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¡Que Payaso!
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| Posted 5/13/2003 7:14 PM (GMT -6) |   | In Doc's paper presenting OV as neo-molinism, I got lost on one initial piece of logic. Doc states, "On a counterfactual square of oppositions, the logical antithesis of the statement, 'agent x would do y in situation z' is not the statement, 'agent x would not do y in situation z.' This is a contrary proposition, not a contradictory proposition. The logical antithesis of 'agent x would do y in situation z' is rather the statement, 'agent x might not do y in situation z.'"
Can anyone splain this to me? I've turned it over and over in my head and I just don't get it.
Payaso 
"I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve." - Bilbo Baggins
Edited by - payaso on 05/14/2003 12:41:11 AM | | Back to Top | | |
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¡Que Payaso!
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| Posted 5/13/2003 7:39 PM (GMT -6) | | I should be more specific. Here's what I don't get:
Why is the contradictory proposition the logical antithesis? Why isn't the contrary proposition the logical antithesis?
Thanks.
Payaso
"I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve." - Bilbo Baggins | | Back to Top | | |
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Starkman
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| Posted 5/14/2003 6:10 AM (GMT -6) | | Well, of course, if you take the antithetical aspect of Bivalence and attempt a cohesive synthesis of both counterfactuals--would/would not--you end up with . . .
Yeah, like I really know what the hek I'm saying!
Starkman
Am I right? I say, am I right?
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Tom
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| Posted 5/14/2003 7:25 AM (GMT -6) | | Payaso: I've turned it over and over in my head and I just don't get it.
Tom: Try standing it on its side. That should turn the lights on.
Doc?
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Tom
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| Posted 5/14/2003 7:31 AM (GMT -6) | | Payaso-
Go this site: http://plato.stanford.edu/entries/square/
But before you do, get VERY drunk, 'cause there ain't NO WAY anybody's gonna undertand what's on DIS HIYA PAGE!
I got dizzy just looking at the screen!
I tell ya, it almost makes a person wanna convert to Greek Orthodoxy and become a mystic.
Tom 
Edited by - TGB on 05/14/2003 12:37:22 PM | | Back to Top | | |
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Alan Rhoda
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| Posted 5/14/2003 8:35 AM (GMT -6) | | quote:
Why is the contradictory proposition the logical antithesis? Why isn't the contrary proposition the logical antithesis?
The answer's fairly simple if you're familiar with the logical square of opposition, or with the precise definitions of the terms.
(1) Two propositions are contrary if they cannot both be true.
(2) Two propositions are sub-contrary if the cannot both be false.
(3) Two propositions are contradictory if both (1) and (2) are the case.
Example of (1): "All grass is green" and "No grass is green". These cannot both be true, but they can both be false (if it turns out that SOME grass is green and SOME isn't).
Example of (2): "Some grass is green" and "Some grass is not green". These can both be true, but they cannot both be false.
Example of (3): "All grass is green" and "Some grass is not green". These cannot both be true AND they cannot both be false. That is why they are logical antitheses.
Hope that helps,
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Tom
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| Posted 5/14/2003 9:11 AM (GMT -6) | | Allan, man, I read your post 37 times. Sometimes I’d get stuck just repeating “Some grass is green” to myself because I wasn’t sure if I’d remember what it meant when I got to the next part! Yeeeow!
You’re heard of the game show “Celebrity Square”? Here’s CVM’s celebrity square:
(1) Tom and Payaso are dumb if they cannot both understand Allan.
(2) Tom and Payaso are stupid if neither understands Allan but they think they do.
(3) Tom and Payaso are complete idiots if both (1) and (2) are the case.
Appreciate ya Allan. 
Tom
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¡Que Payaso!
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| Posted 5/14/2003 4:34 PM (GMT -6) | | Tom, I screwed up. I thought I could go to that website without drinking and still handle it. Boy, was that a mistake!
Alan, thanks for the help. I've seen the square of opposition before, but I didn't take it that seriously. I think your examples will clear up my confusion after I turn them over and on their sides a few times.
