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Tom
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| Posted 7/27/2003 10:10 PM (GMT -6) |   | quote:
Doc: The Square of Opposition doesn't allow for conjoined might counterfactuals. For :
1. if true "x might"
2. false "x would not" (contradictory)
3. hence false "x might not" (sub-alteration)
*** Hence it can never be true that "x might AND might not"
In the sense that you mean “might and might not,” right. But this doesn’t mean that both subcontrary props on the Square can’t both be true. Go to this very cool experiment with the Square and try out what you’ve just suggested:
http://140.209.49.101/Logicw/student/square/square_of_opposition.html
The square won’t let you justifiably deduce from the truth of “x might” to the falsity of “x might not.” Of course, the traditional square is “some x are p.” So, you can validly conclude that the contradictory of this (“No x are p”) is false, but you can’t then validly conclude from this false contradictory to the falsity of its subaltern “some x are not p.” I thought we could do this, but how far you can conclude depends on where you begin. There are some subcontraries that are BOTH true, like “some logicians are professors” and “some logicians are not professors.”
(A) No logicians are professors —contrary— (E) All logicians are professors
(I) Some logicians are professors —subcontrary— (O) Some logicians are not professors
If (I) is true, it follows that (E) is false. But it doesn’t follow that (O) is false even though the subalterns share the truth-value of the top proposition. Subalternism is one-way, from top to bottom. Why (E)'s being false in this case does NOT imply the falsity of (O) is beyond me, becasue in this case the two subcontraries are BOTH true. Some logicians are professors and some are not. So in this case though propositions (E) is false, it does not follow that its subaltern (O) is false. How far you can justifiably conclude beginning with any one particular proposition seems to depend on which true proposition you begin with.
Still, you’re right about there being no room on the square for “might AND might not.” As ONE proposition, yes, there is room. But (and this is what I now see) the “might AND might not” YOU’VE been arguing FOR is NOT the same thing as simply uniting subcontrary propositions. The subcontraries “Some logicians are professors” and “Some logicians are not professors” are BOTH true because they are NOT talking about the SAME “some.” The ‘some’ which are profs is NOT the ‘some’ which are not profs. This is why two subcontraries may sometimes both be true. They don’t predicate opposite claims to the same subject. When we say “Some logicians are profs and some logicians are not profs” we are not at all saying the same thing as when we say, with your conjoined might-counterfactuals, “Bill might eat a cookie if offered AND might not eat a cookie if offered,” because here the “might” predicates to the same ‘something’ (that is, Bill’s eating a cookie if offered). I don’t know if this is clear. Make sense?
quote:
Doc: Now, this means either
a) all conjoined might counterfactuals are logically impossible, absolutely meaningless OR...
b) there is a class of propositions not covered by the Square of Opposition.
Good luck defending a. You might and might not succeed
Oh yeah. I think you’re right. “Might and might not” IS meaningful. And since the “might and might not” you’re talking about is NOT equivalent to simply sticking two true subcontrary propositions together (like “Some logicians are profs and some logicans are not profs”), the only place for conjoined might-counterfactuals on the square is as one indivisible truth claim not amounting to simply uniting subcontraries.” This “might AND might not” is an entirely different animal.
But I’m not sure you have to do the triangle thing. You should still be able to work with the square. “Bob might and might not eat a cookie if offered” should have three other propositions it relates to: a subaltern, a contradictory, and a contrary (or subcontrary). No? What would they be?
(A) ? – contrary – (E) ?
(I) Bob might and might not eat a cookie if offered – subcontrary – (O) ?
quote:
Hence, instead of a Square, we have a Triangle of opposition.
1. If true "x would",
2. false "x might and might not"
3. false "x would not"
And
1. If true "x might and might not"
2. false "x would"
3. false "x would not"
And
1. If true "x would not"
2. false "x might and might not"
3. false "x would"
(TGB, can you diagram this on the board? I again don't know how.)
