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Tom
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| Posted 11/17/2003 11:42 AM (GMT -6) |   | Doc: There's no problem with the distinction between an epistemological and ontological "might." My confusion/hestitation was in (what I thought) was Tom's contention that the square didn't allow for ontological "mights." I didn't see this implied in his "triangle within a triangle" argument. Seems to me that conjoining the mights in a true proposition allows them to be statements of fact, not epistemology. I now think Tom agrees with this, whether he did before or not.
Tom: Right. Conjoined "might and might not" is ontological all the way. The epistemological indeterminacy is only present in "might" when it's 'independently' true, that is, when ALL WE KNOW is that "might" is true. If THAT'S your starting point, then the epistemological indetermintacy is present. Same is true if ALL WE KNOW is that "might not" is true. It's when they're conjointly true that the epistemological in each collapses and we're left with ontologicaly indeterminacy.
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Alan Rhoda
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| Posted 11/17/2003 12:13 PM (GMT -6) | | Alan: And Z~(p ^ q) is the case if and only if either Z~p or Z~q.
Tom: To falsify an “and” you only need to falsify one of the variables. That is “either or both” of them may be false. But to prove an “and” you have to show that both are true. So, if Z~(p ^ q) means both Z~p and Z~q must be the case, then Z~(p ^ q) = Z~p ^ Z~q, right? Isn’t that what you just said?
Alan: Nope, that's not what I said. I have never maintained or suggested that "and" means anything other than "both and". Where we aren't on the same wavelength is not in our usage of "and" but in our understanding of the scope of the operator. In saying Z~(p ^ q) we are saying that the conjuction is determinately not the case. This does not imply that the conjuncts are both determinately not the case. Contrary to what you state, Z~(p ^ q) does not mean that Z~p and Z~q are both the case. Rather, it means that it is not the case that both p and q are the case, which occurs whenever at least one of them is not the case.
Tom: Q(p ^ q) is only the case if both Qp and Qq. ... If this means both Qp and Qq, then there’s only one combination in the entire column that is true, the last one, Qp and Qq.
Alan: Again, the issue is the scope of the indeterminacy operator, Q--in saying Q(p ^ q) indeterminacy is predicated of the conjunction taken as a unit, not of the conjuncts taken severally. Thus, Q(p ^ q) says "It is indeterminate that (both p and q)". This is NOT equivalent to saying "It is indeterminate that p AND it is indeterminate that q" (i.e., Qp ^ Qq), which is how you want to read it.
The truth tables I gave for Q(p ^ q) and Q(p v q) are correct. The ones you give are internally contradictory. To see this, recall that in indeterminacy logic the three metaphysical states (Zp, Z~p, Qp) are mutually exclusive and jointly exhaustive. In other words, EVERY state of affairs is either determinately the case, determinately not the case, or indeterminately the case. Thus, for every state of affairs EXACTLY ONE of those must be the case.
Now in my table the various possible states of affairs are defined by the set of possibilities for p and q. Thus we have (Zp, Zq), (Zp, Z~q), (Zp, Qq), and so on. For each of these states of affairs either Z(p ^ q), Z~(p ^ q), or Q(p ^ q) must be true, and only one can be true. If you look at my truth table, you will see that it satisfies this constraint: In each row exactly one of the metaphysical states is true.
If we examine your tables we see that this is not the case. In your table for Q(p ^ q) six of the nine rows are all false. And in your table for Q(p v q) six of the nine rows have two true values. Both of these results are at odds with the assumptions of indeterminacy logic. Think of it this way. IF state of affairs (Zp, Qq) obtains, how could it be the case that (p ^ q) is neither determinately the case, determinately not the case, nor indeterminately the case, as your table states? Either is it one of those three, or our three metaphysical states are not jointly exhaustive. Similarly, IF state of affairs (Zp, Qq) exists, how could it be the case the (p v q) is both determinately the case and indeterminately the case, as your table states? If you are right, then our three metaphysical states are not mutually exclusive.
God bless,
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Tom
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| Posted 11/17/2003 12:24 PM (GMT -6) | | Alan: In saying Z~(p ^ q) we are saying that the conjuction is determinately not the case.
Tom: Now I got it! Thanks for being patient with me Bro. I was wondering whether or not this was what I was missing in my last post to you above on this same page. I'll rethink my way through it.
But here's what you said back on page two that confused me:
"My thinking was that if Q(p ^ q) then (p and q) is indeterminate, which will be the case when either of them is indeterminate. Now I see that this is not quite right because an "and" statement can be indeterminate in two different ways: (a) both the conjuncts are indeterminate, or (b) one conjunct is indeterminate and the other is determinately true."
It sounded to me then as if you were saying "and" doesn't have to mean "both and" but may mean "either or both," which I gathered from your (b) (one conjunct is something and the other is something else). That's not what you meant, but it wasn't so clear then. Sorry about that.
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Magneton
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| Posted 11/17/2003 12:39 PM (GMT -6) | | Tom & Alan,
It seems to me that something fundamental is missing from this formulation of the logic of indeterminacy so far, and that is the relationship between propositions.
You appear to be assuming that the propositions are not correlated, e.g. that q is not the necessary consequent or contradictory of p. That is, you appear to assume
~Z(p --> q) and ~Z(p --> -q).
For example, one of the theorems states that Q(p^q) is equivalent to Qp ^ Qq.
While it is true that Q(p^q) --> Qp ^ Qq,
it is not true that Qp ^ Qq --> Q(p^q),
because it is possible that p --> -q.
For example, if p = "100 hours from now, Tom will be in Lebanon," and q = "100 hours from now, Tom will be in Greece," then Qp and Qq are true, but Q(p^q) is false: Tom can't be in two places at once, i.e.
Z(p --> -q).
It seems to me that to construct a truth table, one would need additional columns specifying the relational terms. Rather than just the p and q columns, you'd also need columns something like
p -> q; q -> p; p ->-q; q ->-p.
Relational terms are unnecessary in determinate logic, but become a factor in indeterminate logic. Seems to me there's another layer to deal with here that expresses the idea that relationships between entities are just as real as the entities themselves. Or am I missing something?
