What LEM is not

[Skepdick]

THE MEANING OF THE WORD "NEGATION"
( in the context of natural languages as well as LEM )

Ngation is not a word. It's a cognitive process.

The rest is hogwash.

[Skepdick]

In the context of English language, as well as every other natural language; but more importantly, in the context of LEM, the symbol "not X", which is an example of negation, means "anything other than X".

That's nonsense. What does the negation of "anything other than X" amount to?

Negation is a relation like any other. In Classical logic with LEM negation relates true and false via involution.
In other logics the relation may be of a different kind; or it may not even be a well-defined operation.

What's the negation of a cat? Anything other than a cat? Bullshit.

[Magnus Anderson]

Ngation is not a word.

You must be a bot programmed to make the silliest possible objections.

The word "negation" is obviously a word. And that's what I said.

Negation itself is a function that takes a concept and inverts its meaning.

In systems of logic, such as fuzzy logic, it's a function that maps one truth value to another. Different systems of logic use different concepts of negation, as previously explained. Some of those, such as classical logic, use a concept that is based on, or that is entirely the same as, the natural concept of negation.

What does the negation of "anything other than X" amount to?

X.

In Classical logic with LEM negation relates true and false via involution.

Yes. The natural concept of negation, i.e. the one present in natural languages, is involutive.

In other logics the relation may be of a different kind; or it may not even be a well-defined operation.

And? Why should anyone care?

What's the negation of a cat? Anything other than a cat? Bullshit.

You have to tone down your ego because you're actually extremely . . . challenged.

Negation operates on concepts. It does not operate on animals. It takes a concept and produces a different concept by inverting it.

Suppose that C is a symbol that has a concept attached to it that says that C can only be used to represent quantities such as 1, 2 and 3.

The negation of the concept of C would be a concept attached to the symbol "not C" that says that "not C" can be used to represent ANYTHING that is not 1, 2 and 3.

Thus, "not C" could be used to represent quantities such as 4, 5, 6 and so on, but also, non-quantities, such as cats.

[Skepdick]

Negation itself is a function that takes a concept and inverts its meaning.

Surely the inverse of meaning would be meaningless?

In systems of logic, such as fuzzy logic, it's a function that maps one truth value to another. Different systems of logic use different concepts of negation, as previously explained. Some of those, such as classical logic, use a concept that is based on, or that is entirely the same as, the natural concept of negation.

There is no "natural concept of negation".

What does the negation of "anything other than X" amount to?

X.
[/quote]
Wut? If the variable X is assigned the meaning "anything other than X", then the negation of X is itself ?!?

Yes. The natural concept of negation, i.e. the one present in natural languages, is involutive.

No, it's not.

Here is double negation that's NOT involutive.

And? Why should anyone care?

Because English doesn't conform to Classical logic with LEM.

You have to tone down your ego because you're actually extremely . . . challenged.

Nowhere near as challenged as your intelelct.

Negation operates on concepts. It does not operate on animals.

Q.E.D Idiot.

It takes a concept and produces a different concept by inverting it.

What's the inverse of an inverted animal?

Suppose that C is a symbol that has a concept attached to it that says that C can only be used to represent quantities such as 1, 2 and 3.

The negation of the concept of C would be a concept attached to the symbol "not C" that says that "not C" can be used to represent ANYTHING that is not 1, 2 and 3.

Thus, "not C" could be used to represent quantities such as 4, 5, 6 and so on, but also, non-quantities, such as cats.

What's the inverse of 1? Is it ALL integers or ALL real numbers; or ALL numbers? Does it include cats and dogs? Everything except 1? Does the negation of the concept 1 include the symbol 1?

If I negate the concept of "concepts" then what's that ?

[Magnus Anderson]

Surely the inverse of meaning would be meaningless?

Yes but only if you misinterpret your interlocutor. Something that you constantly do without the slightest bit of shame.

There is no "natural concept of negation".

Says Skepdiick.

Wut? If the variable X is assigned the meaning "anything other than X", then the negation of X is itself ?!?

You don't say "Wut" unless you're a kid. And if you're a kid, you need to learn better.

If the symbol "X" means "Anything other than X", then X is a contradiction in terms, an oxymoron, effectively a meaningless symbol.

You are really really trying too hard to be smart.

No, it's not.

Here is double negation that's NOT involutive.

That's not a double negation, Skeppie McDickie. Stop embarrassing yourself at this rate.

Because English doesn't conform to Classical logic with LEM.

What exactly does not conform to "Classical logic with LEM" ?

Nowhere near as challenged as your intelelct.

You never grow tired of these pathetic replies?

What's the inverse of an inverted animal?

Negation does not operate on animals.

What's the inverse of 1? Is it ALL integers or ALL real numbers; or ALL numbers? Does it include cats and dogs? Everything except 1? Is that everything except the symbol 1 or the concept 1?

