# The only form of knowable truth is tautology

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A tautology is a statement of the form "If A then A" or equivalently "A or not A". It is obviously but trivially true, not really very useful.Also a lot of people complain about something being a tautology as if that disproved it, which I find funny because it just proves it is true. But I think I can go one further and say tautology is the only form of knowable truth.

So here is my proof:

Suppose A is true. But I said knowable truth, so how do you know A is true? It has to be proven.

Case 1: A is a tautology, and therefore true.

Case 2: A is not a tautology and must be proven. But to prove A if it is not a tautology, you need some sort of logical proof. But logic preserves truth, that is, you have to start with a true statement to be able to reach a true statement. But how can you prove that statement is true? If it is a tautology it is of course true, but otherwise you need to prove that, ...

So eventually you are left with two things:

1) Tautologies, which are known to be true, and things deduced from the tautology (which would just make them more complicated tautologies)

2) Assertions, which you just say are true and don't bother to prove.

Is there any other option?

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It is possible to say something is true, but lack proof. It might be assumed to untrue due to lack of proof. Later, studies might show it was indeed true. It was always true, but it might be erroneously called untrue, due to lack of protocol. If protocol is not followed, things might be assumed to be untrue, which can be true.

For example, say you are a victim of identity theft. You know it to be true that you did not make all those loans and charges. But your assertion will be assumed untrue, until you follow a elaborate protocol. If done properly, it will turn what was considered untrue, into truth. But it was always true with or without protocol.

Edited by pioneer
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Wouldn't a tautology be a tautology only because we agree that it is so, and not necessarily because it is objectively true?

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A tautology is named a tautology because we agree it is so. Tautologies are always true because we defined them to be that which is always true. Which is a tautology which makes it true.

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At the time I read Karl Popper's critique of Marxist analysis for being tautological, it bothered me because I found Marxian social-economic analysis very useful. However, I did work to understand what tautology means and why it is unscientific. Popper said that if one would understand Marx's theory of class conflict as the cause of social problems, any news item could be explained in terms of class-conflict. Therefore, Popper came up with falsificationism as the measure of good scientific theories. Einstein's theory, for example he claimed, was good because he provided a clear test that would falsify the theory if it didn't pass the test. Since Marx provides no means of falsifying his theory of class conflict, Popper considered it unfalsifiable and therefore unscientific. This doesn't mean that Marx's ideas are completely worthless; just that they are not scientific in the sense of being testable.

Edited by lemur
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Being a tautology doe not make something true, or even false. A Tautology is only self constistant.

For example: I am the King of the worlfd because i said I am the king of the world (and as king of the world I have the power to name the king of the world).

This is a tautology. But it is also false (unless you are all willing to accept me as king of the world ). It is, however, self consistant (as if I was king of the world I could do such things).

So, just because something is a tautology, it does not necesarily make it true (or false for that matter either).

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Being a tautology doe not make something true, or even false. A Tautology is only self constistant.

For example: I am the King of the worlfd because i said I am the king of the world (and as king of the world I have the power to name the king of the world).

This is a tautology. But it is also false (unless you are all willing to accept me as king of the world ). It is, however, self consistant (as if I was king of the world I could do such things).

So, just because something is a tautology, it does not necesarily make it true (or false for that matter either).

No, if it is false it cannot be a tautology (they're always true by definition, so they if its false it automatically isn't one). What you offered fits the second category, assertion. Assertions can't be proven even though many people will claim they know it is true. Specifically, your example is false in the case that you are not the king of the world. A tautology is true in all cases.

What you have is however an example of circular argument.

To modify your example to be a tautology, try this one:

If I am king of the world, then I am king of the world.

or

If as king of the world I say I am king of the world, then I am king of the world.

Both these are always true regardless of the truth or falsity of anything.

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Are people getting that the problem with tautology is that internal consistence/coherence is mistaken for truth? A lie can be internally consistent, which is why it works as a lie. Does internal inconsistency necessarily mean that something isn't true? I don't think so. It could just mean that the truth appears strange within the interpretive framework that is being used to make sense of it. If gravity was defined as the force the causes things to fall to the ground, and the moon's orbit was questioned, it would seem inconsistent that the moon was in fact affected by Earth's gravity. So inconsistence need not indicate falsity. It could just be that the theory hasn't progressed into a form that results in internal consistency among observables.

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"Mathematicians can prove only trivial theorems, because every theorem that’s proved is trivial".- R. Feynman.

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A tautology is named a tautology because we agree it is so. Tautologies are always true because we defined them to be that which is always true. Which is a tautology which makes it true.