I’m not the artist, but I’ll try:
x would do y in z - - - - contrary - - - - x would not do y in z
..... -
......... -
............. -
................ -
................... -
...................... -
............. - x might and might not do y in z
So insted of two subcontraries across the bottom forming a square you want only one (might and might not)? I can't get the line to go back up diagnally to the right.
quote:
And, I'm now wondering, why did we ever disjoin "mights" in the first place? Maybe the square missed mights altogether. Maybe all mights are (as I previously thought) implicitly conjoined mights. Might implies "might not."
There has to be some “might” (whether we use that word or not) to refer to logical possibilities. And not all logically possibilities imply logically possible that not-X, as is the case with the class of all necessary truths. A necessary truth is logically possible but not logically possible NOT, (“God might exist tomorrow” is true because even though God’s exists necessarily it remains logically possible [the other option is that God’s existence is logically impossible] that God exists. But “God might not exist tomorrow” is not true). I think we ought to designate some word other than “might” to denote logical possibilities and reserve “might” and “might not” for (what shall we call them, historical possibilities?) what Doc is talking about.
Tom | | Back to Top | | |
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Tom
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| Posted 7/27/2003 11:07 PM (GMT -6) | | Doc-
Go to this thread NOW!
http://www.gregboyd.org/gbfront/forum/topic.asp?TOPIC_ID=2121&whichpage=3
and look at my third post (June 1, 2003). Among other things, there is this statement:
1. Let’s combine “might” and “might not” and make one indivisible truth claim (which IS the case given the nature of contingency). This one word will be “might/might not.” “Might/might not” is now a single word. We’ll use it to describe contingent events.
See? We WERE related in our former lives. 
Tom | | Back to Top | | |
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Tom
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| Posted 7/28/2003 1:15 AM (GMT -6) | | Heads up Doc. Send ya an email of your TRIANGLE OF COUNTERFACTUALS (call it whatever). Enjoy!
Aristotle...eat your heart out!
Tom | | Back to Top | | |
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GregBoyd
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| Posted 7/28/2003 3:22 PM (GMT -6) | | Dude, we are one,
even as Jesus and the Father are one.
Yeh, so that the world may know
that I am in you,
and you are in me,
and together we philosophize
brilliantly.
Might/might not... ONE and the same.
Of course, they COULD be disjoined (in which case the "can't tell" part of the Square works). But they CAN be CONJOINEd (which resolves the "can't tell" segments as FALSE). Aristotle and the tradition simply didn't conceive of the possibility of MIGHT/MIGHT NOT as ONE proposition, one truth -- the truth value of which an omniscient God must know.
The THREE fold opposition is superior to four
as is of course typically the case.
appreciate all the interaction on this Tom. You are one good egg!!!
Doc
"The responsibility is with the chooser -- God is blameless." Plato, Republic, 10. | | Back to Top | | |
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Tom
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| Posted 7/29/2003 7:07 AM (GMT -6) | | OK, here's the triangle Doc asked for. Thanks to Laika for making this possible! 
Tom | | Back to Top | | |
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Tom
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| Posted 7/29/2003 7:22 AM (GMT -6) | | Houston we have a problem!
Doc-
Comment on this you related-to-me-in-a-previous-life philosopher you.
It's YOUR square. Just remember that!
Now, it seems to me that the "would" and "would not" accross the top can no longer be "contrary" if you have just one proposition at the bottom now.
If the "might and might not" is TRUE, both top propositions must be FALSE. That's OK, because contraries may both be false.
BUT...if the "might and might not" if FALSE then both top propositions must be true and THAT, my related-to-me-in-a-previous-life philosopher friend is impossible. Contraries cannot both be TRUE.
It's your square buddy. Fix it!
...before I have a counterfactual break-down!
Tom 
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Tom
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| Posted 7/30/2003 8:15 AM (GMT -6) | | Doc-
Think I figured it out. Simply change the two “contradictory” lines to “contrary” and everything works fine. It’s “contrary” all the way around.
A = “would do”
E = “would not do”
I = “might and might not do”
If A is true, then both E and I are false (as is the case with contrary propositions: both may be false but both cannot be true). Likewise, if E is true, both A and I are false, while if I is true both A and E are false.
But if one begins by assuming the falsity of one proposition, no deduction can validly be made about the truth-value of the others (except that they are contrary).
