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| Open Theism Discussion Board > Public Forums > The raging debate continues here... > Philosophia Christi Article on "Neo-Molinism" | Forum Quick Jump
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Alan Rhoda
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Date Joined May 2002
Total Posts : 680
| Posted 10/31/2003 2:17 PM (GMT -6) |   | Wow, a lot has happened on this thread in the past couple of days. Tom, Doc, geebob, do you guys ever sleep?  I see I've got some catching up to do.
quote:
Tom wrote:
1) If there are three metaphysically distinct states of affairs, AND…
2) If these metaphysical states of affairs ... are what is behind a proposition’s being true or false), THEN…
3) Which of these three states of affairs makes the supposed “weaker might” true or false, (a), (b), or (c)? Which metaphysical state of affairs makes “It is not determinately not the case that p” (= the weaker “might”) TRUE while also making "It is not determinately not the case that not p" (= the weaker "might not") FALSE, (a), (b), or (c)? ... It seems to me that if the "weaker" might is a genuine “might” distinct from the “might” of indeterminacy, there must be some (weaker?) state of affairs that is metaphysically distinct from the three you’ve already identified which grounds this "weaker might." This would suggest a fourth distinct metaphysical state of affairs. And what, pray tell, would THAT be?
Alan: Good question, Tom. My response is that the "might" of the square corresponds to the state of affairs in which (a) is false and either (b) or (c) is true. Similarly, the "might not" of the square corresponds to the state of affairs in which (b) is false and either (a) or (c) is true.
Tom: I see your point. But your first sentence, as far as I can tell, makes no claim of “fact” to which “I might agree with you” counters which would be why we’d call it ‘counter’-factual, unless your sentence assumes the "facticity" of "the uses of 'might' are not restricted to nonconditional sentences."
Alan: I think you misunderstand the use of the term "counterfactual", Tom. The term refers to a conditional (i.e., if-then statement) in which the antecedent is false. That's all. It doesn't matter what the truth value of the consequent is. And anyway, my example did purport to state a fact, specifically, a conditional fact--IF the uses of 'might' are not restricted to nonconditional sentences, THEN I might agree with you. This conditional is counterfactual because the antecedent is false, but it nevertheless states a FACT. That may sound paradoxical but it's not when you keep in mind that "counterfactual" just means a conditional with a false antecedent. In other words, it is the antecedent, not the consequent that has to "counter" a fact in order to have a counterfactual.
Doc: I wonder if there was some truth in Wethner's claim that I don't believe in middle knowledge. ... Calling future tensed "mights" and "woulds" counterfactual presupposes that the future is exhaustively FACTUAL.
Alan: Au contraire. Counterfactuality has to do with the antecedent of a conditional, not the consequent. That being the case, there is no reason why it can't be a fact that "If God creates Peter and his life runs a certain way, then Peter might not deny Christ." Sans creation, this is a counterfactual, since Peter and the world history up till the time of his decision to deny or not deny Christ don't yet exist. But if Peter still has libertarian freedom with respect to denying Christ, then this "might" counterfactual is true, eternally so.
Doc: So I'm wondering, could the open view of "mights" and "woulds" be collapsed into God's "natural knowledge" and "free knowledge"? God's knowledge of what all possible agents "would" and "might" do is his natural knowledge. God's knowledge of what actual agents "would" and "might " to is part of his free knowledge (knowledge of facts). HENCE IT SEEMS THERE'S NO NEED FOR GOD TO HAVE MIDDLE KNOWLEDGE. ... Is it the case that God's pre-creational knowledge of what possible agent x "would" and "might" do is "natural"? Is God considering, "if I create this agent he would do x in situation y and might do x' in situation y'" beyond his "natural" knowledge? No, I suspect neo-Molinism is sunk.
Alan: I think what you are hitting on, Doc, is a version of the grounding objection to Molinism. For neo-Molinist middle knowledge to reduce to God's free knowledge implies that such knowledge is grounded in God. The Molinist, on the other hand, wants there to be a logical space between God's natural knowledge (his knowledge of all possibilities and necessities) and God's free knowledge (his knowledge of all actualities). It is claimed that God's knowledge of "would" counterfactuals of creaturely freedom lies in such a logical space. What open theists have argued is that the very idea of a "would" counterfactual of creaturely freedom (where "would" implies that the probability = 1) is a contradiction in terms--if it is true that agent X would do Y in conditions Z then X is not free in Z with respect to Y, and if X is free in Z with respect to Y then it is false that the creature "would" do Y in Z; rather, it is true that X might and might not do Y in Z. So I think your observation is correct, but it turns out to be a good thing because it shows that the truth value of "conjoined mights" is in fact grounded. And because it is grounded in God, it is knowledge that he can providentially apply in creation.
Well, that's all I can post for now. My wife is waiting with dinner. God bless.
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Tom
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| Posted 10/31/2003 2:30 PM (GMT -6) | | Doc: I see no reason to deny that some "woulds" are dependent on the nature and character we created with (habitus infusus), though others are dependent on the character we freely develop (habitus acquirus).
Tom: Right. So are you agreeing with me? Couldn't tell. So how are future tense propositions about what an agent "would" do counterfactual in either case (infusus or acquirus)? What's the "fact" being countered?
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Tom
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| Posted 10/31/2003 2:58 PM (GMT -6) | | Alan: I think you misunderstand the use of the term "counterfactual", Tom. The term refers to a conditional (i.e., if-then statement) in which the antecedent is false. That's all. It doesn't matter what the truth value of the consequent is.
Tom: That’s the assumption I WAS working with.  If the antecedent is known to be false, the proposition is counterfactual. No problem. That’s not what I’m talking about.
If counterfactuals are nothing more than conditionals in which the antecedent is false (which I’m conceding), how can future tense conditionals (i.e., a future tense antecedent followed by a “might” or a “would”) constitute a counterfactual? For example: “If Tom comes to town next year, he might bring Cohibas.” The antecedent “If Tom comes to town next year” posits the condition. Do you know this to be false? On what basis, then, do you insist this is a counterfactual proposition? You can only do so by assuming the antecedent to be false. The only truth-value that attaches to the antecedent here is whether or not my visiting St. Paul next year is truly a possibility. And the only thing that can make it false is it’s now being impossible that I visit St. Paul next year. Truth is, I’m planning on visiting next year, but only God knows whether or not this antecedent is true or false. To call ALL “mights” counterfactuals by definition is to assume that ALL future tense conditionals are false. But you don’t do that. So, assuming the antecedent here is TRUE, Alan, do you still want to call “If Tom comes to town next year, he might bring Cohibas” a counterfactual?
Alan: That may sound paradoxical but it's not when you keep in mind that "counterfactual" just means a conditional with a false antecedent. In other words, it is the antecedent, not the consequent that has to "counter" a fact in order to have a counterfactual.
Tom: Exactly. So what about conditionals with true antecedents? Or conditionals with antecedents the truth value of which is unknown to us?
Alan: Counterfactuality has to do with the antecedent of a conditional, not the consequent. That being the case, there is no reason why it can't be a fact that "If God creates Peter and his life runs a certain way, then Peter might not deny Christ." Sans creation, this is a counterfactual, since Peter and the world history up till the time of his decision to deny or not deny Christ don't yet exist.
Tom: The fact that Peter and world history do not yet exist sans creation is why we cannot call “If God creates Peter and his life run a certain way, then Peter might not deny Christ” a counterfactual proposition. The antecedent “If God creates Peter and his life runs a certain way…” is not false just because Peter doesn’t yet exist. The antecedent posits the possibility of Peter’s existing and the possibility of his life running a certain way. Assuming that sans creation Peter’s existence and the course of his life being posited in the antecedent are real possibilities, wouldn’t you call a conditional expressing these possibilities TRUE and not FALSE? And if the antecedent is true, would you still call this a counterfactual?
Alan, you and Doc are the experts here. I just hang around to annoy you both. I know there's not a single trained logician out there who is likely to agree with me either. But I'm ready to question anything and everything! 
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Tom
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| Posted 11/1/2003 9:39 AM (GMT -6) | | I friggin got it!