Magneton
"Only those who will risk going too far can possibly find out how far one can go." - T. S. Eliot | | Back to Top | | |
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Alan Rhoda
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| Posted 11/17/2003 2:04 PM (GMT -6) | | Magneton: It seems to me that something fundamental is missing from this formulation of the logic of indeterminacy so far, and that is the relationship between propositions. You appear to be assuming that the propositions are not correlated. ... For example, one of the theorems states that Q(p^q) is equivalent to Qp ^ Qq.
Alan: That particular theorem is one that Tom and I have been debating over for several posts now. For the record I at least do not accept that Q(p ^ q) = Qp ^ Qq, for the very sort of reasons that you have indicated. Based on his last post, I think Tom may be coming around to the same point of view on this issue.
Magneton: It seems to me that to construct a truth table, one would need additional columns specifying the relational terms. Rather than just the p and q columns, you'd also need columns something like
p -> q; q -> p; p ->-q; q ->-p.
Alan: I think you are right that we do have to discuss the entailment relation "->" at some point. The difficulty, and it is a difficulty shared with other logical systems, is that entailment is NOT plausibly construed as a purely truth-functional relation. The closest approximation one can get in truth functional terms is the so-called "material implication". In standard mathematical logic this says that
(p -> q) = ~p v q
which means that the conditional "p -> q" is true so long as we don't have a true antecedent and a false consequent. This very quickly leads to counterintuitive results known as the "paradoxes of material implication". Thus, on this view, any conditional with a false antecedent (e.g., "If the moon is a cheesecake, then I'm a billionaire") or a true consequent (e.g., "If 2+2=4, then some roses are red") is automatically true. Attempts have been made to patch up the material implication so as to avoid the counterintuitive results (as with C.I. Lewis's proposed "strict implication") while preserving truth functionality, but these don't avoid all the paradoxes.
So basically, the issue of how to construe if-then is an outstanding problem in philosophical logic, and there doesn't seem to be any simple and precise way to describe entailment in extensional (i.e., set-theoretic) terms.
That being said, entailment is the fundamental logical relation, so indeterminacy logic has got to at least try to say something about it, or it will be seriously incomplete as a logic. I'm just not sure at this point how best to proceed.
Suggestions?
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Tom
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| Posted 11/17/2003 5:26 PM (GMT -6) | | Magneton, excellent points. We will (that's Z, not Z~ or Q) get to that (after Alan defends his thesis and takes a short vacation to reward himself on its success)!
Alan: Based on his last post, I think Tom may be coming around to the same point of view on this issue.
Tom: He IS! Sing it with us! (To the tune of "She'll be Comin 'Round the Mountain When She Comes)
Tom will come around the mountain when he comes,
Not might come around that mountain when he comes,
It is not the case that he won't,
Nor the case that he might not come,
Tom WILL come around the mountain when he comes.
He might bring some more dumb theorems when he comes,
He might bring some more dumb theorems when he comes,
It's determinately his case that,
When he tries he screws his case up,
He might bring some more dumb theorems when he comes.
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Tom
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| Posted 11/17/2003 6:10 PM (GMT -6) | | Alan-
Pleeeeeeease! I wanna revise my jive-theorems on the Non-Anal-Retentive Logic thread, but I don’t wanna misconstrue things again, so tell me if I’m understanding the conjunctions and disjunctions correctly:
Z(p ^ q) attributes Z to the conjunction ‘p and q’. That is, ‘p and q’ WILL obtain. All that’s needed to falsify this is for either Zp or Zq to fail to obtain, in which case both Zp and Zq must obtain (as your truth table shows).
Z~(p ^ q) attributes Z~ to the conjunction ‘p and q’. So, “p and q,” taken together, WILL NOT obtain. The conjunction won’t obtain. This doesn’t mean p cannot obtain alone or that q cannot obtain alone. It means only that “both p and q” will not both obtain together. All that’s needed to falsify this is for both Zp and Zq to obtain. Anything else is consistent with the argument.
Q(p ^ q) attributes Q to the conjunction ‘p and q’. That is, ‘p and q’ taken together, as a whole, might and might not obtain together. This is the same as saying the conjunction ~(p ^ q) might and might not obtain (because we’ve already agreed that Qp = Q~p). So all that’s needed to falsify this is for Z or Z~ to appear anywhere in our argument.
OK, now for the “or” arguments.
Z(p v q) attributes Z to the conjunction ‘p or q’ taken together as a single entity. That is, the whole deal ‘p or q’ WILL obtain. All that’s needed to this argument to hold is for either Zp or Zq, or both Zp and Zq, to obtain. Anything else falsifies it.
Z~(p v q) attributes Z~ to the conjunction ‘p or q’. So, ‘p or q’ taken together as a single entity WILL NOT obtain. All of the possible arrangements that would make Zp v Zp true would falsify our argument. Therefore, all that’s needed to falsify Z~(p v q) is for either Zp or Zq to obtain.
Q(p v q) attributes Q to the conjunction ‘p or q’. That is, ‘p or q’ taken together as a whole, might and might not obtain. This is the same as saying the conjunction ~(p v q) might and might not obtain (because we’ve already agreed that Qp = Q~p). So all that’s needed to falsify this is for either Zp, or Zq, or Z~p, or Z~q to appear anywhere in the argument.
I want to get this right. I think I’m following through on the distribution of the operators Z and Q and ~ over the variables just as you specified.
Come on, g’me a high five!
Tom | | Back to Top | | |
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Magneton
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| Posted 11/17/2003 6:56 PM (GMT -6) | | Alan: I think you are right that we do have to discuss the entailment relation "->" at some point. The difficulty, and it is a difficulty shared with other logical systems, is that entailment is NOT plausibly construed as a purely truth-functional relation. The closest approximation one can get in truth functional terms is the so-called "material implication". In standard mathematical logic this says that
(p -> q) = ~p v q
Magneton: I confess I don’t know what a truth-functional relation is or why the logic is required to be expressed in this form. Clearly as you’ve shown, the material implication is an inadequate substitute. I think this is because it is expressed in terms of the entities themselves (p and q) rather than the relation between them.
