Still Wondering about Contradictions

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AlNg said:
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HarryStotle:
Taken “as a whole,” it isn’t “a statement,” it is two statements.
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I disagree. It may be a compound statement, but it is still a declarative sentence, which qualifies it as a statement.
Here is an example of two statements:
I am lying. (period)
I am not lying. (period)
Here is an example of one statement:
I am lying and I am not lying. (period)
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Nope. The two statements aren’t independent of each other in the way that “I am lying and I am not lying. (period)” are.
catholicray said:
Take a blank card/paper and on one side write: “The statement on the other side of this card is false”
On the other side: “The statement on the other side of this card is true”
Examine it for a minute.
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More like: “I am lying if I am telling the truth in the second statement and I am telling the truth if I am lying in the first statement.”

Since we cannot determine the truth value of either statement because of the referential loop, there is no inherent contradiction.
 
catholicray said:
Could you demonstrate this given the specific details of the above contradiction?
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The sentence treats the words as both “objects” (nouns) themselves, as well adjectives describing other objects. In the particular example, the phrase on each side of the card could be diagrammed as below:

“The other side is false” has two meanings:
  1. The other side is factually false (correct, because this side is not the word “true”)
  2. The other side is the word “false” (incorrect, proving the other side is factually true)
"The other side is true has two meanings:
  1. The other side is factually true (correct, because this side is not the word “false”)
  2. the other side is the word “true” (incorrect, proving the other side is factually true)
The example here is really just a riddle. It relies on the ambiguous meaning of the words “true” and “false” to sound contradictory. With context, knowing that it is a riddle playing on the different uses of each word, it can be understood.
 
AlNg said:
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HarryStotle:
Nope.
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I can just as easily say Nope also. I am not buying your explanation.
HarryStotle said:
What good would an illogical system of logic be?
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Nope. The appeal to utilitarianism does not disprove Gödel’s second incompleteness theorem.
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You are missing the logical dependency of the statements upon each other. It isn’t a matter of “appeal to utilitarianism.”

There is a direct reference to the statement “on the other side” in each. That is a logical dependency, not a “utilitarian” connection – whatever that may mean.
Take a blank card/paper and on one side write: “The statement on the other side of this card is false”
On the other side: “The statement on the other side of this card is true”
Examine it for a minute.
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The truth value of each statement is completely dependent on the truth value of the other. Since the truth value of each is supposedly contingent on the truth value of the other by logical implication, and each one leaves the other statement unresolved, the logical implication is an infinite loop of pointing back and forth to determine the truth of both. Since neither definitively resolves the truth, there is no contradiction – merely an unresolved conundrum. That isn’t a contradiction, exactly.
 
AlNg said:
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HarryStotle:
the logical implication is an infinite loop
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It is an infinite loop of contradictions.
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My point is that a contradiction cannot be determined until one of the statements is definitively true or false, but that is impossible because such a determination keeps getting shuffled to the other statement. We can’t know that either statement is true or false so we can’t know that they contradict each other because neither is definitively true or false, no determination, no contradiction.
The first is true only if the second is false and the second is false only if the first is true, but the first can only be false if the second is known to be true, which it can only be true if the first is actually known to be false, which cannot be known. No contradiction because no such determination can possibly be made.
 
HarryStotle said:
My point is that a contradiction cannot be determined until one of the statements is definitively true or false, but that is impossible because such a determination keeps getting shuffled to the other statement. We can’t know that either statement is true or false so we can’t know that they contradict each other because neither is definitively true or false, no determination, no contradiction.
The first is true only if the second is false and the second is false only if the first is true, but the first can only be false if the second is known to be true, which it can only be true if the first is actually known to be false, which cannot be known. No contradiction because no such determination can possibly be made.
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Do you agree that the following is a contradiction:
There is a limbo and
There is not a limbo.
 
I’m of the opinion that what you’re saying is valid but I am also of the opinion that each statement on its own is perpetually true and false. It’s both and rather than either or.
 
It cannot be both-and because neither of the statements can be adjudicated. Neither can it be either-or because each statement depends upon the other.
 
