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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 6/16/2004 10:52 PM (GMT -6) |   | Sloooooowly... 
quote:
Tom: My point is this, bivalent and non-bivalent systems do not define the law of non-contradiction the same way.
Alan: On the contrary, they do. Both bivalent and non-bivalent systems construe the law of non-contradiction as saying that A and not-A cannot both be true (at the same time and in the same respect). That contradictory propositions must have different truth values follows only from the additional assumption of bivalence.
I take bivalence as the more fundamental assumption and add the law of non-contradiction to it. But no matter. This is not my main objection to Prior. I understand the law of non-contradiction as Aristotle expressed it: “It is impossible for the same thing to belong and not belong simultaneously to the same thing in the same respect.” As far as I can tell, Prior essentially denies this when he claims that if a proposition is contingent so is its ‘contradictory proposition’ contingent. But no matter. Let’s move this to the back burner. I don’t “have it out” for multi-valued logic per say, but I wouldn’t agree that the fundamental difference between bivalent and non-bivalent systems is, as I hear you suggesting, one of semantics and that the case for the logical possibility of the open view can be made equally well through both bivalent and non-bivalent logics. On the contrary, I don’t think the case can be made via three-valued logic since I don't see that a case FOR three-valued logic has be made.
Alan: Is the contradictory of a contingent proposition also contingent? I, along with Prior, say Yes. Tom says No.
Tom: But in our paper you agree with me. You argue that the contradiction of Qp IS ~Qp.
Alan: If it is contingent that p, then it must also be contingent that ~p because if p might and might not be true (Qp) then ~p might and might not be true (Q~p).
Tom: Where p is a non-propositional component and not a propositional truth claim, yes. Qp = Qp and Q~p (Qp = p and ~p are both possible). But in this case p and ~p are not, as Prior claims, PROPOSITIONS, they’re non-propositional COMPONENTS.
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Tom: "It is contingent that p." That’s a qualified p. Prior posits a contingent PROPOSITION p. He defines p AS Qp.
Alan: Whoa. The claim is not that p = Qp. Those are different propositions.
Not for Prior they’re not. Prior’s example argues that p IS THE CONTINGENT PROPOSITION.
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Alan: Qp = "It is contingent that p", but p = "p". Plug in any proposition you want for p. Let's say you plug in "It is contingent that q". (We need to pick a different letter to avoid generating a self-referential proposition.) In that case p = Qq. But then "it is contingent that p" does not equal Qq but QQq.
Right. And QQq is nonsense. This is a problem for Prior, not for me. Prior claims that if the PROPOSITOIN p is contingent so is its contradictory PROPOSITION ~p contingent. If that’s the case then “logically contradictory” doesn’t mean anything anymore.
Alan: Let's say you plug in "It is contingent that q". (We need to pick a different letter to avoid generating a self-referential proposition.) In that case p = Qq.
Tom: And the CONTRADICTORY OF THIS PROPOSITION (caps for emphasis not for yelling ), that is of Qq, is?...is?...
is ~Qq, not Q~q.
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Tom: Let’s leave unqualified p (i.e., p without the operator “It is contingent that…”) as a small p and make qualified p (i.e., the proposition “It is contingent that p”) a capital “P", OK?
Alan: Works for me.
Tom: Thus:
p = the component (not the proposition): “...a sea battle tomorrow”
P = the proposition Qp (containing the component p): “It is indeterminately the case that a sea battle obtains tomorrow.”
Alan: p should read "there is a sea battle tommorow". So it is a proposition and not just a component of a proposition.
No, leave it a non-propositional component. The proposition “There is a sea battle tomorrow” is grammatically incoherent and meaningless. So my small p is just “…a sea battle tomorrow” and not a propositional truth claim regarding the sea battle. When you add “There will be…” or “there will not be…” or “There might and might not be…” you’re THEN forming a proposition.
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Tom: Thus “p is contingent” = Qp = P. And the contradictory of THIS is not Q~p, but ~Qp (or ~P). If you qualify a component (“a sea battle tomorrow”) with an operator to form a propositional truth claim and THEN form the contradictory of the proposition, i.e., the contradictory of the truth claim, the “~” is placed before the qualifying operator, that is, before the entire proposition, and not between the operator and the variable. Thus, the contradictory of “It is contingent that p,” or Qp, is ~“It is contingent that p,” or ~Qp.
Alan: I agree with everything you say here, Tom. But I don't see how it bears on the original question, which was whether a contingent proposition must have a contingent contradictory. If we take p as our contingent proposition, then the question becomes whether ~p is contingent. If we take Qp as our contingent proposition, as you seem to prefer, the question becomes whether ~Qp is contingent.
Precisely (though it is P and not p that is the ‘propositin’; p is the component)! But ~Qp is not contingent. Can’t be. It is the denial of contingency. ~Qp means “It is not the case that p is contingent.”
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Tom: Moving on, it seems to me a mistake to say Qp and Q~p are logical equivalents ... By “Qp ^ Q~p” you mean to say “p might and might not occur [that's what Qp means] and ~p might and might not occur [that's what Q~p means].” This if perfectly fine, because here p and ~p are components that contribute to forming their respective propositions (p in "p might and might not obtain" and ~p in "~p might and might not obtain") and not independent propositions making truth claims.
Alan: Whether components or not, p and ~p are propositions. To use the example, p is "there is a sea battle tomorrow" and ~p is "it is not the case that there is a sea battle tomorrow".
But I’m not using your examples. I’m using mine, and in mine p = “...a sea battle tomorrow.” I can posit such a p. It doesn’t make a claim about whether the sea battle will, won’t, or might and might not, happen tomorrow. Take p as a non-propositional component please. Besides, “There IS a sea battle TOMORROW” is grammatically incorrect and yields no meaning. I certainly don’t know what it means. Likewise “It is not the case that there IS a sea battle TOMORROW.” If you want p to be a proposition, then it has to be meaningful one, in which case you have only three options (none of which you use when you posit “There IS a sea battle TOMORROW”): “It is the case that there WILL be a sea battle tomorrow” (and its contradictory), “It is the case that there WILL NOT be a sea battle tomorrow” (and its contradictory), and “It is the case that there might and might not be a sea battle tomorrow” (and its contradictory!). The operators Z and Q are built into these propositions ALREADY because of the way they are worded. You can't further ADD Q to the proposition "It is the case that there might and might not be a sea battle tomorrow."
You know Alan, we need to be specific about whether operators like Z, Z~ and Q are phrases prefixed to propositions to form fuller propositions, or whether the operators are phrases prefixed to phrases to form propositions. Whichever way one goes, one needs to stick with it. Prior mixes them and that's his problem.
Lay it out on the Square:
There will be a sea battle tomorrow There will not be a sea battle tomorrow
There might be a sea battle tomorrow There might not be a sea battle tomorrow.
Replace each with notation:
Zp Z~p
~Z~p ~Zp
If you were to divide the words of the propositions and assign them to those parts of the equation they correspond to, what would you have? You’d have:
Z = “There will be…”
Z~ = “There will not be…”
etc. with ~Z and ~Z~, and…
Q = “There might and might not be…”
p = “…a sea battle tomorrow.”
This is Prior’s mistake. He posits a contingent proposition p and then further adds a contingency operator Q to it. This is mistaken. If p IS a contingent PROPOSITION, then (p = Qr [p the proposition and r the contingent state of affairs]) and not (If p [the proposition] then Qp [the proposition]). He doesn’t see that Q (indeterminacy) is ALREADY present in his proposition p when he posits the proposition p as a contingent proposition.
Had Prior (and Aristotle) claimed that if a state-of-affairs (not a proposition) is contingent then so is its contradictory state-of-affairs contingent, then he'd be fine.
By positing the non-propositional p, or "...a seat battle tomorrow" that's all I'm doing. I'm just positing the state-of-affairs "a sea battle tomorrow." States-of-affairs p and ~p ("...no sea battle tomorrow") CAN be both contingent. But a PROPOSITION claiming the occurence of "a sea battle tomorrow" is contingent (viz., "Tomorrow's sea battle is contingent") is a different matter altogether, for the contradiction OF THIS PROPOSITION is "It is not the case that 'Tomorrow's sea battle tomorrow is contingent'."
Thus, one can affirm contingency by claiming that both state-of-affairs p and its contradictory state-of-affairs ~p are contingent, or one can affirm contingency by claiming that both proposition “S might obtain” and its subcontrary proposition “S might not obtain” are true. But nothing meaningful is said when one claims that a proposition positing a contingent state-of-affairs and the contradictory proposition are logically equivalent.
Alan: Now some propositions have components that are also propositions.
Tom: This sounds like you admit that some propositions have components that are NOT propositions, which is right. And THAT is what my example holds out. P = the proposition “It is contingent that p” or Qp, and p = the component p in the proposition Qp. Qp and Q~p are logically equivalent, yes, but they are NOT contradictory propositions. Prior thinks they are. He’s wrong. Don’t you agree that Qp and Q~p are NOT contradictory propositions? Don’t you argue in fact that Qp and ~Qp are contradictory propositions? Why are you agreeing with Prior?
Alan: Qp, for example, says "It is contingent that p"…
Tom: Right. So give me the contradictory OF THIS PROPOSITION (you know it's ~Qp) and tell me Prior is right in arguing that Qp and Q~p are contradictory propositions.
quote:
Tom: You could add Q~p to Qp ... if you wanted to, but Q~p doesn't add anyting that's not already said in Qp.
Alan: Agreed. That's why I said that Qp and Q~p are logically equivalent.
Exactly! But Prior says they’re logically contradictory.
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Tom: One has to define p consistently throughout. If p is held to be a component and not a proposition, then p and ~p can both be contingent (as you point out). This would give us the logically redundant but not contradictory Qp ^ Q~p. But if p is defined as a contingent proposition, that is Qp (which Prior and Aristotle do), then it would be wrong to claim a) that the CONTRADICTORY PROPOSITION of Qp is Q~p (it isn’t) and wrong also to claim b) that that contradiction of contingency is also contingency.
Alan: Couple points here. First, your distinction between p as a component and p as a proposition is a false distinction. p in Qp is BOTH a component of Qp AND a proposition, namely, "there is a sea battle tomorrow".
But p isn't the entire proposition Qp, which IS what Prior claims. But in any case, please tell me what meaning you understand in the proposition “There IS a sea battle TOMORROW.” I get nothing from it. So I won't concede that it's a proposition. Lay out a grammatically meaningful proposition p claiming that a future state of affaris is contingent, and THEN prefix this contingent proposition with Q. Can't do it.
