The Truth Contradiction

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Skepdick
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Re: The Truth Contradiction

Post by Skepdick »

Agent Smith wrote: Mon Nov 28, 2022 11:33 am You're right of course and on target mon ami. Also it looks like I need to be more specific.

Lemme try again.

1. x > 2
2. x < 2

Do the above 2 statements constitute a contradiction? If no, why? If yes, why is it, if it is, problematic to logic?
I see no problem. Given that x could be ANY Mathematical construction which satisfies property 1 AND 2 the one which trivially comes to mind is the number-line excluding 2. e.g x = (-∞, 2) ∪ (2, ∞)
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Agent Smith
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Re: The Truth Contradiction

Post by Agent Smith »

Skepdick wrote: Mon Nov 28, 2022 11:52 am
Agent Smith wrote: Mon Nov 28, 2022 11:33 am You're right of course and on target mon ami. Also it looks like I need to be more specific.

Lemme try again.

1. x > 2
2. x < 2

Do the above 2 statements constitute a contradiction? If no, why? If yes, why is it, if it is, problematic to logic?
I see no problem. Given that x could be ANY Mathematical construction which satisfies property 1 AND 2 the one which trivially comes to mind is the number-line excluding 2. e.g x = (-∞, 2) ∪ (2, ∞)
I have a feeling something's off.
Skepdick
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Re: The Truth Contradiction

Post by Skepdick »

Agent Smith wrote: Tue Nov 29, 2022 10:53 am I have a feeling something's off.
Well, sure... you are missing a logical connective between 1 and 2.

I could've interpreted what you said as 1 AND 2; 1 OR 2; 1 XOR 2; 1 NOR 2...

But the crux of the issue is that "x" is a free/unbound variable. It could represent anything. If x is a chicken does 1 or 2 hold?
BigMike
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Re: The Truth Contradiction

Post by BigMike »

Agent Smith wrote: Mon Nov 28, 2022 11:33 am
Skepdick wrote: Mon Nov 28, 2022 9:47 am
Agent Smith wrote: Sun Nov 27, 2022 6:08 pm You have a point; there's something amiss in denying contradictions entry into the ideaverse. I'm not saying we should accept them though for if we do pandemonium ensues if you catch me drift mate.
I think claims of "pandemonium" amount to fearmongering. Language is recursive - contradictions are built-in. It's a feature, not a bug. To eliminate contradiction is to eliminate self-reference, but... it would be pretty weird if the discipline which calls itself "the humanities" banned us from talking about our own humanity, don't you think?
Agent Smith wrote: Sun Nov 27, 2022 6:08 pm Have you read paraconsistent logic to sufficient depth to understand what exactly it means to say that it's both true that water is liquid and water is not liquid?
Your particular example doesn't even require para-consistent logic. Liguidity and non-liquidity are properties of water. To say "water is NOT liquid" is to say "water is either gas or solid".

And to say "water is liquid AND not liquid" is to point out that the diagram I showed you has a clear line separating the three distinct phases.
The line represents precisely the uncertain time-period in which water is busy phase-transitioning. The time-period in which the change occurs but you aren't quite certain whether is either gas or solid.
You're right of course and on target mon ami. Also it looks like I need to be more specific.

Lemme try again.

1. x > 2
2. x < 2

Do the above 2 statements constitute a contradiction? If no, why? If yes, why is it, if it is, problematic to logic?
No because they are not negations of each other. I could add a third statement:
3. x = 2
If 3. is true, this would make both 1. and 2. false, so 1. and 2. do not constitute a contradiction.
Skepdick
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Re: The Truth Contradiction

Post by Skepdick »

BigMike wrote: Tue Nov 29, 2022 5:02 pm No because they are not negations of each other. I could add a third statement:
3. x = 2
There are infinitely-many possible completions to 1 and 2.

3. x = chicken
or
3. x = (-∞, 2) ∪ (2, ∞)
BigMike wrote: Tue Nov 29, 2022 5:02 pm If 3. is true, this would make both 1. and 2. false, so 1. and 2. do not constitute a contradiction.
That depends on your logical connectives.

1 AND 2 AND 3 vs 1 OR 2 OR 3.

What if x = (-∞, 2) ∪ {2} ∪ (2, ∞) does that make 1, 2 and 3 true or false?
BigMike
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Re: The Truth Contradiction

Post by BigMike »

Skepdick wrote: Wed Nov 30, 2022 11:22 am
BigMike wrote: Tue Nov 29, 2022 5:02 pm No because they are not negations of each other. I could add a third statement:
3. x = 2
There are infinitely-many possible completions to 1 and 2.

3. x = chicken
or
3. x = (-∞, 2) ∪ (2, ∞)
BigMike wrote: Tue Nov 29, 2022 5:02 pm If 3. is true, this would make both 1. and 2. false, so 1. and 2. do not constitute a contradiction.
That depends on your logical connectives.