OK, I think I can show why “might” and “might not” cannot be other than conjointly true or conjointly false when the truth about reality (viz., Alan’s three metaphysical states of affairs) is known. And I have a new name for it, Doc. It’s not the Triangle of Counterfactuals, it’s the…drum roll please…
Triangle of Non-quantifiables
But FIRST, let me say something about my claim that not all “would’s” and “might’s” are counterfactual…
Alan, you seem to have argued that all “would’s” and “might’s” are counterfactual like this:
P1 All propositions containing antecedents that are, or are believed to be, FALSE constitute counterfactual propositions.
P2 All propositions containing antecedents that are, or are believed to be, false have either a “would” clause or a “might” clause in the consequent to the antecedent.
P3 Therefore propositions containing “would” or “might” in the consequent are all counterfactual propositions.
P4 Therefore all “mights” and “woulds” function as counterfactual operators.
Maybe not so exact, but that’s the gist of what I understood. But this is clearly not a valid argument. P1 and P2 are true. P3 however is false. Not all propositions containing “would” or “might” in their consequent clauses have false antecedents. Some contain antecedents which are, or are believed to be, TRUE. These propositions do not fall under the class of propositions P1 defines as counterfactual. Thus, not all “If…then” propositions are counterfactual and not all “would’s” and “might’s” function as counterfactual operators. If the “If…” clause is a future tense conditional which is, or is believed to be, TRUE, then the requirements of counterfactuality are not met.
OK, on to why I think "might" and "might not" must be conjointly either true or false when the truth about the three metaphysical states of affairs is known.
Alan: Good question, Tom. My response is that the "might" of the square corresponds to the state of affairs in which (a) is false and either (b) or (c) is true. Similarly, the "might not" of the square corresponds to the state of affairs in which (b) is false and either (a) or (c) is true.
Tom: But this “might” appears to be an epistemological deal, what we say when we don’t know. OK. Remember your three states of affairs?
(a) It is determinately the case that NOT p.
(b) It is determinately the case that p.
(c) It is indeterminately the case that p (or neither determinately the case that p nor determinately the case that not p).
OK, I go to a party. Somebody says, “Doc isn’t coming” or “Doc will not come.” The person is claiming state of affairs (a) with regard to Doc’s coming: “It is determinately the case that not p.” I want to falsify this. The only way I can do so (watch this Doc) is to lay claim to one of the other two of Alan's three metaphysical states of affairs OR (this is Alan's weaker "might") to claim that one of the other two states of affairs is the state of affairs that is true. I can say “No, Doc WILL come,” or I can say “Doc might and might not come.” That is, I can say “It is determinately the case that p [viz., Doc will come]” (I almost wrote “It is determinately the case that Doc will p!” )--that is, I can lay claim to metaphysical state of affairs (b)--OR I can lay claim to metaphysical state of affairs (c) and say, “It is indeterminately the case that Doc will come,” OR (and this is a viable third possible response to the guy that falsifies his claim) I can say, "I'm not sure which state of affairs is true, whether 'It is determinately the case that Doc will come' or 'It is indeterminately the case that Doc will come.' But I know that one of these two, and only these two, is true. And since either state of affairs (b) or (c) will falsify your claim that Doc will not come, you're wrong." It's being true that "Either state of affairs (b) or (c) is true" also falsifies "Doc will not come." But--and this is important--laying claim to "Either state of affairs (b) or (c)" is entirely different than laying claim to (b) or to (c). The latter two (claiming state of affaris (b) or claiming state of affairs (c)) express what is metaphysically the case. The third claim expresses only ignorance about what is metaphysically the truth of the matter.
What your solitary “might” does is say this: “It might be the case that it’s determinately the case that Doc will come OR it might be the case that it’s indeterminately the case that Doc will come. Hey buddy, either state of affairs (b) or (c) is true; I don’t know which one is true. But I know it's true that these are the only two possibilities, and so state of affairs (a) regarding Doc's coming is not true.” This is how I understand you, Alan, to have defined “might” on the square.
Several things.
First, this weaker "might" is not a “might” about a metaphysical state of affairs. It can’t be. Gee, I hope I can explain this. Of your three metaphysical states of affairs, only one is characterized by a “might” at all, and that’s your (c). The other two are determinately the case (either that or that not). So your true “might” is merely a DENIAL of one particular metaphysical state of affairs (state of affairs (a) to be precise). It doesn't describe a "state of affairs" itself which might be. It describes what "might" be true with regard to the remaining two states of affairs. It's a might of choice between them, not a might of ontology. And since the falsity of any ONE of your three states of affairs demands that one and only one of the other two states of affairs be TRUE without telling us which, it follows that all we can say is that it “might” be that state of affairs (b) is true or it "might" be that state of affairs (c) is true. That's what your weaker "might" does. It posits epistemological indeterminacy (I think you know what I mean) regarding the truth-value of the remaining two metaphysical states of affairs where the truth value of the fist state of affairs is known to be false.
But it is not helpful to bring such questions onto the square. It's not helpful to insist that props (A) and (E) on the square each express a true metaphyiscal state of affairs (determinately that and determinately that not) but then insist that props (E) and (I) do NOT each express a true metaphysical state of affairs when true; these only express our ignorance about the what is true metaphysically even when they're TRUE! They affirm no true metaphysical state of affairs, that is, when they're true. It's when they're false that "might" and "might not" express a true metaphysical state of affairs about their contradictories. They don't say anything about the determinacy or indeterminacy of the event they describe. You get to affirm truthfully “indeterminately the case that” only by DENYING the other TWO possible states of affairs, and you can't do that by affirming that one of the three is false. You have to say which is TRUE. Saying one is false gives you a "maybe" about the other two, not a "maybe" about the future. The square isn't wrong on this so much as it is bias and incomplete. I can express what is "determinately the case" with ONE TRUE PROPOSITION (A). I can also express what is "determinately not the case" with ONE TRUE PROPOSITION (E). But traditional logic will not let me express what is "indeterminately the case" with one true proposition. To do that I have to falsify (A) and (E) with TWO TRUE PROPOSITIONS (I and O). This is a prejudiced approach to expressing the truth.
You have three metaphysical states of affairs: “determinately that,” “determinately that not,” and “indeterminately that.” Only one can be true and any one, when true, falsifies the other two. Granted, no one, when false, can falsify either of the other two. Either one "might" be true or false. This is what your weaker "might" and "might not" is designed to express, but in my opinion there's no need to find a place for this on the square. There's no place for it on the triangle and it works fine.
But remember, using “might” and “might not” can only be a temporary way of expressing our ignorance about the state of reality, that is, about your three metaphysical states of affairs. As soon as the truth be known about the three states of affairs, both “might” and “might not” MUST collapse and be either conjointly true or conjointly false. To say “might” is true and that “will” and “might not” are simply UNKNOWN on the sole basis of "might" being true is fine so long as we’re expressing our ignorance about two of the three possible metaphysical states of affairs. But to say “‘might’ is true and ‘might not’ is false” is self-contradictory if the truth be known about all three metaphysical states of affairs. There is no metaphysical state of affairs that would render “might” true and “might not” false (unless you want to include necessary truths like "God exists"--but that's another can of worms). There is no metaphysical state of affairs that can render this coherent. So, Alan’s independently true “might” is really only epistemologically independently true. It attributes truth value to our ignorance of the truth of the matter regarding the determinacy of the event posited in the proposition. A true "might" doesn’t entail a truth value for “might not.” In truth, both "might" and "might not" must be either conjointly true or conjointly false. Alan's weaker true "might" is a floating epistemological "might" that expresses our ignorance about whether conjoined "might and might not" is true or false. A true "might" doesn't even tell us the truth about itself ultimately! The standard rule that subcontraries can be one true and the other false in the ultimate sense of truth about reality is not correct. On the contrary, with respect to Alan’s three metaphysical states of affairs, “might” and “might not” collapse into being conjointly either true or false.
It boils down to this, Doc. If you want the square to express epistemological limitation, or rather, ignorance about the truth of the three states of affairs, then we need to leave the square as it is. If we know nothing about the truth value of the props on the square except that prop (I) (“x might come”) is true, then we can only SAY that it “might” (there’s the weaker “might”) be the case that prop (A) is true and (O) false or visa verse. Independently true “might’s” and “might not’s” express only what can be CONCLUDED about one of Alan’s three states of affairs, namely, that that state of affairs in question is false. So if we want a figure that accounts for what can be SAID about reality by less than omniscient beings, then go with the square (though it will still have some problems). But if you want a figure that accounts for reality itself, then go with the triangle.