Thanks,
Payaso
"I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve." - Bilbo Baggins | | Back to Top | | |
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Alan Rhoda
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| Posted 5/15/2003 8:22 AM (GMT -6) | | Hey Tom & Payaso,
I was thinking some more about contradictories, contraries, and the square of opposition this morning (yes, us philosophers do that sort of thing--sick, isn't it?) and I think I've got a better way to explain things.
Start with your basic contradiction: P and not-P. Notice that we have a proposition, P, and the negation of the entire proposition, not-P. Conjoin them together and voila, a contradiction.
So our formula for forming a contradition is to simply take any proposition (e.g., "Some pigs can fly") and negate the whole thing by prefacing it with "It is not the case that..." (e.g., "It is not the case that some pigs can fly") and then rewriting as necessary to put it into more idiomatic English (e.g., "No pigs can fly").
Compare this with the contrary. The contrary of "All pigs can fly" is "No pigs can fly". But the contradictory is "It is not the case that all pigs can fly", which is the same as "Some pigs cannot fly". This is a weaker statement than the contrary "No pigs can fly".
Now compare with the sub-contrary. The sub-contrary of "Some pigs can fly" is "Some pigs cannot fly". But the contradictory is "It is not the case that some pigs can fly", which is the same as "No pigs can fly". This is a stronger statement than the sub-contrary (b/c "No pigs can fly" implies "Some pigs cannot fly" but not vice-versa--assuming, of course, that pigs exist).
Clear as mud?
Alan
Edited by - Alan Rhoda on 05/15/2003 1:23:23 PM | | Back to Top | | |
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Tom
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| Posted 5/15/2003 9:53 AM (GMT -6) | | Thanks Allan!
OK, then, back to Doc’s paper:
Doc: "On a counterfactual square of oppositions…”
Tom: I’m confused already. So there are different squares of opposition? Factual, counterfactual, and what else?
Doc: …the logical antithesis…
Tom: This didn’t appear in your explanation. Logical antithesis? Is this what you call a “contradictory” statement?
Doc: …of the statement, 'agent x would do y in situation z' is not the statement, 'agent x would not do y in situation z.' This is a contrary proposition, not a contradictory proposition. The logical antithesis of 'agent x would do y in situation z' is rather the statement, 'agent x might not do y in situation z.'"
Tom: So, we have the counterfactual “agent x would do y in situation z.”
This has contradictory, contrary, and sub-contrary opposites? But they have to be counterfactual opposites because the proposition you start with is counterfactual? If you had a conditional proposition, would it also have contradictory, contrary, and sub-contrary opposites? Wow.
Let me see if I can do this. To get the contradictory, first stick “It is not the case that…” in front. OK, so "It is not the case that agent x would do y in situation z." Doc simplifies this to: “agent x might not do y in situation z.” Hmmmm. How'd he get there?
Doc says the contrary (which is the strongest opposite possible?) is: “agent x would not do y in situation z.” Now that looks to me like a better simplification of the contradictory “It is not the case that agent x would do y in situation z.”
The sub-contrary of “agent x would do y in situation z”? I haven’t a clue.
Tom
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Tom
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| Posted 5/15/2003 10:04 AM (GMT -6) | | quote:
Doc says the contrary (which is the strongest opposite possible?) is: “agent x would not do y in situation z.” Now that looks to me like a better simplification of the contradictory “It is not the case that agent x would do y in situation z.”
OK, I see something. The "not" is placed at a different spot in the sentence.
Proposition: "Agent x would do y in situation z"
If you basically start again with "not" in front, you get: "Not (the case that) agent x would do y in situation z."
If you place the "not" in front of the verb (and so only negating the predicate?) you get: "Agent x would NOT do y in situation z."
I don't see any difference between these. "It's not the case the agent x would do y in situation z" (to me) is the same as "Agent x would not do y in situation z."
Where does Doc come up with changing the "would" of the original proposition to "might" (and the negated "might not") for the CONTRADICTORY. I thought to get the contradictory all you did was stick a "NO" in front of the claim.
