C is the case with regard to x's doing y, we'd still use "might" to express our ignorance of the matter. It’s like me sitting in a room with two doors. I know one is locked and one is not locked, but I don’t know which is which. What CAN I say about either door? All I can say is, “This door ‘might’ be locked, or it ‘might not’ be locked.” I don’t mean by this “might” that the door isn’t ACTUALLY either locked or not locked. All I mean is that I don’t know, my beliefs about what the truth IS are ‘indeterminate’. My mind is not “made up.” I don’t know, so as far as I can discern, the particular door I'm speaking about "might" be locked and "might not" be locked. But these "might's" say NOTHING whatsoever about the TRUTH of the matter regarding the actualy case with respect to the doors. See the ontology vs epistemology going on here?
This is the “epistemological indeterminacy” I’ve been talking about. It’s undeniable. It’s out there. We talk like this every day. It’s not the ONLY use of might in common speech, but it’s one use. Actually, the agents of the Matrix don’t mind if we use “might” and “might not” like this. They use it themselves and admit that we have to talk about the future this way because we’re not omniscient like God. If we WERE omniscient, we’d only EVER use “will” and “will not” to talk about the future because that’s all the future is. "Might" and "might not" on the square function PARTLY as ontological operators and PARTLY as epistemological operators. When you combine them into Doc's "might and might not" the epistemological in each cancels out and the two collapse like a quantum particle into ontology, that is, into "indeterminacy."
So note the difference. Traditional logic, the logic of the Matrix, tells us that the future can only TRUTHFULLY be described in terms of what “will” and “will not” occur but that our ignorance about the future can be truthfully described in terms of what “might” or “might not” occur. “Might’s” are not ontologically real, they’re only epistemologically real. This epistemological use of “might” will always remain with us, because we often do find ourselves in a room knowing that one door is locked and one is unlocked but not knowing which is which. In such cases we have to say, “Oh well, this door ‘might’ be the one that’s locked.” As long as we’re not omniscient, we’ll be expressing our ignorance about what “will” and “will not” and "might and migh not" happen by using “might.” But the indeterminacy logic I’m talking about isn’t an attempt to wipe out this epistemological use of “might.” What we want to do with our revolution is to introduce another use of “might” for expressing NOT our ignorance about the future (not epistemological indeterminacy) but for expressing the TRUTH about an event which is neither a “will” nor a “will not” but which is itself an ontological “might and might not.” And it’s just as clear to me that in common speech we use “might” with this very meaning ALSO! How do we differentiate it from an expression of ignorance? Context and common sense; two things that the logicians of the Matrix have a hard time with.
When we say “Tom might come to St. Paul, and he might bring Cohibas,” we normal non-anal-retentive non-logicians mean to say something like, “It’s neither settled that Tom’s coming nor settled that he’s not coming, and in the event he DOES come, it’s neither settled that he’ll bring Cohibas nor settled that he won’t bring Cohibas.” The logicians and agents of the Matrix shudder when you say something like this because you’re claiming to express more than ignorance about what is either a “will” or a “will not,” you’re claiming to express truth about what is genuinely, ONTOLOGICALLY, neither a “will” nor a “will not,” but which is a “might and might not.” You’re laying claim to a reality that is not exhaustively determinate.
All that I’ve said so far can be illustrated on the traditional square.
Luckily, the agents of the Matrix couldn’t erase every vestige of ontological indeterminacy from our minds OR our logic. Such ontological indeterminacy found a way to clue us in to its existence. It just wouldn’t go away. And that clue had to come in terms that the agents of the Matrix would understand, through their own sacrosanct Square of Opposition, on their own rules, where the clue that something’s up is seen in conjoining “might” and “might not” into “might and might not.” The square permits this conjoining of “might” and “might not.” Ah, but what is the truth about the future if there actually ARE events which (in the language of the Matrix’s own Square) “might” AND “might not” occur? To ask this is to stand on the brink of the revolution looking out onto the horizon of a new world, a new theology, a new relationship with God. The agents of the Matrix can hardly bring themselves to do this and hate it when other talk of being able to see the horizon of that world. But, given the rules of their own game, they HAVE to admit “might and might not” is a logically possible state of affairs. I suspect the really smart ones can read the handwriting on the wall and are scrambling to find ways to deny the inevitable. To keep the Matrix in tact, they'll have to argue that though “might and might not” is a logically possible state of affairs (ontologically speaking), there are in fact no events in this category! There are no true “might and might not” propositions. And so the revolution plods on.