I am reminded of James Clerk Maxwell, who found that the nature of light was not to be found in Newtonian mechanics, but in the relation between electric and magnetic fields. He also proposed “that the relations between particles in a field of force must be thought of as constituting, in part at least, what particles actually are.” (TF Torrance, in his introduction to Maxwell’s A Dynamic Theory of the Electromagnetic Field http://www.mountainman.com.au/aether_2.html )
It seems (subject to my disclaimer of ignorance above) that to restrict oneself to the language of truth-functional terms is to seek a “Newtonian” solution to the problem, and remain forever at an impasse. A truly relational “Maxwellian” approach, which recognizes that relationships between entities are just as real as the entities themselves, may require different language.
Magneton
“Simplicity is desirable, in scientific and metaphysical explanations. But it is not the only intellectual virtue, and it turns into a vice if it is bought at the price of high improbability, or of omitting a significant range of relevant data.” – Keith Ward - God, Chance, and Necessity, p. 129
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Tom
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| Posted 11/18/2003 8:42 AM (GMT -6) | | Won't hurt to post this here as well.
I want to say that Alan was on the money with his truth table. I had misunderstood how the parentheses were being used. So crucify me! 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.”
So then:
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’.”
Tom | | Back to Top | | |
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Alan Rhoda
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| Posted 11/18/2003 10:26 AM (GMT -6) | | Tom, my comments are in blue, and the specific text commented on is in red. Cool? 
Tom: Z(p ^ q) attributes Z to the conjunction ‘p and q’. That is, ‘p and q’ WILL obtain. All that’s needed to falsify this is for either Zp or Zq to fail to obtain, in which case both Zp and Zq must obtain (as your truth table shows).
Alan: Omit last part. Not correct.
Tom: Z~(p ^ q) attributes Z~ to the conjunction ‘p and q’. So, “p and q,” taken together, WILL NOT obtain. The conjunction won’t obtain. This doesn’t mean p cannot obtain alone or that q cannot obtain alone. It means only that “both p and q” will not both obtain together. All that’s needed to falsify this is for both Zp and Zq to obtain. Anything else is consistent with the argument.
Alan: The part in red should say "All that's needed to falsify this is for either both Zp and Zq to obtain or for one to obtain and the other to be indeterminate."
Tom: Q(p ^ q) attributes Q to the conjunction ‘p and q’. That is, ‘p and q’ taken together, as a whole, might and might not obtain together. This is the same as saying the conjunction ~(p ^ q) might and might not obtain (because we’ve already agreed that Qp = Q~p). So all that’s needed to falsify this is for Z or Z~ to appear anywhere in our argument.
Alan: All that's needed to falsify this is for either p or q to be determinately not the case, or for both of them to be determinately the case.
Tom: Z(p v q) attributes Z to the conjunction ‘p or q’ taken together as a single entity. That is, the whole deal ‘p or q’ WILL obtain. All that’s needed to this argument to hold is for either Zp or Zq, or both Zp and Zq, to obtain. Anything else falsifies it.
Alan: Bingo! 
Tom: Z~(p v q) attributes Z~ to the conjunction ‘p or q’. So, ‘p or q’ taken together as a single entity WILL NOT obtain. All of the possible arrangements that would make Zp v Zp true would falsify our argument. Therefore, all that’s needed to falsify Z~(p v q) is for either Zp or Zq to obtain.
Alan: In other words, both Z~p and Z~q will obtain. All that's needed to falsify this is for either p or q to definitely obtain or for either p or q to be indeterminate.
Note: There may be a new theorem here: Z~(p v q) = Z~p ^ Z~q (an analogue of De Morgan's Law). It doesn't work for Z or Q, however.
Tom: Q(p v q) attributes Q to the conjunction ‘p or q’. That is, ‘p or q’ taken together as a whole, might and might not obtain. This is the same as saying the conjunction ~(p v q) might and might not obtain (because we’ve already agreed that Qp = Q~p). So all that’s needed to falsify this is for either Zp, or Zq, or Z~p, or Z~q to appear anywhere in the argument.
Alan: All that's needed to falsify this is for either p nor q to be determinately the case, or for both to be determinately not the case.
Tom: Come on, g’me a high five!
Alan: You got it, bro!  Appreciate your enthusiasm for this stuff.
God bless,
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Tom
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| Posted 11/21/2003 7:34 AM (GMT -6) | | Check out these two quotes from David Lewis’s Counterfactuals:
“I believe that there are possible worlds other than the one we happen to inhabit. If an argument is wanted, it is this. It is uncontroversially true that things might be otherwise than they are. I believe, and so do you, that things could have been different in countless ways. But what does this mean? Ordinary language permits the paraphrase: there are many ways things could have been besides the way they actually are. On the fact of it, this sentence is an existential quantification. It says that there exist many entities of a certain description, to wit ‘ways things could have been’. I believe that things could have been different in countless ways; I believe permissible paraphrases of what I believe; taking the paraphrase at its face value, I therefore believe in the existence of entities that might be called ‘ways things could have been’. I prefer to call them ‘possible worlds’.”(p. 84)
To which I’d like to say: If there exist ‘ways things could have been’ then there must now exist ‘ways things might and might not yet be’.
But as you read through Counterfactuals you notice that Lewis never thought of applying this to the future. He hints at it a couple of times (possibly in the quote below), but for the most part he talks about possibilities in terms of what “might have” or “would have” been. The indeterminacy logic we’re trying to express now is all there in past tense in Lewis. We just need determinacy and indeterminacy operators (Z and Q!) to provide the means for discussing these ‘ways things might and might not yet be’.