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Second, you are right that the contradictory of Qp is not Q~p, but ~Qp, but this is irrelevant to the question, which is whether contradictories can both be contingent.
No, the question is whether contradictory PROPOSITIONS can both be contingent. And what I said has everything to do with whether contradictory propositions can both be contingent. Prior’s WHOLE argument that if a proposition is contingent so is its contradictory proposition contingent DEPENDS entirely upon Qp and Q~p being contradictories. That's his entire argument. Read him. Here’s what he argues:
1. Qp and Q~p are both contingent
2. Qp and Q~p are contradictory propositions
3. Therefore, if a proposition is contingent so is its contradictory proposition contingent.
This argument of Prior’s is invalid since Qp and Q~p are not contradictories.
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To reiterate, what we want to know is whether two contradictory propositions can both be contingent. To ascertain this we start with an arbitrary proposition, p, assume it is contingent, and see if we can show that its contradictory, ~p, is also contingent. The steps of my proof run as follows:
Question: If p is contingent then is ~p also contingent?
1) p is contingent. (assumption)
2) If (1) then Qp.
3) If Qp then Q~p. (Since Qp and Q~p are logically equivalent.)
4) If Q~p then ~p is contingent.
5) Therefore, ~p is contingent.
This is a deductively valid and completely general proof. It assumes nothing about the nature of the propositions in question, p and ~p.
It DOES assume something about the nature of p. It assumes it’s ‘contingent’. But furthermore, this isn't what Prior argues. Prior's (1) would read: p is a contingent proposition. Is your p in (1) a contingent proposition? And you add Q to this already contingent proposition?
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Moreover, it is assumed at the outset that p and ~p are propositions. So they cannot be construed as non-propositional components of Qp and Q~p.
OK, so they’re propositions. p is a contingent proposition and ~p is the contradictory proposition. Everybody following this?
quote:
The only potentially challengeable premise is (3), but (3) is intuitively obvious. Qp says "there might and might not be a sea battle tomorrow". Q~p says "there might and might not not be a sea battle tomorrow". It is quite clear, I think, that these are two different ways of saying the same thing.
This is easy. If p and ~p are contradictory propositions, spell them out for me, Alan. No notation. Just words. Don’t give me the meaningless “There IS a sea battle TOMORROW.” Give me a grammatically meaningful proposition claiming that some future state of affairs is continget. THEN give me this proposition's contradictory and tell me they’re logically equivalent.
Now, you suggest two propositions.
"There might and might not be a sea battle tomorrow"
"There might and might not not be a sea battle tomorrow”
Are these the propositions p and ~p in your argument above? These ARE meaningful propositions. Problem is, these are not contradictory propositions. These are subcontrary propositions. So they are logically equivalent to p and p~ and not p and ~p. Don't you see that if these are your propositions then Q is already built into them? That's why if your (1) is true, that is, if p = the contingent proposition "There might and might not be a sea battle tomorrow", then (2) cannot read: If p then Qp, for Qp would equal "It is indeterminately the case that there might and might not be a sea battle tomorrow," and THAT my friend, makes no ONTOLOGICAL sense.
I’m standing my ground at the Alamo! Qp and Q~p are not, as Prior claimed and as his argument requires, contradictory propositions, and 2) if a proposition is contingent, its contradictory proposition is (if “contradictory” is to mean anything) the denial of this contingent proposition, or contra-contingent, or not contingent. But I do agree 3) that if a state-of-affairs is contingent, then its contradictory state-of-affairs is also contingent. This is TOOOOOTALLY cool, because the state-of-affairs "a sea battle tomorrow" doesn't make a truth claim UNTIL YOU ADD Z, Z~, or Q! But once we add Q ("There might and might not occur 'a seat battle tomorrow'") you can't claim that the contradictory is this proposition has the same truth value.
Somebody join me at the Alamo!
Blessings,
Tom | | Back to Top | | |
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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 6/17/2004 7:32 AM (GMT -6) | | quote:
Tom: Somebody join me at the Alamo!
I think the following agrees with Tom’s position. I’m not sure, though.
Q only applies if were talking about a meaningful proposition (not a mere component of a proposition), right? A statement that is not a meaningful proposition about something cannot be contingent or necessary or true or false.
Thus, in the case of Qp, “p”should not be understood as “a sea battle tomorrow”, for example. It makes no sense to say whether this statement is contingent or necessarily true or necessarily false until you know what is being affirmed about “a sea battle tomorrow”.
Moreover, Q only applies if we're qualifying a proposition about the future, right? Something that is present or past can't be contingent.
So "p" should be understood as something like "There will be a sea battle tomorrow" (i.e., a simple proposition about the future where "will" is unqualified as to contingency or necessity).
Q and Z serve as qualifiers designed to reflect the three possibilities regarding the present ontological status of any future event, e.g.:
Qp = “It is Contingently the case that there will be a sea battle tomorrow.”
Zp = “It is Necessarily the case that there will be a sea battle tomorrow.”
Z~p = “It is Necessarily Not the case that there will be a sea battle tomorrow.”
Note that Qp is not a statement about the future. Rather, it is a statement about the present, i.e., the present ontological status of a proposition about the future. Thus, it is wrong to say that “Qp” is contingent. Only statements about the future can be contingent. Rather, “Qp” is a way of expressing that the proposition “p” is (presently) contingent. It is “p” that is the contingent proposition. Qp = “p is a contingent proposition”. ~Qp = “p is not a contingent proposition”. Thus, while Qp and ~Qp are contradictories, this doesn’t tell us anything about whether contingent propositions can be contradictories.
On the other hand, “p” and “~p” are clearly contradictories. If “p” is contingent, then clearly “~p” is also contingent.
I need to know. Am I:
1. Merely stating the obvious
2. Way off base
3. Close, but no cigar
Thanks,
Earl | | Back to Top | | |
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Alan Rhoda
Registered Member
Date Joined May 2002
Total Posts : 680
| Posted 6/17/2004 9:08 AM (GMT -6) | | quote:
Alan: Is the contradictory of a contingent proposition also contingent? I, along with Prior, say Yes. Tom says No.
Tom: But in our paper you agree with me. You argue that the contradiction of Qp IS ~Qp.
These are two different issues, Tom. The contradictory of Qp is ~Qp. Neither Prior nor I denies that. You're misinterpreting Prior's claim that the contradition of a contingent proposition is contingent when you represent it as saying that Qp and Q~p are contradictories.
What Prior is saying is simply this: Take any two contradictory propositions: p and ~p. If p is contingent, then so is ~p. In other words, if Qp is true then Q~p is true. He is NOT claiming that Qp and Q~p are contradictories.
Tom: Prior posits a contingent PROPOSITION p. He defines p AS Qp.
Alan: No. He doesn't equate p and Qp. They can't be substituted salva veritate. He says that IF p is contingent then so is ~p. He does not assume that p is contingent. Maybe it is, and maybe it isn't. Again, the claim is only that IF Qp then Q~p.
Tom: And QQq is nonsense.
Alan: Why? If EVERY proposition is either Q, Z, or Z~, as Theorem I in our paper states, then if Qp is a proposition it must be meaningful to iterate the operators and say things like QQp, ZQp, and Z~Qp. Such higher-order propositions are, it seems to me, quite obviously meaningful. Thus, QQp could mean "It is contingent that 'It is contingent that there is a sea battle tomorrow'." This would describe a situation in which, say, God has not yet decided whether to sovereignly decree a sea battle or to leave it open and up to his creatures to settle. In that case whether it is contingent that there is a sea battle tomorrow depends on (is contingent upon) what God decides to do. This is second-order contingency.
quote:
Alan: p should read "there is a sea battle tommorow". So it is a proposition and not just a component of a proposition.
Tom: No, leave it a non-propositional component. The proposition “There is a sea battle tomorrow” is grammatically incoherent and meaningless.
Why do you think "There is a sea battle tommorow" is meaningless? I grant that the tenseless mode of speech here sounds stitled, but there is a reason for avoiding the future-tense here. We need a way of positing states-of-affairs that is neutral between "will", "will not", "might" and "might not". In other words, we need a way of positing states-of-affairs that does not prejudge between Q, Z, and Z~. If I had said, "There will be a sea battle tomorrow" I would have committed myself to Zp, when I want to affirm Qp. Nor could I have let p = "There might and might not be a sea battle tomorrow", for that is what Qp means. So we face the common logician's problem of having to stretch language in funny ways to say what needs saying while preserving systematic rigor. So we get "There is a sea battle tomorrow", which serves to posit the state-of-affairs "a sea battle tomorrow" without making any claim about whether it is contingent or not. Adding Q specifies the modality and makes it "It is contingent that there is a sea battle tomorrow."
Tom: ~Qp is not contingent. Can’t be. It is the denial of contingency. ~Qp means “It is not the case that p is contingent.”
Alan: ~Qp only denies contingency to p. It does not rule out the possibility that ~Qp might be contingent. In other words, it does not rule out the possibility that Q(~Qp) is true.
Tom: You know Alan, we need to be specific about whether operators like Z, Z~ and Q are phrases prefixed to propositions to form fuller propositions, or whether the operators are phrases prefixed to phrases to form larger propositions. Whichever way one goes, one needs to stick with it.
Alan: They should be modifiers that are prefixed to propositions. This is standard in logic, and it is the only way to preserve the full generality of the system because it is the only way to allow for even the conceptual possibility of second-order contingencies (QQp), which we shouldn't rule out a priori.
Tom: One can affirm contingency by claiming that both state-of-affairs p and its contradictory state-of-affairs ~p are contingent, or one can affirm contingency by claiming that both proposition “S might obtain” and its subcontrary proposition “S might not obtain” are true. But nothing meaningful is said when one claims that a proposition positing a contingent state-of-affairs and the contradictory proposition are logically equivalent.
Alan: Couple issues here. First, it is not meaningful to describe states-of-affairs as "contradictory". The law of non-contradiction applies to propositions (not states-of-affairs) because it is propositions (not states-of-affairs) that have truth values. It says that two "dictums" (propositions or statements) that are opposite in meaning cannot both be true. Second, no one (not me and not Prior) has claimed that "a proposition positing a contingent state-of-affairs and the contradictory proposition are logically equivalent." What we are saying is that IF a proposition p is contingent, then the contradictory of that proposition (i.e., ~p) is also contingent. In other words, the claim is that Qp entails Q~p, which I think you agree with. It is not the claim, as you mistakenly take it be, that Qp and Q~p are contradictories. You've simply got Prior wrong on this one.
