∞ is a free variable

[Skepdick]

You can reject it all you want, it won't change a thing. The middle will still be excluded.

You can object all you want. I am rejecting its exclusion anyway.

It has become fashionable, and it is particular so on this forum, to be fanatical about trying to be clever by mindlessly rejecting every widely accepted truth regardless of how basic it is.

A is not A.
1 isn't equal to 1.
2 + 2 is not 4.
Square-circles aren't oxymorons.
And so on.

This place is full of such brilliance.

The Orthodoxy is angry! Success.

When will you be nailing me to a cross for my heresy?

Yes, I am rejecting the foundations of your religion. Suck it up, darling.

[Magnus Anderson]

The Orthodoxy is angry! Success.

When will you be nailing me to a cross for my heresy?

Yes, I am rejecting the foundations of your religion. Suck it up, darling.

Well, it's one thing to re-examine widely accepted beliefs with the aim to correct any mistakes you find along the way and thereby improve the general knowledge and it's another to mindlessly attack healthy cells, i.e. non-mistakes. You're trying so hard to be innovative and unconventional that all you end up being is destructive. Rather than improving human intelligence, you end up destroying it.

And I personally wouldn't mind "nailing you to a cross for your heresy" if by "nailing you to a cross" you mean "banning you from places such as this one until you learn how to cooperate, i.e. abide by the rules of proper conduct". I am fully aware that you don't like rules precisely because they make it difficult for you to spread your negative influence but every serious community must have them if it is to sustain itself.

[Skepdick]

Well, it's one thing to re-examine widely accepted beliefs with the aim to correct any mistakes you find along the way and thereby improve the general knowledge and it's another to mindlessly attack healthy cells, i.e. non-mistakes. You're trying so hard to be innovative and unconventional that all you end up being is destructive. Rather than improving human intelligence, you end up destroying it.

It's literally what I am doing. By rejecting excluded middle I am making the landscape of human ideas richer and more fruitful. More encompassing than your own narrow-minded world-view.

You didn't know that neither infinite nor finite sets exist. And now you do.

The irony should hit you in the nether regions right about now. I am not being destructive - I am being consructive. Literally.

It's called Constructive Mathematics.

And I personally wouldn't mind "nailing you to a cross for your heresy" if by "nailing you to a cross" you mean "banning you from places such as this one until you learn how to cooperate, i.e. abide by the rules of proper conduct". I am fully aware that you don't like rules precisely because they make it difficult for you to spread your negative influence but every serious community must have them if it is to sustain itself.

My influence is overwhelmingly positive. You know - since I am actually adding new knowledge into the heads of ignoramuses...

You just learned about the existence of neither finite nor infinite sets.

Of course, if your community hates knowledge then yeah - I am a negative influence by bringing some.

Fuck your notion of "cooperation". The least you could say for shouldering your ignorance is "thank you".

[Magnus Anderson]

You live in your own delusional little world and are completely unaware of the negative influence your thoughts and actions have on the world around you.

Let me just inform you that, given that I don't think you're capable of genuine self-knowledge, that I don't really care what you think about yourself. As such, you should seriously just stop talking about yourself. It's tiresome.

Well, it's one thing to re-examine widely accepted beliefs with the aim to correct any mistakes you find along the way and thereby improve the general knowledge and it's another to mindlessly attack healthy cells, i.e. non-mistakes. You're trying so hard to be innovative and unconventional that all you end up being is destructive. Rather than improving human intelligence, you end up destroying it.

It's literally what I am doing. By rejecting excluded middle I am making the landscape of human ideas richer and more fruitful. More encompassing than your own narrow-minded world-view.

You didn't know that neither infinite nor finite sets exist. And now you do.

The irony should hit you in the nether regions right about now. I am not being destructive - I am being consructive. Literally.

It's called Constructive Mathematics.

You have a lot of learning to do before you can realize that you're actually destructive.

Surely, you're free to invent your own concepts that are inches or miles away from the standard ones. You're also free to deduce statements that apply to those concepts. That's the constructive part ( though not necessarily particular useful. ) What you're not free to do, and what makes you destructive, is the confusion of your concepts with the standard ones. In other words, what applies to YOUR concepts applies to YOUR concepts and not necessarily to STANDARD ones. Make a distinction, for fuck's sake, and stop playing word games once and for all.

No genius is required to take a standard mathematical concept of a set and create a new version of it by adding a property "color" to it. By doing that, I would be able to speak of the color of a set, but only of the color of MY kind of sets. The standard mathematical sets would remain colorless. To then insist how standard mathematical sets can have color would be pure and utter stupidity, something of which you are very much guilty.

You really are just a child delusionally believing itself to be superior merely because it has discovered the ability to modify existing concepts.

Big deal.

The issue is that you confuse things. You confuse YOUR concepts with STANDARD ones.

[Skepdick]

blah blah blah

Reality doesn't give a damn about what you think either.

And neither do I.

I've literally presented you with a set U. A set that is neither infinite nor finite.

This set exits. By construction.

