2+2=5

[Skepdick]

If I choose to evaluate the expression "2+2" in the Universe of unital semirings of size at most 6, then I will damn well evaluate it that Universe.

Like I say, if you can't define it without looking it up, then you're full of beans.

ps -- Based on our previous conversations, I suspect you couldn't define it even if you did look it up.

pps -- Do you know what a ring is? A semiring? A unital semiring? Can you give some examples of each? If not, then who exactly are you trying to impress by name checking things you know nothing about?

You are grasping at straws trying to test my understanding when you yourself can't define most of the fucking terms you are using. They don't even teach the use-mention distinction in Mathematics *smh*

Do you know what "is" is?" Can you give me an example of "is"? Can you give me some examples of continuums? Infinite precision real numbers? Infinite data structures? If not, then who exactly are you trying to impress by USING things you know nothing about?

Based on our previous conversations, you excell at reciting definitions without understanding what "definition" is.

If you can't define it without looking it up, then you are full of beans. Yet there you are using it. Maybe the reflexive relation went over your head?

Then again, maybe it's just your psychological predisposition - precision breeds nitpickers who tend to miss the forest for the trees...

[wtf]

You are grasping at straws trying to test my understanding when you yourself can't define most of the fucking terms you are using. They don't even teach the use-mention distinction in Mathematics *smh*

Do you know what "is" is?" Can you give me an example of "is"? Can you give me some examples of continuums? Infinite precision real numbers? Infinite data structures? If not, then who exactly are you trying to impress by USING things you know nothing about?

Based on our previous conversations, you excell at reciting definitions without understanding what "definition" is.

If you can't define it without looking it up, then you are full of beans. Yet there you are using it. Maybe the reflexive relation went over your head?

Then again, maybe it's just your psychological predisposition - precision breeds nitpickers who tend to miss the forest for the trees...

You're really funny. You can't even make up your own insults. You're just echoing mine.

So I see you have no idea what a ring is. That's a pretty elementary thing not to know for a guy name checking Andrej Bauer, who I gather you never heard of before you quote-mined him in this thread. You're pathetic. I gave you such an easy opening and you blew it. You actually don't have the slightest idea about the meaning of the link you posted.

[Skepdick]

You're really funny. You can't even make up your own insults. You're just echoing mine.

I didn't realise we were insulting each other? I was only hoping for some reflection...

But reflexivity does seem beyond your Mathematical intuition.

So I see you have no idea what a ring is.

So I see you have no idea what "is" is. Par for the course for somebody who doesn't understand reflexivity.

You sure keep using/name-dropping things you don't understand.

That's a pretty elementary thing not to know for a guy name checking Andrej Bauer, who I gather you never heard of before you quote-mined him in this thread.

You gather I have never heard of the guy whose blog/articles I have pointed you towards; and whom we have mentioned in dialogue before? Do you also gather I haven't read the book he's contributed to? Do you even know which book it is?

I must be such a lucky quote-miner! Always finding precisely the relevant counter-examples on a whim. Almost as if I have it all indexed (and I don't even know how to define indexing).

Do you suffer from any kind of memory problems? Do you not recall reading Sometimes all functions are continuous"; or Representations of uncomputable and uncountable sets?

It's pretty weird, because the very tactic I am using in attcking your regurgitation of other people's definitions (without the ability to reflect on the semantic properties of the objects you are talking about) actually comes from one of those posts.

This would explain a lot...

You're pathetic. I gave you such an easy opening and you blew it. You actually don't have the slightest idea about the meaning of the words you're using.

You wouldn't know irony if it punched you in the face.

You don't seem to know the meaning of the "is"; nor the meaning of "meaning". And yet there you are - using them. Way to demonstrate my point that knowledge of definitions is not a pre-requisite for use.

You don't even know what Mathematics IS but look at you pretending like you do.

[Magnus Anderson]

By telling me that I am taking something "out of context" you implicitly hold some range of Universes (or perhaps even some particular universe) as being THE "correct" Universe for evaluating "2+2".

If that's your cup of tea, you are more than free to define existing mathematical symbols any way you like. For example, you can define "2" to mean what everyone else normally means by "1" and "5" to mean what everyone else normally means by "2". That would, no doubt, allow you to claim that 2+2=5 without being wrong. But you can't then use that to prove that other people are wrong when they say that 2+2=4. That would be equivocation.