Blessings,
Alan | | Back to Top | | |
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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 6/17/2004 10:24 AM (GMT -6) | | Alan: Thus, QQp could mean "It is contingent that 'It is contingent that there is a sea battle tomorrow'." This would describe a situation in which, say, God has not yet decided whether to sovereignly decree a sea battle or to leave it open and up to his creatures to settle. . . .
JET: Wouldn’t this rather be Qp, where:
p = “God decides to sovereignly decree a sea battle rather than leave it open and up to his creatures to settle”
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 6/17/2004 2:01 PM (GMT -6) | | I wrote a huuuuuge amount. Then reread the end of Alan’s post. So I trashed 90% and kept just this bit!
Tom: And QQq is nonsense.
Alan: Why? If EVERY proposition is either Q, Z, or Z~, as Theorem I in our paper states, then if Qp is a proposition it must be meaningful to iterate the operators and say things like QQp, ZQp, and Z~Qp. Such higher-order propositions are, it seems to me, quite obviously meaningful. Thus, QQp could mean "It is contingent that 'It is contingent that there is a sea battle tomorrow'." This would describe a situation in which, say, God has not yet decided whether to sovereignly decree a sea battle or to leave it open and up to his creatures to settle.
Tom: Then the sea battle is contingent, pure and simple Qp. How this state-of-affairs happens to be contingent is something else that doesn’t bear on the fact of indeterminacy itself (assuming you still believe indeterminacy is an attribute of states of affairs and not of propositions).
Alan: In that case whether it is contingent that there is a sea battle tomorrow depends on (is contingent upon) what God decides to do. This is second-order contingency.
Tom: Well, at least you’re attributing the contingency here to a state-of-affairs, i.e., God’s choosing, while Prior’s argument attributes it to propositions.
If you want talk about God’s choice this way, then express this with a proposition about the contingency of God’s choice to render the sea battle determinate or not: Qc (c = God’s choice to determine a sea battle tomorrow) would then be: “God might and might not choose to determine a sea battle tomorrow.” You’re conflating the indeterminacy of one event (God’s choice) with the indeterminacy of another event (a sea battle tomorrow). But if you’re talking about the ontological status of the future with regard to tomorrow’s sea battle, then Qp says everything that can be said about the indeterminacy of the event. QQp doesn’t saying another about the ontological status of p that Qp doesn’t already say.
Likewise, ZQp (which I gather means “It is determinately the case that p might and might not obtain”). This, I think, overlooks that fact that any operator is itself ‘determinately’ what IT IS. Q doesn’t need Z to be determinately what it is. ZQp doesn’t say anything about the ontological status of p that Qp doesn’t say.
Alan: Why do you think "There is a sea battle tommorow" is meaningless?
Tom: Tell me what it means.
Alan: I grant that the tenseless mode of speech here sounds stitled, but there is a reason for avoiding the future-tense here. We need a way of positing states-of-affairs that is neutral between "will", "will not", "might" and "might not".
Tom: Finally! Light at the end of the tunnel! You want to posit states-of-affairs without making claims as to whether they will, will not, or might and might not occur? How about positing the state-of-affairs itself: “…a sea battle tomorrow.” How difficult is that?
Alan: In other words, we need a way of positing states-of-affairs that does not prejudge between Q, Z, and Z~.
Tom: Then you can’t posit a PROPOSITION, Alan. For propositions make truth claims. And a proposition about a sea battle tomorrow cannot BUT make SOME truth claim about tomorrow’s sea battle. If you want to posit the state-of-affairs without laying claim to Z, Z~, or Q, then just plop the state-of-affairs out there on the table: “…a sea battle tomorrow.”
Alan: So we face the common logician's problem of having to stretch language in funny ways to say what needs saying while preserving systematic rigor.
Tom: What systematic rigor is sacrificed if you say the state-of-affairs p = “…a sea battle tomorrow”? Do you want to claim that all states-of-affairs are propositions or cannot be posited apart from propositions?
quote:
Tom: ~Qp is not contingent. Can’t be. It is the denial of contingency. ~Qp means “It is not the case that p is contingent.”
Alan: ~Qp only denies contingency to p. It does not rule out the possibility that ~Qp might be contingent. In other words, it does not rule out the possibility that Q(~Qp) is true.
Come on Alan. Q(~Qp) = “It is indeterminately the case that it’s not the case that there might and might not be a sea battle tomorrow.” “If it’s indeterminately that case that it’s not the case that there might and might not be a sea battle tomorrow” then Qp. There might and might not be a sea battle tomorrow. How far do you wanna push this? QQQQQQQQQQQQQp? God might and might not decide to determine a world whose circumstances determine the birth of a king who is determined to found a kingdom that goes to war by sea? None of this says anything about the ontological status of p that Qp doesn’t say.
quote:
Tom: One can affirm contingency by claiming that both state-of-affairs p and its contradictory state-of-affairs ~p are contingent, or one can affirm contingency by claiming that both proposition “S might obtain” and its subcontrary proposition “S might not obtain” are true. But nothing meaningful is said when one claims that a proposition positing a contingent state-of-affairs and the contradictory proposition are logically equivalent.
Alan: Couple issues here. First, it is not meaningful to describe states-of-affairs as "contradictory". The law of non-contradiction applies to propositions (not states-of-affairs) because it is propositions (not states-of-affairs) that have truth values.
Now we’re friggin getting somewhere! So tell me, Alan, how can you then claim (as you do above) that grammatically stilted “There IS a sea battle TOMORROW” is BOTH a meaningful proposition AND a proposition that avoids making any truth claims?
Now, if you don’t want to say the states-of-affairs “a sea battle tomorrow at noon off the coast of Virginia” and “no sea battle tomorrow at noon off the coast of Virginia” are contradictory because they make no truth claims, fine. How about it’s “opposite”? But it’s certainly meaningful to posit a state of affairs while not making any truth claim about that state of affairs. You believe your “There is a sea battle tomorrow” does just this. And if this is just a state of affairs that makes no truth claim, then why call “There is no sea battle tomorrow” its contradictory (as you have been all along). Secondly, if we can posit truth-valueless state of affairs p, we can certainly posit truth-valueless state of affairs ~p. If you wouldn’t call these contradictory (and I’m not insisting they be called that), what WOULD you call them?
quote:
Alan: Second, no one (not me and not Prior) has claimed that "a proposition positing a contingent state-of-affairs and the contradictory proposition are logically equivalent." What we are saying is that IF a proposition p is contingent, then the contradictory of that proposition (i.e., ~p) is also contingent.
Well, finally! If you and Prior mean what I think you mean, Alan, then a) Prior and you are using Q as a third truth value, i.e., to posit “indeterminacy” as a truth value of propositions and not as an attribute of states of affairs, and b) what is left in our paper that you agree with?
Do you agree that there ARE any such contingent propositions of indeterminate truth value? Do you agree that indeterminacy is an attribute of propositions rather than states-of-affairs?
Prior’s whole reason for bringing this up is to make a case for non-bivalence. He offers Qp. But since he means “a proposition p of indeterminate truth value” he just begs the question. He just assumes there are any such propositions. I’m not saying that the claim “If there are any such propositions…” entails the belief that there are such propositions. But Prior DOES believe there are such contingent propositions. And what he’s saying here he’s saying because he believes there are such propositions. But he never produces a single one. His Qp is the CLAIM that there are such contingent propositions. It’s not an ARGUMENT. I assumed he was arguing his case and assumed that he was using “contingent” as an attribute of states-of-affairs and not a truth value of propositions.
I won’t bother you guys any more. Let me close out:
1) Since Prior’s only example of a “contingent proposition” is HIS Qp (not OUR Qp, for they are two entirely different uses of Q), he just begs the question re: bivalence. Qp is his CLAIM that there are such contingent propositions. It’s not an ARGUMENT. If anyone wants to give an example without any notation, I’m all ears. “There might and might not be a sea battle tomorrow” is not an example. This can be understood perfectly on the assumption of bivalence. Give us an example that actually ARGUES a case for bivalence without assuming bivalence.
2) Prior’s Qp ASSUMES non-bivalence and cannot be a proof OF non-bivalence.
3) It attributes determinacy and indeterminacy to propositions when they are in fact attributes of states-of-affairs. I honestly don’t know what it means to say a ‘proposition’ is indeterminate, Alan.
Alan, I’d like to know whether or not you affirm bivalence and why.
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Alan Rhoda
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| Posted 6/17/2004 2:19 PM (GMT -6) | | Hi, Earl. Nice to have you jump into the mix. Your contributions are always insightful.
JET: Q only applies if were talking about a meaningful proposition (not a mere component of a proposition), right? A statement that is not a meaningful proposition about something cannot be contingent or necessary or true or false. Thus, in the case of Qp, “p” should not be understood as “a sea battle tomorrow”, for example. It makes no sense to say whether this statement is contingent or necessarily true or necessarily false until you know what is being affirmed about “a sea battle tomorrow”.
Alan: I concur.
JET: Moreover, Q only applies if we're qualifying a proposition about the future, right? Something that is present or past can't be contingent.
Alan: I think this is right. If we were talking about the present or past then we couldn't say "might and might not", we'd have to switch to a perfect tense and say "might have and might not have". Perhaps we could figure out a way of generalizing Q, Z, and Z~p to cover the perfect tenses. To do that we'd have to combine indeterminacy logic with some form of tense logic, which could get very messy.
JET: So "p" should be understood as something like "There will be a sea battle tomorrow" (i.e., a simple proposition about the future where "will" is unqualified as to contingency or necessity).
Alan: I accept that as a construal for "p". Hopefully it will mollify Tom's misgivings about my tenseless "There is a sea battle tomorrow." As you mention, however, if we construe p this way it is essential that "will" NOT imply anything as to contingency and necessity. As long as we keep that in mind, your construal is fine. I opted for the tenseless "There is a sea battle tomorrow" in order to avoid the need to continually remind ourselves that "will" in this case doesn't mean "will definitely".
JET: Q and Z serve as qualifiers designed to reflect the three possibilities regarding the present ontological status of any future event, e.g.:
Qp = “It is Contingently the case that there will be a sea battle tomorrow.”