Here’s one passage in Counterfactuals that seems to indicate that Lewis thought of the future in determinate and indeterminate terms. He even created what seems to be to be an indeterminacy operator like our Q. Check it out:
“Suppose that our language has the following resources: (1) propositional variables, grammatically interchangeable with sentences; (2) existential and universal quantifiers E [should be a backwards ‘E’ but I can’t type it] and A [should be an upside down ‘A’ but I can’t type that either] that may be used to bind these variables; (3) the operators [] [a square, but I can’t type it] and * [the * should be a diamond shape figure but I can’t type that either] of…necessity and possibility; (4) the truth-functional connectives; and (5) a special one-place sentential operator O [not the capital ‘O’ but a circle; I can’t type it], called the sphericality operator. A sentence Op is to be true at a world i if and only if there is some sphere S around i such that p is true at all and only the worlds in S.” (p. 45)
Lewis talks about “spheres of accessibility” that I understand to be all the possible worlds accessible from this world i. Lewis’ O sounds like our Q, a future event that is neither necessary nor impossible. “It’s indeterminately the case that p” can only be true if p is accessible, actualizable, obtainable from THIS world. If you can get to p from where you are now, then Op (as Lewis notes it) or Qp (as we’ve been saying it) is true. If you can’t get there, then it’s not true. Not sure if I’m reading Lewis correctly, but given what he says in the first quote about believing this world might have turned out different in many ways, it makes sense to understand his Op as our Qp, as positing an event which might and might not happen.
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Tom
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| Posted 11/23/2003 7:53 AM (GMT -6) | | Consider…
Bring to mind the traditional square of opposites:
A—E
I—O
These four (A, E, I, and O) form the four corners of the square. Furthermore,
A = “will”
E = “will not”
I = “might”
O = “might not”
According to the logic of the square, A and E are contraries (they can both be false but can’t both be true) and I and O are sub-contraries (they can both be true but can’t both be false. Likewise, A and O are contradictory, while I and E are contradictory (they have opposite truth-values).
On a counterfactual square of opposites, the “will” and “will not” are replaced by “would” and “would not,” but the rules governing the relationship of the four props remains the same.
With that in mind, open theists argue that the traditional square allows for the possibility of subcontraries “might” and “might not” BOTH being true, in which case BOTH “will” and “will not” would be false. So, “x might and might not occur” describes and event x about which “x will occur” and “x will not occur” are both by definition FALSE. This is open theism pure and simple. If there is a single true “might and might not” proposition, the future is in that respect open and an omniscient God must know it as such, else God is not omniscient. God must know “x will happen” and “x will not happen” are both false, and God must also believe x’s occurring in this world is neither inevitable nor impossible. In case anybody hasn’t noticed, there is only one group of theists that argues there actually are any TRUE “might and might not” propositions describing the future. That is, of course, open theists.
To falsify the claim that the future is partly open as open theists claim it is, one must argue that THERE ARE NO TRUE “might and might not” propositions. And this is exactly what theological determinists, simple-foreknowledge Arminians, and Molinists attempt to do (each in their own uniquely unsuccessful ways!). All these adhere to ‘exhaustively definite foreknowledge’, meaning the future is entirely a matter of “will” and “will not” (or “would” and “would not” when speaking counterfactually).
I was just contemplating the implications of denying that there are any true “might and might not” propositions. Think about it. If there are no true “might and might not” propositions, then “might” still falsifies “will not” (and “would not”) but it no longer leaves open the possibility of whether “will” is true (and “might not” false) or “might not” true (and “will” false); for “might not” can’t be true (and “will” false) if “might” and “might not” are not in fact ever conjointly true. The effect of denying the existence of any conjointly true “might and might not” propositions is to equate every true “might” with true “will” and every true “might not” with true “will not.” So whenever a person says, “x might do y” she means “x will do y” (or “x would do y” if she’s speaking counterfactually). Likewise, whenever a person says, “x might not do y” she must mean “x will not do y” (or “x would not do y” if she’s speaking counterfactually).
But surely this is an awkward claim to make. Certainly nobody actually speaks this way in normal conversation. When we say, “John might come,” we don’t mean “John will come” or “John would come.” But this is all we could possibly mean if we believe all “might and might not” propositions are false. Every “might” would falsify “will not” leaving us with only one possible TRUE proposition, that is “will.” Likewise, every “might not” would falsify “will” and leave us with only one possible TRUE proposition, “will not.” Every time we said “might” we would necessarily mean “will” and every time we said “might not” we would mean “will not.” Strange indeed, but that’s what our language would mean “strictly” or “logically” speaking if we were to deny that there are any true “might and might not” propositions.
Now, one could argue that there are no true “might and might not” propositions, and that the only true propositions about the future are “will’s” and “will not’s” and still argue a use for “might” that does not entail “will” (and a use for “might not” that does not entail “will not”). For example, we may continue to use “might” and “might not” in normal conversation without implying either “will” or “will not” because we are not omniscient and don’t know what the truth of the matter is regarding x’s doing y. We know it’s either “x will do y” or “x will not do y,” but we don’t know which is which. So how do we talk about x? We can only say, “x might do y” or “x might not do y” depending on our expectations (which could also be fallible). This “might” is entirely epistemic. It’s an expression of ignorance from beginning to end. This sort of “might” (or “might not”) doesn’t even belong on the square and has nothing to do with falsifying either “will” or “will not.” All we mean to say with this “might” and “might not” is we don’t know if “x will do y” or “x will not do y” is true. Could be either one. Maybe “x will do y” is what’s true. Hey, maybe not. Maybe “x will not do y” is what’s true. Maybe not. Gee, we don’t know. Might be one or the other. This is a legitimate use of “might” and “might not” for non-omniscient beings like us humans. Even open theists can use “might” this way.
But I hope you notice that this particular use of “might” has nothing to do with the square of opposites, for it does not falsify anything at all. I wish I could go into this more, but I would bore you more than I already am. I hope others see what I mean here. We often use “might” when nothing whatsoever is known to be true OR FALSE about “what IS the case” with regard to x’s doing y. And THIS sort of “might” has no place on the square of opposites.
