In Support of Trivialism

[wtf]

I'm a human. The Pope is a human. Therefore I am the Pope.

Now go in peace and sin no more. You can cos as much as you like.

[Serendipper]

I'm a human. The Pope is a human. Therefore I am the Pope.

Now go in peace and sin no more. You can cos as much as you like.

Sin and virtue are attributes of action and are therefore equal

[wtf]

We previously talked about the logical rule of inference known as existential instantiation. With the rule of existential instantiation, I would be required to give the rectangle referred to by "a rectangle is not a square" a unique name that is different from the name I give the rectangle referred to by "a rectangle is a square."

That's right. If there exists a rectangle that's a square, we symbolize this as

$$\exists x ( R(x) \land S(x))$$

We say that x is now a bound variable. As Wiki puts it:

That is, free variables become bound, and then in a sense retire from being available as stand-in values for other values in the creation of formulae.

https://en.wikipedia.org/wiki/Free_vari ... _variables

So now if there's some other rectangle that's not a square, and we want to express this fact in conjunction with the earlier fact, we write

$$\exists x ( R(x) \land S(x)) \land \exists y (R(y) \land \neg S(y))$$

One potential flaw with existential instantiation is that it seems to be based off of the implicit assumption that two things that are unequal are not permitted to have the same name.

It's not a flaw, it's a feature. It's how logic works. The purpose of symbolic logic is to be crystal clear in our meaning; to avoid the ambiguity of natural language. That's the entire point.

In mathematics in general, that assumption seems to be made.

Certainly we can use the same name for different objects in different contexts. But in formal logic, we first choose the context, or domain, or universe -- different words for the same idea -- and then within that context, names must refer uniquely to objects.

However, in the real world, two things that are unequal can, and sometimes do, have the same name.

Well sure, a cat is a furry four-legged handwarmer; and a cat is a Caterpillar tractor; and a cat is a person with a hip demeanor, as in a cool cat.

What of it? Again, the entire point of symbolic logic is to remove the ambiguity of natural language, so that we may be sure that we are reasoning correctly. Of course natural language is ambiguous, that's so poets will have something to do. The fog comes on little cat feet.

In poetry, we exploit the ambiguity of natural language; in formal logic, we avoid it. Poetry and logic. Two different human activities.

So, it seems that traditional mathematics is flawed because it seems to have an unnecessary rule that reality does not abide by.

Math is good for doing math, and everyday natural language is good for doing everyday natural things. I don't understand why you think one is "flawed." We use hammers to hammer nails, and flashlights to illuminate the dark. We don't say hammers are flawed because they're not flashlights. We use different tools for different tasks. Surely you agree.

Conflation among different things with the same name may be an inevitable or necessary feature of nature.

No, it's an inevitable or necessary feature of natural language. You are confusing the names of things with the things themselves. You are confusing the words we use to talk about nature and to navigate the world; with the world itself.

This is a philosophical error. There are things, and there are names. The names of things are not the things.

The most questionable step in the above argument is (5), which I provided as a premise. The premise is that the rectangle that is a square is equal to the rectangle that is not a square. The premise's truth is based off of the fact that d and g each have the same name, a rectangle.

I commend you for recognizing that this step is problematic.

But surely you see that just because I am a human and the Pope is a human, that I am not necessarily the Pope!

Here "is" does not mean "equals," which would allow you to use transitivity of equality: if A = B and B = C then A = C.

Rather in this instance, "is" means, "is a member of some class." So you have some horse that "is" an animal; and you have a cat that "is" an animal. But a horse is not a cat.

In this case "is" is being used as set membership, if you like; but not as equality.

[browser32]

Regardless of whether the rectangle referred to in "a rectangle is not a square" is the same rectangle referred to in "a rectangle is a square," the former statement is the negation of the latter statement.

The following Argument 3 is a third attempt to present my argument in symbolic logic.

Argument 3.