Zp = “It is Necessarily the case that there will be a sea battle tomorrow.”
Z~p = “It is Necessarily Not the case that there will be a sea battle tomorrow.”
Alan: Right on, except that Z~p should read "It is Necessarily the case that there will NOT be a sea battle tomorrow."
JET: Note that Qp is not a statement about the future. Rather, it is a statement about the present, i.e., the present ontological status of a proposition about the future. Thus, it is wrong to say that “Qp” is contingent. Only statements about the future can be contingent. Rather, “Qp” is a way of expressing that the proposition “p” is (presently) contingent.
Alan: You are correct that Qp is a statement about the present, but that does not necessarily imply that it is wrong to say that Qp is contingent. QQp can be a meaningful statement if the two Q's affirm contingency with respect to different points in time. Thus, if the first Q described what is contingent at t0 and the second Q described what it contingent at t1, then both refer to what is future relative to the temporal frame in question. For example, I can meaning say "Yesterday (t0) it was contingent that it would now (t1) be contingent that there is a sea battle tomorrow (t2). How can this be? Quite simply. Suppose that something could be done at t0 that would either causally determine that there is a sea battle at t2 or that would leave it causally undetermined. In that case, whether it is contingent at t1 that there is a sea battle at t2 is itself contingent at t0. As long as each successive Q refers to what is contingent at a moment temporally successive to the previous Q, one can meaningfully have as many Q's as one wants in front of p. Thus, QQQQQQQQQQp is potentially a meaningful expression.
Overall, good observations, Earl. Thanks for the input.
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Alan Rhoda
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| Posted 6/17/2004 3:26 PM (GMT -6) | | Thanks for the reply, Tom. It's fun interacting with you.
quote:
Alan: In that case whether it is contingent that there is a sea battle tomorrow depends on (is contingent upon) what God decides to do. This is second-order contingency.
Tom: Well, at least you’re attributing the contingency here to a state-of-affairs, i.e., God’s choosing, while Prior’s argument attributes it to propositions.
If you want talk about God’s choice this way, then express this with a proposition about the contingency of God’s choice to render the sea battle determinate or not: Qc (c = God’s choice to determine a sea battle tomorrow) would then be: “God might and might not choose to determine a sea battle tomorrow.” You’re conflating the indeterminacy of one event (God’s choice) with the indeterminacy of another event (a sea battle tomorrow). But if you’re talking about the ontological status of the future with regard to tomorrow’s sea battle, then Qp says everything that can be said about the indeterminacy of the event. QQp doesn’t saying another about the ontological status of p that Qp doesn’t already say.
You make a fair point, Tom. Successive Q's don't add anything unless they qualify the contingency of p in a different respect. But that doesn't make QQp meaningless. It just means that QQp = Qp. (This is analogous to modal logic where Nec[Nec(p0] = Nec(p) or Poss[Poss(p)] = Poss(p).) But QQp and Qp will not be equivalent if successive Q's qualify the contingency of p in a different respect. We can indicate this as you suggest by subscripting our Q's. If we let t be the time with respect to which something is said to be contingent, and let c be a possible causal situation obtaining at time t, then when can meaningfully generate a succession of Q's as follows:
Q(t0,c0)Q(t1,c1)Q(t2,c2) ... Q(tn,cn)(p)
Tom: Likewise, ZQp (which I gather means “It is determinately the case that p might and might not obtain”). This, I think, overlooks that fact that any operator is itself ‘determinately’ what IT IS. Q doesn’t need Z to be determinately what it is. ZQp doesn’t say anything about the ontological status of p that Qp doesn’t say.
Alan: I agree that ZQp = Qp. My point is simply that it is meaningful to iterate operators. If Qp is meaningful and if ZQp = Qp then ZQp is also meaningful.
Tom: You want to posit states-of-affairs without making claims as to whether they will, will not, or might and might not occur? How about positing the state-of-affairs itself: “…a sea battle tomorrow.” How difficult is that?
Alan: The problem is that "a sea battle tomorrow" does not posit anything. To do that we need to add something like "there is" onto it to make an complete assertion. Here's another way of looking at it. In the prediction "There WILL be a sea battle tomorrow" the force of "WILL" is that the future is settled in that respect. We indicate that with Z. And we can represent the proposition by Zp. Now we want to isolate p, so take out WILL. What's left? You have "There ... be a sea battle tomorrow". It's the phrase "there" + (to be) that actually does the positing, just like "There's food on the table" posits food on the table. Rewording things a bit we get "There is a sea battle tomorrow". We can use WILL as a modifier.
WILL(There is a sea battle tomorrow) = Z(There is a sea battle tomorrow).
Tom: Do you want to claim that all states-of-affairs are propositions or cannot be posited apart from propositions?
Alan: I want to say that states-of-affairs cannot be posited apart from propositions because that's precisely what a posit is.
Tom: Alan, how can you then claim (as you do above) that grammatically stilted “There IS a sea battle TOMORROW” is BOTH a meaningful proposition AND a proposition that avoids making any truth claims?
Alan: I don't claim that it makes no truth claims. It does. All propositions do. It claims that there will be a sea battle tomorrow without implying that this is today either necessary or contingent. If it turns out that there is a sea battle tomorrow, then the claim is true. If not, then it's false. As I point out in the paper, however, we need to distinguish this from the claim that it is true TODAY that there will be a sea battle tomorrow.
quote:
quote:
Alan: Second, no one (not me and not Prior) has claimed that "a proposition positing a contingent state-of-affairs and the contradictory proposition are logically equivalent." What we are saying is that IF a proposition p is contingent, then the contradictory of that proposition (i.e., ~p) is also contingent.
Well, finally! If you and Prior mean what I think you mean, Alan, then a) Prior and you are using Q as a third truth value, i.e., to posit “indeterminacy” as a truth value of propositions and not as an attribute of states of affairs, and b) what is left in our paper that you agree with?
I don't know where you get the idea that I'm positing Q as a third truth value. Prior may do that, but I don't, and I don't see how it follows from what I said. The claim that Qp implies Q~p only invokes two truth values. It says "If it is TRUE that Qp then it is TRUE that Q~p", which implies by contraposition, "If is it FALSE that Q~p, then it is FALSE that Qp". Where do you see a third truth value?
Prior may try to squeeze non-bivalence out of this, but it simply doesn't follow from the claim that Qp implies Q~p. If that's where Prior wants to go, then here's where I part company with Prior.
Tom: Alan, I’d like to know whether or not you affirm bivalence and why.
Alan: Yes, I do affirm it. The reason is basically the same as what you've been emphasizing. Insofar as reality is indeterminate, there ought to be a TRUE description of it as such. But if there is a TRUE description of reality that communicates the respects in which it is indeterminate, then there is no need to invent an indeterminate truth value to accomplish the same job. Moreover, while one could invent a consistent language game with multiple truth values to describe real indeterminacy, such an endeavor is at the very least misleading, for it suggests that indeterminacy is a property of a proposition's correspondence with reality--which could be merely epistemic--rather than a property of reality.
In summary, I'm with you, Tom, in affirming bivalence. And if Prior wants to reject bivalence, then I agree with you that he's made a mistep. But I don't think that mistep occurs when he claims that the contradictory of a contingent proposition is also contingent. On that issue I think he's correct.
God bless,
Alan | | Back to Top | | |
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Tom
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| Posted 6/17/2004 3:46 PM (GMT -6) | | Come on guys, let me sleep! It’s 4:45 AM.
JET: Q only applies if were talking about a meaningful proposition (not a mere component of a proposition), right? A statement that is not a meaningful proposition about something cannot be contingent or necessary or true or false.
Tom: Before or after you add Q?
JET: Thus, in the case of Qp, “p” should not be understood as “a sea battle tomorrow”, for example. It makes no sense to say whether this statement is contingent or necessarily true or necessarily false until you know what is being affirmed about “a sea battle tomorrow”. (Alan concurs).
Tom: How lame can ya get. Come on! Q renders p contingent. That’s what the bloody operator does. If p is a contingent proposition apart from Q, then why add Q?
If p = a proposition positing a contingent state-of-affairs: “It is indeterminate that p occurs”
And if Q = “It is indeterminate that…”
Then Qp conjoins these two: “It is indeterminate that it is indeterminate that p occurs.” But that’s NOT what we claim Qp means.
On the other hand:
If Qp = “It is indeterminately the case there occurs a sea battle tomorrow”
Then what is left for Q to mean if p is the proposition “It is indeterminately the case there occurs a sea battle tomorrow”?
JET: Moreover, Q only applies if we're qualifying a proposition about the future, right? Something that is present or past can't be contingent.
Tom: Q just doesn’t apply to what we’re qualifying. Q IS THE QUALIFICATION.
JET: So "p" should be understood as something like "There will be a sea battle tomorrow" (i.e., a simple proposition about the future where "will" is unqualified as to contingency or necessity).
Alan: I accept that as a construal for "p". Hopefully it will mollify Tom's misgivings about my tenseless "There is a sea battle tomorrow." As you mention, however, if we construe p this way it is essential that "will" NOT imply anything as to contingency and necessity. As long as we keep that in mind, your construal is fine. I opted for the tenseless "There is a sea battle tomorrow" in order to avoid the need to continually remind ourselves that "will" in this case doesn't mean "will definitely".
Tom: Grrrrrr. First, “There is a sea battle tomorrow” is not tenseless. Secondly, “There will be a sea battle tomorrow” is not tenseless and is, as far as I can tell, exactly what Zp claims. Sure, you follow immediate with the qualification that you don’t mean Zp and you want it understood that no truth claim is being made. You guys want to put as much distance between how normal human beings speak and how logic works. Why? Maybe that’s just my pet issue. But if we can get it right in average Joe’s language, then by golly we ought to.
Now, if you’re claiming that p posits the state-of-affairs stripped bare of any truth claims then a) why say (as JET does above and as Alan concurs) that it makes no sense to posit state-of-affairs p without knowing what is being affirmed about p? and b) what objection is left to saying the state-of-affairs p = “a sea battle tomorrow”?
quote:
JET: Q and Z serve as qualifiers designed to reflect the three possibilities regarding the present ontological status of any future event, e.g.:
Qp = “It is Contingently the case that there will be a sea battle tomorrow.”
Zp = “It is Necessarily the case that there will be a sea battle tomorrow.”