But arguing this use of “might” and “might not” doesn’t help determinists, Molinists, or simple-foreknowledge Arminians much, for though it’s perfectly understandable for a being that is NOT omniscient to talk this way, it’s quite difficult to account for how an omniscient being would use “might” or “might not” with this meaning if it’s the case that there are no true “might and might not” propositions. If “might” and “might not” (logically, or strickly, speaking) each entail “will” and “will not” respectively, what would an omniscient being who knows whether any future-tense “will” or “will not” (or “would” or “would not”) is true of false, be doing using “might” or “might not”? There’s no epistemological gap, not ignorance of the truth, to speak of in the case of omniscience that would account for an omniscient being using “might” as we ignorant humans might justifiably use “might” (as explained above) without intending to falsify or affirm anything regarding the “x will do y” or “x will not do y.” So, with this epistemic use of “might” out of the way, what other possible meaning could we give to God’s use of “might”? Remember, if there are no true “might and might not” props, then presumably for an omniscient being, every true “might” is a true “will” and every true “might not” is a true “will not.” That’s what “might” and “might not” would MEAN if it were believed to be the case that there exist no true “might and might not” props.
So, the implications for denying that there exist any true “might and might not” props is having to admit that every time God uses “might” he means “will” and every time God says “might not” he means “will not.” But what happens to the divine-human conversation when we interpret it this way? Very strange indeed.
Now, to be fair, we have to admit there is one meaningful use of “might” for an omniscient God which would not justify our concluding that the event in question is a “will,” and that would be a case in which God, knowing the truth regarding “x will do y” and “x will not do y,” nevertheless wished us to remain ignorant regarding this truth. In this case, God might say “x might happen” meaning, “As far as YOU’RE concerned x might happen (though you correctly believe I eternally know whether or not x will happen). Yet I require your ignorance on this matter.” I personally wouldn’t have a problem with God sometimes approaching things this way. As a parent I have to admit to often times approaching things this way. Perhaps it was best that my kids NOT know the truth about what would certainly happen. But I find it impossible to believe that EVERY divine use of “might” in Scripture can be made sense of on this basis.
I really don’t feel like proof-reading this, so I hope there aren’t too many typos!
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Tom
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| Posted 11/24/2003 1:34 AM (GMT -6) | | I’d like to suggest we distinguish between the following three uses of “might” and ask ourselves which one applies to God when God uses "might."
1) “Might” = Exhaustively Epistemic Indeterminacy
This is simple. Let’s assume that future event x is either determinately the case or determinately not the case. Either “x will happen” is true or “x will not happen” is true. Let’s assume also that I know this much about x. But I don’t know which is true. What can I say about x’s occurring? I’m talking normal conversation here, not logic-lingo. In every day conversation, what would I say about x? I’d say “x might happen.” But this is not intended to falsify “x will not occur” (which “might” on the square DOES do). Here I know that either “will” or “will not” is true but I don’t know which is which, so I say “x might happen.” As I said in the previous post, this “might” doesn’t appear on the traditional square. This is exhaustively, entirely, an expression of epistemic indeterminacy.
Example. Given certain circumstances, I know that a burglar either “will” or “will not” break into my home tonight. It’s true either that “It is determinately the case that the burglar will break into Tom’s home tonight,” or “It is determinately the case that the burglar will not break into Tom’s home tonight.” But I don’t know which is true. So what do I say? I saw to Anita, “Honey, a burglar ‘might’ break into our home tonight.” Am I thereby falsifying “A burglar will not break into Tom’s home tonight”? The “might” on the square would certainly falsify this. But is that what I mean? No, it’s not. And it’s perfectly logical that I use “might” this way, for epistemology and ontology are both at work. If a logician said, “Hey, you said ‘A burglar might break into your home tonight’? You must therefore believe that he ‘will not’ break into your home.” I’d reply, “Get a life outside your logic textbooks dude! I know that a burger either ‘will’ or ‘will not’ break in. But I DON’T know which is the truth, so I CAN’T falsify either one. Either one ‘might’ be true. So I’m sitting here on the sofa with my shotgun just in case.”
See? This “might” is exhaustively epistemological. It doesn’t express anything about the truth-value of either “will” or “will not.” What’s indeterminate here is my own beliefs about whether a burglar “will” or “will not” break into my home.
This is a legitimate use of “might” for us non-omniscient folks who often don’t know the truth about ANY of the possible propositions that embrace future event x. However, it is only non-open theist theists who are limited to “will” and “will not” regarding the future. Open theist who use this sort of “might” may in fact include “will,” “will not,” and “might and might not” in this use of “might.” I could retell the example above about the burglar and only change the fact that I know, for example, that one of the following three claims is TRUE: “A burglar will break into my house,” “A burglar will not break into my house,” and “A burglar might and might not break into my house.” I can know that one of these is true but NOT KNOW which is true. How would I describe the future break in? I’d say “A burglar ‘might’ break into my house.” But by this I would not be falsifying “will not.” I actually believe “will not” is possibly true. So I wouldn’t want to rule it out by falsifying it. I simply don’t know which is true. So my “might” is entirely an admission of ignorance about the truth of the matter, not a claim know what the truth of the matter is. We all use this “might.” Open theists embrace more by it than non-open theists. But in both cases it’s entirely, or exhaustively, epistemologically indeterminacy that’s being expressed.
2) “Might” = Partial Epistemic Indeterminacy. We’ve talked about this a lot. When all you know is that “x might happen” (on the square) is true, then you can conclude only ONE thing about the truth values of the other three propositions on the square, and that is “x will not happen” is false. You cannot know whether “x will happen” is true (and “x might not happen” false) or “x might not happen” is true (and “x will happen” false). The square allows for either possibility. So THIS “might” falsifies an ontological state of affairs (that state of affairs responsible for “x will not happen” being false), but that’s all the ontology it speaks to. With regard to the truth values of “will” and “might not” it is epistemologically open.
And we certainly speak this way in normal conversation. Somebody says, “Doc will not come to the party” and someone else falsifies this with, “No, Doc ‘might’ come to the party.” What’s the reply mean? Does it mean “Doc will come to the party”? No. All it means is that it’s not determinately the case that Doc will not come. He might show up. He might not. It might be determinately the case that he will come. It might be indeterminately the case that he comes. All that “might” on the square tells for sure is that “Doc will not come” is false.
