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

[Ben_Sinner]

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…

 

[JuanFlorencio]

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…

Ok, let’s suppose “A and ~A” is true. Then

1. A and ~A
2. A (from 1. by simplification)
3. ~A (from 1. by simplification)
4. A or P (from 2. by addition of P)
5. P (from 4. and 3. by disjunctive syllogism)

But P can be whichever proposition you like, for example: “The law of non-contradiction is both true and false at the same time and the same way”, or “My skeptic friend is a cow”…

 

[dshix]

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.

 

[Tomdstone]

Some things can only be expressed in a contradictory fashion. For example: “The only certain knowledge we have outside of our immediate experience is that there is no certain knowledge outside of our immediate experience.”
This would be false only if it were true, etc.
Other things may be true or false, depending.
For example, if you take one dollar from a rich man’s account he is still a rich man. True or false? Most people will say true, but suppose that you do that continuously, then there will come a point when he will not be a rich man. So it is also false.
And I seem to recall that there was a person on CAF who wrote that God was somehow above logic with the implication that God was not bound by logical constrictions, although I disagreed with him on that.

 

[JuanFlorencio]

Some things can only be expressed in a contradictory fashion. For example: “The only certain knowledge we have outside of our immediate experience is that there is no certain knowledge outside of our immediate experience.”
This would be false only if it were true, etc.

This is better written this way: “The only certain knowledge we have outside of our immediate experience is that, besides this, there is no other certain knowledge outside of our immediate experience.” Then it expresses what is meant.

 

[St_Francis]

Some things can only be expressed in a contradictory fashion. For example: “The only certain knowledge we have outside of our immediate experience is that there is no certain knowledge outside of our immediate experience.”
This would be false only if it were true, etc.
Other things may be true or false, depending.
For example, if you take one dollar from a rich man’s account he is still a rich man. True or false? Most people will say true, but suppose that you do that continuously, then there will come a point when he will not be a rich man. So it is also false.
And I seem to recall that there was a person on CAF who wrote that God was somehow above logic with the implication that God was not bound by logical constrictions, although I disagreed with him on that.

If you take one dollar more than once, you are taking more than one dollar.

Plus, one would need to define “rich.”

 

[Tomdstone]

If you take one dollar more than once, you are taking more than one dollar.

Not really. Say the man has 10 billion dollars and you take one dollar from him. Then he is still rich. Now you take one dollar from the man who has 9999999999 dollars. He is still rich. Now you take one dollar from the man who has 9999999998 dollars. He is still rich. Consider the general statement. If you take one dollar from a rich man, he is still rich? Is it true or false.

 

[Tomdstone]

This is better written this way: “The only certain knowledge we have outside of our immediate experience is that, besides this, there is no other certain knowledge outside of our immediate experience.” Then it expresses what is meant.

That is not the statement I wrote. That is a different statement. The question is whether the statement I wrote was true or false. I can agree that your statement is true, but that is not my proposition.

 

[JuanFlorencio]

Not really. Say the man has 10 billion dollars and you take one dollar from him. Then he is still rich. Now you take one dollar from the man who has 9999999999 dollars. He is still rich. Now you take one dollar from the man who has 9999999998 dollars. He is still rich. Consider the general statement. If you take one dollar from a rich man, he is still rich? Is it true or false.

The answer is: “it depends on how much he still has”.

 

[JuanFlorencio]

That is not the statement I wrote. That is a different statement. The question is whether the statement I wrote was true or false. I can agree that your statement is true, but that is not my proposition.

What is your proposition then? Please rewrite it in a formal way, so that I can see it better.

 

[Tomdstone]

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?

 

[StJoseph8]

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…

You are trying to prove a first principle of logic, which in classical logic is impossible. You cannot create an argument if you deny this first principle. So the skeptic just has to accept it.

 

[Bradski]

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?

All the problems brought up so far are questions requiring a determination on subjective or objective grounds.

