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

  • Thread starter Thread starter Ben_Sinner
  • Start date Start date
Status
Not open for further replies.
Ben_Sinner said:
I’m trying to solve this. Can someone help me prove that the Law of non-contradiction has to apply to EVERY situation?

Skeptic: A thing can be and not be at the same time and the same way.

Objection: That is false. That breaks the law of non-contradiction.

Skeptic: The law of non-contradiction is false.

Objection: Then that would mean the law of non-contradiction is both true and false at the same time and the same way.

**Skeptic: ** That is only if I meant *All *things can be both true and false at the same time and the same way. I meant Some things can be both, not all. “The law of non-contradiction is false” is a statement that wouldn’t fall under that category though, so saying that statement has to be both true and false at the same time and the same way is a false statement. It is one of the things that doesn’t break the law of non-contradiction. There can be other things out there that do though.

This is where I have trouble…
Click to expand...
While it is certainly true that some philosophers have rejected the law of non-contradiction, it doesn’t not necessarily seem to me that they actually believe that a thing can “be and not be at the same time and in the same respect”, but rather that they don’t have a concept of “in the same respect”.
 
Tomdstone said:
Suppose Bob and John get married in New York Is it true or false that they are married? It is both true and false.
According to the state of NY, they are married.
But according to Saudi Arabia and the Vatican they are not married.
So the statement “Bob and John are married” is both true and false.
Click to expand...
That is not a contradictory statement since the term “marriage” changes meaning from NY to the Vatican. The Vatican says marriage is lifelong intimacy between one man and one woman. NY says that marriage is emotional love between anyone. Not to start an argument over the definition of marriage but a term has to be inflexible and mean only one thing.
 
Tomdstone said:
Here is another question. Is it true or false that if you take one grain of sand from a heap of sand, you will still have a heap of sand left?
Click to expand...
The answer is: “If I can see how many grains are left then it is not a heap of sand, but if I still can’t, then it still is a heap of sand”.
 
Tomdstone said:
The only certain knowledge we have outside of our immediate experience is that there is no certain knowledge outside of our immediate experience.
Click to expand...
Well, if you mean to express a contradiction, then it can be formalized as “A and ~A”. And, as I have shown in my post #2, it implies whatever proposition you like. For example, it implies that “Tomdstone is 6 meters high”.
 
Entwhistler said:
That is not a contradictory statement since the term “marriage” changes meaning from NY to the Vatican. The Vatican says marriage is lifelong intimacy between one man and one woman. NY says that marriage is emotional love between anyone. Not to start an argument over the definition of marriage but a term has to be inflexible and mean only one thing.
Click to expand...
Look at it from the legal point of view only.
Is it true or false that Bob and John are legally married.
It is both true and false.
It is true in the state of NY.
It is false in Saudi Arabia.
 
dshix said:
Doesn’t the skeptic have the burden of proof?

If he can’t provide a founded reason for this belief that some things do not fall under the law of non-contradiction, then he hasn’t said anything more compelling than the statement that there is a pink teapot in space. Can’t be proven or disproven, therefore it is meaningless.
Click to expand...
Whomever made the accusation has the burden of proof.
 
Ben_Sinner said:
I’m trying to solve this. Can someone help me prove that the Law of non-contradiction has to apply to EVERY situation?

Skeptic: A thing can be and not be at the same time and the same way.

Objection: That is false. That breaks the law of non-contradiction.

Skeptic: The law of non-contradiction is false.

Objection: Then that would mean the law of non-contradiction is both true and false at the same time and the same way.

**Skeptic: ** That is only if I meant *All *things can be both true and false at the same time and the same way. I meant Some things can be both, not all. “The law of non-contradiction is false” is a statement that wouldn’t fall under that category though, so saying that statement has to be both true and false at the same time and the same way is a false statement. It is one of the things that doesn’t break the law of non-contradiction. There can be other things out there that do though.

This is where I have trouble…
Click to expand...
Not really much of a logician here, but personally, I just wouldn’t bother . . . :rolleyes: ---- Fuzzy logic, Fuzzy control system
 
Tomdstone said:
Look at it from the legal point of view only.
Is it true or false that Bob and John are legally married.
It is both true and false.
It is true in the state of NY.
It is false in Saudi Arabia.
Click to expand...
The definitions of marriage are different. You are talking about two different things. A typical statement from Saudi would be: They are not married because the process they have gone through does not constitute ‘marriage’.
 
JuanFlorencio said:
Such set does not exist; so, the question makes no sense.
Click to expand...
If the set R does not exist then x is not a member of R. But then you have a contradiction because that implies that x is a member of R. In any case, who determines whether a set exists or not? A set is simply a collection of objects written as x| A(x)} where A(x) is some statement qualifying x. Under that condition, {x| x is not a member of R} does exist as a set. In this case A(x) is the statement that x is not a member of R.
For example, suppose that R is the set of even numbers. {x| x is an integer and x is not a member of R} will be the set of all odd numbers: {…,-3, -1, 1, 3, 5,…}.
 
Bradski said:
The definitions of marriage are different. You are talking about two different things. A typical statement from Saudi would be: They are not married because the process they have gone through does not constitute ‘marriage’.
Click to expand...
So it is both true and false that the process they have gone through constitutes ‘marriage’.
It is true in NY.
It is false in Saudi Arabia.
 
Tomdstone said:
So it is both true and false that the process they have gone through constitutes ‘marriage’.
It is true in NY.
It is false in Saudi Arabia.
Click to expand...
Whether they are married or not is a subjective opinion. Which can be true and false depending on a person’s viewpoint. See earlier post.

Objective facts are either true or false. Never both.
 
Tomdstone said:
If the set R does not exist then x is not a member of R. But then you have a contradiction because that implies that x is a member of R. In any case, who determines whether a set exists or not? A set is simply a collection of objects written as [x| A(x)} where A(x) is some statement qualifying x. Under that condition, {x| x is not a member of R} does exist as a set. In this case A(x) is the statement that x is not a member of R.
Click to expand...
So, if your set does exist, what is its cardinality, Tomdstone?
Tomdstone said:
For example, suppose that R is the set of even numbers. {x| x is an integer and x is not a member of R} will be the set of all odd numbers: {…,-3, -1, 1, 3, 5,…}.
Click to expand...
So, in this case you are saying that

R = {x| x is an odd number}

And another set (let’s call it Q) is

Q = {x| x is an integer and x is not a member of R}

That is okay, this makes sense. But your previous question, concerning your other R “set”, still doesn’t make any sense.
[/quote]
 
JuanFlorencio said:
So, if your set does exist, what is its cardinality, Tomdstone?.
Click to expand...
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”.
 
Status
Not open for further replies.
Back
Top