Does it blow up your paradigm? Yes, it does.

That's your problem.

Well, it's one thing to re-examine widely accepted beliefs with the aim to correct any mistakes you find along the way

Your mistake is staring you in the face. Neither finite nor infinite sets.

The issue is that you confuse things. You confuse YOUR concepts with STANDARD ones.

Non-contradiction isn't a standard concept to you? Heh...

[Magnus Anderson]

There he goes again.

[Skepdick]

There he goes again.

If you don't think paradigm-level counter-examples are useful in Mathematics, then I have no idea what you mean by "useful".

That's usually a weasel word.

I think you need some of this...

glide copy.png

[Will Bouwman]

The irony should hit you in the nether regions right about now. I am not being destructive - I am being consructive. Literally.

It's called Constructive Mathematics.

Constructive Mathematics eh?

"Constructive mathematics is distinguished from its traditional counterpart, classical mathematics, by the strict interpretation of the phrase “there exists” as “we can construct”. In order to work constructively, we need to re-interpret not only the existential quantifier but all the logical connectives and quantifiers as instructions on how to construct a proof of the statement involving these logical expressions."
https://plato.stanford.edu/entries/math ... structive/

This set exits. By construction.

Given your keenness to expand our minds, are there limits to what might be constructed?

[Magnus Anderson]

I can construct a set that is neither finite nor infinite provided that you let me redefine the terms "finite" and "infinite" in the following ways.

A set is said to be finite if its number of elements is an integer greater than or equal to 1.

A set is said to be infinite if its number of elements is greater than every integer.

Thus, a set containing zero elements, i.e. an empty set, would be a set that is neither finite nor infinite.

Voila!

Proof by construction.

Except that . . . I'm merely playing a word game.

And that is all Skepdick is doing.

Playing word games.

[Skepdick]

Given your keenness to expand our minds, are there limits to what might be constructed?

Obviously. When you lose an axiom - you lose perks with it.

Anything which implicitly depends on the full axiom of choice can't be constructed. It's a long list.

If you want a more intuitive grasp... anything which requires you to presuppose that you are omniscient is problematic.
I may be a dick, but I am less of a dick than anybody who believe they are omniscient.

https://ncatlab.org/nlab/show/principle+of+omniscience

In logic and foundations, a principle of omniscience is any principle of classical mathematics that is not valid in constructive mathematics. The idea behind the name (which is due to Bishop (1967)) is that, if we attempt to extend the computational interpretation of constructive mathematics to incorporate one of these principles, we would have to know something that we cannot compute.

The main example is the law of excluded middle (EM); to apply p∨¬p computationally, we must know which of these disjuncts hold; to apply this in all situations, we would have to know everything (hence ‘omniscience’).

[Skepdick]

I can construct a set that is neither finite nor infinite provided that you let me redefine the terms "finite" and "infinite" in the following ways.

A set is said to be finite if its number of elements is an integer greater than or equal to 1.

A set is said to be infinite if its number of elements is greater than every integer.

Thus, a set containing zero elements, i.e. an empty set, would be a set that is neither finite nor infinite.

Voila!

Proof by construction.

Except that . . . I'm merely playing a word game.

And that is all Skepdick is doing.

Playing word games.

That's all Mathematics is, child. Games with rules.

Different rules - different games.

https://plato.stanford.edu/entries/form ... thematics/

One common understanding of formalism in the philosophy of mathematics takes it as holding that mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than playing ludo or chess are normally thought to have.

[Magnus Anderson]

That's all Mathematics is, child. Games. With with rules.

Different rules - different games.

You wish but it isn't actually.

If you want to examine the truth value of a statement, whether that statement is a mathematical one or not, you have to understand the meaning that the speaker has assigned to the words he's used to construct his statement. You have to actually understand what he's trying to say instead of misinterpreting him. You are not free to take his words and imbue them with your own meaning for that would be a misinterpretation of his statement, a substitution of what he said with something he did not say. When done with the intention to make it easier to attack, it's called a strawman argument. And that's all you're doing. You're constructing strawman arguments against everything conventional. You're substituting other people's statements with the ones that are easy to refute, hoping that the deception will go unnoticed.

Dummy . . .

When they say, "There are no sets that are neither finite nor infinite", they are not using the word "finite" to mean "of a size that is equal to an integer greater than or equal to 1".

GET OVER IT.

[Skepdick]

blah blah blah

*yawn*

Given the standard Mathematical meanings for "finite" and "infinite" tell me whether the constructed set is finite or infinite.

[Magnus Anderson]

blah blah blah

*yawn*

Given the standard mathematical meanings for "finite" and "infinite", there is no such thing as a set that is neither finite nor infinite. Thus, the set you constructed is finite, infinite or an oxymoron.

[Skepdick]

blah blah blah

*yawn*

Given the standard mathematical meanings for "finite" and "infinite", there is no such thing as a set that is neither finite nor infinite.

Thus, the set you constructed is finite, infinite or an oxymoron.

Good to know!

Classify it then.

Is it finite or infinite?