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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 6/17/2004 8:14 AM (GMT -6) |   | Consider the following statements:
p “There is a sea battle tomorrow”
Qp “It is Contingently the case that there is a sea battle tomorrow.”
Zp “It is Necessarily the case that there is a sea battle tomorrow.”
Z~p “It is Necessarily Not the case that there is a sea battle tomorrow.”
It seems to me that bivalence holds for the last three, i.e.,:
Qp is either True or False
Zp is either True or False
Z~p is either True or False
But not for the first, i.e.,:
“p” is either True or False or Indeterminate [Edit: Actually, as argued below, "p" is not a proposition. Thus, "p" cannot be True, False or Indeterminant, but rather, "p" is either Z or Z~ or Q]
What is the difference between the first statement and the last three? [Edit: see next post] | | Back to Top | | |
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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 6/17/2004 10:03 AM (GMT -6) | | The Principle of Bivalence only purports to apply to propositions.
From http://www.philosophypages.com/dy/index.htm . . .
Bivalence, principle of: Supposition that every proposition must be either true or false.
Proposition: What is conveyed by a declarative sentence used to make a statement or assertion.
In order to retain bivalence, perhaps the indeterminist must argue that the statement ...
S: “There is a sea battle tomorrow”
by itself, does not convey a proposition.
That is, “S” does not affirm or declare or assert anything about "a sea battle". Not only does it fail to assert any details about the "sea battle tomorrow", "S" does not even assert that there "will" or “will not” or “might” be a sea battle tomorrow. It is merely a description of an event (“a sea battle”) that is described in terms placing the event in the future (“tomorrow”). It is no different than saying:
“a sea battle tomorrow”
Thus, S is not “a declarative sentence used to make a statement or assertion”. Therefore, S does not convey a proposition.
In order to convey a proposition, more needs to be said about “a sea battle tomorrow”. At a minimum, we need to say either that it “will” occur or that it “will not” occur or that it “might” occur. If it will or might occur, we could assert more details about "a sea battle tomorrow" (e.g., that it will occur at a certain time tomorrow or it might occur at a certain place). But in order to declare or assert something meaningful about "a sea battle tomorrow" we must, at a minimum, declare that it "will" or "will not" or "might" occur.
Once you qualify S with Q or Z or Z~ , you then have a proposition and bivalence is not a problem. | | Back to Top | | |
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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 6/17/2004 1:01 PM (GMT -6) | | If the foregoing is correct, then perhaps bivalence can co-exist with 3-valued logic when understood as follows:
Propositions are bivalent. Thus, each of the following propositions are either True or False:
Qp
Zp
Z~p
Statements that merely describe future events have one of three values. However, the three values are not true, false and nueter. Rather, the three values are Z, Z~ and Q. Thus, the statement:
“There is a sea battle tomorrow”
(which is the same as saying, “a sea battle tomorrow”)
is either Z or Z~ or Q. The principal of bivalence is not violated because it does not apply. The principal of bivalence does not apply with respect to such statement because it is not a proposition (i.e., it is not “a declarative sentence used to make a statement or assertion”.)
So bivalence and multi-valued logic are both true!
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Tom
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Date Joined Jul 2001
Total Posts : 10353
| Posted 6/17/2004 2:38 PM (GMT -6) | | JET: Consider the following statements:
p “There is a sea battle tomorrow”
Qp “It is Contingently the case that there is a sea battle tomorrow.”
Zp “It is Necessarily the case that there is a sea battle tomorrow.”
Z~p “It is Necessarily Not the case that there is a sea battle tomorrow.”
Tom: Unless I’ve totally lost my mind, Z~p means “It is necessarily the case that there is not a sea battle tomorrow.” Your ““It is Necessarily Not the case that there is a sea battle tomorrow” is ~Zp.
JET: It seems to me that bivalence holds for the last three, i.e.,:
Qp is either True or False
Zp is either True or False
Z~p is either True or False
But not for the first, i.e.,:
“p” is either True or False or Indeterminate [Edit: Actually, as argued below, "p" is not a proposition. Thus, "p" cannot be True, False or Indeterminant, but rather, "p" is either Z or Z~ or Q]
Tom: If p is not a proposition then it’s not either Z or Z~ or Q. And if it IS one of Z, ~p, or Q then, as you just said above, it is a bivalent truth claim.
JET: In order to retain bivalence, perhaps the indeterminist must argue that the statement ...
S: “There is a sea battle tomorrow” by itself, does not convey a proposition.
Tom: S isn’t a proposition. Alan suggested is was a proposition but suggested that it didn’t make any truth claim. But that contradicted his own claim that "propositions make truth claims." I suggest that if you want to posit a state-of-affairs without making any truth claim about it, “a sea battle tomorrow” is perfect.
JET: That is, “S” does not affirm or declare or assert anything about "a sea battle". Not only does it fail to assert any details about the "sea battle tomorrow", "S" does not even assert that there "will" or “will not” or “might” be a sea battle tomorrow. It is merely a description of an event (“a sea battle”) that is described in terms placing the event in the future (“tomorrow”). It is no different than saying: “a sea battle tomorrow”
Tom: Fancy that! But “There is a sea battle tomorrow” does affirm something about “a sea battle tomorrow.” It affirms that it “is.” I don’t know what it means because its not a meaningful proposition. “A sea battle tomorrow” is where it’s at.
