Law of Non-Contradictions...HELP

#1

Ight, Phil 101 teach said if we can come up with an example that defies Aristotle's Law of Non-Contradictions we get an automatic A for the class (Law states that something cannot be A and not A at the same time and with the same respect).

I did some research, and came up with this...

(from a website..please read!!...the italics are not as important in my opinion...make sure you get the last part tho)

The problem of the paradox is that it seems to show that common beliefs about truth and falsity actually lead to a contradiction. Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with grammar and semantic rules. Consider the simplest version of the paradox, the sentence This statement is false. If we suppose that the statement is true, everything asserted in it must be true. However, because the statement asserts that it is itself false, it must be false. So the hypothesis that it is true leads to the contradiction that it is true and false. Yet we cannot conclude that the sentence is false for that hypothesis also leads to contradiction. If the statement is false, then what it says about itself is not true. It says that it is false, so that must not be true. Hence, it is true. Under either hypothesis, we end up concluding that the statement is both true and false. But it has to be either true or false (or so our common intuitions lead us to think), hence there seems to be a contradiction at the heart of our beliefs about truth and falsity.

However, the fact that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is neither true nor false. This response to the paradox is, in effect, to reject one of our common beliefs about truth and falsity: the claim that every statement has to be one or the other. This common belief is called the Principle of Bivalence, and is related to the law of the excluded middle.

The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox:

This statement is not true.

If it is neither true nor false, then it is not true, which is what it says; hence it's true, etc.

This again has led some, notably Graham Priest, to posit that the statement is both true and false (see paraconsistent logic).

Nevetheless, even Priest's analysis is susceptible to the following version of the liar:

This statement is only false.

If it is true and false then it is true, which means that it is only false since that's what it says, but then it can't be true, so it is false, etc.

A. N. Prior claims that there is nothing paradoxical about the Liar paradox. His claim (which he attributes to Charles S. Peirce and John Buridan) is that every statement includes an implicit assertion of its own truth. Thus, for example, the statement "It is true that two plus two equals four" contains no more information than the statement "two plus two is four", because the phrase "it is true that..." is always implicitly there. And in the self-referential spirit of the Liar Paradox, the phrase "it is true that..." is equivalent to "this whole statement is true and ...". Thus the statement "This statement is false" is said to be equivalent to
This statement is true and this statement is false.

The latter is a simple contradiction of the form "A and not A", and hence is false. There is no paradox because the claim that this two-conjunct Liar is false does not lead to a contradiction.

(now these are my thoughts)

Go back to the "this statement is only false." How does this not defy the law?? Adding Prior's claim (as in the example) does make it false...(as pointed out in the last part of the article..) OR DOES IT? How can you add Prior's claim once but not again...It seems to me, that to consistently use Prior's claim, you would have to say:

IT IS TRUE that this statement is true and that this statement is false.

Since they agreed that the "this statement is true and this statement is false" is false, the implicit assertion of its own truth makes it both...right? It may be Bivalent, (idk, maybe not) but it seems that could be worked around..

WHAT DO YOU GUYS THINK? AM I SOUND HERE? IF NOT, ANY OTHER IDEAS HOW TO BREAK THE LAW?

#2

So that we're clear...

Must we make the example in sentence form..?

#3

He just said that if we could show an instance where this law is denied, we get an automatic A. As far as I'm concerned, throw out whatever you've got!

#4

I had this one posited to me by a mentor. My answer blew him away, and he was a former professor of philosophy.

(in the common instance of speaking to a person named Never)

Say "Never say never."

the command becomes a contradictory demand both adhered to, and disobeyed in any instance.

-------------

Besides, in Taoism one learns to thrive on contradiction.

Toa ko Tao - Tao Fei Tao.

The Tao called Tao is not The Tao.

i personally don't believe in the Law of Non-Contradictions. See, this is what i see. Man creates a sensible dependence based on his accumulated evidence, and forms preconcieved notions... these he assigns a value of true. When they are disproven, he is in chaos, and buffers his initial notions with new findings, adjusting them accordingly.

but to me, there is no fixed Law, there is a "tangent" independent of discovery, and unique to each person. and to know this "law, certainty, or TRUTH" is the goal of all.

That TRUTH is called by the Hebrew, Aemeth. and it is not spoken, It is witnessed. Just as Lao Tse tries to portray the Tao.

Words undo themselves; but the Logos is Eternal.

#5

Umm...I don't really understand...

So this only applies if you are speaking to a person named Never? or...

Could you elaborate a little more please raum..? I kinda get what you're saying, but don't get it well enough to explain it...

Also, is "this statement is only false" a violation of the law as well?

#6

Thinking out of the box here, in reference to people and objects based on the law as expressed:

"one cannot say of something that it is and that it is not in the same respect and at the same time"

What about phase changes in materials..? For instance, H2O ‚» Water ‚» Ice ‚» Vapor..?

An ice cube is water, yet it is an ice cube...

Or, defining gender...What about hermaphrodites..?

Sorry if I am off base, just trying to maybe go in another direction...

#7

Good examples. I will try those as well.

#8

I always liked this one

From the Doctor Who eposide (not the curent one version) "Pyramids of Mars" - 1975

http://en.wikipedia.org/wiki/Pyramids_of_Mars

There is not much time as Sarah has a limited air supply within the chamber and will suffocate unless he can find out from them which is the right switch to activate. One robot will always tell the truth and the other always lie, but which is which?
Since the Guardians are contra-programmed so that one will always give a false answer, the Doctor asks one Guardian, if he were to ask the other Guardian which was the life switch, which would the other indicate? The Doctor reasons that if the Guardian he asks tells the truth then it must indicate the death switch and the if it is the liar then it would still indicate the death switch. The Doctor presses the other switch and the chamber and Guardians disappear, freeing Sarah.

#9

Yea I like that too, it is clever but I am afraid it doesn't really help me much /sad.gif" style="vertical-align:middle" emoid=":(" border="0" alt="sad.gif" />
Thanks tho.

#10

What's the status on this..?

I'm anxious to see how my ideas were discredited... /:D" style="vertical-align:middle" emoid=":D" border="0" alt=":D" />