In the sand example, you’d need to define what a heap of sand is objectively for it to be true OR false. Otherwise ‘a heap of sand’ is a subjective term so could be true for one person and false for another.

Objective facts are always true or false: there is a pen on my desk (there is or there isn’t). Subjective statements are always true or false: I think that’s a nice pen (he is either telling the truth or lying).
Subjective opinions, by definition, can be both: I think it’s a nice pen, Jane thinks it’s not.

 

[Tomdstone]

What is your proposition then? Please rewrite it in a formal way, so that I can see it better.

The only certain knowledge we have outside of our immediate experience is that there is no certain knowledge outside of our immediate experience.

 

[Tomdstone]

All the problems brought up so far are questions requiring a determination on subjective or objective grounds.

In the sand example, you’d need to define what a heap of sand is objectively for it to be true OR false. Otherwise ‘a heap of sand’ is a subjective term so could be true for one person and false for another.

Objective facts are always true or false: there is a pen on my desk (there is or there isn’t). Subjective statements are always true or false: I think that’s a nice pen (he is either telling the truth or lying).
Subjective opinions, by definition, can be both: I think it’s a nice pen, Jane thinks it’s not.

How do you explain what Chuang Tsu says: “That which makes things has no boundaries with things, but for things to have boundaries is what we mean by saying ‘the boundaries between things’. The boundaryless boundary is the boundary without a boundary” ?

 

[St_Francis]

Not really. Say the man has 10 billion dollars and you take one dollar from him. Then he is still rich. Now you take one dollar from the man who has 9999999999 dollars. He is still rich. Now you take one dollar from the man who has 9999999998 dollars. He is still rich. Consider the general statement. If you take one dollar from a rich man, he is still rich? Is it true or false.

What I am saying is that if you take one dollar away from a rich man, then you’ve taken one dollar. If you take $1 each day for a year, then you’ve taken $365, not $1.

It is also necessary to define rich. To the man who has no money at all, the man with $1 might be rich, and if you took a dollar from him, he would then be poor.

So the L of NC applies to things that are well-defined, not relatively defined. The state of being rich is not well-defined.

The L of NC does not apply to all statements about all things. Is yogurt palatable? Some think so, others not so much, right? But whether or not there is yogurt in the refrigerator is something which either is or is not true, it can not be both at the same time.

 

[Tomdstone]

All the problems brought up so far are questions requiring a determination on subjective or objective grounds.

In the sand example, you’d need to define what a heap of sand is objectively for it to be true OR false. Otherwise ‘a heap of sand’ is a subjective term so could be true for one person and false for another.

Objective facts are always true or false: there is a pen on my desk (there is or there isn’t). Subjective statements are always true or false: I think that’s a nice pen (he is either telling the truth or lying).
Subjective opinions, by definition, can be both: I think it’s a nice pen, Jane thinks it’s not.

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.

 

[Tomdstone]

All the problems brought up so far are questions requiring a determination on subjective or objective grounds.

In the sand example, you’d need to define what a heap of sand is objectively for it to be true OR false. Otherwise ‘a heap of sand’ is a subjective term so could be true for one person and false for another.

Objective facts are always true or false: there is a pen on my desk (there is or there isn’t). Subjective statements are always true or false: I think that’s a nice pen (he is either telling the truth or lying).
Subjective opinions, by definition, can be both: I think it’s a nice pen, Jane thinks it’s not.

Is the following objective statement true or false?
“This statement is false.”

 

[Tomdstone]

What I am saying is that if you take one dollar away from a rich man, then you’ve taken one dollar.

But after you have done one time that is he still a rich man or not?
Is it true or false that if you take one dollar from a rich man, that he will still be a rich man?

 

[St_Francis]

But after you have done one time that is he still a rich man or not?
Is it true or false that if you take one dollar from a rich man, that he will still be a rich man?

Define what a rich man is.