JET: Thus, S is not “a declarative sentence used to make a statement or assertion”. Therefore, S does not convey a proposition.
In order to convey a proposition, more needs to be said about “a sea battle tomorrow”. At a minimum, we need to say either that it “will” occur or that it “will not” occur or that it “might” occur. If it will or might occur, we could assert more details about "a sea battle tomorrow" (e.g., that it will occur at a certain time tomorrow or it might occur at a certain place). But in order to declare or assert something meaningful about "a sea battle tomorrow" we must, at a minimum, declare that it "will" or "will not" or "might" occur. Once you qualify S with Q or Z or Z~ , you then have a proposition and bivalence is not a problem.
Tom: I don’t think it's a problem. Prior would think it was. I’m not sure about Alan. Alan?
Prior has a problem with “will” and “will not” both being false just in case the sea battle is a contingent state-of-affairs (gotta say state-of-affairs now!) and DOES come to pass. Actually, in a paper of his Prior argues that if the battle is contingent BUT DOES occur, then “will” and “will not” were neither true nor false but of indeterminate truth value BEFORE the sea battle and BECOME true and false (respectively) AFTER the sea battle. Chew on that for a while!
JET: If the foregoing is correct, then perhaps bivalence can co-exist with 3-valued logic when understood as follows: Propositions are bivalent. Thus, each of the following propositions are either True or False:
Qp
Zp
Z~p
Tom: So far so good.
JET: Statements that merely describe future events have one of three values. However, the three values are not true, false and nueter. Rather, the three values are Z, Z~ and Q.
Tom: Are you calling Z and Q “values” but not “truth values”? Ouch. Don’t do that. Call them operators. Calling them "values" confuses them with "truth values."
JET: Thus, the statement:
“There is a sea battle tomorrow”
(which is the same as saying, “a sea battle tomorrow”)
is either Z or Z~ or Q.
Tom: Well, in a sense. I mean, you can just posit the state-of-affairs “a sea battle tomorrow” if you want and leave it at that. But in reality, there IS a truth (Z, Z~, or Q) about every future state-of-affairs. So yes, in reality (and not just in logical discussion) every future state of affairs p is either Z, Z~, or Q. Our first theorem claims this: Zp v Z~p v Qp.
JET: The principal of bivalence is not violated because it does not apply.
Tom: It doesn’t apply to a non-propositional presentation of a state-of-affairs, like “a sea battle.” But once you add Z, Z~, or Q, then you definitely DO have a proposition making a specific truth claim.
JET: So bivalence and multi-valued logic are both true!
Tom: Nice try. But proponents of multi-valued logics don’t limit their denial of bivalence to non-propositional presentations of states-of-affairs (like “a sea battle tomorrow”) like you do. They argue there are meaningful proposition making truth claims about future events that are non-bivalent.
There is a difference, and the difference is more than just semantics.
Tom | | Back to Top | | |
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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 6/17/2004 4:58 PM (GMT -6) | | Tom: If p is not a proposition then it’s not either Z or Z~ or Q. And if it IS one of Z, ~p, or Q then, as you just said above, it is a bivalent truth claim.
Tom: Are you calling Z and Q “values” but not “truth values”? Ouch. Don’t do that. Call them operators. Calling them "values" confuses them with "truth values."
JET: I guess I'm just trying to say that the ontological status of a future "state of affairs" is one of three possibilities: Necessary, Necessarily Not, or Contingent. Because this "threeness" is so fundamental to indeterminancy, I intuitively felt there might be something to a 3-valued logic. But the more I think about it, the more I think you're right about bivalence.
Tom: But “There is a sea battle tomorrow” does affirm something about “a sea battle tomorrow.” It affirms that it “is.” I don’t know what it means because its not a meaningful proposition.
JET: I agree it seems meaningless. And I'm not sure it really affirms anything about "a sea battle tomorrow". What could "is" possibly mean? There "now exists" a sea battle tomorrow? Can't be. Isn't it really just a convention that has been used by logicians who have generally assumed a settled future and have understood "there is a sea battle tomorrow" to be a (supposedely) tenseless version of "there will be a sea battle tomorrow"? Well, if you don't assume a settled future, "there is a sea battle tomorrow" is meaningless. And if its meaningless, then its not a proposition, right?
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 6/17/2004 5:04 PM (GMT -6) | | quote:
Tom: But “There is a sea battle tomorrow” does affirm something about “a sea battle tomorrow.” It affirms that it “is.” I don’t know what it means because its not a meaningful proposition.
JET: I agree it seems meaningless. And I'm not sure it really affirms anything about "a sea battle tomorrow". What could "is" possibly mean? There "now exists" a sea battle tomorrow? Can't be. Isn't it really just a convention that has been used by logicians who have generally assumed a settled future and have understood "there is a sea battle tomorrow" to be a (supposedely) tenseless version of "there will be a sea battle tomorrow"? Well, if you don't assume a settled future, "there is a sea battle tomorrow" is meaningless. And if its meaningless, then its not a proposition, right?
If it's meaningless then it's not a proposition. Right. But Alan argues it is meaninful and does make a truth claim, namely, Zp. So what happened to positing just the state-of-affairs without assuming Z, Z~, or Q? How does one make a claim about future state of affairs p but not claim Zp, Z~p, or Qp?
Know what JET? Logic sucks. I don't mean it's not real. And I don't mean its not important. I just mean...
...it sucks.
Tom | | Back to Top | | |
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