This is why, Doc, we were earlier forced to admit that the relationship between the THREE points on our new triangle (determinately the case that, determinately the case that not, and indeterminately the case) is “contrary” all the way around and not “contradictory.” The reason is: If you know that one metaphysical state of affairs is TRUE, you know the truth values of the other two. But if all you know is that one is false, you cannot know the truth value of the other two. And this is all that independently true "might" on the square does; it only knows that one of the three states of affairs is not the case. It can't tell us what the case is about the other two states of affairs. Look at the three points of our triangle again (“will do y,” “will not do y,” “might and might not do y”).
But we really must insist that a) if one begins with the independent truth of either “might” or “might not” on the square, nothing can be known about the determinacy or indeterminacy of the event in question, and b) as soon as the truth be known about the event in question, that is, as soon as the truth be known about Alan’s three metaphysical states, both “might” and “might not” collapse into being conjointly either true or false. It can never be metaphysically the case (the truth being known about Alan's three metaphysical states of reality) the “might” is true and “might not” is false. That’s what has been friggin hounding Doc and me for months. You have THREE possible metaphysical states of affairs regarding the determinacy and indeterminacy of future events, but we're trying to account for the truth values of these three states with a FOUR sided square. And to boot, the subcontraries "might" and "might not" are left on the square to give non-omniscient beings like us a way to logically express our ignorance about the ultimate truth of reality.
There is no square for God when it comes to the future. There is only a triangle.
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Tom
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| Posted 11/1/2003 11:13 AM (GMT -6) | | One final objection to the square.
If we begin with the truth of “x will come” the standard rules for the square demand that a) the subaltern “x might come" be true, that b) the contrary "x will not come" be false, and that c) the contradictory “x might not come” be false. Thus, it would seem that the square has pinned down the four corners of reality. All four describe what is ultimately the truth about x's coming. Trouble is, you cannot fit Alan's three metaphysical state of affairs onto this four-cornered claim to reality. None of Alan's three states of affairs can be behind its being true that “x might come” and false that “x might not come” (the subcontraries). Consider Alan’s three metaphysical states of affairs again:
“Determinately the case that p”
“Determinately the case that not p”
“Indeterminately the case that p”
If it’s true that “x will come,” then the state of affairs behind THIS is the first in the list above, that is, “It is determinately the case that x will come.” Boom. There ya are. But if it’s determinately the case that x will come, then it is FALSE that “It is indeterminately the case that x will come,” in which case it’s false that “x might and might not come,” in which case we have on the square a true “might” and a false “might.” Now we finally catch the square with its pants down to the floor. We have at one and the same time on one and the same square a true “might” (“x might come” which MUST be true as the subaltern of “x will come”) and a false “might” (the first “might” of the false “x might and might not come”). Other similar irreconcilable combinations can be produced. It's getting more rediculous by the hour. I'm going to bed!
Now, someone might object, "But the true 'might' that is the subaltern of the true 'will' in this case is NOT the SAME 'might' (doesn't occupy the same place on the square) as the (false) 'might' which appears first in the conjointly false "might and might not." Oooo, that's interesting. So where are we going to place the conjointly false "might and might not" which expresses the truth value of Alan's third metaphsical state of affairs, or that fact that "It is not indefinitely the case that x might and might not come"? Where does this fit on the square? Well, it's right there living on the same two subcontrary points of the square! On the one hand the false "x might not come" of the conjointly false "x might and might not come" is right there on its spot as the contradictory of our true "x will come." We don't notice the freakiness going on because "x will not come" (to which "x might not come" is subaltern) is also false. We only notice the pants are down when we try to overlay Alan's three metaphysical states of affairs with it being true that "x might come" and false that "x might and might not come." Lay 'em over top one another and there they are, a true "might" and a false "might" coexisting on the same little corner of the square.
The square sucks for attributing truth values to propositions laying claim to what is determinately or indeterminately the case about the future. We must keep to the triangle when discussing the future. If we know only that “It is determinately the case that x will come” is FALSE, then let’s express our ignorance about which of the other two options is the true metaphysical state of affairs and not insist that our triangle express this ignorance in propositional terms ON THE TRIANGLE as the square attempts to do on the square.
Doc, you have your revolution. Go for it twin.
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Tom
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| Posted 11/2/2003 10:39 AM (GMT -6) | | I know I know, you’re getting tired of me. Sorry. I just wasn’t sure I explained myself well at all the past two or three posts. After reading through it I thought it was a bit convoluted at times.
A true “might” on the square amounts to a denial of one of Alan’s three metaphysical states of affairs, in other words, it is false that “it is determinately the case that not p.” This is all the truth value a true “might” posits regarding a metaphysical state of affairs. At the same time a true “might” posits an epistemological state of affairs (as opposed to a metaphysical state of affairs) regarding the truth value of the remaining two props (A and O) on the square.
A true “might not” does the same thing. It denies “It is determinately the case that p” (one of Alan’s three metaphysical states of affairs). This is all the truth value a true “might not” posits regard the truth of reality. At the same it a true “might not” posits an epistemological state of affairs (as opposed to a metaphysical state of affairs) regarding the truth value of the remaining two props (E and I) on the square.
But notice this too. When a true “might” says, “Hey, ‘will not’ is false and either ‘will’ or ‘might not’ is true,” we should be careful. The “might not” held out as possibly true by a true “might” is NOT the independently true “might not” that’s staring at you from the lower right hand corner of the square. It can't be. See, a true "might" affirms the possibility of a true "might not." But an INDEPENDENTLY true "might not" affirms that "might" could be false and "will not" true! See it? But an independently true "might" cannot affirm the possibilty of it's own falsity (which it would be doing if the "might not" it affirms as possibly true is the independently true "might not"). Tell me you all see this! The "might not" that a true "might" affirms as possibly true, then, is the true “might not” of the conjointly true “might and might not” that’s knocking on the door of the square from our triangle! Boy, now I'm REALLY confident that the triangle is the only way to go when discussing this stuff.
There are two levels or spheres constantly bumping into each other and trading off between the traditional square (which deals with ontological AND epistemological states of affairs) and the triangle Doc and I have been toying with (which deals only with ontological states of affairs).
The reason the square works fine all the way round for some props and not for others is that some props describe quantifiable states of affairs and other do not. You can have a true “might” and a false “might not” in ontological terms IF the state of affairs is quantifiable. We discussed an example above: “All grass is green.” In this case the state of affairs being described is quantifiable. Consequently, “Some grass is green” is true (that’s the I prop on the square) and “No grass is green” is false (that’s the O prop on the square). End of story.
But this won’t work for non-quantifiable (not sure that’s the term I want to use) states of affairs, like “x will do y.” If we follow through and fill out the truth values of the other props on the square according to its own rules, we’re left with “x might do y” being true and “x might not do y” being false. But the reality behind "x will do y" being true cannot be quantified in such terms. If it’s TRUE that “x will do y” then it’s false that x’s doing y is indeterminately the case. Sorry to repeat it, but it’s important because it shows how the square is prejudiced against one possible state of affairs, Alan’s “indeterminately that case that….” The only prop that can express “indeterminately the case that…” when TRUE is “x might and might not do y.” And if “x will do y” is true then it's false that "It is indeterminately the case that x do y." If we leave this on the square and fill out all the truth values that follow from "x will do y" being true, we'd have a true “might” (the independent subaltern of “x will do y”) and a false “might” (the conjoined “might” in the false “x might and might not do y”).
My whole point is simple. Independently true “might” and independently true “might not” affirm an epistemological state of affairsp, that being, “We don’t know which of Alan’s three possible states of affairs is TRUE; we only know it’s EITHER ‘determinately the case that x do y’ OR ‘indeterminately the case that x do y’.” In this case independently true "might" means “Either determinately the case that p OR indeterminately the case that p.” So long as we are ignorant of which state of affairs is TRUE, independently true “might” remains true and no truth value can be assigned to “x will do y” and “x might not do y”. But once the metaphysical truth be known about “x will" the epistemological state of affairs (viz., our ignorance regarding whether x’s doing y is determinately or indeterminately the case) resolves itself to reality (to what is and is not the case) and “might” and “might not” collapse into conjointly true or conjointly false “might and might not.”