If A is false, no deduction can be made about the truth-value of E or I. E may be true and I false, or E may be false and I true. One cannot determine which is which solely on the basis of A’s being false. Likewise if one begins by assuming E is false or by assuming I is false.
It’s CONTRARY all the way around. It’s that simple.
You got your triangle back!
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Tom
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| Posted 7/31/2003 1:29 AM (GMT -6) | | Triangle vs Square
The traditional square expression of propositions describing future contingencies reveals its inherent inability to account for simultaneously true counterfactual subcontraries (that is, “might” and “might not”). The square is also confuses historical contingency expressed in “might” propositions with logical possibility.
Example: It is true that “Bob would not eat a cookie if offered one”
Bob would eat a cookie if offered one Bob would not eat a cookie if offered one
(Necessarily FALSE as the Starting point (TRUE)
contrary of “would not” And
the contrdictory of “might not”)
Bob might eat a cookie if offered one Bob might not eat a cookie if offered one
(necessarily FALSE as (necessarily TRUE as the
the contradictory of “would not”) subaltern of “would not”)
So far so good. But are subcontraries ever both true? Yes. Here’s an example:
All logicians are professors No logicians are professors
FALSE FALSE
Some logicians are professors Some logicians are not professors
TRUE TRUE
So there are three reasons for believing the traditional square incapable of accounting for propositions describing contingent events.
First, “might” cannot describe mere logical contingency. If “x might” and “x might not” are to falsify their contradictories then they do so only if the are assertions of historical contingency and not mere logical consistency.
Secondly, if might-counterfactuals describe historical contingency, then it can never be the case that “might” and “might not” are not both either true or false. It cannot be true that and event is both historically contingent (“might”) and not historically contingent (“might not”). If “might” means more than “is logically possible that,” that is, if it describes a historic contingency, then “might” and “might not” are in fact conjoined and together describe one and the same contingency.
Thirdly, “might” and “might not,” when they are both true, are not true in the way non-counterfactual subcontraries are true. When we conjoin the subcontraries “some are and some are not,” for example, we are making a compound sentence, one which compounds TWO claims about TWO different subjects (those who are profs and those who are not). But when we conjoin “might and might not” we are making one claim about one and same event subject. This means “might” and “might not” subcontraries which are both true on the square of opposites are NOT logical subcontraries at all. They are in fact two sides of ONE indivisible truth, whereas “some logicians are profs” and “some logicians are not profs” are two independent truths. “Might and might not” is not the logical equivalent of “some are and some are not” (or any other propositions formed by conjoining subcontraries).
These three points account for the inability of the traditional square to account for separate “might” and “might not” propositions. The square is not suited to accommodate propositions expressing contingent events. If one objects that subcontraries “might” and “might not” are required on the square to account for propositions describing logical possibilities, then one faces the problem of accounting for how it is they falsify their contradictories, for its being merely logically possible that “Bob might not eat a cookie if offered one” cannot falsify “Bob would eat a cookie if offered one.”
Alan has argued that instead of conjoining mights all one has to do is show that there exist some true “mights” which do not follow subalternately from true “woulds.” This is indeed all we have to show. But the only case in which “x might” is true and “x would” is not also true is when BOTH subcontaries (“might” and “might not”) are true. And as is also true, the only way for “might” and “might not” to falsify their contradictories is if “might” means more than “is logically possible that,” that is, unless “might” describes what is historically possible. So, Alan is right, but to accomplish what he admits is required one necessarily comes to terms with conjoining “might” and “might not.”
I temporarily conclude then that there is no such thing as a “counterfactual square of opposites.” Counterfactuals are necessarily triangular. We must argue for a “counterfactual triangle” of opposites.
Loose ends.
Nobody, including God and others who speak in the Bible, goes around saying “might and might not.” If “might” and “might not” each entail each other, then it’s only necessary to say “might” or “might not” to express historical contingencies. But this returns us to the confusion between the using “might” to express both historical and logical possibilities. On what grounds are open theists to insist that any particular “maybe” or “perhap” in the Bible means anything more than “logically possible that”? This needs to be considered.
