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, ∞)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?
The Truth Contradiction
Re: The Truth Contradiction
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Re: The Truth Contradiction
I have a feeling something's off.Skepdick wrote: ↑Mon Nov 28, 2022 11:52 amI 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, ∞)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?
Re: The Truth Contradiction
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?
Re: The Truth Contradiction
No because they are not negations of each other. I could add a third statement:Agent Smith wrote: ↑Mon Nov 28, 2022 11:33 amYou're right of course and on target mon ami. Also it looks like I need to be more specific.Skepdick wrote: ↑Mon Nov 28, 2022 9:47 amI 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 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.
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".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?
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.
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?
3. x = 2
If 3. is true, this would make both 1. and 2. false, so 1. and 2. do not constitute a contradiction.
Re: The Truth Contradiction
There are infinitely-many possible completions to 1 and 2.
3. x = chicken
or
3. x = (-∞, 2) ∪ (2, ∞)
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?
Re: The Truth Contradiction
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.
Re: The Truth Contradiction
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
Re: The Truth Contradiction
And I just demonstrated that the two statements do not constitute a contradiction, according to your definition.Skepdick wrote: ↑Wed Nov 30, 2022 12:29 pmThat'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
Re: The Truth Contradiction
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!
Re: The Truth Contradiction
Re: The Truth Contradiction
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!
Re: The Truth Contradiction
I just noticed that you couldn't answer the original question, so I jumped in to clear things up.Skepdick wrote: ↑Wed Nov 30, 2022 12:59 pmMarvelous! 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!
Re: The Truth Contradiction
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?
Re: The Truth Contradiction
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.
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Re: The Truth Contradiction
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.