Another important point is this: An omniscient being would NEVER know "might" on the square to be independently true, for that implies ignorance regarding the truth value of "will" and "might not." For God there IS NO SQUARE when it comes to the future. There is only a triangle.
Lastly, I was reading David Lewis’s Counterfactuals (which is why I can’t sleep; that book is giving me a migrane!), I read where he agreed with me (though he’d probably say I agree with him!) that “would” and “might” are only sometimes counterfactual. It was like I was reading my previous post! Lewis came right out and said (don’t have the quote here) that the antecedent must be false, or be believed to be false, in order for the consequent “would” or “might” to constitute a counterfactual. He also pointed out that the antecedent of a counterfactual proposition can’t be future tense. So I’m in good company. I feel a little better!
A might-counterfactual (which Lewis admits is actually a “might have” because the antecedent is past tense and assumed false, so the consequent describes what “might have been”) can only be true if the consequent describes a state of affairs that was actualizable/possible before the antecedent was rendered false. Here Lewis sounded like an open theist.
So, Doc, I’m wondering if your calling all “might’s” counterfactuals was confusing to Werther. If he’s familiar with Lewis (and he did reference him) he might have assumed you meant what Lewis meant when he limited might-counterfactuals to propositions having false antecedents. You, of course, were talking about might-counterfactuals with antecedents assumed to be true (If z obtains, x might do y) and simple indicative conditionals (“x might do y”). Perhaps if you could be more specific from here on out. If you’re talking about what “might have been” (consequent) had things been different (false antecedent) you’re talking about might-counterfactuals. But if you’re talking about what “might be” then you’re talking about simple indicative conditionals.
Finally, in my opinion (haven’t found it in writing yet and am not likely too, but I’m pretty confident of this now) you can have a true past-tense “might” (“might have”) with a true antecedent. The open view demands this actually. We now argue that given the same conditions, agent x might have done differently. We might say, “If the conditions under which Oswalt shot Kennedy were no different than they were (true antecedent), Oswald might not have shot Kennedy (assumed true consequent).” Only God knows if this is true, but it’s certainly possible that it’s true. All it amounts to is saying “What is now history was once an open future and could have turned out differently under the same circumstances.” Lewis has a section on props employing “would” and “might” with true antecedents too. I’m not sure whether “might” in my example about Kennedy is a counterfactual. The antecedent is true (so it doesn’t fit the standard definition of counterfactuals), but it is past tense (and so historically necessary).
Fun stuff!
Tom
Somebody say I'm not crazy!
Mephi, I don't know about Neo-Molinism. I think it might be history. | | Back to Top | | |
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Tom
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| Posted 11/2/2003 7:53 PM (GMT -6) | | Mephi and geebob-
It seems to me that we don’t need middle knowledge either. I’d say simply that before creation God’s knowledge included all logically possible worlds with all the logically possible choices and scenarios. This knowledge itself includes “would’s” and “might’s” whose antecedents are true. That is, “If I create world x with agent y and she becomes through free choice solidified with respect to z, she WOULD do q in situation p.” Some may want to call this a counterfactual. I wouldn’t. But it doesn’t matter. The entire proposition is conditional. World x MIGHT be created with agent z. Then, agent z only MIGHT become solidified with respect to z. Then again, solidified agent z only might find herself in situation p in which case she WOULD do q.
Once God creates a specific world all the other possible worlds that this world doesn’t include become false. They could have existed and so were true. Now that can’t and so are false. NOW you have the possibility of counterfactual propositions, and their antecedents would all describe these once possible worlds (and perhaps worlds that never were possible) and so would be false. As time moves forward in our world also, you have the stuff of counterfactuals because you can now form false antecedents with consequents describing what WOULD HAVE or MIGHT HAVE happened. Now, granted, you can have a counterfactual with a false future-tense antecedent describing (an "If...then" where the "If" is future tense AND false). But usually only God would know if these are true or false antecedents since it describes the future (and we're not omniscient). But some such props are obviously false, like: “If Tom wakes up a woman tomorrow morning, he would have his hair done.” This is false, or at least is assumed false, because my waking up a woman is not possible (as far as we know). This “would” is a counterfactual. Let me adjust what I previously said then: Some future tense antecedents can be false (I earlier said they couldn't be; but this doesn't change much at all) and so the “would” or “might” of the consequent can be counterfactual. But all such counterfactuals would be FALSE (because their antecedents are false). If we believe a future tense antecedent to be TRUE, however, the requirements for counterfactuality are not met and the "would" or the "might" in the consequent is not counterfactual. These props simply describe an open future (EVEN those with "would" in their consequent clauses. Why? Because the antecedents posit "that which is indeterminately the case" and the "would" depends upon this possibility occuring.).
All God needs to act providentially is knowledge of all these possible states of affairs. God does know “would’s”, for sure, but a true “would” can only be providentially useful to God if the antecedent is TRUE, that is, if it describes what is possible (in the “might and might not” sense). But in this case it wouldn’t be a counterfactual. True counterfactuals provide God with no providential advantage. They’re no more useful to God than simple foreknowledge, because God would come by knowledge of them too late logically speaking to use them or do anything about them.
Tom | | Back to Top | | |
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Tom
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| Posted 11/2/2003 10:12 PM (GMT -6) | | I friggin got it, got it, got it!
This is getting clearer by the hour. Check this out. Let’s look at the square with each of Alan’s three metaphysical states of affairs in the place of the propositions that affirm them. Can't fit the props onto the square here. The square is:
A-E
I-O
A= "will" = "It is determinately the case that p"
E= "will not" = "It is determinately the case that not p"
I= "might" = "It is either determinately the case that p or indeterminately the case that p"
O= "might not" = "It is either determinately the case that not p or indeterminately the case that p"
This is what the traditional square gives us. The “might” (I) and “might not” (O) do NOT posit indeterminacy when independently true. But (and this is what I see now) neither can they both be TRUE. It can’t be true BOTH that it is “Either determinately the case that p or indeterminately the case that p” AND “Either determinately the case that not p or indeterminately the case that p.” This confirms that the “might” and “might not” of the square express an ontological state of affairs with regard to the falsified proposition but only an epistemological states of affairs with regard to the other two propositions. So, even with the square you're really only working with a triangle with regard to ontology.
What about our “might and might not” positing “it is indeterminately the case that p”? Isn’t this merely the conjoining of the same “might” and “might not” of the square? Friggin NO! If you conjoin the “might” and “might not” of the square you conjoin (that is ADD together) their INDEPENDENTLY TRUE MEANINGS and get:
It is false that "x will not do y" and either "determinately the case that x will do y" or "indeterminately the case that x do y" (that's your independently true "might" for ya) AND at the same time it is false that "x will do y" and thus either "determinately the case that x will not do y" or "indeterminately the case that x do y” (that's your independently true "might not" for ya).
This appears to be a self-contradictory claim to me. The “might and might not” we open theists argue posits ontological indeterminacy is an "IS" (a single indivisible truth claim) and isn't and "ARE" (two independently true claims that "are" indeterminacy). It's something else that isn't even acknowledged on the square! Calling it conjoined "might and might not" is not really accurate because conjoining "might" and "might not" of the square gives you a self-contradictory proposition, not indeterminacy.
The square only accidentally acknowledges “indeterminately the case that p” by conceding the possibility that both “will” and “will not” can be false. But there's no single prop on the square that falsifies both "will" and "will not." You can't get to it by afirming both "might" and "might not" as true because adding the independently true meanings of each gives you garbledigook. We have to hand it to the undeniable power of indeterminacy itself for not allowing Western logic to silence its voice. Indeterminacy, like love(!), will find a way! It keeps popping its head up in what the square says is logically possible (conjointly false “will” and “will not”) but which the square gives us no way of AFFIRMING. It has nothing to do with “might” and “might not” on the square. Our indeterminacy operator is knocking on the door of Western logic asking for a place at the table.
