Anyone study multivalent logic? Some help needed
 

I have an assignment and my study was having some difficulty with a problem. We worked for about 2 hours on this problem without coming close to a consensus on how to solve it, and we think some fresh faces might be able to contribute something we have overlooked. Evaluate this argument:

1. If A is contingent, then A is neither necessarily true nor necessarily false
2. If A is indeterminate, then A is neither true nor false, hence neither necessarily true nor necessarily false
3. Therefore, any sentence that has an indeterminate truth value is contingent

We already pointed out that the conlcusion makes a generalization about "any sentence" from the specifc example of A, but the professor said he was looking for something deeper than that. Any ideas or input would be appreciated.

What in the- H- E -double hockey sticks - are you talking about???
;)

I think it's that 'fuzzy logic' stuff.

Its a non sequitur.

1. If A is contingent, then A is neither necessarily true nor necessarily false
2. If A is indeterminate, then A is neither true nor false, hence neither necessarily true nor necessarily false
3. Therefore, any sentence that has an indeterminate truth value is contingent

OR

1. If A is in Paris, he is not in New York
2. If A is in London, he is not in New York.
3. Therefore, any person who is not in New York must be in Paris.

what happened to London?

or someone's underpants for that matter...

A sentence is not contingent. It just is.

Fuzzy logic is a form of multivalent logic. That's where the issue lies. Multivalent logic allows for an indeterminate truth value that is itself neither true nor false.

Right, I should have explained more.
Contingent is symbolized as [upside down triangle]. A statement is contingent if and only if it is possibly true and possibly false
This can be used to turn statement 1 into a biconditional, or a conjuct of the two conditionals:
1a. If A is contingent, then A is neither necessarily true nor necessarily false
1b. If A is neither necessarily true nor necessarily false then A is contingent
Using this, one could show that if A is indeterminate, then it is contingent.

The problem that is that this would rely on the definition of contingent statements. When contingent isn't symbolized, are we to assume that it means the same thing as [upside down triangle] which is what we have been using to symbolize contingent? Do we know that A is a statement? Even if it is, would the example of A hold true for all statements?

Now, assuming that we can use 1a and 1b, which requires assuming contingent = [upside down triangle], which actually hasn't been stipulated to for this system, the conditional "if A is indeterminate then A is contingent" can be shown to be true.

For a conditional proof, begin by assuming A is indterminate (the antecedent of the conditional conclusion) and apply it using modus ponens to premise 2 to derive "A is neither true nor false, hence neither necessarily true nor necessarily false."
Which is actually a conjunction unto itself and be broken down to "A is neither true nor false" and "A is neither necessarily true nor necessarily false."
Now applying modus ponens to "A is neither necessarily true nor necessarily false" and 1b the conditional conclusion has been shown to be true. Conditional proof works by assuming the antecedent of the conclusion in order to the consequent, which has just been done.
Now that prrof should be taken in light possibility and necessity:
Possibly true = not necessarily false
Possibly false = not necessarily true
So premise 1 actually means:
If A is contingent, then A is neither Possibly true nor possibly false
This statement actually contradicts our defintion of contingent. So where do I got from here? It appears to me that argumetn is flawed, but I can only show it assuming that contingent = [upside down triangle] can I assume that? Another point to consider is does the argument exist in bivalent or multivalent universe? If it exists in a bivalent universe where there is no such truth value as indeterminate, is the conclusion true or false?

Yes. Just ask Schroedinger.

I think I was sleeping that day in class.

Just throw in some quantum effects and it's true and false at the same time. Problem done.

I can see the skills I aquired in Logic 101 when I was 18 are not needed here.

quietly backs out of room......

Probably equally interesting to here what Herr Schroedinger´s cat had to say about it. Now you see me, now you don´t - for God sake, quit open and close the damn box lid !!

Do they not teach basic math anymore?!?!?

My cats breath smells like catfood.

Has anybody seen the cat? I heard some yelling a bit ago...