In Support of Trivialism

[browser32 (Paul E. Mokrzecki)]

Mad Man P:

I have not abandoned the law of non-contradiction. If there is a contradiction, then through the principle of explosion, the law of non-contradiction is true. If there is not a contradiction, the law of non-contradiction is true. Either way, the law of non-contradiction has not been abandoned.

My language use in my argument may be poor, but it does seem to be permitted. One concern I have is that my use of the indefinite article a whenever referring to one of the two rectangles may be grammatically prohibited. However, if the use is prohibited, my earlier given Argument 3, and even Arguments 1 and 2, still succeed since they do not violate that linguistic prohibition.

[Mad_Man_P]

@browser32

My language use in my argument may be poor, but it does seem to be permitted.

The word “permitted” implies a standard, system or authority that is “permitting”… From who or what are you seeking this permission?

I contend that it cannot be “logic”, as logic strictly prohibits that kind of ambiguity in language, equivocation is a fallacy, after all…
If you are operating by some alternative in which equivocation is not a fallacy, then you have successfully shown that this alternative generates contradictions.

[browser32 (Paul E. Mokrzecki)]

@Mad Man P

From who or what are you seeking this permission?

I am seeking this permission from the rules of the English language.

As my opponent had suggested to me in the comments section for a past debate I participated in, a debate that was cited indirectly in the second paragraph of the original post for this thread and is located at viewtopic.php?p=2695639#p2695639,

@browser32

while the rectangle in the quoted statement “a rectangle is a square” may not be the same rectangle in the quoted statement “a rectangle is not a square,” the quoted noun phrase “a rectangle” has the same meaning in both statements. That common meaning is “one quadrilateral that has four right angles.”

The statement “a rectangle is a square and a rectangle is not a square” is, in some sense, a syntactic contradiction. Since the syntactic contradiction exists, a contradiction exists. So, the principle of explosion brings about trivialism. Also, the syntactic contradiction suggests some semantic contradiction. A semantic contradiction, through the principle of explosion, brings about trivialism.

[Mad_Man_P]

I think we’ve come near the conclusion of our disagreement.

@browser32

I am seeking this permission from the rules of the English language.

I wish you’d made this clear earlier… It’s not controversial at all to state that you can make unclear and ambiguous statements using the english language.
It’s nevertheless logically fallacious to draw any conclusions based off of that ambiguity.

@browser32

I am not equivocating because the noun phrase “a rectangle” is used in the same sense at all times in my argument. That sense can be a fixed definition such as “one parallelogram that has four right angles.”

You’ve misunderstood the source of the equivocation.
Your argument is derived from “some rectangles are squares” which implies at least “one rectangle is a square”, so the phrase “a rectangle” in your argument is not a matter of definition, it’s the identity of a specific item, the existence of which is granted.

Where you equivocate is where you change the referent of “a rectangle” from the item that is a square to the item that is not a square…
Essentially you’ve given two distinct items the same name and are confusing yourself.

“Bob watched tv last night” and “Bob did not watch tv last night” are not contradictory statements, unless they both referred to the same “Bob”.

Like I said, equivocation is a fallacy so this is not a contradiction, just a demonstration of poor use of language.

[browser32 (Paul E. Mokrzecki)]

@Mad Man P

It’s not controversial at all to state that you can make unclear and ambiguous statements using the english language.
It’s nevertheless logically fallacious to draw any conclusions based off of that ambiguity.

The statement “a rectangle is a square” is neither unclear nor ambiguous.

@Mad Man P

Where you equivocate is where you change the referent of “a rectangle” from the item that is a square to the item that is not a square…

In some sense, I have not equivocated. In the sense, the referent of “a rectangle” is never changed in my argument. In the sense, the referent is always the same, one parallelogram that has four right angles. It is in such a sense that I am working in.

@Mad Man P

Essentially you’ve given two distinct items the same name and are confusing yourself.