Conclusion? There is no single proposition on the square that affirms “indeterminately the case that p.” You have to trip into indeterminacy accidentally by conceding the possibility that “will” and “will not” may both be false, but, counterfactually speaking, “might” and “might not” cannot both be true (that is a self-contradiction), so there’s no way to GET to falsifying “will” and “will not.”
When logicians admit the possibility of “might” and “might not” both being true they are equivocating on the meaning of “might.” “Might” cannot at the same time mean “either determinately the case that p or indeterminately that case that p” and conjoin with “might not” (which means “either determinately the case that NOT p or indeterminately the case that p”) and produce anything coherent, much less “indeterminately the case.”
Now we MUST have a triangle. It’s not optional. I previously thought it didn’t matter because we can get to affirming “indeterminately the case that p” by affirming the truth of both “might” and “might not.” But you can’t conjoin THESE two operators. You have to have a proposition which AFFIRMS “indeterminately the case.” If you don’t have such a proposition you have no way of affirming an indeterminate state of affairs.
Done, finished, outta there!
So, there IS NO SUCH THING as a SQUARE of propositions expressing all that can be expressed about the determinacy vs indeterminacy of future events. There is no such animal. There is only a Triangle of Non-quantifiable truths.
What about if all we know is that ONE prop on the triangle is false? Isn’t it still the case that all we can SAY is that either of the other two “might” be true? Yes. But we do this math in our heads. Don’t mix propositions expressing epistemological states of affairs with propositions expressing ontological states of affairs. If you do, then make sure you have a separate point on your figure for each prop. If you enlarge the square to a five sided pentagram (pentegon?), and make the fifth point “indeterminately the case” then fine. Work it out. Or if you’re working with the triangle and you want to include propositions expressing what “might” be true about two of Alan’s metaphysical states of affairs if all that is known is that one is false, then enlarge the triangle and make it a square (which I'll try to do below). But don’t remove the only proposition which, BEING TRUE, affirms “indeterminately the case that p.”
Check this out. What I suggest is a Triangle of Alan’s metaphysical states of affairs. It’s the same triangle we posted before. Here it is:
(I don't think affirming indeterminacy with "might and might not" is helpful anymore. I'm looking for another way to say it. Nor would I call this a Triangle of Counterfactuals, 'cause there's nothing counterfactually going on here whatsoever. But we'll deal with that later.)
Now, using your imagination, add a floating epistemological quantifier, a guy that stands opposite a solitary false proposition (any one of the three, doesn’t matter--just draw an imaginary line from the false prop through the triangle and out again then stop, that's where we'll place our epsitemological quantifier) and says, “Either one of the remaining two props is true since this prop is false.” He floats around the triangle and stands opposite a prop and falsifies it. That’s all this quantifier is responsible for doing. (I ventured that determinacy and indeterminacy are themselves not quantifiable, and I still hold to that; maybe “epistemological quantifier” isn’t the right term to use for our friend. I think it’s OK, ‘cause he’s not quantifying what is known about reality [that’s done: “x will do y” is FALSE. He’s quantifying what is NOT known about reality, viz., whether “will not” or “might/might not” is TRUE]). If ALL we know (that’s important too, ‘cause if you know two props that are false then Mr. Quantifier goes away) that “x will do y” is false, the quantifier (who is not an official member of our ontological triangle, he’s just a floating epistemological handyman) stands way opposite THIS false prop (forming a square actually, where the “might not” would be) and falsifies it and in falsifying it says, “It is either determinately the case that x will not do y or indeterminately the case that x do y.” If on the other hand we know that “x will not do y” is false, the quantifier stands opposite THIS false prop (forming a square—dotted line please, not a solid line!) and falsifies “x will not do y” and in so doing affirms, “It is either determinately that case that x will do y or indeterminately the case that x do y.” Lastly (and this options is completely missing form the standard square), if we know that the bottom prop, the “might and might not” (whatever we call it), is false, then our epistemological quantifier (not ontological quantification, which is an impossibility) stands opposite this false prop and affirms, “It is either determinately the case that p or determinately the case that not p.”
(I have a great .pdf file with a graphic of this. Can anybody post it on a website and give us the URL for it? Laika? Did you URL the last triangle for us? Can I send you this one too?)
So, we can only posit true states of affairs on a triangle of determinacy vs indeterminacy, and the three points would be Alan’s three metaphysical states of affairs. It would only be a square (with a dotted line too!) in as much as our epistemological quantifier is able ONLY to deny the truth of one of the three props on the triangle.
Tom
PS I see that as I've evolved in the past few posts I earlier argued that conjoined "might" and "might not" on the square can, when the truth of all three metaphysical states of affairs be known, only be either conjointly true or conjointly false. Now I hope it's clear that the "might" and "might not" of the square can only be conjointly FALSE when the truth of the matter be known, since these both express ignorance regarding the truth of the matter. We need to find a way to express "indeterminately the case that p" other than "conjointly true 'might and might not'." Any suggestions? | | Back to Top | | |
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Tom
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| Posted 11/3/2003 4:40 AM (GMT -6) | | Thanks Laika! I sent you the pdf file. Let us know what you have a URL for it.
Tom | | Back to Top | | |
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Tom
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| Posted 11/3/2003 8:17 AM (GMT -6) | | Alan-
Perhaps this question will force my issue to the surface…
Given your three metaphysical states of affairs…
(a) It is determinately the case that p.
(b) It is determinately the case that not p.
(c) It is indeterminately the case that p.
We can with one true proposition (viz., “might not”) falsify (a) “determinately the case that x will do y” and be left with “either (b) determinately the case that x will not do y OR (c) indeterminately the case that x will do y.”
AND
We can with one true proposition (viz., “might”) falsify (b) “determinately the case that x will not do y” and be left with “either (a) determinately the case that x will do y OR (c) indeterminately the case that x will do y.”
BUT…
Where do we go on the square to with one true proposition falsify (c) “It is indeterminately the case that x will do y” SO THAT (and this is the clincher) we are left with “It is either (a) determinately the case that x will do y OR (b) determinately the case that x will not do y”?
Now, we CAN falsify (c) “indeterminately the case that x will do y” with one true proposition, either “x will do y” or “x will not do y”, but this is not to falsify (c) in such a way as to leave us with “either ‘will’ or ‘will not’.” I trust you see this inconsistency in the square. I can only guess as to the presuppositions about creation and reality that are behind this strangeness of the square. It ought not be so.
Notice that in falsifying state of affairs (a) or (b) we do not posit a TRUE metaphysical state of affairs that does the falsifying. We posit only an “either/or” between the remaining two states of affairs. Not so with falsifying state of affairs (c). You can’t falsify this on the square and leave yourself ignorant of whether state of affairs (a) or (b) is the truth. Why?
Why in the world would logicians and philosophers give us a single proposition for affirming “determinately the case that p” and a single proposition for affirming “determinately the case that not p” but not give us a single proposition for affirming “indeterminately the case that p” (and instead make it as difficult as possible to get to state of affairs (c))?
Doc, I’m spent. I’m done. I’m finished. I’m empty. My brain is mush. The revolution is in your hands.
Tom | | Back to Top | | |
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Tom
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| Posted 11/3/2003 9:09 AM (GMT -6) | | Thank you Laika! Great!
OK, the graphic Laika posted illustrates what I mean by working with a triangle with respect to propositions expressing Alan's three metaphysical states of affairs. Assuming "x will do y" is FALSE, we can only then affirm that it 'might' be the case that "x will not do y" is true OR it 'might' be the case that "x might/might not do y (for lack of a better term; it's "indetermiantely the case" that I mean)" is true. I think the graphic is pretty self-explanatory.
Point is: It's a triangle with respect to ontology, but a square with respect to epistemology. But when you DO have the square come into play (that is, when we DON'T know which state of affairs is TRUE but only that one is FALSE) you have only ONE quantifer (not two quantifiers ["might" and "might not"] as in the case of the traditional square).
I'm calling the proposition that falsifies "x will do an "epistemological qualifier" because though it falsifies a real state of affairs it cannot affirm a TRUE state of affaris. It's epistemologically open with respect to what state of affairs is true, thus "epistemological quantifier."
I'm hoping Laika will be kind enough to post just one more. I took this example of "x will do y" being false to illustrate my point, but the next graphic will illustrate this with all three states of affairs and one floating quantifier.