Z~p = “It is Necessarily Not the case that there will be a sea battle tomorrow.”
Alan: Right on.
Alan, I can’t for the life of me comprehend your support of Prior.
quote:
Alan: You are correct that Qp is a statement about the present, but that does not necessarily imply that it is wrong to say that Qp is contingent. QQp can be a meaningful statement if the two Q's affirm contingency with respect to different points in time. Thus, if the first Q described what is contingent at t0 and the second Q described what it contingent at t1, then both refer to what is future relative to the temporal frame in question. For example, I can meaning say "Yesterday (t0) it was contingent that it would now (t1) be contingent that there is a sea battle tomorrow (t2). How can this be? Quite simply. Suppose that something could be done at t0 that would either causally determine that there is a sea battle at t2 or that would leave it causally undetermined. In that case, whether it is contingent at t1 that there is a sea battle at t2 is itself contingent at t0. As long as each successive Q refers to what is contingent at a moment temporally successive to the previous Q, one can meaningfully have as many Q's as one wants in front of p. Thus, QQQQQQQQQQp is potentially a meaningful expression.
But a) QQQQQp says nothing about the ontological status of p that Qp doesn’t say, b) each Q in the line is a separate indeterminate state-of-affairs. This is clear in “whether it is contingent at t1 that there is a sea battle at t2.” Two independent events or states-of-affairs are consider here. One is “whether it is contingent at t1 that there is a sea battle at t2” and the second is “whether there is a sea battle at t2.” If yesterday it was contingent that it would now be contingent that a sea battle would occur tomorrow, then yesterday’s contingent event at t1 is not tomorrow’s sea battle at t2, but rather that state-of-affairs which TODAY at t1 determines whether tomorrow’s sea battle at t2 remains contingent or not. Thus each Q is a different event and each Q ought to have its own variable even if each impact the p. And c) every Q but the last precedes the moment at which the claim is made and thus are no longer Q’s really, viz., “It is indeterminately the case that” but posit instead a past contingency (and one which is no longer contingent—it is no longer contingent at t1 plus a minute that “it is contingent at t1 that a sea battle would occur tomorrow at t2). What all the preceding Q’s posit is “It WAS indeterminately the case that….” If one should want to say “Yesterday it was contingent that it would now be contingent that there would be a sea battle tomorrow” why not introduce an operator H (for history!) meaning: “It was contingently the case that…”? And “r” would be today’s moment in time when the contingency of p was put to the test. Then you could say Hr(Qp). You could add ‘em up all you wanted to provided you added different variables showing that each previous contingency is a separate state-of-affairs from the others and that each is no longer a contingent state-of-affairs, for each of them resolved itself so as to leave p contingent: HaHbHcHdHeHfHgHgHiQp. Not sure if you need parentheses or not. Got for it.
Tom | | Back to Top | | |
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Tom
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| Posted 6/17/2004 4:08 PM (GMT -6) | | Alan: I don't claim that it makes no truth claims. It does. All propositions do. It claims that there will be a sea battle tomorrow without implying that this is today either necessary or contingent. If it turns out that there is a sea battle tomorrow, then the claim is true. If not, then it's false. As I point out in the paper, however, we need to distinguish this from the claim that it is true TODAY that there will be a sea battle tomorrow.
Tom: How does one today make the truth claim “There will be a sea battle tomorrow” without implying anything as to its necessity or contingency? How does it not equal Zp? And how does “If it turns out that there is a sea battle tomorrow, THEN the claim is true” not amount to retroactive causation of some kind, that is, today’s claim “There will be a sea battle tomorrow” is rendered true or false tomorrow when there is or isn’t a sea battle?
Publish it Alan and Doc, but I don’t understand a single line.
Alan: In summary, I'm with you, Tom, in affirming bivalence. And if Prior wants to reject bivalence, then I agree with you that he's made a mistep. But I don't think that mistep occurs when he claims that the contradictory of a contingent proposition is also contingent. On that issue I think he's correct.
Tom: Is the contingency an attribute of the contingent proposition or an attribute of a state-of-affairs posited in the proposition? If the former, then your doing what only non-bivalent proponents do, namely, ascribing “contingency” to propositions. If the latter, then kindly give me a proposition which ascribes contingency to a state-of-affairs and show me how this proposition and its contradictory are logically equivalent.
I’m giving up. It’s 5 AM and I haven’t slept.
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Tom
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| Posted 6/17/2004 4:46 PM (GMT -6) | | Ah, so what, now it’s 5:45 AM and I gotta wake up in 15 minutes anyhow!
Alan-
1) You affirm bivalence.
2) You deny that a proposition positing a contingent state-of-affairs and the proposition’s contradictory are logically equivalent.
3) But you affirm that if a proposition is contingent (in some way OTHER than positing a contingent state-of-affairs) so is the proposition’s contradictory contingent.
4) You agree that “contingency” is to be attributed to states-of-affairs and not to propositions.
Here’s what I need from ya. Give me a proposition, either true or false, which does not posit a contingent state-of-affairs but which is itself contingent in such a way that the contingency is not an attribute of the proposition but of states-of-affairs.
I really need to see such a proposition.
Tom  | | Back to Top | | |
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JET
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| Posted 6/17/2004 6:23 PM (GMT -6) | | quote:
JET: Thus, in the case of Qp, “p” should not be understood as “a sea battle tomorrow”, for example. It makes no sense to say whether this statement is contingent or necessarily true or necessarily false until you know what is being affirmed about “a sea battle tomorrow”. (Alan concurs).
Tom: How lame can ya get. [jet: lol] Come on! Q renders p contingent. That’s what the bloody operator does. If p is a contingent proposition apart from Q, then why add Q?
JET: Moreover, Q only applies if we're qualifying a proposition about the future, right? Something that is present or past can't be contingent.
Tom: Q just doesn’t apply to what we’re qualifying. Q IS THE QUALIFICATION.
JET: So "p" should be understood as something like "There will be a sea battle tomorrow" (i.e., a simple proposition about the future where "will" is unqualified as to contingency or necessity).
Alan: I accept that as a construal for "p". Hopefully it will mollify Tom's misgivings about my tenseless "There is a sea battle tomorrow." As you mention, however, if we construe p this way it is essential that "will" NOT imply anything as to contingency and necessity. As long as we keep that in mind, your construal is fine. I opted for the tenseless "There is a sea battle tomorrow" in order to avoid the need to continually remind ourselves that "will" in this case doesn't mean "will definitely".
Tom: Grrrrrr. First, “There is a sea battle tomorrow” is not tenseless. Secondly, “There will be a sea battle tomorrow” is not tenseless and is, as far as I can tell, exactly what Zp claims. Sure, you follow immediate with the qualification that you don’t mean Zp and you want it understood that no truth claim is being made. You guys want to put as much distance between how normal human beings speak and how logic works. Why? Maybe that’s just my pet issue. But if we can get it right in average Joe’s language, then by golly we ought to.
Tom, I have to apologize. I've been all over the place. I did a reversal between the time I posted above in this thread and the time I finished all my edits in my other thread. (I'm basically in over my head, but, hey, I wanna learn too.) I thought about deleting my post above or adding a disclaimer, but never got around to it.
Anyway, what I want to say now (for the reasons stated in the other thread, and your reasons above) is that "There is a sea battle tomorrow" does not constitute a proposition and is meaningless (unless it simply refers to the state of affairs "a sea battle tomorrow"). (It could also refer to the proposition Zp, "There will necessarily be a sea battle tomorrow", but as Alan has established, that is not what is intended by "There is a sea battle tomorrow".)
One of your initial objectives was:
quote:
I’m trying to nail down exactly where we (Doc, Alan, and I) would argue Prior goes wrong in arguing FROM p and ~p are contradictories (which they are) and both are contingent (which they are) TO denying bivalence since both a proposition and its contradictory cannot both be true or false.
If Q = "It is contingently the case that there is" and p = "a sea battle tomorrow", then p is not a proposition. Likewise, if Q = "It is contingently the case that" and p = "there is a sea battle tomorrow", p is not a proposition (assuming we're correct.) If p is not a proposition, then p and ~p are NOT contradictory propositions. Moreover, bivalence does not require that p (or require that ~p) be either true or false because the law of bivalence only applies to propositions.
On the other hand, if p = "It is contingently the case that there will be a sea battle tomorrow", then what we're positing is actually Qp, the contradictory of which is not Q~p but rather ~Qp. And clearly both Qp and ~Qp are bivalent.
I think you've said this (right?), and (just so I'm clear) isn't this all tied to the conclusion that "There is a sea battle tomorrow" is not a proposition? Isn't that the key to explaining where Prior goes wrong?
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Tom
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| Posted 6/17/2004 11:32 PM (GMT -6) | | JET: (just so I'm clear) isn't this all tied to the conclusion that "There is a sea battle tomorrow" is not a proposition? Isn't that the key to explaining where Prior goes wrong?
Tom: I think we’re splitting hairs. I don’t know anymore. Until Alan gives me a proposition, either true or false, which does not posit a contingent state-of-affairs but which is itself contingent in such a way that the contingency is not an attribute of the proposition but of some state-of-affairs, I have no idea what I’m dealing with.
See, Alan agrees with Prior that Qp and Q~p are an example of “if a proposition is contingent then so is its contradictory.” But Qp and Q~p are only an example of this claim IF a) p and ~p are contradictory propositions (I'm not settled on this either because I still haven't seen in English what these two contradictory propositions are) and b) Q, or contingency, is an attribute of the propositions p and ~p and not an attribute of the states-of-affairs posited by the propositions p and ~p. That’s what Alan claims Prior means by “contingent proposition” and Alan seems to agree. In Prior’s Qp, Q renders the entire ‘proposition p” contingent, not the ‘state-of-affairs’ posited in the proposition. But then Alan has said that he agrees that contingency is not an attribute of propositions but only of states-of-affairs.
I don’t get it.
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JET
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| Posted 6/18/2004 1:04 AM (GMT -6) | | TJB: See, Alan agrees with Prior that Qp and Q~p are an example of “if a proposition is contingent then so is its contradictory.” But Qp and Q~p are only an example of this claim IF a) p and ~p are contradictory propositions (I'm not settled on this either because I still haven't seen in English what these two contradictory propositions are) and b) Q, or contingency, is an attribute of the propositions p and ~p and not an attribute of the states-of-affairs posited by the propositions p and ~p. That’s what Alan claims Prior means by “contingent proposition” and Alan seems to agree. In Prior’s Qp, Q renders the entire ‘proposition p” contingent, not the ‘state-of-affairs’ posited in the proposition. But then Alan has said that he agrees that contingency is not an attribute of propositions but only of states-of-affairs.