In some sense, the two items you allege are distinct are actually indistinct. The two items are each a rectangle. So, like I’ve previously argued in this thread, the items are, in some sense, the same.

@Mad Man P

“Bob watched tv last night” and “Bob did not watch tv last night” are not contradictory statements, unless they both referred to the same “Bob”.

You do seem to be correct. However, the statements I’m using do not involve definite subjects. They involve indefinite subjects, as is indicated by the indefinite article a.

@Mad Man P

Like I said, equivocation is a fallacy so this is not a contradiction, just a demonstration of poor use of language.

I am not equivocating; I am operating in a sense you do not believe I am operating in. My use of language is not poor; it is commonly used and accepted. What I have actually demonstrated is an ingenious use of language.

[Mad_Man_P]

@browser32

@Mad Man P

“Bob watched tv last night” and “Bob did not watch tv last night” are not contradictory statements, unless they both referred to the same “Bob”.

You do seem to be correct. However, the statements I’m using do not involve definite subjects. They involve indefinite subjects, as is indicated by the indefinite article a.

Then, by your own admission, there is no contradiction… you cannot generate a contradiction without contradictory statements.
If the subject of your statements are not the same, then there is no contradiction… but you’ve just committed yourself to there being no definite subject, meaning you cannot generate a contradiction.

“Something is a ball” and “something is not a ball” are likewise not contradictory statements.

I am not equivocating; I am operating in a sense you do not believe I am operating in. My use of language is not poor; it is commonly used and accepted. What I have actually demonstrated is an ingenious use of language.

It is not commonly used or accepted… it’s uncommonly confused and moronic. A child could do better…
At this point I’m convinced that I am locked in battle with your ego and not your reason…
Every single person who has spoken with you thus far has contributed to utterly debunking your nonsense beyond any REASONABLE doubt, and since I have no intention of making an appeal to your ego for the sake of convincing you…
It’s best to simply withdraw and let you insist on your own genius to whomever cares to listen.

[browser32 (Paul E. Mokrzecki)]

@Mad Man P

If the subject of your statements are not the same, then there is no contradiction… but you’ve just committed yourself to there being no definite subject, meaning you cannot generate a contradiction.

The subject of both statements is the same. The subject of each is a rectangle. An indefinite subject is always a subject just as a definite subject is always a subject.

The following conditional statement (1) is true.

(1) If a rectangle is a square, then some rectangles are squares.

However, its inverse (2) is false.

(2) If a rectangle is not a square, then it is not true that some rectangles are squares.

Since the contrapositive of a conditional statement is logically equivalent to the conditional statement, the contrapositive of (2), (3), is also false.

(3) If some rectangles are squares, then a rectangle is a square.

However, (3) seems to be an implicit rule of inference that is used in my argument, as I quote.

@browser32

Some rectangles are squares. So, a rectangle is a square.

Since (3) is false, it has a counterexample. The counterexample is: some rectangles are squares, but a rectangle is not a square.

So it appears there’s a fallacy in my argument where I’ve quoted it. However, the argument I’ve previously cited at twitter.com/paulemok/status/975234801409118208 avoids this fallacy. It does not have “some rectangles are squares” as a premise.

@Mad Man P

“Something is a ball” and “something is not a ball” are likewise not contradictory statements.

They are likewise contradictory statements. Those statements have the same subject, something. What that something is does not matter. Whether that something is different in the second statement from what it is in the first statement does not matter. As long as we are considering something, we are not violating any rules.

@Mad Man P

It is not commonly used or accepted… it’s uncommonly confused and moronic.

As I’ve previously explained, it is commonly used and accepted. It is not just personally used and accepted by me; it is personally used and accepted by society in general. It’s not just used and accepted in the United States, either. I have a book apparently from Canada, which claims to be published outside of North America as well, that invokes such language use. Its name is Modal Logics and Philosophy, 2nd Edition (2000, 2009) by Rod Girle. The book claims to be printed and bound in the United Kingdom.