In the unrestricted sense, everything except for the number 1. So yes, "not 1" would also be able to represent cats. But if you say, "A natural number that is not 1", that's a different thing.

[Skepdick]

Yes but only if you misinterpret your interlocutor. Something that you constantly do without the slightest bit of shame.

I am not misinterpreting you. I am interpreting you.

You insist that the inverse of X is anything other than X.
So the inverse of something meaningful is anything other than something meaningful.

Says Skepdiick.

Well done, captain obvious.

You don't say "Wut" unless you're a kid. And if you're a kid, you need to learn better.

Yet here I am. Saying "Wut?". And I am not a kid. So there goes another one of your principles...

If the symbol "X" means "Anything other than X", then X is a contradiction in terms, an oxymoron, effectively a meaningless symbol.

Why? One's a bound X, one is a free X.

You are really really trying too hard to be smart.

I am not in this game to be smart. I am in this game to avoid stupidity.

That's not a double negation, Skeppie McDickie. Stop embarrassing yourself at this rate.

There are literally TWO negatives in the phrase "No, it's not".

What exactly does not conform to "Classical logic with LEM" ?

Natural languages. Or any language without involutive negation.

You never grow tired of these pathetic replies?

Neither do you.

Negation does not operate on animals.

You said it operates on the concepts.

What's the inverse of an inverted animal (the concept)?

In the unrestricted sense, everything except for the number 1.

Why do you assume "not 1" negates the number and not the symbol?

So yes, "not 1" would also be able to represent cats. But if you say, "A natural number that is not 1", that's a different thing.

I am saying "not 1". Without qualification.

Is the symbol 1 in that set?
Is the number 1 in that set?
Is the letter 1 in that set?

[Magnus Anderson]

I am not misinterpreting you. I am interpreting you.

Yes, you're interpreting me. Incorrectly. And that means you're misinterpreting me.

There are literally TWO negatives in the phrase "No, it's not".

Two negatives isn't enough to constitute a double negation.

Even statements such as "We don't need no education" do not contain double negation.

You said it operates on the concepts.

Yes. Animals aren't concepts.

What's the inverse of an inverted animal (the concept)?

The word "animal" does not denote a concept.

I am saying "not 1". Without qualification.

Is the symbol 1 in that set?
Is the number 1 in that set?
Is the letter 1 in that set?

Why should I bother answering these questions?

Give me a reason . . . or be ignored.

[Magnus Anderson]

LEM IS NOT AN OPEN STATEMENT

Moving on, this will be a post where I address the idea that LEM is sometimes true and sometimes false, or more specifically, that it is true within some systems of logic but false within some other systems in logic. This is the kind of thinking that can be found among people who subscribe to formalism.

To understand why this is false, one must first understand the difference between open and closed statements.

An open statement is a statement that contains at least one free variable. An example would be, "Given human being H, H is a male". Such statements do not represent a specific proposition, but instead, an entire category of propositions. That's why the concept of truth value does not apply to them -- they are a collection of propositions rather than a single proposition, a collection that can even consist of propositions that have different truth values. That's why they have no truth value until you turn them into a closed statement by assigning each free variable a value.

An open statement can be said to have a conditional truth value, i.e. its truth value depends on the values that are assigned to its free variables. It can always be true, in every case, but not necessarily. It can also be sometimes true and sometimes false.

The only way a statement can be sometimes true and sometimes false is if it's an open statement. And that's why when they say that LEM is true in one system of logic but false in another, you can safely conclude that they think that LEM is an open statement.

They literally believe, albeit they won't say it or even admit it, that LEM is stated as, "Given negation N and truth-value T, for every proposition P, either the truth value of P is T or the truth value of N( P ) is T".

If you think this way, then obviously, whether LEM is true or not depends on the values that are assigned to N and T.

In fuzzy logic, they use the word "true" for "1". They also define negation of P as "1 - P".

Thus, if we set T to 1 and N to 1 - P, we get a closed version of LEM which goes like this:

"For every proposition P, its truth value A is 1 or 1 - A is 1".

Let A be 0.8. The above says that A is either 1 ( which it is not ) or that 1 - 0.8 = 0.2 is 1 ( which is also not the case. )

So this instance of LEM is very clearly false.

The problem is that LEM is NOT an open statement and what these people are doing is merely misinterpreting what it is.

[Skepdick]

Yes, you're interpreting me. Incorrectly. And that means you're misinterpreting me.

I am interpreting you verbatim. If that's incorrect - it's got nothing to do with me.

Here - let me remind you:

in the context of LEM, the symbol "not X", which is an example of negation, means "anything other than X".

Substiutute "X" for "meaningful". The negation of "meaningful" means "anything other than meaningful".

Which is just a long fucking way of saying "The negation of something meaningful is NOT meaningful"

Two negatives isn't enough to constitute a double negation.

