Can truth contradict itself?

[exchemist]

13 hours ago, rufus mosley said:

How?

The question you originally asked seems to me to make a category error. "Truth", as @joigus observed back in July last year, is a value applied to a proposition. In other words, truth is not an entity in itself, but "true" or "false" are attributes of a proposition. "Truth" cannot contradict anything, because it is not a verifiable proposition.  

[Genady]

48 minutes ago, exchemist said:

The question you originally asked seems to me to make a category error. "Truth", as @joigus observed back in July last year, is a value applied to a proposition. In other words, truth is not an entity in itself, but "true" or "false" are attributes of a proposition. "Truth" cannot contradict anything, because it is not a verifiable proposition.  

I thought that the word "truth" is just a shortcut for "true proposition", like in "The truth is that he was not there."

[dimreepr]

23 minutes ago, Genady said:

I thought that the word "truth" is just a shortcut for "true proposition", like in "The truth is that he was not there."

It depends, how many bears did you drink???

[Genady]

12 minutes ago, dimreepr said:

It depends, how many bears did you drink???

I don't drink bear because of an allergy.

[dimreepr]

13 minutes ago, Genady said:

I don't drink bear because of an allergy.

You lucky duck...

[exchemist]

56 minutes ago, Genady said:

I thought that the word "truth" is just a shortcut for "true proposition", like in "The truth is that he was not there."

Exactly, it has no meaning except in relation to a proposition, or a collection of propositions judged to be true.

[iNow]

43 minutes ago, Genady said:

I don't drink bear because of an allergy.

Sounds like a grizzly situation, Yogi. No difference between brown bears or black? They seem to be polar opposites. Maybe we can hibernate on it. 

[Genady]

20 minutes ago, iNow said:

Sounds like a grizzly situation, Yogi. No difference between brown bears or black? They seem to be polar opposites. Maybe we can hibernate on it. 

I didn't try a polar though...

[TheVat]

This is why I support the Constitutional right to arm bears.  As was crafted by John Grizzly Adams.  

[rufus mosley]

On 7/8/2024 at 6:00 PM, swansont said:

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

Group - Swansont says that the statement is a tautology. Do we need some proof of this?

On 7/8/2024 at 6:35 PM, joigus said:

 

Joigus - Are there some linguistic rules that would alert us to a tautology here?

On 7/9/2024 at 12:26 AM, Eise said:

 

Else - What type of tautology is this?

On 7/9/2024 at 8:09 AM, dimreepr said:

 

Dimreaper - Can a tautology contradict itself?

On 7/9/2024 at 9:32 AM, iNow said:

 

iNow - Is this a definition or a proposition?

On 7/9/2024 at 9:36 AM, dimreepr said:

 

Dimreaper - If this a definition, what are the rules for definitions, and does this statement adhere to the rules?

On 7/9/2024 at 9:37 AM, iNow said:

 

iNow - If this a proposition, what is the premise?

On 7/9/2024 at 1:02 PM, Ghideon said:

 

Ghideon - Can a tautology contradict itself?

On 7/9/2024 at 5:48 PM, studiot said:

 

Studiot - If this is a tautology, would the opposite be a tautology also? - Truth can contradict itself?

On 7/10/2024 at 3:48 PM, MSC said:

 

MSC - If the language demands that the opposite is also a tautology, why choose one over the other, since both statements are equal, being tautological?

Edited Friday at 11:33 PM by rufus mosley

[studiot]

Just now, rufus mosley said:

Group - Swansont says that the statement is a tautology. Do we need some proof of this?

Joigus - Are there some linguistic rules that would alert us to a tautology here?

Else - What type of tautology is this?

Dimreaper - Can a tautology contradict itself?

iNow - Is this a definition or a proposition?

Dimreaper - If this a definition, what are the rules for definitions, and does this statement adhere to the rules?

iNow - If this a proposition, what is the premise?

Ghideon - Can a tautology contradict itself?

Studiot - If this is a tautology, would the opposite be a tautology also? - Truth can contradict itself?

MSC - If the language demands that the opposite is also a tautology, why choose one over the other, since both statements are equal, being tautological?

If and only if you are genuinely interested in discussing this you will have to work harder yourself.

 

Yes swansont says this (ie some) statement is a tautology.

So what ?

 

Under what system of logic, propositional (first order) or predicate (second order) or what?

Since I consider examples are really helpful I have given you several, and again you have not responded to any of them.

Why not ?

swansont also said

On 2/3/2025 at 8:54 PM, swansont said:

Yes, tautology. Can you ask a more specific question?

to which you responded

On 2/3/2025 at 10:21 PM, rufus mosley said:

How?

 

Well I suggest to you that 'how?' is answered by providing an example for discussion.

 

Here is an example of a first order logic being defeated by a second order answer

In Irish Mythology there was a superhero who was apparantly invincible.

So magic was cast so that he could not be killed either inside a house or outside one.

Yet he was eventually slain.

 

Would you like to discuss how and is his invincibility a tautology ?

 

[swansont]

3 hours ago, rufus mosley said:

Group - Swansont says that the statement is a tautology. Do we need some proof of this?

A tautology is a statement that is true by definition (in rhetoric, it says the same thing twice). “True statements are true” seems to fit that. By inspection.

If you want a syllogism

A tautology is a statement that is true by definition
‘True statements are true’ is true by definition
Therefore it is a tautology

Do we need this proof? I wouldn’t think so, but YMMV

Can you refute it? 

 

 

[rufus mosley]

1 hour ago, swansont said:

A tautology is a statement that is true by definition (in rhetoric, it says the same thing twice).

