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It seems that to prove this statement, you cannot assume the notion of true or false, otherwise its circular, meaning that the proof contains no reference to the concepts of true or false.

This invites a new definition of proof (maybe?), lets say, we need to show "truth exists" with absolute certainty.

But, does absoloute certainty exist? To prove it does, we cannot use notions of certainty, or truth or falsity, since that would be circular, so we must again re-define the notion of proof,

But this will go on for infinity, so any proof will be infinite regress. Hence anything you say with a notion of true or false, will require infinite regress, circular reasoning or assumptions?

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  • In general yes, every "proof" needs assumptions. Commented Jan 9 at 8:04
  • You can assume the notion of truth, indeed, you must. If you wanted to define truth using truth, that would be circular, but having a notion does not require what it describes to exist, so there is no circularity in using it to prove existence. Indeed, it is hard to see what proving that X exists even means if there is no notion of what X is supposed to be.
    – Conifold
    Commented Jan 9 at 8:08
  • @Conifold in the proof you "assume" something, i.e. take an axiom, but you can't do this? How do you know that the axiom is true?
    – Demon
    Commented Jan 9 at 8:12
  • @MauroALLEGRANZA Doesn't this make every proof invalid? Since you are relying on things you don't really know
    – Demon
    Commented Jan 9 at 8:13
  • The word "assume" is ambiguous. That you "assume" a notion does not mean assuming that anything is true, it just means that you are using it. You "assume" mathematical notation when writing formulas in it in the same sense, they may very well be false or nonsensical.
    – Conifold
    Commented Jan 9 at 8:15

5 Answers 5

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U cannot prove it. It is an axiom. Human reasoning generally seeks to prove something in order to have absolute certainty of its truth, i.e, to justify something through another claim. But that either goes infinitely (and nonetheless fails to provide a complete explanation), or u have to assume a indemomstrable/unprovable principle as an absolute truth. The third option is being circular. The second option is the only one that is viable, and there really is no way to go deeper because we would already be assuming atleast one of these options as a starting point. And yes, that sort of is Agripa's trilemma.

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    – Community Bot
    Commented Jan 10 at 14:17
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Why would you expect or want to prove it in the way that you mean? Truth is a word, so you would expect to define it, not to prove it. What truth, the word, refers to is a matter of usage and convention. Truth can be used to mean correspondence with the reality. If I say I went to the Vatican yesterday, you can check the truth of my claim by watching the CCTV footage of an un-named pope asking how far I had got with the draft of the authorised biography his publisher has commissioned me to write, and whether I had remembered to leave out the episode with the actress in Valparaiso (which I had). Truth can also refer to the quality of a statement which has been derived from axioms in accordance with established rules. Do those kinds of truth 'exist'? Well, we encounter them everyday, so in that sense they exist, and if you think what we encounter everyday might just be the imagination of a brain in a vat then they exist in that sense.

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  • Sure, assuming truth exists, I can accept how truth is perceived in Everday reality. I was meaning Moreso the actual concept of it, not it's symbolic (verbal, or written) form, I'm really trying to say debates over "is it really possible to attain knowledge" (epistemology) ? are just straight up pointless.
    – Demon
    Commented Jan 9 at 8:30
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It helps to split the question into two parts and to deal with each part separately:

  • How is truth defined?

    Truth and its opposite falseness are properties of statemens. A statement is a sentence like “Today there is snow in Manhattan.” By definition, this sentence is true exactly when today there is snow in Manhattan. Otherwise the statement is false.

    Hence a statement is true if its content is a matter of fact.

  • How to determine whether a statement is true?

    To determine whether a statement is true, requires to determine whether the corresponding event happens or does not happen.

    How to do this, depends on the statement. In the case above, one could ask today's wetter broadcast for Manhattan or the webcams installed in Manhattan. In case of confirmation one has found a true sentence. In the OP’s formulation “there exists a true sentence”.

The problem with truth and falseness is not the above definition, due to Tarski. The problem is to find a method of confirmation or falsification of general statements like those of scientific theories. The latter problem and its solution is the subject of Popper's theory of philosophy of science.

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Sure.

  1. no statements are true
  2. 1 is a statement
  3. therefore 1 is not true
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  • That's absolutely not what I am saying, I am saying we can't prove "truth exists" that is not saying "no statements are true", its saying we can't know with certainty, even the one I just wrote, but it's better to not give a fuck, and just assume truth exists, and go on with everyday life
    – Demon
    Commented Jan 9 at 9:18
  • @Demon justifying complete certainty of anything beyond the fact that experience is occurring is not possible, at least, not that I'm aware. That is an old thought, thousands of years old, and comes up repeatedly.
    – philosodad
    Commented Jan 9 at 20:04
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Yes. It is very easy to prove that truth exists.

All conditioned phenomena are impermanent.

The above statement is true , regardless of who speaks it , where it is spoken ,when it is spoken and how reality is understood by any species of life.

The truth may not be visible at all times but just as Sun is bound to shine upon Earth , the above truth is bound to unravel itself.

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