I know, I know. I'm nuts. But I'm right on this one. I might be off a bit here and there on expressing it, but the basic claim is right on I think.
Tom
PS The lines across the top and alon the right side (each with a question mark with regard to the truth value of "will not" and "might/might not") were supposed to be dotted lines, but when I wrote them to pdf they bled. Oh well. I wanted dotted lines to point out that the quantifier lies outside the triangle.
Tom | | Back to Top | | |
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DrBob
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| Posted 11/3/2003 9:43 AM (GMT -6) | | Mr. Boyd,
This is truly interesting. Your discussion on this thread sounds very much like the discussion I heard last March. I was invited to attend a conference last year and the discussion centered on the open theism debate and the possibility that this theological category was outside theological orthodoxy. It seemed to me that the speakers were all agreed that your propositions were logically consistent with themsleves, but were not clearly in line with Scripture. I read your "Letters to a Skeptic" and was thoroughly entertained with your encounter with your father, but found numerous faults in your presuppositions, for example about God's love. You categorically state that the "only way" certain things can be true is to see God from your open view. As I read, I noted other theologically and logically consistent ways to explain your view. I am sure you have heard all of these before, but it amazes me that you continue down the path that lowers God to the level of a finite creature. And then your discussions of molinism and intelligence intrigue me. Where can I get a copy of this article, and in it, do you explain what you think is the infinite intelligence of God, (and do you differentiate it from infinite knowledge)? These probably sound sophmoric to you, but I have just begun this quest.
Bob | | Back to Top | | |
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Alan Rhoda
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| Posted 11/3/2003 11:02 AM (GMT -6) | | Whoa, Tom. Slow down. I'm still trying to catch up.
Tom: On the standard square of opposites, the subcontraries I and O are ‘quantifiers’.
Alan: Not exactly. The terms "some", "all", and "no" are the quantifiers. A, E, I, O propositions are not quantifiers but quantified expressions.
Tom: They express the relationship between quantities, or parts, of a whole.
Alan: More generically, they express relations among sets. Virtually all formal logic reduces in one way or another to set theory. Thus, "some" is a subset of "all". And "none" refers to an empty set. In modal logic, the modal terms are defined on the set of possible worlds, where a "world" is a maximal state of affairs. Given bivalence, a maximal state of affairs is one in which every propositions is either true or false.
Tom: The question our discussion has led me to is this: Are ALL states of affairs quantifiable? If yes, then "X will do y in z" is quantifiable, and “might” and "might not" are its quantifiers.
Alan: Are all states of affairs quantifiable? I would say "yes" in principle, though the quantity would have to be a nondenumerable order of infinity. My reason is this: take any two maximal states of affairs S1 and S2. These states are either distinct or they are not. If not distinct then by the law of the identity of indiscernables we only have one state of affairs. If they are distinct then by the same law we have two (count 'em) states of affairs. So any two states of affairs that differ in any respect are distinct. So we can form the set of all mutually distinct states of affairs and quantify on that set, though, as already mentioned, the quantity will be nondenumerable.
geebob: I would think that when you combine possible worlds with presentism, interestingly, you get something that is very much like a process metaphysic as the world is always becoming a new world. But of course your not commited to any of the baggage of process. ... True counterfactuals fluctuate through time and they are not frozen in God's "free knowledge" or his middle knowledge. For example, we could say that if joe passes a bar on his way home, he may or may not stop at the bar to drink his sorrows away. As if he continues to stop at the bar, his character will continue to develop in the wrong way to the point that joe would stop at the bar to drink his sorrows away if he passes it on the way home. And that counterfactual may hold until joe makes some other libertarian free choices that will move that would back into the arena of the might such as joining AA.
Alan: I agree with you, geebob. As a maximal state of affairs, a possible world is kinda like a freeze-frame snapshot, a way things could be at some particular instant. But the actual state of affairs is continually changing, and if the future is partially open then we are not locked into one possible world from eternity past. Rather our world, the actual world, moves around within the space of possible worlds depending on the free decisions of God's creatures. Future-tense counterfactuals can then be defined relative to the currently actual possible world.
Tom: If counterfactuals are nothing more than conditionals in which the antecedent is false (which I’m conceding), how can future tense conditionals (i.e., a future tense antecedent followed by a “might” or a “would”) constitute a counterfactual? For example: “If Tom comes to town next year, he might bring Cohibas.” The antecedent “If Tom comes to town next year” posits the condition. Do you know this to be false? On what basis, then, do you insist this is a counterfactual proposition?
Alan: The truth value of a proposition depends on whether it corresponds to the currently actual possible world. The proposition "Tom comes to town next year" claims it to be a settled fact that Tom will come to town next year. Thus, its truth value depends on whether or not that fact is now settled as true. If it is, then the antecedent is now true and we have no counterfactual. If it is not, then we have a counterfactual. Now whether we call a given conditional a counterfactual depends on our assumptions about what the currently actual possible world is like. Your coming to town next year might in fact be settled as true, yet if it doesn't seem settled to me then I will regard it as a counterfactual. If I thought your coming was in fact settled as true, then I would say "when Tom comes" and not "if".
Tom: The fact that Peter and world history do not yet exist sans creation is why we cannot call “If God creates Peter and his life run a certain way, then Peter might not deny Christ” a counterfactual proposition. The antecedent “If God creates Peter and his life runs a certain way…” is not false just because Peter doesn’t yet exist. The antecedent posits the possibility of Peter’s existing and the possibility of his life running a certain way.
Alan: I disagree. The antecedent "God creates Peter ..." affirms more than a mere possibility. It affirms that God has in fact created Peter, a claim which is not true unless and until God does in fact do so. So sans creation the antecedent is false.
Love the interaction, Tom. I'll try to engage with your more recent posts later today if I get a chance.
Alan
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Alan Rhoda
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| Posted 11/3/2003 12:17 PM (GMT -6) | | Welcome to the discussion, Bob.
quote:
I read your "Letters to a Skeptic" and was thoroughly entertained with your encounter with your father, but found numerous faults in your presuppositions, for example about God's love. You categorically state that the "only way" certain things can be true is to see God from your open view. As I read, I noted other theologically and logically consistent ways to explain your view. I am sure you have heard all of these before, but it amazes me that you continue down the path that lowers God to the level of a finite creature.
I would appreciate it if you would specify what you think Dr. Boyd's faulty presuppositions are, what these other theologically and logically consistent explanations are in your view, and why you think open theism lowers God to the level of a finite creature. Thanks.
quote:
Where can I get a copy of this article, and in it, do you explain what you think is the infinite intelligence of God.
The article is in the latest edition of the journal Philosophia Christi, and yes it does develop the idea of the infinite intelligence of God.
Alan | | Back to Top | | |
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DrBob
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| Posted 11/3/2003 12:57 PM (GMT -6) | | I will pull my copy out and return to this discussion board and post my thoughts, probably Wednesday.
Bob | | Back to Top | | |
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Tom
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| Posted 11/3/2003 6:17 PM (GMT -6) | | quote:
Tom: On the standard square of opposites, the subcontraries I and O are ‘quantifiers’.
Alan: Not exactly. The terms "some", "all", and "no" are the quantifiers. A, E, I, O propositions are not quantifiers but quantified expressions.
OK, they’re quantified expression. Close enough. Plus, I only suggested that I and O are quantified expressions, not A and E.
quote:
Tom: If counterfactuals are nothing more than conditionals in which the antecedent is false (which I’m conceding), how can future tense conditionals (i.e., a future tense antecedent followed by a “might” or a “would”) constitute a counterfactual? For example: “If Tom comes to town next year, he might bring Cohibas.” The antecedent “If Tom comes to town next year” posits the condition. Do you know this to be false? On what basis, then, do you insist this is a counterfactual proposition?
Alan: The truth value of a proposition depends on whether it corresponds to the currently actual possible world. The proposition "Tom comes to town next year" claims it to be a settled fact that Tom will come to town next year. Thus, its truth value depends on whether or not that fact is now settled as true. If it is, then the antecedent is now true and we have no counterfactual.