Looks like you just changed your mind on LEM. Again.

the negative of the negative of P is P.

Yes. Animals aren't concepts.

I am literally using your own nomenclature, moron.

The symbol "animals" is attached to the concept" animals"

The word "animal" does not denote a concept.

Contradiction. "animal" is an abstract category ergo - a concept.

Give me a reason . . . or be ignored.

The reason is because you are a confused cunt. Good enough?

[Magnus Anderson]

I am interpreting you verbatim. If that's incorrect - it's got nothing to do with me.

In other words, you're not making any effort to understand, so you're misunderstanding and shifting the blame on me.

You don't even know which of the statements of mine you've misunderstood.

Looks like you just changed your mind on LEM. Again.

the negative of the negative of P is P.

And you don't know what a double negation is.

I am literally using your own nomenclature, moron.

Not quite.

The symbol "animals" is attached to the concept" animals"

In that case, you should ask, "What does the symbol 'not animal' mean?"

Instead, you're asking, "What's the inverse of an animal?"

And, "What's the inverse of an inverted animal?"

Holy fucking shit, an inverted animal! I don't even want to picture what that looks like.

Contradiction. "animal" is an abstract category ergo - a concept.

You're not following and you're not going to be getting an explanation as to why.

The reason is because you are a confused ****. Good enough?

You choose to be ignored. Thanks.

[godelian]

Moving on, this will be a post where I address the idea that LEM is sometimes true and sometimes false, or more specifically, that it is true within some systems of logic but false within some other systems in logic. This is the kind of thinking that can be found among people who subscribe to formalism.

The concern about the LEM is staunchly constructivist and not formalist.

Formalism is about the fact that mathematics is not about the physical universe.

A very small part of mathematics may naturally map to physical reality but in the greater light of things, that is actually irrelevant. This part, i .e. physical mathematics, is indeed available from our built-in biological firmware, but it is so small that it is barely worth mentioning.

By systematizing and axiomatizing physical mathematics since Greek antiquity, we have managed to see a much bigger picture, i.e. the enormous abstract Platonic world of which physical mathematics is just a minute part. By obsessing over the mere shadows, visible in the physical cave, you will fail to see the much larger Platonic truth.

This is not a consideration that originates from formalism but from Platonism.

In the much larger Platonic world of mathematics, the LEM is indeed sometimes true and sometimes false.

[Magnus Anderson]

In the much larger Platonic world of mathematics, the LEM is indeed sometimes true and sometimes false.

So you ignored the post where I said that 1) only open statements can be conditionally true or false, and 2) LEM is not an open statement.

By obsessing over the mere shadows, visible in the physical cave, you will fail to see the much larger Platonic truth.

You're talking about extremely narrow subjects and you're calling them "the much larger Platonic world of mathematics".

You need to get out of these caves and see the big picture.

[godelian]

So you ignored the post where I said that 1) only open statements can be conditionally true or false, and 2) LEM is not an open statement.

The LEM indeed has no free variables.

However, it iterates ("for each") over propositions ... of what set or domain exactly?

Physicalist propositions -- representing a state in physical reality -- are just a small subset of all possible propositions. In fact, the LEM is itself also a proposition and it is not physicalist. Therefore, in your take on the matter, the LEM does not even apply to itself.

[Magnus Anderson]

The LEM indeed has no free variables.

And because only statements that have free variables have conditional truth value ( which isn't really truth value in the classical sense of the word ), LEM does not have a conditional truth value. In other words, it can't be true in one context and false in another.

However, it iterates ("for each") over propositions ... of what set or domain exactly?

It says, "For each proposition P". It's speaking about the set of all propositions that can be conceived. But one has to understand what is meant by the term "proposition", among other things, that propositions aren't the same thing as sentences.

Physicalist propositions -- representing a state in physical reality -- are just a small subset of all possible propositions. In fact, the LEM is itself also a proposition and it is not physicalist. Therefore, in your take on the matter, the LEM does not even apply to itself.

What is a physicalist proposition and how does it differ from non-physicalist propositions?

Can you give some examples?

[godelian]

What is a physicalist proposition and how does it differ from non-physicalist propositions?

You defined a proposition as a logic sentence representing a state in physical reality. Let's call this a "physicalist" sentence.

The LEM itself is not such proposition, as it is about other propositions and not about a state in physical reality. Hence, in your take on the matter, the LEM does not even apply to itself.

It says, "For each proposition P". It's speaking about the set of all propositions that can be conceived.

This sounds like a psychologically defined set. Which person would we take as the benchmark for the "psychological conceiving"? How do you guarantee that the proposition that one person can conceive, is also conceivable to another person?

Furthermore, the "for each" quantifier is not supported for every set. On what grounds do you believe that this psychological set of propositions is recursively enumerable? What algorithm is capable of enumerating this set?