Now, open theists have no problem using this “might” (falsifying “will not” and leaving open the question of “will” and “might and might not”). But here Molinists, determinists, and simple-foreknowledge Arminians have something to say. Since these all deny the possibility that conjoined “might and might not” is EVER TRUE, that is, that there are any true “might and might not” propositions, then they MUST argue that “might” and “might not” on the square are actually “contradictories” and not sub-contraries. Take note. If “might” is known to be true, then “will not” is known to be false and—since there are not conjointly true “might and might not” propositions—“will” must be true. Same applies on the other side with “might not.” If “might not” is true, then “will” is false and—given that there are not true “might and might not” propositions—“will not” must be true. Hence my point: If you deny that there are any true “might and might not” propositions, then there are only “will” and “will not” (or “would” and “would not” if you’re speaking counterfactually) propositions about the future, in which case “might” = “will” and “might not” = “will not.” I can’t think of a single example, biblical or otherwise, of how “might” and “might not” would be used in this way.
If follows then that if “might and might not” propositions are by definition false, then not only are “might” and “might not” contradictories (instead of sub-contraries) but so also are “will” and “will not” contradictories (instead of contraries). For as contraries, “will” and “will not” may both be false. But the only case in which “will” and “will not” may both be false is if “might” and “might not” are both TRUE. And if conjoined “might and might not” propositions are by definition false, then “will” and “will not” are by definition contradictory. They can no longer both be false. And they can’t both be true. That’s what “contradictory” props are!
To conclude, this second use of “might” (independently true) can meaningfully be used by open theists. But non-open theists, who deny that “might” and “might not” may be conjointly true, end up equating every true “might” with “will” and every true “might not” with “will not.”
3) "Might" (acutally, conjoined “might and might not”) = Ontological Indeterminacy. No need to belabor the point here. Open theists are the ONLY theists around who are arguing that there exist any true “might and might not” propositions. But it’s important to note that in every day conversation nobody does around conjoining the two. We simply say “might,” just as we would in cases (1) and (2) above. How do we know the difference in normal conversation between the “might’s” of (1), (2), and (3)? Usually context tells us what’s intended. Sometimes it may impossible for a hearer to judge which particular meaning of “might” is intended by somebody saying, “x might happen.” Usually context will fill in the blanks are people will understand either (1), (2), or (3) (except for non-open theists of course, who deny (3) and so redefine (2) to mean “might” = “will” and “might not” = “will not.”
The Divine “might”. What do non-open theists do here? The divine “might” is what corners non-open theists, because being omniscient, God cannot be thought of as expressing either might (1) or might (2) above. God knows all truths and believes no falsehoods. So what in the world could God be expressing about the future by saying, “x might happen” if he knows “x will happen” or “x will not happen” is true? The only possible explanation I can come up with is that God uses “might” when he knows “will” (or “will not”) because he wants us to remain in (1) above; that is, he wants us to remain ignorant of what the truth is regarding x’s occurrence. I admit this may work sometimes (gotta think on it), but it can’t explain every divine use of “might” or “if” or “maybe” or “perhaps.”
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Magneton
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| Posted 11/26/2003 7:53 AM (GMT -6) | | Tom,
Thanks for spelling out the meanings of ‘might.’ It’s helpful. If I may paraphrase the 3 forms of might,
(1) I know that there are deterministic laws in place that will determine whether or not x will happen. I don’t know the form of the laws, so I don’t know whether x will happen.
(2) I know there’s not a deterministic law preventing x from happening.
(3) I know there are no deterministic laws that would cause or prevent event x. The uncertainty is ontological.
It seems to me there is yet another case:
(4) I don’t know whether deterministic laws are in place that would cause or prevent event x. This is the case of total ignorance: as Sgt. Schultz of Hogan’s Heroes would say, “I know NOTHING.” 
I’m not clear on why you say only (3) is a “might and might not.” It seems to me in any of these uses of “might,” that “might not” is implied. To say “x might occur” is to say I’m not sure (or that no one could be sure as in case 3), which means that x might not occur.
The controversy relative to OVT lies in whether there is a truly ontological “might”. That “might” is conjoined to “might not” seems quite obvious and noncontroversial. Or am I missing something here?
It would also be helpful to clarify what you mean by “will” and “will not” (maybe even spelling out the various meanings of “will” and “will not” like you did with “might”).quote:
Tom: With that in mind, open theists argue that the traditional square allows for the possibility of subcontraries “might” and “might not” BOTH being true, in which case BOTH “will” and “will not” would be false. So, “x might and might not occur” describes an event x about which “x will occur” and “x will not occur” are both by definition FALSE. This is open theism pure and simple.
I find the language quite confusing. In this language, “x will occur” could be false, but later on, lo and behold, x does indeed occur. When you say, “x will occur” you apparently mean, “x is sure to happen,” or “it is inevitable that x will occur,” which could indeed be false even if later x does happen. So why not say it that way?
It seems more natural to me to say that “x will occur” and “x will not occur” are both INDETERMINATE in this case, and that “it is inevitable that x will occur” and “it is inevitable that x will not occur” are both FALSE.
And Tom, when you sort out what "will" and "will not" mean, you might as well go all the way, in honor of our former President, and spell out what the meaning of "is" is. 
Magneton
We are getting into semantics again. If we use words, there is a very grave danger they will be misinterpreted. - H. R. Haldeman | | Back to Top | | |
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Alan Rhoda
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| Posted 11/26/2003 8:47 AM (GMT -6) | | Laika: The way I look at it is, "will" has probability 1.0, "will not" has probability 0.0 and "might" has probability n. What I don't know is, why couldn't "might" include the end points? "will" and "will not" are just a subset of "might". "will" is a "might" whose probability is 1.0, "will not" is a "might" whose probability is 0.0. Then saying it's a "might" (indeterminate) doesn't make the case that a "will/will not" (inevitable) is false.