1 AND 2 AND 3 vs 1 OR 2 OR 3.

What if x = (-∞, 2) ∪ {2} ∪ (2, ∞) does that make 1, 2 and 3 true or false?
Maybe I misunderstood the question. I believed the question asked whether the two statements contradict each other, not whether some logical conjunction between them is true or not.
Skepdick
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Re: The Truth Contradiction

Post by Skepdick »

BigMike wrote: Wed Nov 30, 2022 12:17 pm Maybe I misunderstood the question. I believed the question asked whether the two statements contradict each other, not whether some logical conjunction between them is true or not.
That's a pretty weird statement when "contradiction" is defined as the negation of a logical conjunction: ¬(p ∧ ¬p) ⇔ ⊤

So please explain to me why the expression "¬(p ∧ ¬p)" evaluates to False in this system?

Code: Select all

[1] pry(main)> $toggle = false
=> false
[2] pry(main)> def p
[2] pry(main)*   $toggle = not($toggle)
[2] pry(main)* end
=> :p
[3] pry(main)> not(p and not(p))
=> false
BigMike
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Re: The Truth Contradiction

Post by BigMike »

Skepdick wrote: Wed Nov 30, 2022 12:29 pm
BigMike wrote: Wed Nov 30, 2022 12:17 pm Maybe I misunderstood the question. I believed the question asked whether the two statements contradict each other, not whether some logical conjunction between them is true or not.
That's a pretty weird statement when "contradiction" is defined as the negation of a logical conjunction: ¬(p ∧ ¬p) ⇔ ⊤

So please explain to me why the expression "¬(p ∧ ¬p)" evaluates to False in this system?

Code: Select all

[1] pry(main)> $toggle = false
=> false
[2] pry(main)> def p
[2] pry(main)*   $toggle = not($toggle)
[2] pry(main)* end
=> :p
[3] pry(main)> not(p and not(p))
=> false
And I just demonstrated that the two statements do not constitute a contradiction, according to your definition.
Skepdick
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Re: The Truth Contradiction

Post by Skepdick »

BigMike wrote: Wed Nov 30, 2022 12:40 pm And I just demonstrated that the two statements do not constitute a contradiction, according to your definition.
The entire point I am making is that the answer to the question "What constitutes a contradiction?" is an arbitrary choice!

Given the "standard definition" ¬(p ∧ ¬p) is supposed to be a tautology, but I have provided an empirical, real-world computational system in which ¬(p ∧ ¬p) IS NOT a tautology.

e.g LNC mandates ¬(p ∧ ¬p) ⇔ ⊤, but I am SHOWING a system in which ¬(p ∧ ¬p) ⇔ ⊥

Thus demonstrating that the LNC is a prescriptive, not a descriptive statement e.g an arbitrary CHOICE.

What constitutes a contradiction? Whatever you want to define "contradiction" as!
BigMike
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Re: The Truth Contradiction

Post by BigMike »

Skepdick wrote: Wed Nov 30, 2022 12:47 pm
BigMike wrote: Wed Nov 30, 2022 12:40 pm And I just demonstrated that the two statements do not constitute a contradiction, according to your definition.
The entire point I am making is that the answer to the question "What constitutes a contradiction?" is an arbitrary choice!
That is one of the most shocking assertions I've ever heard.
Skepdick
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Re: The Truth Contradiction

Post by Skepdick »

BigMike wrote: Wed Nov 30, 2022 12:55 pm That is one of the most shocking assertions I've ever heard.
Marvelous! You should be absolutely pleased with the fact that you are feeling shock/surprise. It signifies the arrival of new information - you just learned somethig you didn't know before!

I this is as shocking to you as learning that God doesn't exist is shocking to a theist. Slaughter those sacred cows!
BigMike
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Re: The Truth Contradiction

Post by BigMike »

Skepdick wrote: Wed Nov 30, 2022 12:59 pm
BigMike wrote: Wed Nov 30, 2022 12:55 pm That is one of the most shocking assertions I've ever heard.
Marvelous! You should be absolutely pleased with the fact that you are feeling shock/surprise. It signifies the arrival of new information - you just learned somethig you didn't know before!

I this is as shocking to you as learning that God doesn't exist is shocking to a theist. Slaughter those sacred cows!
I just noticed that you couldn't answer the original question, so I jumped in to clear things up.
Skepdick
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Re: The Truth Contradiction

Post by Skepdick »

BigMike wrote: Wed Nov 30, 2022 1:35 pm I just noticed that you couldn't answer the original question, so I jumped in to clear things up.
And I noticed that you could answer the original question.

Meaning you made up some criteria for what contsitutes an acceptable answers to a meaningless question.

The fact remains - you have no dequate answers to the questions: What is a contradiction; why is it defined that way; and is the definition correct?
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shelby
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Re: The Truth Contradiction

Post by shelby »

Christianity is the largest religion in the world with over 2 billion followers. There are a lot of funny things about Christianity that people don't know about. For example, there's a Christian sect called "The Church of Jesus Christ of Latter-day Saints" which is also known as Mormons. They believe that Jesus appeared to Joseph Smith in 1820 and told him to restore the church on earth.
popeye1945
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Re: The Truth Contradiction

Post by popeye1945 »

Eodnhoj7 wrote: Thu Oct 06, 2022 10:00 pm Given truth A is not the same as truth T it necessitates that truth is contradictory given both A and T are truths.
Truth is what your senses tell you is true, on an individual level truth is experience, to the group it is agreement or collective experience. The only way contradiction enters is with differing or altered biologizes, different biology different perception.
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