Theorems for the non-anal-retentive to come…
Tom  | | Back to Top | | |
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Tom
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| Posted 11/16/2003 10:06 AM (GMT -6) | | OK, here are the theorems for indeterminacy logic we’ve come up with so far. I’ll list them in notation and then spell ‘em out in jive-talk.
1. Zp v Z~p v Qp
“Hey Joe, p either will occur, will not occur, or might/might not occur.” It is either determinately the case that p, determinately the case that not-p, or indeterminately the case that p.” The “or” here is exclusive, meaning “either but not both.”
2. Zp --> ~Z~p ^ ~Qp
”Hey dude, check it out: If it’s true that p will occur, then it’s false that ‘p will not occur’ and false that ‘p might/might not occur’.”
3. Z~p --> ~Zp ^ ~Qp
“Yo girl, if it’s true that p will not occur, then it’s false that ‘p will occur’ and false that ‘p might/might not occur’.”
4. Qp --> ~Zp ^ ~Z~p
“Here we go: if it’s true that ‘p might/might not occur, then it’s false that ‘p will occur’ and false that ‘p will not occur’.”
5. Qp = Q~p
“OK, so here it is: ‘p might/might not occur’ is the same as saying ‘p might not/might occur.’ Ha!”
6. ~Zp = Z~p v Qp
“Alright, saying ‘p might not occur’ is the same as saying ‘Either p will not occur or p might/might not occur’.”
7. ~Z~p = Zp v Qp
“Saying ‘p might occur’ is the same as saying ‘Either p will occur or p might/might not occur’.”
8. ~Qp = Zp v Z~p
“Dig it: Saying ‘It’s not true that p might/might not occur’ is the same as saying ‘Either p will occur or p will not occur’.”
Conjuntions:
9. Z(p ^ q) = Zp ^ Zq
“Hang on: Saying ‘p and q will both occur’ is the same as saying ‘p will occur and q will occur’.”
10. Z~(p ^ q) = Z~p ^ Z~q
“Check it out baby: Saying ‘p and q will both not occur’ is the same as saying ‘p will not occur and q will not occur’.”
11. Q(p ^ q) = Qp ^ Qq
“Saying ‘p and q might/might not occur’ is the same as saying ‘p might/might not occur’ and ‘q might/might not occur’.”
Disjunctions:
Now you in fo a ride hunny—
12. Z(p v q) = (Zp ^ Zq) v (Zp ^ Z~q) v (Zp ^ Qq) v (Z~p ^ Zq) v (Qp ^ Zq)
“Saying ‘Either or both of p or q will occur’ is the same as saying: Either ‘p and q will occur’ or ‘p will occur and q will not occur’ or ‘p will occur and q might/might not occur’ or ‘p will not occur and q will occur’ or ‘p might/might not occur and q will occur’. Dude!”
13. Z~(p v q) = (Z~p ^ Z~q) v (Z~p ^ Zq) v (Z~p ^ Qq) v (Zp ^ Z~q) v (Qp ^ Z~q)
“Hang on: Saying ‘Either or both of p and q will NOT occur’ is the same as saying: Either ‘p will not occur and q will not occur’ or ‘p will not occur and q will occur’ or ‘p will not occur and q might/might not occur’ or ‘p will occur and q will not occur’.”
14. Q(p v q) = (Qp ^ Qq) v (Zp ^ Qq) v (Z~p ^ Qq) v (Qp ^ Zq) v (Qp ^ Z~q)
“One more: Saying ‘Either or both of p and q might/might not occur’ is the same as saying: Either ‘p might/might not occur and q might/might not occur’ or ‘p will occur and q might/might not occur’ or ‘p will not occur and q might/might not occur’ or ‘p might/might not occur and q will occur,’ or ‘p might/might not occur and q will not occur’.”
Forget theorems 15-20 in jive-talk for now.
21. Q(p --> q) = p --> Qq
“Yo my main man: Saying “It might/might not happen that ‘if p then q’ is the same as saying ‘If p occurs then q might/might occur’.”
Note: Hmmmm?
22. Z(p --> q) = Zp ^ Zq
“Listen up Jack: Saying “It WILL be the case that ‘if p then q’ is the same as saying ‘p will occur and q will occur’.”
Note: This seems sound.
23. Z~(p --> q) = Z~p ^ Z~q
“Duuudes: Saying ‘It will NOT be the case that ‘if p then q’ is the same as saying ‘p and q will not occur.”
