Can truth contradict itself?

[rufus mosley]

This seems to be an axiom (self evident truth) of philosophy and in all areas of knowledge. What reasons are there for accepting or rejecting this first principle?

[swansont]

If truth contradicted itself it would not be true. True statements are true seems like a tautology.

[joigus]

Within the confines of propositional logic (binary logic, that is) a proposition cannot be true and not true at the same time. I suppose that's what you're pointing at here.

It makes sense to discuss whether a proposition is true or not true. It makes sense to discuss whether a proposition contradicts another, and therefore only one of them can be true.

Truth is a value you assign to a proposition. A function, if you will. You do not assign truth/not truth to truth itself.

Does that make sense?

[Eise]

What does 'contradiction' mean, according to you? Can one 'thing' ('truth' in this case) be a contradiction?

Also, you only have to find one case where 'truth contradicts itself', and your question is answered. 

[dimreepr]

18 hours ago, rufus mosley said:

This seems to be an axiom (self evident truth) of philosophy and in all areas of knowledge. What reasons are there for accepting or rejecting this first principle?

The point of a paradox is that it can't be real.

[iNow]

1 hour ago, dimreepr said:

The point of a paradox is that it can't be real.

Unless it highlights a flaw in our model, one which suggests an update is needed

[dimreepr]

2 minutes ago, iNow said:

Unless it highlights a flaw in our model, one which suggests an update is needed

That was kinda my point.

[iNow]

My bad. I didn't see that, but in retrospect now can.

[Ghideon]

In traditional propositional logic, truth cannot contradict itself, as a proposition cannot be both true and false simultaneously.
Maybe paraconsistent logic* is what you are interested in? In paraconsistent logic it is possible to handle contradictions without rendering the entire logical system meaningless. Managing something that is both true and false in a controlled and meaningful way, allowing for the coexistence of contradictory truths within a logical framework, can have applications in for instance software systems. Disclaimer: I have no deeper knowledge in these matters, and especially not in philosophy; possibly my connection to software does not apply.

*)https://en.wikipedia.org/wiki/Paraconsistent_logic

[studiot]

On 7/8/2024 at 8:03 PM, rufus mosley said:

This seems to be an axiom (self evident truth) of philosophy and in all areas of knowledge. What reasons are there for accepting or rejecting this first principle?

Would not a negative logic OR gate not achieve your objective with both inputs set to false ?

[MSC]

On 7/9/2024 at 9:09 AM, dimreepr said:

The point of a paradox is that it can't be real

Indeed, although something like the liars paradox fits the question somewhat, your point is that outside a thought excercise, if we made a game out of telling who is the liar in a small group of people, the expectation is that at some point the liar will reveal truthfully, they were the liar all along for the sake of the game. There is as far as we know, no being bound to lying or bound to telling the truth with 100% consistency. 

So I suppose my response to OP is that truth can contradict itself in a language game where the language contradicts itself. In physical reality however, no, truth cannot contradict itself. 

[studiot]

@rufus mosley

Your original post was rather too widely set, as can be seen from the range and  breadth of the replies.

I note you haven't replied to any of them, although you have been back since you first posted.

If you are still interested in the subject (and it is an interesting one) please tighten up on the seeting in which we are supposed to discuss this.

 

[rufus mosley]

OK. I am looking for reasons to accept or reject the premise that truth cannot contradict itself.

What have you seven posters come up with? Is there some consensus? or debate?

I would not know what to say about truth, having never encountered it.

I would not know whether I had encountered it.

Is the premise (or axiom) true? Why or why not?

[TheVat]

Truth (or falsity) isn't a thing.  It's an attribute of a statement about some aspect of the world.  If a statement is true, then it corresponds accurately to some state of affairs in the world.  So it does not contradict itself.   The statement simply remains true so long as it corresponds to reality.  If I say Dubai has a hot climate, it will be true so long as that is the reality of Dubai.  If the Earth changes in some drastic way and becomes coated with ice, then the statement will become false.  So truth value of a statement can change when a statement no longer accurately describes reality, but that is not an inherent contradiction in the statement: it has simply shifted from true to false.   (due to fuzzy word meanings, sometimes with gray areas between T and F)

[Peterkin]

1 hour ago, rufus mosley said:

I would not know what to say about truth, having never encountered it.

