How to refute "a thing can be true and false at the same time"?

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Tomdstone said:
Consider the following set: R = {x | x is not a member of R}.
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The problem with that statement is your assertion that R is a set. R = U (the universe), which is not a set. That is why R is not contained in itself.
 
Bradski said:
Objective facts are either true or false. Never both.
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What is an objective fact? Can there be objectivity in reality? According to quantum mechanics, the observer may influence the measurement of an object. Nonobjectivity of physical properties enters reality with the standard interpretation of quantum mechanics. Observation has a disturbing effect on reality and limits our access to the objective properties of atomic realities. This is well known for QM, but also there is a question of how objective any observer can be even in the classical case. Take for another example, the question of the objectivity of the moral law. Many people will deny that the moral law is objective.
 
Peter_J said:
The problem with that statement is your assertion that R is a set. R = U (the universe), which is not a set. That is why R is not contained in itself.
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the question as to whether or not R is a set is both true and false.
It is true that R is not a set in Zermelo Fraenkel set theory.
It is false that R is not a set in naive set theory.
 
Take the statement:
Parallel lines never meet.
It is both true and false.
It is true in Euclidean geometry.
It is not true in elliptic geometry.
 
Definitions:

Truth - knowledge that conforms to reality.
False - knowledge that does not conform to reality.

Premise: Reality is singular and independent of all knowledge.

Therefore, any knowledge about reality cannot be true and false at the same time.
 
Tomdstone said:
Take the statement:
Parallel lines never meet.
It is both true and false.
It is true in Euclidean geometry.
It is not true in elliptic geometry.
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But I’m not sure what your point is with this example. Remember that the law of non-contradiction says that something cannot be true and false at the same time and in the same respect (emphasis added). “Parallel lines never meet” isn’t both true and false in Euclidean geometry (or in elliptic geometry for that matter).
 
o_mlly said:
Definitions:

Truth - knowledge that conforms to reality.
False - knowledge that does not conform to reality.

Premise: Reality is singular and independent of all knowledge.

Therefore, any knowledge about reality cannot be true and false at the same time.
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Reality is not singular but dual. For example, a photon is both a particle and a wave (not a particle).
 
Peter_J said:
But I’m not sure what your point is with this example. Remember that the law of non-contradiction says that something cannot be true and false at the same time and in the same respect (emphasis added). “Parallel lines never meet” isn’t both true and false in Euclidean geometry (or in elliptic geometry for that matter).
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Consider the statement: parallel lines never meet. Is it true or false or both?
 
Tomdstone said:
Russell’s paradox is independent of considerations of cardinality. this has been shown by Alonzo Church:[1974] “Set theory with a universal set.” Proceedings of Symposia in Pure Mathematics XXV, ed. L. Henkin, Providence RI, Second printing with additions 1979, pp. 297−308. Russell’s set does not exist in Zermelo Fraenkel set theory, but it will exist in Frege’s system of unrestricted comprehension or naive set theory.
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Rusell’s paradox was a problem within the theory that was called “naive set theory”. So, let’s not be naive and forget about it, unless you are a historian.

On the other hand, the question about cardinality is valid either in the naive set theory or in the modern set theory. But you don’t have an answer. Just say so.
Tomdstone said:
To take a simple example: Is the following statement true or false:
“This statement is false”.
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Once again? “This statement is false” is a pseudo- statement, not a statement. You said it was objective, but you have not responded to my question: “if it is objective, how do you verify that it is truly false?”
 
Tomdstone said:
According to quantum mechanics, the observer may influence the measurement of an object. Nonobjectivity of physical properties enters reality with the standard interpretation of quantum mechanics. Observation has a disturbing effect on reality and limits our access to the objective properties of atomic realities. This is well known for QM, but …]
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Is this observation of the Quantum Mechanics guys objective or not, Tomdstone? You tell me, please.
 
Tomdstone said:
Take the statement:
Parallel lines never meet.
It is both true and false.
It is true in Euclidean geometry.
It is not true in elliptic geometry.
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No, Tomdstone, the equivalent of “Parallel lines never meet” is an axiom in the Euclidian geometry and it is not an axiom for other geometries. As a result, the geometries that result from considering a different axiom are different from the Euclidean geometry. Why it is not an axiom in other geometries? Because the mathematician decided to try with a different axiom.
 
Tomdstone said:
Reality is not singular but dual. For example, a photon is both a particle and a wave (not a particle).
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I am sorry, but what you are saying is false: the phenomena that is called “photons” sometimes resemble the phenomena that we call “particles” and sometimes resemble the phenomena that we call “waves”; but one set of phenomena is not the other.
 
Tomdstone said:
Reality is not singular but dual. For example, a photon is both a particle and a wave (not a particle).
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Reality is still singular.

Light has properties of particles (photons) and waves. True.
Light does not not have properties if particles (photons) and waves. False.
 
Tomdstone said:
Russell’s paradox is independent of considerations of cardinality. this has been shown by Alonzo Church:[1974] “Set theory with a universal set.” Proceedings of Symposia in Pure Mathematics XXV, ed. L. Henkin, Providence RI, Second printing with additions 1979, pp. 297−308. Russell’s set does not exist in Zermelo Fraenkel set theory, but it will exist in Frege’s system of unrestricted comprehension or naive set theory.

To take a simple example: Is the following statement true or false:
“This statement is false”.
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The statement “this statement is false” would have to apply to another statement.
 
Tomdstone said:
A surface plasmon polariton does act like a wave and does not act like a wave at the same time (simultaneously).
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Alright. But again, what’s the point of this example? The Law of Non-contradiction allows that something can be both true and not true at the same time.
 
Like trying to argue with someone who thinks the law of gravity on earth is false.

Do not waste your breath.

Yes the law of non-contradiction is true. Denying it that it is is like the above or like a child who says “is not!” when one says “is”. And keeps repeating…“is not!”

No need to stop an argue with hissing geese…🙂
 
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