Given: p = "A rectangle is a square," p, ¬p, q is a statement.
Prove: q

Statements (Reasons)
1. p (Given)
2. ¬p (Given)
3. ꓕ (ꓕ introduction from (1) and (2))
4. q (ꓕ elimination from (3))
This concludes the argument.

Premise (1) is justified by the fact that some rectangles are squares. Premise (2) is justified by the fact that some rectangles are not squares.

I'm a human. The Pope is a human. Therefore I am the Pope.

I know it sounds odd, but in a sense you are the Pope. You are the Pope in the sense that you and the Pope each is a human. There may be contexts in which you would use such discourse.

Example. You are talking to aliens that are not humans and are not from earth. You indicate to them that, among the numerous species of life on earth, you and the Pope are of the same species. You told the aliens you are not a cat, you are not a spider, you are not a giraffe, and you are not a penguin. You told the aliens, however, that you are the Pope. The aliens understand that you meant that there are some differences between you and the Pope, but that you and the Pope are of the same species. This concludes the example.

Here "is" does not mean "equals," which would allow you to use transitivity of equality: if A = B and B = C then A = C.

Again, there are multiple senses of equality. Since you are a human and the Pope is a human, there is a sense of equality in which "you = a human" and "the Pope = a human." This sense of equality may be syntactic only, or it may be syntactic and semantic. You and the Pope have properties in common that can be used to pair you two up and regard you two in the same way.

No, it's an inevitable or necessary feature of natural language.

Natural language is a part of nature.

It doesn't matter what language a contradiction is asserted in; if a contradiction exists, then through the principle of explosion, all statements of all languages are true. Thus, if a contradiction exists in natural language, then by the principle of explosion, all statements of first-order logic, all statements of all natural languages, and all statements of all unnatural languages are true.

The names of things are not the things.

The names of things are not always the things. The names of things can be considered properties of the things. It actually seems the name of a thing is often considered a property of the thing. For example, in computer software, the name of an object is often considered one of the most important properties of the object.

[wtf]

The names of things are not always the things. The names of things can be considered properties of the things. It actually seems the name of a thing is often considered a property of the thing. For example, in computer software, the name of an object is often considered one of the most important properties of the object.

Yes, and in biology a cat is a four legged furry handwarmer, while in popular culture it's an especially hip hipster. What of it?

Regarding your equivocation of "is", consider a mathematical example.

2 is a number and 3 is a number, but 2 is not equal to 3.

If we let N be the set of natural numbers, then we say 2 ∈ N and 3 ∈ N. That means "2 is a member of the set of natural numbers, and 3 is a member of the set of natural numbers."

In this case the natural language "is" refers to set membership.

When we say that 2 = 1 + 1 and 1 + 1 = 5 - 3, that's equality. It's a transitive relation, so that we may conclude that 2 = 5 - 3.

You are simply equivocating "is" as set or class membership, and "is" as the equality relationship.

[browser32]

Yes, and in biology a cat is a four legged furry handwarmer, while in popular culture it's an especially hip hipster. What of it?

Some words have multiple senses. Equality is one of those words.

2 is a number and 3 is a number, but 2 is not equal to 3.

2 is not equal to 3 in a well known mathematical sense. But both are, as you have suggested in your post, natural numbers. So, in the sense that 2 and 3 each is a natural number, 2 is equal to 3.

When we say that 2 = 1 + 1 and 1 + 1 = 5 - 3, that's equality. It's a transitive relation, so that we may conclude that 2 = 5 - 3.

The expressions 2 and 1 + 1 are not equal; there is an obvious syntactic inequality. In another sense of equality, however, the expressions 2 and 1 + 1 are equal; the value of the expressions are equal. This example is similar to the example I previously gave involving two dimes. Each pair of expressions (1 + 1, 5 - 3) and (2, 5 - 3) can be used in another similar example.

You are simply equivocating "is" as set or class membership, and "is" as the equality relationship.

I am not equating naively. My equations have been justified.