Alan: In at least one sense, "might" can include the endpoints. The "might" on the much-discussed square of oppositions is like this. The "might of ontological indeterminacy", however, cannot, for to say that something is really indeterminate would imply that its probability of occuring is greater than 0.0 and less than 1.0.
Happy Thanksgiving
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Alan Rhoda
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| Posted 11/26/2003 2:27 PM (GMT -6) | | Tom, I like your breakdown of possible meanings of "might". I can see that you've really thought about this. Good work!
One comment, which may just be another way of reiterating Magneton's point that there may be a fourth usage of "might": Why can't "might" occasionally have BOTH ontological AND epistemological significance? I don't mean PARTLY epistemic and PARTLY ontological (your second category), but your first and third categories together. It seems to me that some colloquial uses of "might" carry both senses at the same time. What do you think?
Alan
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Tom
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| Posted 11/26/2003 8:38 PM (GMT -6) | | Hi Magneton!
quote:
1) I know that there are deterministic laws in place that will determine whether or not x will happen. I don’t know the form of the laws, so I don’t know whether x will happen.
(2) I know there’s not a deterministic law preventing x from happening.
(3) I know there are no deterministic laws that would cause or prevent event x. The uncertainty is ontological.
It seems to me there is yet another case:
(4) I don’t know whether deterministic laws are in place that would cause or prevent event x. This is the case of total ignorance:
Your (4) is my (1): total ignorance. A non-open theist would use “might” in the sense of (1) above (and your (4)) to say “it’s either determinately the case that x will happen or determinately the case that x will not happen. I don’t know which is true, so all I can is, ‘x might happen.’” But an open theist, if totally ignorant about the truth of the matter, would have to include THREE states of affairs in this ‘might’ and say, “it’s either determinately the case that x will happen, or determinately the case that x will not happen, or indeterminately the case that x will happen. I don’t know which is true, so all I can is, ‘x might happen.’” It’s OK to use this sort of ‘might’. We do so all the time. It’s just that, logically speaking, open theists include more in it than non-open theists.
Also, on (2), remember that an open theist who knows that “will not” is false and therefore says, “x might happen,” remains ignorant about whether “will” or “might and might not” is true, that is, about whether “it is determinately the case than x will occur” or “it is indeterminately the case that x will occur” is true. But a non-open theist who KNOWS that “x will not occur” is false cannot remain ignorant about whether “will” or “might and might not” is true because he believes there ARE NO true “might and might not” propositions. So if he knows “will not” is false, he has to conclude “will” is true (and vice versa).
quote:
I’m not clear on why you say only (3) is a “might and might not.” It seems to me in any of these uses of “might,” that “might not” is implied. To say “x might occur” is to say I’m not sure (or that no one could be sure as in case 3), which means that x might not occur.
I used to think this too. But Doc and Alan went to work on me. Let’s say that you admit the three metaphysical states of affairs we’ve been talking about relative to x’s occurring:
(A) It is determinately the case that x occur
(B) It is determinately the case that x not occur
(C) It is indeterminately the case that x occur
Now, if any one of these is known to be TRUE, the other two are necessarily false, right? But if you only know that one is FALSE, can you conclude which of the other two is true and which is false? No. So, we should be able through whatever logical apparatus (square or triangle or notation, whatever) we employ to falsify any one of A, B, or C and leave open the question regarding the truth values of the other two.
OK, if you’re say that saying “x might occur” is to say…“x might not occur” you’re saying every “x might occur” entails the truth of “x might not occur.” You’re saying “might” and “might not” are either conjointly true or conjointly false. But the logic of the square (and our new triangle!) won’t allow this. Sub-contraries can be both true, but they can’t both be false. They may also be one true and one false. So let’s say you wanted to falsify (B) (x will not occur) but you don’t know which is true (“will” or “indeterminately that…”). What do you say? You say “x might occur.” But this cannot imply the truth that “x might not occur,” for if your “might” leaves open the possibility that “x will occur” is TURE, then it leaves open the possibility that “x might occur” is FALSE.
quote:
The controversy relative to OVT lies in whether there is a truly ontological “might”. That “might” is conjoined to “might not” seems quite obvious and noncontroversial. Or am I missing something here?
The truly ontological might you’re talking about IS the conjoined “might and might not” of the square. We’re saying there are some true “might and might not” propositions about the future. Our opponents are saying there are NO true such propositions. They wouldn’t deny that you can conjoint “might” and “might not” from the square, they just believe that all such propositions are by definition false.
quote:
It would also be helpful to clarify what you mean by “will” and “will not” (maybe even spelling out the various meanings of “will” and “will not” like you did with “might”).
Well, “will” means “it is determinately the case that p” while “will not” means “determinately the case that not p.” Does that not do it?
quote:
I find the language quite confusing. In this language, “x will occur” could be false, but later on, lo and behold, x does indeed occur.
Exactly! The propositions “John Kennedy WILL be assassinated in 1963” spoken before Kennedy was assassinated was a FALSE proposition, even though Kennedy was assassinated, for it was (for all we know) presumably the case before he was assassinated the he might and might not be assassinated. It’s a little strange, I know, to say of some contingent event when it happens to occur that it was false before it occurred that “it will occur,” but that’s in fact the essence of what the open view claims: given the history of the world up to the instant x occurs, that history could conceivable be repeated exactly as it occurred with x not occurring. And if that’s the case, if there are some events that are contingent in this sense, then it’s false to say they “will” occur even though they end up occurring.
quote:
It seems more natural to me to say that “x will occur” and “x will not occur” are both INDETERMINATE in this case, and that “it is inevitable that x will occur” and “it is inevitable that x will not occur” are both FALSE.
OK I see. But I don’t think this works. “x will occur” = “it is inevitable that x occur” and “x will not occur” = “it is inevitable that x not occur.” “x will occur” = “it is determinately the case that x occur” and “x will not occur” = “it is determinately the case that x not occur.” You can’t say “It is DETERMINATELY the case that x occur” is INDETERMINATE and be using “determinate” and “indeterminate” in the same ontological sense.
quote:
And Tom, when you sort out what "will" and "will not" mean, you might as well go all the way, in honor of our former President, and spell out what the meaning of "is" is.