HarryStotle said:
neither of the statements can be adjudicated
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Adjudication is not relevant as to whether or not a collection of statements is contradictory. It cannot be adjudicated as to whether or not Limbo exists. Yet the following constitutes a logical contradiction:
Limbo exists and
Limbo does not exist.
 
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AlNg said:
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HarryStotle:
neither of the statements can be adjudicated
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Adjudication is not relevant as to whether or not a collection of statements is contradictory. It cannot be adjudicated as to whether or not Limbo exists. Yet the following constitutes a logical contradiction:
Limbo exists and
Limbo does not exist.
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Again, you are completely missing the point. Your first statement “Limbo exists,” stands on its own and its truth can be determined without reference to what your second statement about Limbo says. There is no logical dependency on the second. The second statement need not even be made. The existence of Limbo depends on other determinations, not solely nor merely on the declaration of the statement “Limbo does not exist” as false. The truth value of neither statement is not get established by a simple tautological declaration regarding the other one.

There is, actually, no independent means of determining the truth of either of the following statements, except with reference to the other.
“The statement on the other side of this card is false”
On the other side: “The statement on the other side of this card is true”
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That is the point. The existence of Limbo can, theoretically at least, be determined independently of either of the statements about Limbo. The truth of either the two statements above cannot be determined or verified, in principle, because they each completely and solely depend on the other, and neither depends on actual reality, nor can they be independently determined to be true or false.
 
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AlNg said:
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HarryStotle:
neither depends on actual reality
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Logical consistency can vary from material reality.
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Not when the logical truth or falsity of the statement relies on material reality to be determined.

Unicorns exist. The logical truth of the statement depends on what is the case in material reality and cannot be determined aside from that. Whether limbo exists depends upon reality, though perhaps not the material reality we presently experience.

The truth of each of the following two statements is indeterminate because while the truth of each depends upon what is materially on the card, each side merely points to the other so the actual truth of each one is pushed back to the other, repeatedly, in an endless loop.
HarryStotle said:
The statement on the other side of this card is false”
On the other side: “The statement on the other side of this card is true”
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There is no logical way to determine the truth of either because the truth value is flipped on and off by the very act of reading each side in sequence. There is no definitive way to determine which is true and which isn’t.

You cannot claim that one is true and the other false because as soon as you do the one becomes false and the other true. They could only contradict if the truth value of one could be determined to begin with. They can’t, though.
 
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HarryStotle said:
They could only contradict if the truth value of one could be determined to begin with.
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I don’t think so.
You cannot determine the truth value of the following, but it is still a contradiction.
In a parallel universe, there are people who speak Chinese and
In any
parallel universe, there are no people who speak Chinese.
HarryStotle said:
It is a nonsensical word puzzle
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It is nonsensical because the statements are contradictory.
HarryStotle said:
The logical truth of the statement depends on what is the case in material reality
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There are statements in mathematics that are logically true and do not depend on what is the case in material reality. Take for example statements about the continuous real line. There is only discreteness in material reality. There is no such thing as a real continuous line in material reality because material reality has grain or discreteness. There is no such thing in our material universe as an infinite set of real entities corresponding to the uncountable infinity of the real line.
It is logically true that the continuous image of the real line interval [0,1] is a connected set. But there is no such thing as the real line interval [0,1] in material reality. Material reality is discrete, but many statements about continuity are logically true and of course there are others that are logically false.
 
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catholicray said:
Take a blank card/paper and on one side write: “The statement on the other side of this card is false”
On the other side: “The statement on the other side of this card is true”
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Let side A be: “The statement on the other side of this card is true”
Let side B be: “The statement on the other side of this card is false”
A is either true or false.
Suppose A is true, then B is true,. Since B is true, then A is false.
So A is both true and false, and therefore a contradiction.
Suppose A is false, then B is false. Since B is false, then A is true.
So A is both false and true, and therefore a contradiction.
You are dealing here with a simple logical contradiction.
 
If A is true then A is true and false
If A is false then A is false and true
 
If it is indeed a logical contradiction then would you say that it is true that it exists? If it exists then would you say that it is therefore possible for God to create a square circle? That His omnipotence is absolute?
 
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