The words of the statement for consideration are: Truth cannot contradict itself or Can truth contradict itself? These four words are the topic we are discussing. Is there any logical progression of thought present in any of these statements? Is this a definition of truth or a proposition concerning truth. What are the rules of definition? What are the rules for the construction of a proposition? Do we need a premise? Suppose that truth does contradict itself? Then when we go searching for truth we will miss it entirely. So, I remain unconvinced. All I knew is that I would flunk if I did not accept this proposition. That is the one and only reason I accepted it in my youth. Fear. There does not seem to be any logical reasoning here. This seems to violate the rules of definition as I know them. it is against the rules of definition to refer to the definiendum in the definiens.

https://g.co/gemini/share/0b247bcdb467

If you want say that it is not a definition but is a proposition about truth, where is the premise? Someone else on the other side of the internet, a very learned philosopher argued that it's neither a definition or a proposition - it's a statement. What do you think of that? Are not all definitions and propositions also statements? He seems to have desired to remove himself from the discussion.

Now what happens to the truth by definition argument, if the definition violates the rules of definition? What can any of you say to Swansont? A tautology is a truth by definition. So it is a tautology, particularly a circular definition. And it must be a definition in order to be truth by definition. And it violates the rules of definition. Are you all standing on terra firma? Discuss these things among yourselves.

The only other avenue is to treat it as proposition without a premise. You may want to resort to the history of philosophy to find the unstated premise(s).

Edited Saturday at 03:51 AM by rufus mosley

[Ghideon]

12 hours ago, rufus mosley said:

Ghideon - Can a tautology contradict itself?

What type of tautology are you interested in? Logical and computational tautologies are within my area of expertise.

(Language and legal tautologies for instance, not so much.)

[dimreepr]

9 hours ago, rufus mosley said:

The words of the statement for consideration are: Truth cannot contradict itself or Can truth contradict itself?

It will be what it is... 😉

[swansont]

10 hours ago, rufus mosley said:

The words of the statement for consideration are: Truth cannot contradict itself or Can truth contradict itself?

No, those are not my statements, those are yours.

My statement was “true statements are true” which is a tautology. You asked for proof, and I gave it. You can’t rebut it by considering some other statement. 

As for your statement, give an example of truth contradicting itself.

[Genady]

13 hours ago, studiot said:

In Irish Mythology there was a superhero who was apparantly invincible.

So magic was cast so that he could not be killed either inside a house or outside one.

Yet he was eventually slain.

This is the only meaningful piece in this whole thread so far, IMO.

I can think of several ways to solve this apparent contradiction, basically by separating its parts in space or in time.

I'll wait for the "textbook answer."

[dimreepr]

41 minutes ago, Genady said:

I'll wait for the "textbook answer."

It can only be what it is... 🙂

[Genady]

14 hours ago, studiot said:

In Irish Mythology

I found on the Internet (with no LLM help) a story of the king with initials B.B., which fits one of the solutions I've thought about. Is that the one?

P.S. An LLM's answer was wrong, again.

[joigus]

17 hours ago, rufus mosley said:

Joigus - Are there some linguistic rules that would alert us to a tautology here?

Where?

[Genady]

The solution that I referred to in the previous post (https://www.scienceforums.net/topic/134306-can-truth-contradict-itself/page/2/#findComment-1284392) is weak, IMO. I think my other solution is rather strong, but I couldn't find it in the Irish myths I looked at.

 

[studiot]

Just now, Genady said:

The solution that I referred to in the previous post (https://www.scienceforums.net/topic/134306-can-truth-contradict-itself/page/2/#findComment-1284392) is weak, IMO. I think my other solution is rather strong, but I couldn't find it in the Irish myths I looked at.

 

I was only a child when I read those stories.

I had a quick look on the net but can't find any of the stories I remember  -  even the names are spelled differently now.

 

However the 'solution' to the story was that the hero was slain in a doorway  -  neither inside nor outside the house.

The fact remains that first order logic is unable to resolve the issue as it is based on absolute (usually binary) non intersecting classes in all cases.

 

It is also interesting the the mythology of the four 'home' nations is quite different from the mythology in Europe, Russia, China and the middle East which have much commonality.

[dimreepr]

19 hours ago, joigus said:

Where?

lol +1

21 minutes ago, studiot said:

It is also interesting the the mythology of the four 'home' nations is quite different from the mythology in Europe, Russia, China and the middle East which have much commonality.

So many paths, but only one place to find.

 

 

[Genady]

42 minutes ago, studiot said:

I was only a child when I read those stories.

I had a quick look on the net but can't find any of the stories I remember  -  even the names are spelled differently now.

 

However the 'solution' to the story was that the hero was slain in a doorway  -  neither inside nor outside the house.

The fact remains that first order logic is unable to resolve the issue as it is based on absolute (usually binary) non intersecting classes in all cases.

 

It is also interesting the the mythology of the four 'home' nations is quite different from the mythology in Europe, Russia, China and the middle East which have much commonality.

Yes, that was one of the solutions I thought about. Then I search Internet for "Irish mythological hero killed in doorway" and found this story of Brian Boru (thus the "initials B.B." that I've mentioned earlier): Brian Boru: historical figure and mythic hero

Quote

Brian himself was dead – killed by an axe thrown by a Manx Norseman Brodr, as he stood in the doorway of his tent awaiting news of victory

 

However, I think that this solution is weak, because it can be reasonably argued that a doorway is still part of the house as without a house there would not be a doorway.

My other solution, which I consider strong, is also based on going beyond the first order logic, but instead of adding possibilities to the binary notion "inside"/"outside" the house, it adds possibilities to the notion "here"/"not here" of the location of killing.