Note: I’m doubting this. It doesn’t seem right. All the left side of the equation seems to say is that p will not occur and q will not follow as p’s implication, but this doesn’t mean that q will not under OTHER circumstances occur.
24. Q(p --> q) = Qp ^ Qq
“Listen up: Saying ‘It might/might not be the case that ‘if p then q’ is the same as saying ‘p might/might not occur and q might/might not’ occur.
Note: Not sure about this either, for the same reasons as I doubt 23.
There ya go friends! Logic in street talk.
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GregBoyd
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Date Joined Jul 2001
Total Posts : 1818
| Posted 11/17/2003 1:54 AM (GMT -6) | | [Splendidly clear restatement of your previously manic, hyper-technical, frenzied reflections. (Your "jive" lingo, however, sounds like a white guy in Lebanon trying to sound hip. "Yo dude, if it is determinately the case that p, then not indeterminately the case that q…" Yeh, people on the street talk like this Tom! )
TGB: So, those who maintain the Matrix insist that the future is entirely a matter of states of affairs (A) and (B). Everything is either "determinately x will occur" or "determinately x will not occur." State of affairs (C) is not ONTOLOGICALLY the case at all. It only exists in our minds and language as a way of expressing our ignorance (thus, EPISTEMOLOGY) about the future. Doc and Alan seem not to be so convinced of my distinction here. But I think it’s crucial to note as the revolution gets rolling.
Doc: I heartily agree with this TGB, if by "those who maintain the Matrix" you mean "those who hold to exhaustively definite foreknowledge (this phrase probably should be abandoned, heh?) and thus hold that the future is exhaustively encompassed by truths about what will and will not occur. My only reservation concerned a claim I thought you were making about the square – that it only could express epistemological, not ontological, indeterminacy. But I now see that you don’t claim this, for you grant that "conjoined mights" require ontological indeterminacy.
Great job.
Doc
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Tom
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| Posted 11/18/2003 8:34 AM (GMT -6) | | A few corrections. I want to say that Alan was on the money with his truth tables on the “Logic of Indeterminacy” thread. I had misunderstood how the parentheses were being used. Now I GOT it! When I worked through the conjunctions and disjunctions again, I came out with the same deal Alan worked out. Here’s his truth table in normal-people talk:
M-M stands for "might and might not"
We need to correct my 9-14 a bit.
Conjuntions:
9. Z(p ^ q) = Zp ^ Zq
“‘p and q will both’ will occur” is the same as saying “‘p will occur’ and ‘q will occur’.”
10. Z~(p ^ q) = (Zp ^ Z~q) v (Z~p ^ Zq) v (Z~p ^Z~q) v (Z~p ^ Qq) v (Qp ^ Z~q)
“‘p and q will not both occur” is the same as saying “‘p will occur and q will not occur’ or ‘p will not occur and q will occur’ or ‘p will not occur and q will not occur’ or ‘p will not occur and q might and might not occur’ or ‘p might and might not occur and q will not occur’.”
11. Q(p ^ q) = (Zp ^ Qq) v (Qp ^ Zq) v (Qp ^ Qq)
“‘p and q’ might and might not occur” is the same as saying “‘p will occur and q might and might not occur’ or ‘p might and might not occur and q will occur’ or ‘p might and might not occur and q might and might not occur’.”
Disjunctions:
12. Z(p v q) = (Zp ^ Zq) v (Zp ^ Z~q) v (Zp ^ Qq) v (Z~p ^ Zq) v (Qp ^ Zq)
“‘Either or both of p or q’ will occur” is the same as saying: “Either ‘p and q will both occur’ or ‘p will occur and q will not occur’ or ‘p will occur and q might and might not occur’ or ‘p will not occur and q will occur’ or ‘p might and might not occur and q will occur’.”
13. Z~(p v q) = (Z~p ^ Z~q)
“‘Either or both of p and q’ will not occur” is the same as saying “Neither p nor q will occur’.”
14. Q(p v q) = (Qp ^ Qq) v (Zp ^ Qq) v (Z~p ^ Qq) v (Qp ^ Zq) v (Qp ^ Z~q)
“‘Either or both of p and q’ might and might not occur” is the same as saying “‘Either p might and might not occur and q might and might not occur’ or ‘p will occur and q might and might not occur’ or ‘p will not occur and q might and might not occur’ or ‘p might and might not occur and q will occur,’ or ‘p might and might not occur and q will not occur’.”
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