I am aware of the two different uses of is that you have mentioned. I described the set membership use in my earlier post at viewtopic.php?p=2697521#p2697521, exclusively between the first and second quotations from Serendipper that I provided. I also described the set membership use in my earlier post at viewtopic.php?p=2697589#p2697589, in my first paragraph after the first quotation from Serendipper that I provided.

[Serendipper]

So, in the sense that 2 and 3 each is a natural number, 2 is equal to 3.

2 is equal to 3 in that sense only. You cannot make further conclusions.

1) things
2) shapes
3) more-specific shapes
4) even more-specific shapes.

You cannot say because everything is a thing, therefore everything is equal in all senses.

If you can't see this by now, maybe you can't see it. Or perhaps you're not giving it moral consideration because you need your proposition to pan out for some reason. Either way, this is going to go on forever because you can't or won't see reason. Isn't there some other topic that you'd rather dive into? You seem like a nice guy. Why not comment on something else of interest and abandon this?

[Mad Man P]

We previously talked about the logical rule of inference known as existential instantiation. With the rule of existential instantiation, I would be required to give the rectangle referred to by "a rectangle is not a square" a unique name that is different from the name I give the rectangle referred to by "a rectangle is a square." One potential flaw with existential instantiation is that it seems to be based off of the implicit assumption that two things that are unequal are not permitted to have the same name. In mathematics in general, that assumption seems to be made. However, in the real world, two things that are unequal can, and sometimes do, have the same name. So, it seems that traditional mathematics is flawed because it seems to have an unnecessary rule that reality does not abide by.

I think we might have found the problem...
I agree in reality we can have many different things that are identified by the same name... A kid could name a rock "bob", he could name an imaginary friend "bob", there is no end to the number of things we could call "bob" on a whim.

Language is a human invention, the naming conventions we employ are more for practical functionality than accurate representation... You'd be perfectly happy to simply call Bob your work friend "Bob" and Bob your childhood friend "Bob"... but if you were speaking to a friend who knew both Bobs then you'd feel the need to distinguish them by name for the sake of clarity... you'd say "work Bob" or "Original Bob" or use their last names... or simply bob1 and bob2

We rename things and add extra identifiers to how we name things all the time for the sake of clarity and communication...

In the second argument, it is postulated that there is a rectangle that both is and is not a square. The basis for that contradiction is that the rectangle that is a square and the rectangle that is not a square are the same because each is a rectangle. They each have the property of being a rectangle. They each have the name a rectangle. They each share the noun phrase a rectangle.

You have correctly identified a failure of you own chosen naming convention... the term "A rectangle" is insufficient to distinguish distinct objects and therefor misrepresents them as the same thing.
Like with the two Bobs, the solution is to rename them for clarity... given how the "square/not square" aspect is generating the contradiction and not the rectangle part, perhaps including that detail in the naming convention would be useful.

Perhaps you could name them as you did above and stick to that naming convention: "The Rectangle that is a square" and "The Rectangle that is not a square"

At which point you'd be spouting a tautology "The Rectangle that is a square, is a square" and "The rectangle that is not a square, is not a square"... There is no contradiction when employing a more clear use of language.

[browser32]

Mad Man P:

I don't have to rename the rectangles. I don't have to give each rectangle a unique name. It is permitted that both rectangles simultaneously have the same name. That is how it is in real life.

[Mad Man P]

Mad Man P:

I don't have to rename the rectangles. I don't have to give each rectangle a unique name. It is permitted that both rectangles simultaneously have the same name. That is how it is in real life.

I understand...
But what I'm suggesting is that your refusal to be precise or even practical with your use of language does not logically constitute sufficient cause to abandon the law of non-contradiction.

You are not demonstrating a contradiction... merely poor language skills.

[browser32]

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]

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]

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 http://www.debate.org/debates/God-Exists/164/, 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." I said something similar in a reply to Carleas at viewtopic.php?p=2695639#p2695639,

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.

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.

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]

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.

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.

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.

"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.

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]

"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]

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.

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 https://twitter.com/paulemok/status/975234801409118208 avoids this fallacy. It does not have "some rectangles are squares" as a premise.

"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.

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.