Exactly. IF you know the antecedent to be false you have a counterfactual. But you appear to be only admitting as candidates for ‘true’ and ‘false’ antecedents those conditionals that express either state of affairs (a) “determinately the case that p” or (b) “determinately the case that not p.” But if state of affairs (c) “indeterminately the case that p” can be just as equally as (a) or (b) the TRUTH about the future, by what logic are you saying it cannot be the antecedent of an "If...then" conditional? It can NOW be true that state of affairs (c) is the truth about my coming next year, in which case the only truthful way to express it would be "Tom might come to town next year." It's “indeterminate.” What decides whether “If Tome comes to town next year” is a true antecedent or not is whether or not Tom's coming to town next year coheres to one of your three states of affairs regarding the future. And in the case we can assume (though only God knows for certain) that my coming IS a possibility.
quote:
Your coming to town next year might in fact be settled as true, yet if it doesn't seem settled to me then I will regard it as a counterfactual. If I thought your coming was in fact settled as true, then I would say "when Tom comes" and not "if".
Again, for some reason you’re admitting antecedents expressing either state of affairs (a) or (b) of your metaphysical states of affairs. But these aren’t the only REAL states of affairs. If “Tom might come to St. Paul next year” can be true with regard to reality (state of affairs (c)), then you cannot refuse it as a candidate for a true antecedent, and we’d express this true possibility as an antecedent with “IF Tom comes to town next year….”
quote:
Tom: The fact that Peter and world history do not yet exist sans creation is why we cannot call “If God creates Peter and his life run a certain way, then Peter might not deny Christ” a counterfactual proposition. The antecedent “If God creates Peter and his life runs a certain way…” is not false just because Peter doesn’t yet exist. The antecedent posits the possibility of Peter’s existing and the possibility of his life running a certain way.
Alan: I disagree. The antecedent "God creates Peter ..." affirms more than a mere possibility. It affirms that God has in fact created Peter, a claim which is not true unless and until God does in fact do so. So sans creation the antecedent is false.
But I didn’t say “God creates Peter…” and so imply more than a mere possibility. All I expressed in the antecedent was the possibility that God create Peter, and the possibility that Peter become solidified, and the possibility that Peter find himself in circumstances y. You don’t seem to want to recognize the possibility that true POSSIBILITIES can be antecedents.
Of your three states of affairs (determinately the case that p, determinately that case that not p, and indeterminately the case that p), assuming the TRUTH is that “It is indeterminately the case that p” and assuming p is Tom’s coming to town next year, this would be expressed as “Tom might/might not come to town next year.” Let’s assume that there exists another TRUE “indeterminately the case that…” which follows if I DO end up coming to town, and that is “Tom might bring Cohibas.” Thus, “IF Tom comes to town next year, he might bring Cobhibas.” The antecedent expresses the truth that Tom’s coming to town is “indeterminate” and the consequent expresses the truth that Tom’s bringing Cohibas is “indeterminate” provided I come.
Blessings,
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Tom
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| Posted 11/4/2003 1:52 AM (GMT -6) | | Buckle your seat-belt Alan...
Here’s the graphic expanding on the previous one I posted arguing for a triangle of metaphysical states of affairs with a floating epistemological quantifier. Here is the same thing but with all three of Alan’s states of affairs involved. The inner triangle is solid, but the outer larger triangle is supposed to be a dotted line only.
Some comments:
I called this the Triangle of "Quantifiable" States of Affairs. Ooop. I earlier offered that Alan's three states of affairs were not quantifiable. Maybe I'm using these words to mean something else. Not sure. Just ignore the title. We'll get to that later.
I have no idea if “epistemological quanitifier” is the right expression. It is certainly true that “might” and “might not” on the standard square FALSIY one of the three possible states of affairs. But after that it’s epistemologically ignorant regarding the truth value of the remaining two states of affairs. So, on my graphic you’ll see the smaller inner circle with A, B, and C, Alan’s three metaphysically distinct states of affairs. If any one is true, the other two are false. But if any one is false, it’s the case that one of the remaining two is true and the other false, but one cannot conclude which is which if the only truth value known is that the first is false. This falsifier, or EQ, Epistemological Quantifier, stands OUTSIDE the triangle of metaphysically distinct states of affairs and falsifies. It should be pretty self explanatory. Again, the falsifer does speak directly regarding a metaphysical state of affairs but only in that it falsifies one of the three (and so I place a solid arrowed line from the EQ to the falsified state of affairs) but it doesn't attribute truth value to the other two states of affairs. On this the EQ is ignorant and so if we draw lines from the EQ to each of the two states of affairs to its left and right, the line ought to be a dotted line to show that truth value is not being attributed.
Notice this. You have a triangle of metaphysical states but you have a square (for those of you who like squares) when the only truth value known is that one state of affairs is false. The fourth prop added is the EQ. But you don’t have ONE square. You have THREE squares depending on which of the three metaphysical states of affairs is falsified. If any one EQ prop is true, then a square is formed with that EQ prop and the three metaphysical states. The false metaphysical state stands opposite the EQ and the truth value of the other two states is unknown. There can only be ONE EQ relating to the triangle of states at a time. For two EQ’s to be true, two metaphysical states would be false, in which case we’d know which is true and wouldn’t need the EQ’s at all.
See the three squares the are formed with each EQ and the three metaphyisical states?
Look at this. The standard square is there also. Remove the top EQ that falsifies “inderterminately the case that p.” The traditional square doesn’t even recognize the existence of such a falsifier (evidence of it’s prejudiced worldview). Now, remove the bottom center point of the inner triangle that affirms state of affairs (C), or “indeterminately the case that p.” With (C) removed and the top EQ that falsifies (C) removed, what d’ya have left? You have the friggin traditional square! It's right there. I'll I've done to the traditional square is add the bottom center prop expressing "indeterminately the case that p" (and why should logic NOT recognize this state of affairs independently just like state of affairs (A) and (B)?) and add a falsifier for this prop. “Determinately the case that p” ("will") and “determinately the case that not p” ("will not") across the top, and “might” and “might not” (the two EQ's at the bottom far left and right), each falsifying its contradictory, is the traditional square we're familiar with. What is missing from the traditional square is a prop that affirms as true “indeterminately the case that p” and a prop (like “might” and “might not”) which only falsify this.
Jump in Doc, the water’s warm!
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Tom
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| Posted 11/4/2003 2:17 AM (GMT -6) | | Mephi: 2) The four-sided shape formed by your EQ(s) is a rhombus, not a square.
Tom: THAT's the word! A rhombus or something. Obviously not a square. But it is a four sided figure, and since wer'er talking about logical relations, it gets the job done.
Mephi: 3) It'd be nice if you did a little something on the Peter thread. You're Doc's twin, remember.
Tom: I'm scared to go near that thread!
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Alan Rhoda
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| Posted 11/4/2003 12:42 PM (GMT -6) | | Tom: Exactly. IF you know the antecedent to be false you have a counterfactual.
Alan: I didn't say that counterfactuality depends on our state of knowledge. I said it depends on the truth value of the antecedent with respect to the currently actual state of affairs.
Tom: But you appear to be only admitting as candidates for ‘true’ and ‘false’ antecedents those conditionals that express either state of affairs (a) “determinately the case that p” or (b) “determinately the case that not p.”
Alan: Not so. For the purpose of assessing whether a given conditional is a counterfactual or not, we treat the antecedent as a proposition that is affirmed to be determinately true. The justification for this is that ALL propositions, even "mights", make determinate truth claims. That's just what it is to assert a proposition. Thus if you say "It is possible that Tom comes to town next year" then you are claiming that it is determinately true that it is possible for Tom to come to town next year. With respect to conditionals, the antecedent is FALSE just in case the proposition is not determinately true as posited. This follows from bivalence--if it ain't true, then it must be false. For example, if the antecedent is "Tom comes to town next year" but it is not now settled that Tom will come to town next year, then the antecedent is false. It could be true, however, if it made a weaker claim like "Tom might come next year" or "Tom will probably come next year". But that's not what the given antecedent states.
In other words, we need to distinguish between the determinacy of the TRUTH of a claim, and the determinacy of what is claimed to be true. Unless we give up bivalence, we have to insist that the TRUTH of every claim is fully determinate, even if what it claims is that something is indeterminate, such as whether you come to town next year.
Tom: But I didn’t say “God creates Peter…” and so imply more than a mere possibility.