Yes, but how would you have any knowledge distinguishing that from a non-tautological claim of truth?

Or was that the point of the thread...

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A tautology is the most beneficial when applied in a heuristic fashion.

Because the best way to measure things is sometimes using something the same and not different.

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No, if it is false it cannot be a tautology (they're always true by definition, so they if its false it automatically isn't one). What you offered fits the second category, assertion. Assertions can't be proven even though many people will claim they know it is true. Specifically, your example is false in the case that you are not the king of the world. A tautology is true in all cases.

What you have is however an example of circular argument.

To modify your example to be a tautology, try this one:

If I am king of the world, then I am king of the world.

or

If as king of the world I say I am king of the world, then I am king of the world.

Both these are always true regardless of the truth or falsity of anything.

Maybe I should have used the word "real" rather than "true".

To continue my example:

You reinterpereted my first example as: "If I am king of the world, then I am king of the world.", but if this is true, then does this mean I am king of the world? No.

Yes, if the initial premise (being king of the world) is either true or false, thenn the the conclusion (being king of the world) is logically consistent (this is what I ment by internally consistent - that is the whole statement does not have a logical incosistency), and in this view it is "true". But, whether it is internally consistent (or true if you want), does not make what the statement is about true or false.

So you might be abel to argue that the statemnt is true, but this has no relevence to anything else. It makes it meaningless.

In terms of programming it is like a statment that reads:

If (A = A).

Of course A = A, but this does not allow you to do anyhting at all useful with it (like determine if A is actually true or false). You might as well have not included that line of code at all.

To sum up what I mean. A tautology is only a statment where the syntax is true, and it has no impact on whether the subject the statement is about is true or false.

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Yes, but how would you have any knowledge distinguishing that from a non-tautological claim of truth?

Or was that the point of the thread...

A tautology will always be true, no matter what is true. A non-tautological claim of truth could be false if other things were true/false. The tautology will be of the form (A or not A) whereas the non-tautological claim of truth would be one or more sentences that cannot be reduced to (A or not A). It will be true if it is true but false if it is false. Saying a tautology is false would be a contradiction.

Maybe I should have used the word "real" rather than "true".

To continue my example:

You reinterpereted my first example as: "If I am king of the world, then I am king of the world.", but if this is true, then does this mean I am king of the world? No.

Yes, if the initial premise (being king of the world) is either true or false, thenn the the conclusion (being king of the world) is logically consistent (this is what I ment by internally consistent - that is the whole statement does not have a logical incosistency), and in this view it is "true". But, whether it is internally consistent (or true if you want), does not make what the statement is about true or false.

So you might be abel to argue that the statemnt is true, but this has no relevence to anything else. It makes it meaningless.

Yup, tautologies are in fact rather meaningless. By virtue of necessarily being true, asserting it is true tells you nothing. But true is not the same as logically consistent. Being logically inconsistent does however make something necessarily false (a contradiction, or the negation of a tautology). For example, "If pineapples are prickly then pineapples grow on pine trees" is logically consistent but false.

In terms of programming it is like a statment that reads:

If (A = A).

Of course A = A, but this does not allow you to do anyhting at all useful with it (like determine if A is actually true or false). You might as well have not included that line of code at all.

To sum up what I mean. A tautology is only a statment where the syntax is true, and it has no impact on whether the subject the statement is about is true or false.

Yes. That's what I meant by them being trivially true.

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A = A is a statement of identity. A in itself is an interactive function, therefore it becomes irrelevant what "A =" in itself because the issue is how A interacts with other variables.

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"All green unicorns are green" is, I think, a tautology. But as far as I can see, it's totally unhelpful. It doesn't tell you anything.

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"All green unicorns are green" is, I think, a tautology. But as far as I can see, it's totally unhelpful. It doesn't tell you anything.

Well tautologies aren't totally unhelpful. Consider the mathematical theorems, for example.

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do we know the sun will rise tomorrow?

why? Because we have seen it rise so many times before?

you also have to consider the difference between a doubt and a reasonable doubt.

the laws of physics could conceivably change tomorrow but I have no reason to doubt them.

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"All green unicorns are green" is, I think, a tautology. But as far as I can see, it's totally unhelpful. It doesn't tell you anything.

It tells you they recycle and buy re-usable shopping bags. It's really quite a coincidence considering their green color, don't you think?

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• 6 years later...

"Mathematicians can prove only trivial theorems, because every theorem thats proved is trivial".- R. Feynman.

Hehe! In a similar vein, if any two persons disagree then one or both of them is thinking irrationally.

Edited by Rasher Null

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