That said, your original claim is that "there are very many mathematical theories in which 2+2=5", and if all you're saying is that "there are very many ways people can use the expression '2+2=5' to represent something that is true", then you are right, and in fact, you aren't saying anything that is disputed by others.

As far as the original post of this thread is concerned, I find it to be quite incomprehensible.

[Skepdick]

By telling me that I am taking something "out of context" you implicitly hold some range of Universes (or perhaps even some particular universe) as being THE "correct" Universe for evaluating "2+2".

If that's your cup of tea, you are more than free to define existing mathematical symbols any way you like. For example, you can define "2" to mean what everyone else normally means by "1" and "5" to mean what everyone else normally means by "2". That would, no doubt, allow you to claim that 2+2=5 without being wrong. But you can't then use that to prove that other people are wrong when they say that 2+2=4. That would be equivocation.

It's not equivocation! It's polymorphism. The meaning of the operator "+" changes depending on what it operates on.

1 + 1 = 2 when operating on apples.
1 + 1 = 1 when operating on averages.

That said, your original claim is that "there are very many mathematical theories in which 2+2=5", and if all you're saying is that "there are very many ways people can use the expression '2+2=5' to represent something that is true", then you are right, and in fact, you aren't saying anything that is disputed by others.

I am not saying that at all because "truth" is meaningless without a specifying a model. 2+2=5 could evaluate to true; or false; or itself; or something else entirely depending on what the symbols mean; and depending on how they are being evaluated. My perspective is non-representational - it's entirely relational/algebraic.

There are infinitely many Mathematical universes. Ala pluralism in which to interpret the meaning of the expression "2+2=5".

So now all you have to do is to define "provability". I think that's pretty easy - proofs are programs.

What's not so easy is defining what you mean by "wrong" when you make statements such as "proving other people wrong".

[commonsense]

2 + 2 = 5 for very large values of 2

[Eodnhoj7]

This thread is misunderstood. In stating a contradiction, such as 2+2=5, the contradiction requires non-contradictory elements to compose it. Because of this even the contradiction contains elements of truth.

[Magnus Anderson]

It's not equivocation! It's polymorphism. The meaning of the operator "+" changes depending on what it operates on.

1 + 1 = 2 when operating on apples.
1 + 1 = 1 when operating on averages.

Before you can determine whether any given claim is true or false, you have to properly understand it. You have to understand what portion of the universe it is talking about and what it is saying about it. Generally, when people say "1 + 1 = 2" they are basically saying "If you take one apple and add to it another apple, you will end up with two apples". That's what is normally meant by that expression. You can, of course, change the meaning of that expression to anything you like e.g. you can say it's a code for "Chuck Norris is the 46th president of the US". In that case, "1 + 1 = 2" would be false, but only because you changed its meaning. It no longer has anything to do with the original claim.

There are infinitely many Mathematical universes. Ala pluralism in which to interpret the meaning of the expression "2+2=5".

There is absolutely nothing insightful and important about the claim that you can take any false expression and make it true by changing its meaning (and vice versa.) That's all you're saying -- that whether or not any given expression is true depends partly on the meaning assigned to it. It's true but kind of banal. Most importantly, it's dangerous, since it paves the way for logical fallacies such as equivocation.

[Skepdick]

It's not equivocation! It's polymorphism. The meaning of the operator "+" changes depending on what it operates on.

1 + 1 = 2 when operating on apples.
1 + 1 = 1 when operating on averages.

Before you can determine whether any given claim is true or false, you have to properly understand it. You have to understand what portion of the universe it is talking about and what it is saying about it. Generally, when people say "1 + 1 = 2" they are basically saying "If you take one apple and add to it another apple, you will end up with two apples". That's what is normally meant by that expression. You can, of course, change the meaning of that expression to anything you like e.g. you can say it's a code for "Chuck Norris is the 46th president of the US". In that case, "1 + 1 = 2" would be false, but only because you changed its meaning. It no longer has anything to do with the original claim.

I am not doing anything that you are accusing me of doing. I am pointing out that the "+" operator is polymorphic. I am not "changing its meaning" - I am pointing out that absent an explicit model the operator "+" in the expression "1+1" can take on multiple (potentially infinitely many) meanings.

It only appears to you as if I am "changing" something because I am not taking any particular meaning to be the "normal" one - I am not even assuming that "1+1" is talking about integers, so you are only upset because I am not defaulting to your own cultural biases/assumptions/denotation. If I am allowed to (and excused for) depart(ing) from courtesy and politeness...