Alan: The conditional "If God creates Peter ... then ..." does not assert that God creates Peter, but the antecedent most emphatically does assert this. To ascertain what the antecedent claims you have to extract it from the conditional and take it as a stand-alone assertion. The antecedent states "God creates Peter ...". Thus it asserts as true that God creates Peter.
Again, bear in mind the distinction between the determinacy of the truth of a claim and the determinacy of what is claimed to be true. I can claim any of those three metaphysically distinct states of affairs to be true, or posit any of them in the antecedent of a conditional, but whether my claims or my posits are true is always a fully determinate fact. They are true just in case they correspond to what is the case. If I claim that some state of affairs is indeterminate, then that claim is determinately true if and only if that state of affairs is indeterminate. Otherwise it is false.
Hope that clarifies my position.
Alan
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Tom
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| Posted 11/5/2003 3:00 AM (GMT -6) | | quote:
Tom: Exactly. IF you know the antecedent to be false you have a counterfactual.
Alan: I didn't say that counterfactuality depends on our state of knowledge. I said it depends on the truth value of the antecedent with respect to the currently actual state of affairs.
Right. I didn’t mean to suggest that our “knowing” is what MAKES a proposition counterfactual. As you say, every antecedent is either true or false (bivalence) and false antecedents are what make their propositions counterfactual. My point was that we can only SAY propositions are counterfactual if we know their antecedents are false. If you agree that antecedents can be true, and that propositions with true antecedents are not counterfactual, then we are in agreement.
One example at least (there may be more) of a true antecedent, I suggested, is one which posits state of affairs (c), “indeterminately the case that p,” with respect to my coming to St. Paul next year. I assumed “If Tom comes to St. Paul next year” does just this. Now, I’ll concede you’re correct that the extrapolated antecedent of this (“Tom comes to town next year”) doesn’t mean “indeterminately the case that Tom comes to town next year.” Fine. So tell me, Alan, how I CAN express “indeterminately the case that p” with respect to my coming to town next year and do so in logically acceptable lingo. What would I say? [If you go running to the traditional square of opposites for a proposition you won't find one, 'cause traidtional Western logic HAS NO ONE PROPOSITION that it recognizeas as AFFIRMING as true "indeterminately the case that p." The square is ill-fitted for expressing indeterminacy; my Triangle above however, allows for any possible proposition regarding such states of affairs.]
I could say, “IF it is indeterminately the case that Tom comes to town next year, THEN it is indeterminately the case that he’ll bring Cohibas with him.” Or I could say, “IF Tom might and might not come to town next year, THEN he might and might not bring Cohibas.” True antecedent, thus no counterfactuals. I could even say “IF it is indeterminately the case that Tom comes to town next year, THEN he 'WOULD' bring Cohibas.” Given the truth of the antecedent, the “would” here is not counterfactual. All I’m trying to say is that not ALL “would’s” and “might’s” are counterfactual. Do you want to deny this?
Now, logicians and philosophers aside, NOBODY talks like this. Nobody says, “Gee, if Tom might and might not…” or “Hey, if it is indeterminately the case that Tom…” No, your average Joe (like me) simply says, “If Tom comes to town next year…” and we all know what I mean. Now, you’re right that this is technically/logically/philosophically NOT the way to express it. So what SIMPLE way is there for me to say it? Hey, could I say, “If Tom were to come to town next year, he might bring Cobhibas” or “If Tom might come to town next year, he might bring Cohibas”? Hey, in this case the “might” of “If Tom ‘might’ come to town next year” doesn't even posit state of affairs (c) with respect to my coming! It's the same “might” of the traditional square. So it simply falsifies “Tom will not come to town next year” and thus (as a TRUE antecedent) leaves open the question of whether it is determinately the case that Tom will come to town or indeterminately the case that Tom will come to town. BUT it’s a TRUE antecedent, and thus NOT a counterfactual.
quote:
Alan: The conditional "If God creates Peter ... then ..." does not assert that God creates Peter, but the antecedent most emphatically does assert this. To ascertain what the antecedent claims you have to extract it from the conditional and take it as a stand-alone assertion. The antecedent states "God creates Peter ...". Thus it asserts as true that God creates Peter.
Tom: Hmm. You got the degree Bro., so I’m in quick sand here. But OK, how about if I said:
“If God were to create Peter, and were Peter to become solidified with respect to situation x, THEN Peter would do y in x”?
According to the definition of counterfactuality, this "would" would not constitute a counterfactual. Or how about if we said:
“If God might create Peter, and if Peter might become solidified with respect to situation x, THEN Peter would do y in x”?
The “might” here only falsifies “God will not create Peter” and thus affirms “it is either determinately the case that God creates Peter or indeterminately the case that God creates Peter,” and so forth. We have every reason to assume the antecedent to be true (although we weren't around sans creation, so only God knows if it was true sans creation!) and thus “would” and “might” here would not meet the requirements for counterfactuaality.
My frustration is also this--nobody goes around talking like this. If we have to play the game for the professionals in academic journals, cool. But you and I both know that when I say, “Hey, if I come to town next year, I might bring some Cobhibas” EVERYBODY knows I mean “I might come to town, I might not come to town. And if it turns out that I DO come to town, then I might bring Cobhibas and I might not bring Cobhibas.” Logic, Arthur Prior argued, ought to make better sense of the way people actually speak. So, maybe the textbooks need a tune up.
Now, you did say that you do think indeterminate states of affairs are candicates for true antecedents of conditional propositions. Now that I think of it, I gather you’d agree also that a true independent “might” falsifying “will not” and affirming as true either “will...” or “indeterminately that...” may also constitute true antecedents. Good. Either way, we agree:
Not all “would’s” and “might’s” are counterfactual.
So...
Why call the square OR our triangle a square or triangle of counterfactuals? This assumes that all conditional proposition to be discussed on the square or triangle have false antecedents. But we admit they don’t. Why talk of "might-counterfactuals" as if this includes all might-propositions?
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Tom
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| Posted 11/5/2003 8:14 AM (GMT -6) | | Alan-
I'm actually beyond the counterfactual thing. Call 'em what you will, in the end it's just nomenclature. We both admit "indeterminately the case that..." as a metaphysically distinct state of affairs. In the end, it's getting THIS state of affairs recognized in propositional terms just as the other two states of affairs are. I'm not a philosopher or a logician, but if I had the credentials I think this would be my passion--clearing room at the table for state of affairs (c).
I’m still searching (David Lewis and Arthur Prior at present, plus what I can find online) for a modal operator for Alan’s state of affairs (c) “It is indeterminately the case that” and have come up with nothing. Modal (Temporal) logic offers the following tensed operators:
G "It will always be the case that..."
F "It will be the case that..."
H "It has always been the case that..."
P "It was the case that..."
That's it. Anything missing? Friggin YEAH! Amazing really. No operator whatsoever for "It is indeterminately the case that." I think part of the problem may be that even Prior, when it comes to finding operators for tense-logic, has limited himself to propositions ON the square, the WHOLE square, and nothing BUT the square so help him God. And since there IS NO PROPOSITION on the square affirming “it is indeterminately the case that…” nobody seems to have bothered with finding a modal operator for expressing this state of affairs EVEN IF THEY BELIEVED IT a metaphysically distinct state of affairs! It kill me. What have logicians been doing with themselves all this time?
Alan, don’t you find it extremely bothersome (I do) that of the three metaphysically distinct states of affairs…
a) Only two can be affirmed as true by all the logics (propositional, modal, tensed, whatever) known to Western academia, and
b) Only these two can be falsified with a proposition (“might” on the one hand, “might not” on the other) that does not also affirm as true any state of affairs?
There is no proposition IN LOGIC that affirms or denies indeterminacy! Come on, think about it. Here’s a metaphysically distinct state of affairs (“indeterminately the case that p”), just a real as the other two, and no logician to date has bothered to argue its right for a place at the table (or square, or triangle, or anything).
I mean, come on ya’ll? What gives? Anybody wanna do a Ph.D. dissertation? Here it is. You’ll go down in history as the Martin Luther of Western logic. Somebody puuuuleease nail this thesis to the door!
Give us an operator for INDETERMINACY for heaven’s sake! (I have one and I'm now using it, but I'm a friggin nobody so it doesn't matter!)
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