Let’s let Bill Clinton do that!
quote:
Alan: One comment, which may just be another way of reiterating Magneton's point that there may be a fourth usage of "might": Why can't "might" occasionally have BOTH ontological AND epistemological significance? I don't mean PARTLY epistemic and PARTLY ontological (your second category), but your first and third categories together. It seems to me that some colloquial uses of "might" carry both senses at the same time. What do you think?
Not sure what you mean. Perhaps an example would help. But I think epistemology and ontology DO both overlap entirely whenever we know the truth about all three states of affairs regarding some future-tense proposition. There would be no gap between what we know about the determinacy vs indeterminacy of x’s occurring and what there is to know about the determinacy vs. indeterminacy of x’s occurring. Is that close? Another possibility of their overlapping might be a correct “guess.” Prior talks about this. One could not know the truth about x’s occurring and so guess that “x will occur," and then x occurs. Let’s assume that the truth of the matter was in fact that “x will occur” was true. In this case epistemology and ontology overlapped. But I don’t know how the guesser would know that they really overlapped, since x’s actually occurring can just as easily be explained on the basis of its having been entirely contingent. Only God would know if his guess was REALLY correct! Hey, but this means that when we GUESS that “Tom WILL bring Cohibas next time he visits St. Paul” and I do in fact bring them next time I visit, it could still be the case that my guess was, logically speaking, FALSE, even though I brought Cohibas, for my bringing Cohibas was presumably contingent! I might NOT have brought them! But no one would want to deny that my guess was correct. Hmm. So we may have a popular use of “will” and “will not” that is epistemological as well, that is, that does not claim it is NOW determinately the case that “Tom will bring Cohibas.” It only “guesses” what the outcome might be and though this is expressed in terms of what “will” happen, it’s not the “will” of the square. More to obsess with!
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Tom
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| Posted 11/27/2003 10:16 PM (GMT -6) | | Magneton-
Hope you had a nice Thanksgiving! I’m on leftovers for the next four days!
Do it this way (it’s rather simple)…
1) Take our three states of affairs. You’ve already expressed them. They are a) It is determinately the case that x occur (x’s occurring is inevitable; given the present state of the world, x is gonna happen), b) It is determinately the case that x not occur (x’s occurring is impossible; given the present state of the world, x will certainly not happen), and c) it is indeterminately the case that x occur (x is neither inevitable nor impossible).
2) Keep in mind that these are ONTOLOGICAL states of affairs. They represent the only possible realities that form the future. So if any one of these three states of affairs is true (and only ONE can be true about a proposed event) then the other two must be false. But it follows that if you ONLY know that one is FALSE, you cannot on this basis alone know which of the other two propositions describing a proposed event is true and which one is false.
3) Lay the three states of affairs out there and one by one, think through how YOU would go about falsifying each one. I mean, how you would ONLY falsify it. Obviously you can falsify any one of the three by correctly claiming another of the three is TRUE. But right now you don’t know which one is true. All that you know is that one, and only one, is false.
So, start with:
a) “It is determinately the case that x occur” (or “x will occur’).
Falsify this, but not by positing as true either of the other two—(b) or (c). How would you do it? All you know is that this is false. You don’t know what the truth is about the other two states of affairs. Whatever word(s) you choose to falsify this cannot amount to affirming anything regarding the truth value of the other two. Falsify away!
Then do the same for:
b) “It is determinately the case that x not occur” (or “x will not occur”).
Falsify this without affirming what the truth values of the other two (a and c) are.
Then lastly, do the same for:
c) “It is indeterminately the case that x occur.”
Falsify THIS without saying anything about the other two (a and b) of our three states of affairs.
So, tell me. How did you word your three falsifiers in every day conversational speech?
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Tom
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| Posted 11/28/2003 10:27 PM (GMT -6) | | quote:
Magneton: Tom, I’ll try to falsify these statements:
(1) It is determinately the case that x occur
(2) It is determinately the case that x not occur
(3) It is indeterminately the case that x occur
with these:
(1) There is nothing that guarantees that x will happen.
(2) There is nothing that prevents x from happening.
(3) Whether x happens or not is already determined.
I’m not sure if this meets your criteria, but I still don’t see what this has to do with conjoined mights.
Hi Magneton-
Here’s what it has to do with “might’s”: On the square of opposition, “might” and “might not” falsify (1) and (2):
“x will occur’ is falsified by “x MIGHT NOT occur” (which is just like your first falsifier; x is not inevitable). All you need to falsify “x will occur” is to show that “x might not occur.”
“x will not occur” is falsified by “x MIGHT occur” (which is just like your second falsifier; x is not impossible or out of the question). All you need to fafsify “x will not occur” is to show that “x might occur.”
Your third falsifier is right on too. Here’s where Doc’s conjoined “might and might not” come in. Look at the double reference in your third falsifier: “whether x happens or not is already determined.” You’ve just falsified “x might and might not happen.” Or in other words, if “It is indeterminately the case that x occur” is true then both “will” and “will not” are false. And if BOTH “will” and “will not” are false then BOTH the “might” and the “might not” that falsify “will” and “will not” are true. See that? Thus, “indeterminately the case that x” = “x might and might not occur.” There’s your conjoined “might and might not.” There’s indeterminacy.
But we can’t assume that “might” by itself, when true, posits this indeterminacy. It may be the case that “will” is true (and “might not” false). Think of it this way. If you only know that your (2) second falsifier “There is nothing that prevents x from happening” is true (that is, “x might happen” is true), what could you conclude about states of affairs (1) and (3)? Could you conclude that since “x might happen” is true that state of affairs (3) is the truth of the matter? No. It might be that state of affairs (1) (“x will occur”) is the truth of the matter. If all you know is that “x might occur” is true you know that “x will not occur” is false, but you wouldn’t know whether “x will occur” is true or whether “x might and might not occur” (i.e., x’s occurring is indeterminate) is true.
See how indeterminacy is expressible in terms of “might and might not” but how “might” by itself or “might not” by itself do not necessarily posit indeterminacy?
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