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Tom
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| Posted 7/31/2003 1:40 AM (GMT -6) | | Most excellent Laila! Thanks for correcting the Triangle of Opposites above! You put "contrary" in the place of "contradictory."
Most excellent!
I haven't convinced Doc yet that this is correct. But he'll come around.
Tom
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Tom
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| Posted 7/31/2003 5:18 AM (GMT -6) | | Tom: On what grounds are open theists to insist that any particular “maybe” or “perhaps” in the Bible means anything more than “logically possible that”? This needs to be considered.
Mephi: This is what I think is a big issue. I predict that this whole thing is going to go in circles because the whole thing is based on a METAPHYSICAL presupposition that backs a desired THEOLOGICAL assertion. Tom seems right in saying that the only way to say that the set of true “mights” that don’t entail true “woulds” is not empty is by conjoined the “might” and “might not” But this just illustrates the problem. If one is bound by METAPHYSICAL ASSUMPTION that God does know all future events exhaustively…and believes that “might” only needs to be “it is logically possible that”, then they don’t need any triangle. Why? Because though they may not say it, they don’t believe in historical contingency in the metaphysical sense, but only the appearance of it the phenomenologicall sense because this suits compatibilism.
Tom: Man I miss hearing you big time Bro! Big time.
I think you’re right here Mephi. First, the square itself cannot tell us whether or not it ever actually is the case that both subcontraries “might” and “might not” are true. That is a metaphysical question as you say. I’m not into the whole square/triangle thing to argue a metaphysical point. All I want to show is that if one believes on other grounds that both subcontraries “might” and “might not” (or Doc’s conjoined “might and might not”) are in fact sometimes both true there can be no “logical” objection to this. It is not “logically” impossible for both “might” and “might not” to be TRUE. One can be an open theist without transgressing the square or any other law of logic. And I haven’t heard a non-open theist concede this yet. Bill Craig is a perfect example. He rejects the open view because (among other reasons) he claims it “logically” attributes ignorance to God; God cannot know the truth-value of all propositions if he knows true “maybe’s” that are not entailed by true “would’s.” Craig doesn’t see the point you just made. I think he assumes his metaphysical beliefs ARE what the square is all about.
But I do think that openness metaphysical assumptions make better sense of the square than other metaphysical assumptions. The traditional square’s inability to account for true counterfactual subcontraries “might” and “might not” encourages us to suspect that something’s up. One cannot logically deny the meaningfulness of “might and might not” (though one can attempt to deny on metaphysical grounds that “might and might not” is ever true). It’s accounting for this meaningfulness on the square that’s awkward.
Secondly, I don’t see how embracing apparent contingency (in the phenomenological sense) while denying historical contingency (in the metaphysical sense) provides any framework or basis for defending compatibilism. What do “apparent contingencies” appear to be if one denies any metaphysical reality supporting them? Compatibilists have to argue what you’re saying, yes. It’s all that’s left them. But belief in apparent contingency couple with the denial of metaphysical contingency is not a livable metaphysic. Once one denies metaphysical contingency, nothing can “appear” contingent, for one now KNOWS the truth that it is NOT contingent. What is “apparent contingency” supposed to do for one who knows otherwise?
This leads directly into all the biblical passages that describe the future in terms of what “might” be, including passages in which God is the one doing the talking. What existential sense can be made of divine offers and descriptions of conditions if one denies any metaphysical reality behind the offers and conditions and instead claims they are merely “logically” possible? If a prophet of God says to me, “Tom, God is offering you one last chance to change you ways. You can avoid judgment if you repent now. But if you don’t repent you’ll lose everything.” If I believe my repenting and being restored and not repenting and being judged are not metaphysically contingent but only propositions describing logically possible states of affairs, how do I relate to the offer? I do end up relating to it. I must relate to it. Even compatibilists end up relating to it. But I honestly believe that in relating to such offers they unconsciously detach from their metaphysical beliefs and live as open theists. Whatever theology they might SAY they embrace, compatibilists and determinists cannot demonstrate in the actual manner in which they deliberate God’s offer the belief that the contingency of the offer and threat of judgment is only apparent.
