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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 11/10/2004 12:31 AM (GMT -6) |   | Bivalence again—
Can’t get away from it. The challenge to bivalence comes from three sorts of proposition (I think). (1) The first is future contingents. (2) The second is propositions (don’t know what to call them) like the following: “The present King of France is bald.” (3) The third class is “vague” sentences about what exactly, for example, constitutes a “heap,” or the difference between “red” and “pink,” or what percentage of a man's head has to have no hair in order for the properties of universal “baldness” to be met.
(1) The first class of propositions thought to undermine bivalence (future contingents) has been talked about a lot here. Future contingents are thought to undermine bivalence because “Laika will travel to Amsterdam” and “Laika will not travel to Amsterdam” are believed to be the only options we have for describing the state of affairs “Laika’s traveling to Amsterdam.” For folks who deny LFW, there’s no problem. These can affirm bivalence while believing “…will travel…” and “…will not travel…” are the only two options we have for positing the fact of the matter about Laika’s traveling to Amsterdam. But for those of us who affirm LFW, that is, who affirm the real indeterminacy of Laika’s traveling to Amsterdam, we either have to a) deny bivalence (which means “Laika will travel to Amst” and “Laika will not travel to Amst” are both neither true nor false), or b) come of with some third proposition other than “will” and “will not” for describing Laika’s travellling to Amsterdam. Alan, Greg, and I hope very soon to explode our bombshell on the playground of logic by offering a semantics, a way of talking, about the future that affirms bivalence and the indeterminacy of the future by expanding the options beyond “will” and “will not” to include “might and might not.” This isn’t new. We’ve talked a lot about “might and might not” propositions. [Note: Some, like Craig, agree with LFW, that is, affirm real indeterminacy, but still argue that the future is expressible exclusively in terms of what “will” and “will not” happen; they just deny the problem.]
(2) The second class of propositions, like “The present King of France is bald” is thought to threaten bivalence. If we claim this prop is false, then we are thought to be affirming its contradictory, that “The present King of France is not bald.” But this latter proposition is also surely not true since there IS no present king of France to speak of. But a proposition and its contradictory can’t BOTH be false if bivalence holds. So, deny bivalence. In this case both these props are neither true nor false.
But this smells fishy. “The present King of France is bald” and “The present King of France is not bald” are not contradictories. They’re contraries, and by definition may both be false, which is just what they are. To contradict “The present King of France is bald” one places the negation symbol in front of the ENTIRE prop (viz., “It is not the case that the present king of France is bald”) and not in front of the predicate “…is bald” (to form “…is NOT-bald) only. Placing the negation in front of the predicate “...is bald” gives us a ‘contrary’ proposition. So, both "The present King of France is bald" and "The present King of France is not bald" are false. What is true? This: "It's neither the case that the present King of France is bald nor the case that he is not bald." This being the case does NOT commit us to belief in a King in present-day France. It only commits us to the falsity of claims regarding a present day King of France, for obvious reasons. In other words, there doesn't need to BE a present King in France for contradictory predicates attributed to a present King in France to both be false.
I take all such examples as are in this class as offering no threat to bivalence.
(3) I’d like to talk about the THIRD class: vagueness. What constitutes a “heap” of sand? One grain? Surely not. Two grains? Surely not? A trillion grands of sand placed together that stands two stories high and 30 feet wide? Surely. At some point we passed from "is not a heap" to "is a heap." But precisely WHERE? Many philosophers argue there simply is no fact of the matter about when exactly one crosses the line, or whether there is a distinct line. That is, in spite of the fact that our sand pile crosses from “is not a heap” to “is a heap,” there is no exact number of grains of sand that constitutes a “heap”; no universal "heapness" that defines the line between it and, say, "pile-ness" or "mound-ness." Same can be said about baldness. Just when does a man become “bald”? What percentage of hair loss DEFINES baldness? 50%? 75%? 98%? What if the guy has a singe hair on top of his head? Is he bald? Is he not bald?
Now, such “vagueness” is believed by many to undermine “bivalence.” Saying of particular pile or mound of sand “This is a heap” or “This is not a heap” are believed to be neither true nor false since there is no fact of the matter that defines “heap-ness.” Same with baldness. To say of a man with hair on only 1/9th of his head “He’s bald” or “He’s not bald” is to say what is neither true nor false. There is no fact of the matter that defines “baldness” except to say that a man with not a single hair on his head is bald.
Of the three sorts of challenge to bivalence, the third in my view poses the most serious threat. Anybody interested in talking about (3)? Any of you bald guys? Any of you ladies with husbands who are bald?
Tom
PS Here's an introduction to the issues: http://plato.stanford.edu/entries/vagueness/
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 11/10/2004 4:11 AM (GMT -6) | | Mr. EinSHtein-
Did you wear your bedroom slippers outside of the house today? Perhaps while visiting the present King of France? Hmm.
You haven't visited Amsterdam have you?
Sorry about re-editing the original post so often. I can't figure out where the line is between acceptable and unacceptable typos.
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 11/10/2004 4:23 AM (GMT -6) | | OK, OK, let's keep this thread SERIOUS! If you can't understand vagueness, Albert, then take this!
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 11/10/2004 4:36 AM (GMT -6) | | I don't understand. Duh. Give me an example.
Tom
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JET
Registered Member
Date Joined Jun 2002
Total Posts : 397
| Posted 11/10/2004 4:54 AM (GMT -6) | | Here’s my initial reaction:
If the vague term is not important in terms of what is being asserted, then the vagueness has no implications for bivalence. Consider the proposition:
P1: “That heap of sand [pointing to a particular group of sand particles] was not there yesterday.”
Here, the term “heap”, while vague, is unimportant. The proposition is true or false regardless of the vagueness of the term “heap”. In fact, the proposition could be expressed without using the term “heap” (e.g.,: “That particular group of sand particles [pointing to a particular group of sand particles] was not there yesterday”). So, in this case, vagueness has no implications for bivalence.
On the other hand, if the vague term is important in terms of what is being asserted, then I would say you haven’t really expressed a proposition (for purposes of bivalence) unless some meaning is attributed to the vague term–and then the proposition is either true or false in accordance with whatever meaning is attributed to the vague term. Consider the proposition:
P2: “That particular group of sand particles [pointing to a particular group of sand particles] constitutes a heap.”
If this statement constitutes a proposition, then “heap” must have some meaning. (If “heap” has no meaning, then we don’t have a proposition and bivalence is inapplicable.) So, in order to determine whether the proposition is true or false, we just need to know what the meaning of “heap” is.
If “heap” has an objective meaning for purposes of the declaration, then the proposition is either true or false in accordance with whatever that objective meaning is.
More often, when dealing with vague terms, the meaning is subjective. For example, “heap” may mean one thing to the declarant and another thing to another person who also observes the thing being pointed to. In that case, you really have two separate propositions, each of which is either true or false in accordance with whatever subjective meaning is being applied.
Hey, I don’t know what I’m talking about, but playing amateur philosopher is more fun than my real job.
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 11/10/2004 5:03 AM (GMT -6) | | So that's it? We're done? That was easy.
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 11/11/2004 2:56 AM (GMT -6) | | Nice site there. Can't believe all the time people spend on this stuff! Some people just don't have enought to do! ;o)
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