You are berating me for being objective, impartial and unbiased when reading the expression "1+1". That makes you a bit of a cunt.

There are infinitely many Mathematical universes. Ala pluralism in which to interpret the meaning of the expression "2+2=5".

There is absolutely nothing insightful and important about the claim that you can take any false expression and make it true by changing its meaning (and vice versa.) That's all you're saying -- that whether or not any given expression is true depends partly on the meaning assigned to it.

Indeed, the point has absolutely gone over your head. Devoid of a model the expression "1+1=2" is meaningless. It doesn't even mean "true"; or "false"! It doesn't mean anything.

So I am most certainly NOT taking a "false expression and making it true", I am taking a meaningless expression; I am assigning meaning to the symbols and I am evaluating the expression to mean "true". Given the model!

The fact that you think the expression is "false" says far more about your state of mind than it does about the expression.

It's true but kind of banal.

Well, if it's so "banal" then would you kindly make explicit the model in which the meaningless English expression "It's true but kind of banal." becomes true?

Or perhaps you are up for a challenge? GIve us a model in which the expression "x = x" becomes false?

Most importantly, it's dangerous, since it paves the way for logical fallacies such as equivocation.

That is a really hypocritical criticism from somebody who seems to embrace classical mathematics/logic. Your ilk constantly equivocates proof BY contradiction and proof OF contradiction.

Much like that nuance is lost on classical mathematicians/logicians; so is the nuance between equivocation and polymorphism lost on you.

[commonsense]

I am not doing anything that you are accusing me of doing. I am pointing out that the "+" operator is polymorphic. I am not "changing its meaning" - I am pointing out that absent an explicit model the operator "+" in the expression "1+1" can take on multiple (potentially infinitely many) meanings.

It seems you’re saying that the addition of potentially infinite many meanings is not a change of meaning. Is that what you’re implying?

[Skepdick]

I am not doing anything that you are accusing me of doing. I am pointing out that the "+" operator is polymorphic. I am not "changing its meaning" - I am pointing out that absent an explicit model the operator "+" in the expression "1+1" can take on multiple (potentially infinitely many) meanings.

It seems you’re saying that the addition of potentially infinite many meanings is not a change of meaning. Is that what you’re implying?

No, I am saying that the meaning of the "+" verb/operator itself depends on the nouns it acts upon.

It means one thing when adding apples, and another thing when adding degrees Celsius.

No different to how the verb "taking" describes one behaviour in "taking a nap", and a completely different behaviour in "taking an apple".

[commonsense]

I am not doing anything that you are accusing me of doing. I am pointing out that the "+" operator is polymorphic. I am not "changing its meaning" - I am pointing out that absent an explicit model the operator "+" in the expression "1+1" can take on multiple (potentially infinitely many) meanings.

It seems you’re saying that the addition of potentially infinite many meanings is not a change of meaning. Is that what you’re implying?

No, I am saying that the meaning of the "+" verb/operator itself depends on the nouns it acts upon.

It means one thing when adding apples, and another thing when adding degrees Celsius.

No different to how the verb "taking" describes one behaviour in "taking a nap", and a completely different behaviour in "taking an apple".

I see your point. I could say that “taking” means “obtaining” in both situations, but then it could be said that “obtaining” has different meanings in different situations.

[Skepdick]

I see your point. I could say that “taking” means “obtaining” in both situations, but then it could be said that “obtaining” has different meanings in different situations.

Exactly that. And trying to insist that any given word/verb has a "default" , "standard" or "normal" meaning is just a statement of one's own cultural biases at best; or an argumentum ad populum at worst.

[commonsense]

I see your point. I could say that “taking” means “obtaining” in both situations, but then it could be said that “obtaining” has different meanings in different situations.

Exactly that. And trying to insist that any given word/verb has a "default" , "standard" or "normal" meaning is just a statement of one's own cultural biases at best; or an argumentum ad populum at worst.

Cool idea.

Taking nothing away from what you’ve presented, another way to resolve the conundrum is by considering what is meant by the values themselves.

[Skepdick]

Cool idea.

Taking nothing away from what you’ve presented, another way to resolve the conundrum is by considering what is meant by the values themselves.

That's kinda the entire point. The meaning of "2" determines the meaning of "+" in "2+2".

But what does 2 mean? It means absolutely nothing without context.

Given two ???
Given spotted ???