So, not only is Western logic as understood in the square of opposites ill-suited to account for a class of meaningful proposition (“might and might not”), but life is equally ill-suited to demonstrate the denial of that contingency which makes this class of proposition meaningful.
Mephi: One would only have to grant the triangle of counterfactuals if one were inclined to CHANGE their metaphysical assumptions.
I totally agree. But at least now open theists can justifiably request that their opponents concede the logical possibility of open theism.quote:
Doc: I personally think a number of philosophical conundrums or errors arise because confuse LOGICAL POSSIBILITY with what we might call "HISTORICAL POSSIBILITY. For example, some argue that an agent is free if it was "possible" for them to do otherwise... but they mean simply that it was LOGICALLY possible for them to do otherwise. This of course is compatible with compatiblism. But it is also TOTALLY inadequate for a definition of freeodm, for it applies to a mosquito as much as a human.
Mephi: The only philosophical conundrum I see here is because Doc places such high value in the metaphysical (rather than just phenomenological) verity of “historical possibility” because of his view of human freedom.
Tom: I don’t see this as philosophical conundrum at all. It’s an existential conundrum (for theological determinists that is), and an insurmountable one at that.
Mephi: He’s going by his assumption that freedom (as he conceives of it) is CORE to what makes a human being 1) in the image of God and 2) distinct from a mosquito. But one can just plain disagree with this for good reasons. (One still can be a Nevillian, you know!). And “poof” the incessant need for historical possibility to be distinct from logical possibility disappears.
Tom: Yeah, we’ve been here. I remember your discussing the Nevillian take on things. But I remember absolutely nothing about it. Give me the one-post review! And also tell me--are you a Nevillian? Or are you suggesting that something you don’t believe in is a good reason for rejecting something you do (?) believe in--libertarian freedom? Apart from being a Nevillian, what other “good reasons” do you have in mind for rejecting libertarian freedom as at least part of what is essential to human personhood and uniqueness as God’s image?
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GregBoyd
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| Posted 7/31/2003 5:27 AM (GMT -6) | | TGB: On what grounds are open theists to insist that any particular “maybe” or “perhap” in the Bible means anything more than “logically possible that”? This needs to be considered.
Doc: Two grounds: 1) In ordinary language we never mean by "might" merely "logically possible." We mean possible given the state of reality at the present time -- what I want to call "historical possibility." 2) The Square of Opposition turns into absurdity if we supply "logically possible" as the meaning of "might," for "might" need not entail "might not." Yet "logically possible that x" always entails "logically possible that not x" -- unless we are dealing with logical necessity. And it would be odd indeed to argue that "x might" means "x is logically necessary" (esp. if we add that "might" is distinct from "would" in that "might" is logically necessary while "would is not!)
MephEternal: If one is bound by METAPHYSICAL ASSUMPTION that God does know all future events exhaustively…and believes that “might” only needs to be “it is logically possible that”, then they don’t need any triangle. Why? Because though they may not say it, they don’t believe in historical contingency in the metaphysical sense, but only the appearance of it the phenomenological sense because this suits compatibilism.
Doc: But we CAN show that this metaphysical assumption requires that FOR GOD all conjoined might counterfactuals (why assume they are counterfactuals... different issue) are logically impossible, which means they must be meaningless. But how can they be meaningful to us and meaningless to God?
Meph Eternal: The only philosophical conundrum I see here is because Doc places such high value in the metaphysical (rather than just phenomenological) verity of “historical possibility” because of his view of human freedom. He’s going by his assumption that freedom (as he conceives of it) is CORE to what makes a human being 1) in the image of God and 2) distinct from a mosquito. But one can just plain disagree with this for good reasons. (One still can be a Nevillian, you know!) And “poof” the incessant need for historical possibility to be distinct from logical possibility disappears.
Doc: I'm not here working from anthropology to logic, but from logic to anthropology (actually anthropology is for the moment irrelevant). The point is that it is that
* conjoined might counterfactuals are meaningful, so
* they cannot all be logically entailed by would counterfactuals, so
* they constitute a distinct class of propositions an omniscient God must know which...
* is the case even if God decided to create a world in which all of them were rendered false
No metaphysics dude. ]
the Doctor
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