JET: (Again, I'm backtracking from my earlier post and I'm now agreeing with you . . . )
It seems to me that a "state of affairs" only becomes a proposition when you posit that it (the state of affairs) has some ontological status. If the "state of affiars" is a future event, its ontolgical status is one of three possibilities: Z, Z~ or Q. So a description of a future "state of affairs" is not a proposition without attributing to it Z, Z~ or Q. Without Z, Z~ or Q, you haven't made any truth claim about the future state of affairs that you've described. Without Z, Z~ or Q, all you've done is described or identified a future state of affairs. Describing or identifying something does not, by itself, make any truth claim about what is being described. "A red apple tomorrow" is not a proposition. "There is a red apple tomorrow" is a proposition only if it is understood to mean "There will be a red apple tomorrow" (i.e., only if we attribute Z to "a red apple tomorrow"). Likewise with "There is a sea battle tomorrow".
Thus, Qp and Q~p is not an example of “if a proposition is contingent then so is its contradictory.” The proposition is Qp and the contradictory is ~Qp.
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Humphrey Bogart
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| Posted 6/18/2004 1:19 AM (GMT -6) | | OK guys, my exams are over and I can get back into this stuff. If you don't mind, I'd like to take a step back a few posts, since I think that there is an issue which people think is resolved, which isn't.
Alan wrote: Exactly. A disjunction can be true simply because it's disjuncts are jointly exhaustive (as is the case when they are contradictory) and not because one of the disjuncts is in fact true. For example, "Either 'x < 0' or 'x > 0' or 'x = 0'" is true for any x that is a member of the set of real numbers. But which disjunct is true depends on the value of x. Until that is specified, we cannot say of any one disjunct that it is true or that it is false. But we can know that the disjunct is true BEFORE the value of x is specified because the disjuncts are jointly exhaustive.
Tom wrote: Alan’s comments about noting whether or not disjunctions are exhaustive are very good and I think they fix things, Albert. We can say with regard to any claim at T0 regarding any claim regarding p at T1, “Either p or ~p at T1.” This doesn’t rule out p’s contingency, viz., it’s being true that “p might or might not obtain at T1” and false both that “p will obtain at T1” and “p will not obtain at T1.”
Albert's response:
OK, I don't think this solves the problem, and here's why. A disjunction that is jointly exhaustive is true only for the same reason that any disjunction is true; because one of the disjuncts is true. It's just that with a disjunction that is jointly exhaustive, we know that one of the disjuncts has to be true, whereas with other disjuncts, we don't know that. The statement "X or Y" can only be true if X is true or Y is true or both.
Now to address Alan's example. The reason we know that "either x<0 or x>=0" is true (just to simply things to two disjuncts instead of three) for a real x is that it is logically impossible for x to be a real number and for both x<0 and x>=0 to be false. In other words, for any x, one of the disjuncts must be true, which is why the overall disjunction is true.
However, this is completely unlike the situation with "will" and "will not". On the kind of indeterminacy logic which Tom, Greg, and others including myself have been espousing, the statements "X will" and "X will not" can both be false (if X is something that is open and not determined). In this case, the disjunction "either X will or X will not" must also be false. There is no way around that, guys.
Furthermore, the argument that "either X will or X will not" exhausts all the possibilities is also false on our indeterminacy logic. There is one other possibility: namely that "X might" and "X might not" are both true, and hence "X will" and "X will not" are both false. So here is the disjunction that is true on our theory, and which does exhaust all the possibilites:
Either "X will" or "X will not" or "X might and X might not"
The statement "Either X will or X will not" on our theory says that either X is determined or not-X is determined. But this omits the possibility that neither X nor not-X is determined. In fact, if the statement "Either X will or X will not" is true for all X, then determinism is true.
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Tom
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| Posted 6/18/2004 1:32 AM (GMT -6) | | JET: It seems to me that a "state of affairs" only becomes a proposition when you posit that it (the state of affairs) has some ontological status. If the "state of affiars" is a future event, its ontolgical status is one of three possibilities: Z, Z~ or Q. So a description of a future "state of affairs" is not a proposition without attributing to it Z, Z~ or Q.
Tom: Good point. You know, JET, when I obssessed over a year ago on this stuff and we all got to talking about it, we agreed then (Alan included I believe) on the following:
For any future tense p, either Zp, Z~p, or Qp.
See it? There are no propositions regarding future states of affairs that are not either Zp, Z~p, or Qp. To posit a p regarding some future state of affairs is to posit one of these even if you don't explicitly mention the operator. Thus, there is no "extracting p" from Zp (or Z~p or Qp). There is only 'waking up' logically to the the fact that all future tense p's are each by definition either Zp, Z~p, or Qp. There are no propositions describing future tense states of affairs that are not by definition an embodiment of either Z, Z~, or Q. With regard to the future, there's only Z-future, Z-~future, and Q-future. We've said it already: these three are conjointly exhaustive and mutually exclusive. So what business do we then have positing propositions about the future that are neither Z, Z~p, or Q? There are no such propositions.
Remember this Alan? I do. Still on board with this?
Now, if we try to argue (because of some existing principle of logic) that p MUST be extractable from Z, Z~, and Q and remain a proposition making a claim about some future state of affairs, THEN I don't see how ADDING Q (or Z, or Z~) to this proposition does not reduce the operators to being attributes of propositions, which we have sworn we want to avoid. If you want the operator to be an attribute of states-of-affairs, then it seems our earlier claim that for any future tense p, either Zp, Z~p, or Qp. This is not adding a new logic of the future. It's uncovering the logic of the future. Qp and Q~p are not an example of contradictory contingent propositions.
Doc, get your drumming butt in here! 
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Tom
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| Posted 6/18/2004 1:44 AM (GMT -6) | | Albert: Either "X will" or "X will not" or "X might and X might not"
Tom: This is I think the first theorem of our paper: For any future tense p, either Zp, Z~p, or Qp. This disjunction is true because the disjuncts are jointly exhausitive and mutually exclusive. Right on.
Albert: The statement "Either X will or X will not" on our theory says that either X is determined or not-X is determined. But this omits the possibility that neither X nor not-X is determined. In fact, if the statement "Either X will or X will not" is true for all X, then determinism is true.
Tom: Right. And when you read Aristotle’s struggle to maintain bivalence in the face of what he believed was the only available disjunction—“Either ‘There will be a sea battle tomorrow’ or ‘There will not be a sea battle tomorrow’”—you can understand why he saw future contingents as an exception to bivalence. Had he admitted “…or there might and might not be a sea battle tomorrow” to the disjunction, he could have maintained bivalence and claim his disjunction was true.
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Alan Rhoda
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| Posted 6/18/2004 5:29 PM (GMT -6) | | quote:
Originally posted by TGB
Alan-
1) You affirm bivalence.
2) You deny that a proposition positing a contingent state-of-affairs and the proposition’s contradictory are logically equivalent.
3) But you affirm that if a proposition is contingent (in some way OTHER than positing a contingent state-of-affairs) so is the proposition’s contradictory contingent.
4) You agree that “contingency” is to be attributed to states-of-affairs and not to propositions.
Here’s what I need from ya. Give me a proposition, either true or false, which does not posit a contingent state-of-affairs but which is itself contingent in such a way that the contingency is not an attribute of the proposition but of states-of-affairs.
Thanks for the summary, Tom. Before I answer your challenge, I need to clarify some terms.
First, what is a state-of-affairs? It's a MUCH broader category than you might initially think. It includes things that are actual (e.g., Doc's being a pastor) and things that are not (e.g., My being a pro football player). It includes things that are physically possible (e.g., A rock's falling) and some are not (e.g., A rock's flying upward on its own power). It includes not only a sea battle's occuring tomorrow, but also its being contingent that there is a sea battle tomorrow and its being true that it is contingent that there is a sea battle tomorrow. And it also includes things that are logically necessary (e.g., 2+2's being equal to 4) and things that are logically impossible (e.g., a circle's being square). Basically, just about anything expressible in the form (possessive noun, pronoun, or noun phrase)+(gerund) is a state-of-affairs.
Second, contingency is opposed to both necessity and impossibility. If a state-of-affairs is contingent then it is possible but not necessary. Something is possible (or not) in relation to a field of possibilities, which is generated by a system of constraints or background assumptions. Logical possibility, for example, is constrained by the law of non-contradiction. Something is logically contingent iff is it logically possible but not logically necessary. Physical possibilty is constrained by physical laws. So something is physically contingent iff it is physically possible but not physically necessary. And so on. There are as many possible types of contingency as there are different possible systems of constraints.
Now a system of constraints or background assumptions is itself a state-of-affairs. For example, the state-of-affairs an omnipotent God's existing generates a different field of possibilities than does God's not existing. If God does not exist, then some things (e.g., resurrections) are not possible, as they would be if he does exist. In any case, every state-of-affairs constrains a field of possibilities. For example, the cat's being on the mat right now rules out such states-of-affairs as no cats' existing, no mats' existing, and the cat's not being on the mat right now.
Thus contingency is a dyadic relation between two states-of-affairs. A state-of-affairs is contingent on some field of possibilities iff, in relation to another state-of-affairs that defines the relevant field of possibilities, it is both possible and not necessary.
Third, you distinguish in (3) above between (a) "contingent proposition" and (b) "proposition positing a contingent state-of-affairs". The latter phrase is ambiguous, however, for it could mean (b.1) "proposition positing THAT a state-of-affairs is contingent" or (b.2) "proposition positing a state-of-affairs that happens to BE contingent".
Given the above characterizations of "states-of-affairs" and of "contingent" here's how I interpret (a), (b.1), and (b.2):
As for (a), a proposition is contingent (i.e., is a "contingent proposition") with respect to a field of possibilities iff the truth of that proposition is possible but not necessary on that field. The contingency applies not to the proposition as such, but to the state-of-affairs the proposition's being true with respect to that field of possibilities.
With respect to (b.1), the operator "Q" affirms THAT a state-of-affairs is contingent. So (b.1) is properly denoted by Qp, where "p" is a proposition positing some state-of-affairs. Qp is false if the state-of-affairs posited by p is not in fact contingent. For example, Q(2+2=4) is false because it claims THAT (2+2=4) is contingent when it is not.