I'm totally confused.
Tom
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¡Que Payaso!
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| Posted 5/15/2003 2:52 PM (GMT -6) | | OK, Tom, now you're making it worse. I was almost there until you had to write those last two posts. Thanks alot.
Payaso
"I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve." - Bilbo Baggins | | Back to Top | | |
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Tom
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| Posted 5/15/2003 6:15 PM (GMT -6) | | Payaso: I was almost there...
Tom: OK, try it now: "I was almost there."
Contradictory: "It was not the case that I was almost there."
Contrary: "I was NOT almost there"
Sub-contrary: Either "I was almost NOT there" or "Somebody was almost there but it wasn't me"?
Tom
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Springs
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| Posted 5/15/2003 7:09 PM (GMT -6) | | Well I'm definitely not almost there.
But I think it might be possible that I may get almost there as long as nobody contradicts themselves.
-S
"Dreams are illustrations...from the book your soul is writing about you." -Marsha Norman
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Alan Rhoda
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| Posted 5/16/2003 2:24 PM (GMT -6) | | | | |
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Tom
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| Posted 5/16/2003 7:31 PM (GMT -6) | | Thanks Allan! Appreciate it. I'm gonna study that baby until I understand it.
Tom
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Starkman
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| Posted 5/17/2003 5:35 AM (GMT -6) | | And Tom, as you are so apt, please translate it into the clear, thinking language the rest of us meatheads can understand! 
Okay, I don't get something(and here's where Allan's probably just going to shake his head with clenched fists or shout hallelujah): Shouldn't the sub-contraries read Agent x might do y in situation z (and not "x")? (As I say, Tom: translate!)
The Starkman
Am I right? I say, am I right?
Charlie Brown
Edited by - Starkman on 05/17/2003 10:44:55 AM | | Back to Top | | |
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Alan Rhoda
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| Posted 5/17/2003 9:58 AM (GMT -6) | | quote:
Shouldn't the sub-contraries read Agent x might do y in situation z (and not "x")?
Good eye, Starkman. That's a typo on my part. Should be 'y', not 'x'. I'll fix it on the link I posted.
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One Love
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| Posted 5/17/2003 11:41 AM (GMT -6) | | Let me try...
Meph Attempts to Do Philosophisticated Junk
Each of these is in derivatives of the following main form:
Agent...........ACTION DEFINER........action..........Conditioning Situation
(Person X) (will/will not/may/may not) (do Y) (in Situation Z)
Being more specific...
Meph WILL go to see the Matrix if it's a Friday. (affirmative DEFINITE action)
Meph WILL NOT go see the Matrix if it's a Friday. (negative DEFINITE action)
Meph MIGHT go to see the Matrix if it's a Friday. (affirmative POSSIBLE action)
Meph MIGHT NOT to see the Matrix if it's a Friday. (negative POSSIBLE action)
************************************
Contrary:
It cannot be true that I both WILL and WILL NOT see the Matrix on a Friday. Either one or the other will be true at any given time. BUT both claims can be FALSE. How, you ask? By me changing the DEFINITE action into a POSSIBLE one! If I say I may or may not go see the Matrix on a Friday, it is not true either that I WILL or WILL not definitely see it! If I were to use either of the possible action statements (may or may not), then BOTH definite claims would be logically false.
As you can see, both definite action claims cannot be true at the same time, but both can be false.
******************************************
Sub-alteration:
Simple question. Can it be a CERTAINTY that I go to the Matrix on a Friday if it's not even POSSIBLE that I do so? How about "Hell, no!" Something has to be POSSIBLE before it can actually happen, right? Right. So, let's extend the thought. It must be POSSIBLE for me to NOT go to the Matrix on Friday...before I can say that I WILL NOT go. If, by some strange irresistable means, I was forced to go to the movies, then it would be silly of me to say that I MIGHT NOT go. I KNOW that I'm going for certain. See the issue? An action must exist as a true possibility BEFORE it can be true CERTAINTY.