Of course you have. Many times. It mostly comes in small, insignificant statements. "It's raining." "You have some parsley in your teeth." "The game starts at 8:00 pm."

How you know whenever you encounter it is through empirical verification: look out the window, into a mirror, at the program guide.

When you encounter falsehood, the most common way you recognize it is by comparing with your own observation of reality. If the statement contradicts the evidence of your senses, you generally assume it's a false statement. It takes a great deal more evidence to convince a person that their own experience is false than that a statement by someone else is false. If it were otherwise, none of us could navigate life. 

Can you give a theoretical example of a true statement that is self-contradictory?

[studiot]

11 hours ago, rufus mosley said:

OK. I am looking for reasons to accept or reject the premise that truth cannot contradict itself.

What have you seven posters come up with? Is there some consensus? or debate?

I would not know what to say about truth, having never encountered it.

I would not know whether I had encountered it.

Is the premise (or axiom) true? Why or why not?

Please note that axioms and premises are different things.

Please note you have not answered anyone's questions or addressed their comments, which contain some very valuable information.

This is a discussion site and you need to participate in the discussion not just repeat your question without adding anything further.

 

OK some further helpful background.

In Philosophy and more particularly formal logic there is not such thing as the truth.

Truth, or more correctly, truth value, is as noted above a property we attribute to or deduce for some statement or other, as @TheVat states.

We recognise 'orders of logic' because matters can become complicated.

First order logic is as @joigus states contains what is known as the law of the excluded middle or that every statement has one of two truth values, True or False (T or F ) but there is no room for overlap, don't know , other value etc.

We can obtain a false statement by the process of negation of a true statement and vice versa.  (more of this in a moment)

Statements can be simple in that they contain only one single idea or they may be compound or complex by combination of more than one simple statement.

There are various connectives for combining simple statements into compound ones., including rules for combining their truth values to obtain an overall truth value.

Herein lies the issue because mostly the rules work well, but some combinations lead to paradoxes or other troubles.

For instance combining the statements

In a village, the barber shaves every man in the village except himself.

Every man in the village is clean shaven.

So who shaves the barber ?

These are two statments either of which or both could be assigned a T value.

But their combination leads to an issue, given by the end question.

 

Second order logic was introduced to analyse such statements by doing away with the law of the excluded middle.

 

OK so back to negation.

Within the confines of Euclidian Geometry there are 5 postulates or axioms.

Over the millenia the last one has received considerable attention.

Through every point, not on a given straight line, only one parallel line may be drawn.   -  Truth value  T

Now negate this to obtain a false truth value.

Through every point, not on a given straight line, it is possible to draw more than one parallel line 

Now the truth value is F

And in this form the statement will work perfectly well as an axiom.

 

A final point.

In the world of engineers, machinists, carpenters and other practical folk there is a process called 'truth testing'

Does my wheel bearing run true?

Is my spirit level true enough to build my brick wall ?

Is this rope strong enough to support the weight ?

The last one giving the clue as to the meaning in this context  of conformity to some standard or criterion.

 

 

 

Edited July 25 by studiot

[Sensei]

11 hours ago, rufus mosley said:

I would not know what to say about truth, having never encountered it.

I would not know whether I had encountered it.

Computer programmers use 'true' and 'false' all day long in software.

Logical (boolean) operators return "true" or "false". e.g. if( x > y ) then do something #1 else do something #2.

However, we can imagine a bug where the result of an operator depends on the result of the same operator (which depends on the result of the same operator etc.), resulting in an infinite recursion that is infeasible and will cause the software to crash (stack overflow due to not having infinite amount of memory).

 

 

Edited July 25 by Sensei

[dimreepr]

21 minutes ago, Sensei said:

Computer programmers use 'true' and 'false' all day long in software.

Indeed, but not every programme work's... 🙂

[Sensei]

2 minutes ago, dimreepr said:

Indeed, but not every programme work's... 🙂

There is an adage: "There is no software without bugs, but only software in which no one has yet found them."

 

[joigus]

Context is essential, yes, as everyone has said. As a further example,

1+1=0 is false in standard arithmetic, but it is true in mod-2 modular arithmetic.

And @studiot's example of Russell's paradox is an example in which one seems to be led to the conclusion that some statements can both be true and not true. Of course, what happens is that the context, or the axioms/premises must be re-examined.