(b.2) differs from (b.1) because it doesn't claim THAT a certain state-of-affairs is contingent. So, where p is a proposition positing a state-of-affairs that happens to be contingent, it should be represented by p and not by Qp, for we can't represent something as Qp unless it is claimed to be contingent.
Fourth, with respect to your summary of my position in points (1)-(4). I agree with (1), (2), and (4), but not (3). You say there that I "affirm that if a proposition is contingent (in some way OTHER than positing a contingent state-of-affairs) so is the proposition’s contradictory contingent."
As I have explained, to say that a proposition is contingent is to say that the state-of-affairs the proposition's being true is possible but not necessary in relation to some other state-of-affairs that grounds the relevant field of possibilities. In other words, to say that a proposition is contingent is to posit THAT some state-of-affairs (i.e., the proposition's being true) is contingent. This is not necessarily the same thing as positing a contingent state-of-affairs, however, for one may be mistaken in what one posits. Thus, if the proposition's being true is in fact necessary, then positing THAT that state-of-affairs is contingent fails to posit a contingent state-of-affairs. One the other hand, if the proposition's being true is in fact contingent, then positing THAT that state-of-affairs is contingent does succeed in positing a contingent state-of-affairs. In other words, your assumption that one can affirm THAT a proposition is contingent iff one posits a contingent state-of-affairs is false.
In short I accept (3) IFF you remove the qualification in parentheses.
Fifth You say, "Give me a proposition, either true or false, which does not posit a contingent state-of-affairs but which is itself contingent in such a way that the contingency is not an attribute of the proposition but of states-of-affairs."
If the proposition is not to posit a contingent state-of-affairs then it has to posit a necessary state-of-affairs. What counts as necessary or contingent is relative to given field of possibilities. Let's take the field of possibilities defined by Euclidean geometry. In that field, "the sum of the interior angles of a triangle equals 180 degrees" is a necessary truth. This proposition posits the non-contingent state-of-affairs the-sum-of-the-interior-angles-of-a-triangle's equaling 180 degrees.
Now you want this proposition to be itself contingent. Since it can't be contingent wrt Euclidean geometry, we have to shift reference frames. If we drop Euclid's parallel line postulate, then we open up the field of possibilities to curved geometries in which the sum of the interior angle's of a triangle may or may not equal 180 degrees, depending on the curvature of space. In that frame of reference the proposition is contingent, not necessary.
Finally, you want this contingency to be an attribute, not of a proposition, but of a state-of-affairs. That's easy. The contingency applies to the state-of-affairs the-sum-of-the-interior-angles-of-a-triangle's equaling 180 degrees.
Sorry for rambling on so long. But I hope you have a better understanding of where I'm coming from. To reiterate the main point, your position seems to me to conflate (b.1) positing THAT a state-of-affairs is contingent with (b.2) positing a contingent state-of-affairs. The two are different because one can posit THAT something is the case and be mistaken.
God bless,
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Tom
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| Posted 6/19/2004 1:04 AM (GMT -6) | | Alan: Sorry for rambling on so long. But I hope you have a better understanding of where I'm coming from. To reiterate the main point, your position seems to me to conflate (b.1) positing THAT a state-of-affairs is contingent with (b.2) positing a contingent state-of-affairs. The two are different because one can posit THAT something is the case and be mistaken.
Tom: I did wanna just say that I noticed you expressed nearly all your states-of-affairs as non-propositional components after dismissing my doing so. You also use “contingent” sometimes to mean “logically contingent” and sometimes to mean “historically contingent” without expressly mentioning which you mean. Seems to me that your "contingent proposition" is simply a proposition whose truth value is what it is neither necessarily nor impossibly, that is, its truth value is logically contingent. I understood that our paper was exclusively about historical contingency. I also don't see the import of your distinction between propositions positing THAT a state-of-affairs is contingent and propositions positing states-of-affairs THAT are in fact contingent. All propositions positing a state-of-affairs that is in fact contingent also claim THAT their states-of-affairs are contingent (though not vice-versa, if that's the distinction you were making; but that's hardly news). If a proposition that posits THAT a state-of-affairs is contingent is a true proposition, it's true because the state-of-affairs it describes is in fact contingnet. And if a proposition posits a state-of-affairs that is in fact contingent, the proposition is true. I don't see much to hang my hat on in the distinction between these.
BTW, would you still agree, as you once did, that: For any future tense p, either Zp, Z~p, or Qp?
Anyhow, I tried to write a bit of a response but the electricity kept going on and off and I'd lose a portion of work each time. The infrastructure in Beirut here is still not working well. When it finally came back on to stay, it dawned on me that I really don’t understand much of anything about indeterminacy logic, bivalence, contingency, and the open future! You and Doc are gonna have to carry this torch. If I can’t follow the arguments, I can’t argue the arguments!
Peace,
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JET
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| Posted 6/19/2004 3:46 AM (GMT -6) | | I think we need to clearly distinguish between Truth Values and Ontological Values.
Truth Values describe propositions. Ontological Values describe states of affairs.
Truth Values indicate whether or not a proposition corresponds to present reality. Ontological Values, on the other hand, merely describe (truthfully or not) the ontological status of a state of affairs given present reality.
There are only two Truth Values: True or False. Either a proposition corresponds to reality (ie, the proposition is True) or it does not (ie, it is False). Hence, bivalence.
There are several Ontological Values. For example, for any state of affairs, it either obtains, did obtain, did not obtain, will obtain, etc. With respect to future states of affairs, there are three possible Ontological Values: either it necessarily will obtain or it necessarily will not obtain or it might obtain. Hence: (Z v Z~ or Q).
Now, if you assume a settled future, then for any future state of affairs, “reality” (i.e., everything that is presently true) includes the fact that such state of affairs either “will” (Z) or “will not” (Z~) occur. If you assume an open future, then for any future state of affairs, present reality includes the fact that such state of affairs either “will” (Z) or “will not” (Z~) or might (Q) occur. However, we are not talking about three Truth Values. Rather, we are talking about three Ontological Values. (Note, we are here talking about future “states of affairs” not “propositions”.)
So bivalence is irrelevant to the debate about the ontological status of the future. The debate is not over whether there are two or three Truth Values. The debate is over whether (when it comes to future states of affairs) there are two or three Ontological Values.
Notes:
When we refer to a “contingent proposition”, we are not referring to the Ontological Value of the proposition. Rather, we are referring to the Ontological Value of the state of affairs posited by the proposition. The Truth Value of the proposition is either True of False (not True or False or Contingent).
A statement constituting purely a “state of affairs” can have no express or implied ontological value attributed to it. If an ontological value is attributed to a state of affairs, then a truth claim has been made about the state of affairs (viz, that it has such and such ontological value) and so you now have a proposition instead of purely a state of affairs.
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Tom
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| Posted 6/19/2004 9:57 AM (GMT -6) | | JET: I think we need to clearly distinguish between Truth Values and Ontological Values.
Tom: I know what you're getting at, but "ontological values" doesn't work for me because a value attaches to something as a property, whereas ontology is that TO WHICH properties attach themselves. Ontology is too fundamental to be a value (though again, I know what you're getting at). Doesn't ontological states-of-affairs work better?
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JET
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| Posted 6/19/2004 1:55 PM (GMT -6) | | Tom: I know what you're getting at, but "ontological values" doesn't work for me because a value attaches to something as a property, whereas ontology is that TO WHICH properties attach themselves. Ontology is too fundamental to be a value (though again, I know what you're getting at). Doesn't ontological states-of-affairs work better?
JET: “Ontological states-of-affairs” sounds (to me) like its referring only to states-of-affairs that ontologically exist. I want to be able to attribute what I’ve called “Ontological Values” to states of affairs that exist as well as those that don’t exist and those that might exist. I thought about “Ontological Status”, but I don’t know the plural of “status”.
I’m not sure I understand your objection to saying “Ontological Values”. The ontological status or quality of any future state-of-affairs is one of three possibilities: Z, Z~, or Q. My dictionary defines “value” as “the quality or number represented by a figure or symbol”. I want to say that Necessarily, Necessarily Not, and Contingently are the ontological qualities represented by the symbols Z, Z~ and Q, respectively (hence, “Ontological Values”).
Similarly, corresponding to reality and not corresponding to reality are the qualities represented by the symbols True and False (hence, “Truth Values”).
Make sense?
The question is whether Qp and Q~p are an example of “if a proposition is contingent then so is its contradictory.” If what I'm trying to say is true, then the answer is no. Because Qp and Q~p are not "contingent propositions". If what I'm saying is true, no proposition is technically "contingent". Contingency is not a property of propositions. Contingency is an "Ontological Value" and thus only applies to "states of affairs". If what I'm saying is true, the "Ontological Value" of contingency applies only to the state of affairs, p, not to the proposition Qp. (See "notes" in my post, above).
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Tom
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| Posted 6/19/2004 6:48 PM (GMT -6) | | JET: “Ontological states-of-affairs” sounds (to me) like its referring only to states-of-affairs that ontologically exist.
Tom: Naw, state-of-affairs can be past, presently actual, historically contingent (i.e., Q), etc. Hey, call ‘em ‘ontological STATES’.
I think too that you’ll want to think about ‘truth conditions’. The truth condition of a proposition is that by virtue of which the proposition is true or false, that which determines the truth value of propositions. This condition IS a state-of-affairs, or a state-of-reality if that's better, and it always is that state-of-affairs that exists at the time the proposition is spoken. But again, it’s confusing to call ontological states-of-affairs ‘values’ since values DERIVE FROM states-of-affairs while ontological states-of-affairs are more fundamental. In other words ‘values’ are attributes of ontological states-of-affairs, so why call those states-of-affairs ‘values’? Just call them ‘states’!
So now you’ve got...
Truth values: true and false
Truth conditions: ontological states-of-affairs which determine the truth value of propositions
Propositions: assertions that make truth claims
states-of-affairs: Want it in fancy logic-lingo or common jive-talk? I’d say a state-of-affairs is simply ‘a way the world is’ (or ‘was’ or ‘can’ be), ‘a slice or reality’ is even better.