So, any DEFINITE claim is a subalternation of it's POSSIBLE form, whether positive or negative. This means entails that the definite claim can ONLY be true if and only if it's possible form is true.
**************************************
Sub-contrary:
Think about what we said about subalterations. From this, we know that it may be the case that only one possible claim to be true, like when one definite claim is made. For example, when I say it's CERTAIN that I will go to the movie, this implies the genuine possibility that I might go. But this means that the possibility that I might NOT go is false, right? Right.
But both possible action claims may be TRUE. It can be true that Meph MAY or MAY NOT see the Matrix on a Friday. Why can both be true at the same time? Because of the nature of possibility! If there is NO definite action claims being made, then the nature of possibility makes both claims true. For it to be a pure possibility, rather than any type of CERTAINTY, that I attend the movie on Friday, both the "may" and the "may not" have to apply to the situation. Therefore, both claims must be true. And the only thing that would make one of the possible action claims false if some type of SUBALTERATION were going on. (Now aren't you glad I did that one before this??
But it can never be the case that NEITHER possibility is open to me, by the definition of possibility. By subalteration, we see that possibilities are ALWAYS in the equation...even when we are dealing with just definite action claims.
So...either one or both possible action claims can be true at the same time, but both cannot be false at the same time.
*********************************
Contradictories:
Short answer...A given definite claim is ALWAYS contradictory to it's related OPPOSITE-TYPED possible claim and vice versa. This means that a positive definite action is always contradictory to the NEGATIVE POSSIBLE form of the action's claim and vice versa.
Example. If I were to say that I was CERTAINLY going to see the Matrix on Friday...but then turned around and told you that it MAY NOT be POSSIBLE that I go, what would you say? How about "What the @&$#? That makes no sense, Meph! You just contradicted yourself!"
What about if I said that it MAY be possible for me to see the movie...but it is a CERTAINTY that I WILL NOT see it. Same thing.
You try it. Take any action claim we use here. Now flip it's TYPE and DEFINITENESS. And see if I tell you true.
Meph WILL CERTAINLY drool if he sees Krispy Kreme doughnuts. (positive definite)
Now let's flip it...
Meph MIGHT NOT drool if he sees Krispy Kreme doughnuts. (negative possible)
Hmmm...they seem to contradict to me!
And common sense kicks in. They seem contradictory because both claims can't be true at the same time...AND they can't be false at the same time either!
*************************************
Now I bet if you read this in combination with Alan's picture, things may (or may NOT...heh) become clearer!
Holla,
Edited by - MephEternal on 05/17/2003 4:46:09 PM | | Back to Top | | |
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CalvinnHobbes
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| Posted 5/20/2003 6:27 PM (GMT -6) | | Alan, you say the truth of subalternation flows downward in the square [Agent x would (T) --> Agent x might (T)]. Is this square supposed to possess all the properties of the traditional square? If so, does falsity then flow upward as well [Agent x might (F)--> Agent x would (F)]? And if "Agent x would" is false, is "Agent x might" then logically undetermined (as a type I proposition would be according to the traditional square) or can we infer from a false "would" a false "might" as well [Agent x would (F) --> Agent x might (F)] which would be an immediate deduction not allowed by the traditional square? I haven't familiarized myself with a whole lot of material on the OV and haven't read Doc's Neo-Molinism paper yet, so forgive any potentially stupid questions.
quote:
If I were to say that I was CERTAINLY going to see the Matrix on Friday...but then turned around and told you that it MAY NOT be POSSIBLE that I go, what would you say? How about "What the @&$#? That makes no sense, Meph! You just contradicted yourself!" --meph
Does "Agent x might not" (alleged contradictory of "Agent x would" and our type O stand-in) mean to say "It might not be possible that Agent x would" or does it mean to say "It is possible that Agent x might not. . ."? What are the implications of and what is the relation between these options (if the statements entail different things)?
"The longer I live, the more I read, the more patiently I think, and the more anxiously I inquire, the less I seem to know." ~President John Adams | | Back to Top | | |
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GregBoyd
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| Posted 5/20/2003 8:07 PM (GMT -6) | |
Calvin H. Alan, you say the truth of subalternation flows downward in the square [Agent x would (T) --> Agent x might (T)]. Is this square supposed to possess all the properties of the traditional square? If so, does falsity then flow upward as well [Agent x might (F)--> Agent x would (F)]? And if "Agent x would" is false, is "Agent x might" then logically undetermined (as a type I proposition would be according to the traditional square) or can we infer from a false "would" a false "might" as well [Agent x would (F) --> Agent x might (F)] which would be an immediate deduction not allowed by the traditional square?
Doc: As I understand it, "would" logical encompasses "might," but "might" does not logically encompass "would." Hence, there's a category of truths -- "might counterfactuals" -- that an omniscient God would know, but which have been excluded from consideration on the part of classical theists. On the basis of feedback I've gotten form my proposal, its because they assume that since "would" implies "might," "mights" are already covered under God's knowledge of "woulds." I'm told that William Lane Craig is coming out in Philosophi Christi with a response to my proposal. It will be interesting to see how he responds.
And Alan, thanks for your input. You have a gift for breaking stuff down to bite size units.
Doc
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Tom
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| Posted 5/21/2003 12:29 AM (GMT -6) | | Isn't Philosophi Christi the journal Bill Hasker edits? Oh, I hope hope hope they give you a rejoinder. Or better yet, publish both Craig's article and your response in one issue.
Tom
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Tom
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| Posted 5/21/2003 4:26 AM (GMT -6) | | Does it sometimes happen that when someone publishes a response to another person’s work, that person publishing sends a copy of their response to the person in question? Is that an academic courtesy? Are you likely to see Craig’s response before it’s published (if only to have an opportunity to confirm Craig’s interpretation of you for his own sake)?
Here are two really good threads on Molinism. Perfect prep for Craig’s article. When is that due out by the way?
“A Refutation of Molinism” http://www.gregboyd.org/gbfront/forum/topic.asp?TOPIC_ID=1830&ARCHIVE=&whichpage=1
“The Principle of Bivalence” http://www.gregboyd.org/gbfront/forum/topic.asp?TOPIC_ID=1626&ARCHIVE=&whichpage=1
Tom
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Alan Rhoda
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| Posted 5/21/2003 2:16 PM (GMT -6) | | quote:
Alan, you say the truth of subalternation flows downward in the square [Agent x would (T) --> Agent x might (T)]. Is this square supposed to possess all the properties of the traditional square? If so, does falsity then flow upward as well [Agent x might (F)--> Agent x would (F)]? And if "Agent x would" is false, is "Agent x might" then logically undetermined (as a type I proposition would be according to the traditional square) or can we infer from a false "would" a false "might" as well [Agent x would (F) --> Agent x might (F)] which would be an immediate deduction not allowed by the traditional square?
CH, it seems to me that the counterfactual square possesses the same properties as the traditional square. Thus, falsity does flow upward along the subalternate relations. And if "Agent x would ..." is false then "Agent x might ..." is logically underdetermined.quote:
Does "Agent x might not" ... mean to say "It might not be possible that Agent x would" or does it mean to say "It is possible that Agent x might not. . ."?
Neither. The closest modal translation would be something like "Possibly, x does not do y in z".
Alan | | Back to Top | | |
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Alan Rhoda
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| Posted 5/21/2003 2:26 PM (GMT -6) | | Doc: ... They assume that since "would" implies "might," "mights" are already covered under God's knowledge of "woulds."
Alan: The only "mights" that are covered by "woulds" are those that follow directly from them. If God knows the "woulds" then He knows the corresponding "mights". But if neo-Molinism is true then there are some "mights" that are not covered by any "woulds" that God knows. Thus God knows the "mights" but not the corresponding "woulds". Craig would have to show that the set of "mights" not covered by a "would" is empty. I imagine that he will argue that there is no good reason to suppose that there are any "mights" that do not follow from "woulds" that God knows and that to suppose otherwise compromises God's omniscience and/or sovereignty.
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