Now, the state-of-affairs ‘a cow jumping over the moon’ is a proposed state-of-affairs. But since it’s physically impossible (as Alan pointed out) it’s not an actual state-of-affairs. So it’s not a slice of reality. It’s a state-of-affairs in that it proposes to be a state-of-reality, it presents itself for our consideration, it runs for membership, but it doesn’t qualify. When I say “ontological state-of-affairs” I mean “a slice of reality” or “a way the world is.”
JET: I’m not sure I understand your objection to saying “Ontological Values”. The ontological status or quality of any future state-of-affairs is one of three possibilities: Z, Z~, or Q. My dictionary defines “value” as “the quality or number represented by a figure or symbol”. I want to say that Necessarily, Necessarily Not, and Contingently are the ontological qualities represented by the symbols Z, Z~ and Q, respectively (hence, “Ontological Values”).
Tom: “States” would work well for this then. But since “values” attach to something other than themselves that determine what they are (while ontological states do not), calling ontological states “values” seems confusing. But hey, that’s just me! And I’m understanding less and less of this stuff.
Now, since states-of-affairs can be such that they determine future states-of-affairs (Z or Z~) or determine a range of future states-of-affairs (Q), we can speak of the “status” of ontological states-of-affairs, and that’s what Z and Q do. Z and Q tell us what the “status” of a particular state-of-affairs is, that is, whether the actual state-of-affairs at the time the proposition is made (viz., the truth conditions of the proposition) is such that the state-of-affairs about which the proposition makes some truth claim follows determinately or indeterminately from the state-of-affairs that constitute the proposition’s truth conditions.
JET: Similarly, corresponding to reality and not corresponding to reality are the qualities represented by the symbols True and False (hence, “Truth Values”).
Make sense?
Tom: Well, yeah, but corresponding and not corresponding to reality are what is generally called the “truth conditions” that yield a score, a value, or T or F.
JET: The question is whether Qp and Q~p are an example of “if a proposition is contingent then so is its contradictory.” If what I'm trying to say is true, then the answer is no. Because Qp and Q~p are not "contingent propositions". If what I'm saying is true, no proposition is technically "contingent". Contingency is not a property of propositions. Contingency is an "Ontological Value" and thus only applies to "states of affairs".
Tom: Other than wanting to avoid calling ‘contingency’ a value, I agree completely. Well, I thought I did. But like I said, I’m pretty confused right now about all of this. I’d also agree with you so long as by “contingency” you mean historical contingency and not logical contingency. A state-of-affairs can be historically determined (i.e., it can be already actual or determined to be actual) but logically contingent (i.e., the state-of-affairs is not what it is necessarily like the state-of-affairs ‘God’s existing’ is what it is necessarily).
It sure looks to me like Alan attributes historical contingency to propositions and their truth values as opposed to states-of-affairs, but I’m swamped with having to pack my house up and move to the other side of the planet! So…
Peace,
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Tom
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| Posted 6/19/2004 7:33 PM (GMT -6) | | Alan: As for (a), a proposition is contingent (i.e., is a "contingent proposition") with respect to a field of possibilities iff the truth of that proposition…
Tom: The truth VALUE of the proposition? Or (assuming the proposition IS trut) the proposition’s being in fact true?
Alan: As for (a), a proposition is contingent (i.e., is a "contingent proposition") with respect to a field of possibilities iff the truth of that proposition is possible but not necessary on that field. The contingency applies not to the proposition as such, but to the state-of-affairs the proposition's being true with respect to that field of possibilities.
Tom: It looks to me like you’re defining a ‘contingent proposition’ as a proposition whose truth value is logically contingent. I can’t tell if by “the state-of-affairs the proposition's being true” you mean to say:
(A) …the proposition IS true (in which case the state-of-affairs of its being true is simply the proposition’s truth conditions) or,
(B) …whether the proposition is true or not is not a determinate matter.
(A) Affirms bivalence but takes “contingent” to mean “logically contingent.”
(B) Denies bivalence and attributes “contingency” to propositions.
Re: (A), assuming bivalence, and that Tom is married, then “Tom is married” is true BUT is a logically contingent proposition. Though my being married is now historically determined, it is logically contingent. It’s not logically necessary that I be married. But since nearly every proposition excluding mathematical truths would qualify as contingent in this sense, I’m guessing you mean something else. But I still can’t conceive of what the something else is if bivalence is to hold.
Once again:
Alan: As for (a), a proposition is contingent (i.e., is a "contingent proposition") with respect to a field of possibilities iff the truth of that proposition is possible but not necessary on that field. The contingency applies not to the proposition as such, but to the state-of-affairs the proposition's being true with respect to that field of possibilities.
Tom: Let me ask for an example of such a proposition. No notation and no definitions. Just a contingent proposition in English with a truth value of TRUE, please.
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JET
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| Posted 6/19/2004 8:12 PM (GMT -6) | | TGB: In other words ‘values’ are attributes of ontological states-of-affairs, so why call those states-of-affairs ‘values’?
JET: I'm not calling states-of-affairs "values". I'm calling the ontological attributes of states-of-affairs "values". Future states-of-affairs have one of three ontological attributes (which you just called "values" in your quote above).
TGB: Just call them ‘states’!
JET: But I don't want the attributes ("values") to be confused with the "states".
The reason I like "Ontological Values" is because it sounds close enough to "Truth Values" to highlight the distinction between the two. It is an important distinction for purposes of the question of bivalence, because it shows that it is "states of affairs" that have three possible values (not propositions) and the three possible values are Ontological Values, not Truth Values. The "threeness" inherent in indeterminancy relates to the ontological status of future states of affairs. But this "threeness" is compatible with bivalence because bivalence only applies to truth claims about future states of affairs, not the ontological status of those future states of affairs.
TGB: So now you’ve got
Truth values: true and false
Truth conditions: ontological states-of-affairs which determine the truth value of propositions
Propositions: assertions that make truth claims
states-of-affairs: Want it in fancy logic-lingo or common jive-talk? I’d say a state-of-affairs is simply ‘a way the world is’ (or ‘was’ or ‘can’ be), ‘a slice or reality’ is even better.
JET: "States-of-affairs" may or may not correspond with reality, though, right? "Earl smoking a cohiba" is a state of affairs, even though the proposition "Earl is smoking a cohiba" is False, right?
TGB: Now, the state-of-affairs ‘a cow jumping over the moon’ is a proposed state-of-affairs. But since it’s physically impossible (as Alan pointed out) it’s not an actual state-of-affairs. So it’s not a slice of reality. It’s a state-of-affairs in that it proposes to be a state-of-reality, it presents itself for our consideration, it runs for membership, but it doesn’t qualify.
JET: Why not just say "a cow jumping over the moon" is a state of affairs, while the proposition "a cow is jumping over the moon" is False? Let's make it a future state of affairs: "a cow jumping over the moon tomorrow". This state of affairs has one of three possible "Ontological Values" : Z, Z~ or Q. The proposition "a cow will jump over the moon tomorrow" has one of two possible Truth Values. We happen to be in an epistemic position to know in this case that the Ontological Value of the future state of affairs "a cow jumping over the moon tomorrow" is Z~. Thus, the proposition: "a cow will jump over the moon tomorrow" is False. Likewise, the proposition "a cow might jump over the moon tomorrow" is False. The proposition "a cow will not jump over the moon tomorrow" is True.
It seems to work. It seems tight.
quote:
JET: I’m not sure I understand your objection to saying “Ontological Values”. The ontological status or quality of any future state-of-affairs is one of three possibilities: Z, Z~, or Q. My dictionary defines “value” as “the quality or number represented by a figure or symbol”. I want to say that Necessarily, Necessarily Not, and Contingently are the ontological qualities represented by the symbols Z, Z~ and Q, respectively (hence, “Ontological Values”).
Tom: “States” would work well for this then. But since “values” attach to something other than themselves that determine what they are . . .
JET: I don't understand what you mean by this. "Ontological Values" attach to something other than themselves (states of affairs). What do you mean by ". . . that determine what they are"?
TGB: Now, since states-of-affairs can be such that they determine future states-of-affairs (Z or Z~) or determine a range of future states-of-affairs (Q), we can speak of the “status” of ontological states-of-affairs, and that’s what Z and Q do. Z and Q tell us what the “status” of a particular state-of-affairs is, that is, whether the actual state-of-affairs at the time the proposition is made (viz., the truth conditions of the proposition) is such that the state-of-affairs about which the proposition makes some truth claim follows determinately or indeterminately from the state-of-affairs that constitute the proposition’s truth conditions. (JET’s emphasis)
JET: Or doesn’t follow at all (ie, Z~), right? Do we agree that “states of affairs” can include things that are actual and things that are not actual, as Alan says?
Tom: . . . so long as by “contingency” you mean historical contingency and not logical contingency. A state-of-affairs can be historically determined (i.e., it can be already actual or determined to be actual) but logically contingent (i.e., the state-of-affairs is not what it is necessarily like the state-of-affairs ‘God’s existing’ is what it is necessarily).
JET: I’m not sure I totally understand, but I think I have been talking about historical contingency.
TGB: I’m swamped with having to pack my house up and move to the other side of the planet!
JET: Thanks for taking the time to respond. It’s been helpful (as always).
Thanks,
Earl
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Humphrey Bogart
Registered Member
Date Joined Jun 2003
Total Posts : 205
| Posted 6/19/2004 11:22 PM (GMT -6) | | Regarding the "three valued future" of Z, ~Z and Q:
I would distinguish between "truth values" (propostions being true or false) and "ontological values" only if by this you mean things either existing or not existing (although I still don't like the term "ontological values"). But the point is, if you want to use the term "ontological values", there are still only two ontological values: existence or non-existence. There are no others. Ontology is bivalued just like truth; in fact the reason truth is bivalued is because ontology is bivalued.
Now as for the future, statements about the future are three-valued because their truth value is logically dependent on the present, not on the future. They are not, strictly speaking, ontological statements, but logical inferences from ontological statements. The wonderful irony of the position we are advocating is that future-tensed statements derive their truth value from the present, not the future. Now for any X there are three types of logical entailment from the present: X being logically entailed by the present, not-X being logically entailed by the present, and neither X nor not-X being logically entailed by the present (and both being logically consistent with the present). For this reason, future-tensed statements appear to have three values (Z, ~Z and Q). But this is because they are not ontological or existential statements (which only have two values, X exists and X does not exist), but logical inferences from existential statements.
Just as things either exist or do not exist, so states of affairs either are the case or are not the case. So "states of affairs", like ontology and truth, are bivalued also.
Does this make sense?
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