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felipec  unbelief  1yr ago (felipec.substack.com)   3218 thread views

2+2 = not what you think

felipec.substack.com

Changing someone's mind is very difficult, that's why I like puzzles most people get wrong: to try to open their mind. Challenging the claim that 2+2 is unequivocally 4 is one of my favorites to get people to reconsider what they think is true with 100% certainty.

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(2+2=4 (mod 4)) might be the same statement as (2+2=0 (mod 4)), but not (2+2=4).

So you're now saying that 2+2=4 without further context is not the same statement as 2+2=4 (mod 4)?

Dare I hope you finally saw reason? That you accept that you are not allowed to say "2+2=4" without context and pretend you mean modular arithmetic, and that "2+2=4" is simply true?

(And if you're just going to say the () change the meaning, then you should start off defining your idiosyncratic notation, and by "start off" I mean you should have done it 10 posts ago when you first used it. And then you should retract your argument, since it's a non-sequitur obfuscated by misleading notation.)

So you're now saying that 2+2=4 without further context is not the same statement as 2+2=4 (mod 4)?

No, I said (2+2=4 (mod 4)) might not be the same as (2+2=4). I very clearly never said what you claim I'm supposedly "now saying": I said "might not be", never said "is not".

This is a smoke screen though. I'm talking about what YOU said, and you are very conveniently trying to distract from that.

YOU claimed (2+2=4) is just another representation of (2+2=0 (mod 4))... that is 100% false, as you yourself now admitted. They are different statements.

And you also avoided to comment on the obvious conclusion from your misrepresentation, and instead chose a distraction from what YOU said.

No, I said (2+2=4 (mod 4)) might not be the same as (2+2=4). I very clearly never said what you claim I'm supposedly "now saying": I said "might not be", never said "is not".

You also said

(2+2=4 (mod 4)) exists, which is not the same as (2+2=4)

So yes, you said it. Do you want to retract that statement now?

YOU claimed (2+2=4) is just another representation of (2+2=0 (mod 4))...

I claimed that 2+2=4 (mod 4) is another representation of 2+2=0 (mod 4). I specified "in Z/4Z" the first time I made my statement, I referred to modular arithmetic the second time, I clarified my statement to the literal same when you asked.

The question I answered referred to 2+2=4 in standard arithmetic(although it took you 5 comments to finally clarify your ambiguous question), which makes it a different question with a different answer.

You're trying to cut out the context, which makes it a misrepresentation of me. Retract and apologize.

I specified "in Z/4Z" the first time I made my statement, I referred to modular arithmetic the second time, I clarified my statement to the literal same when you asked.

You are trying to distract from what you said, this is what you said:

But the existence of modular arithmetics doesn't make 2+2=4 incorrect. It merely makes 2+2=0 another representation of the same statement. So "most people" remain correct.

You also said:

Did you just claim less than 0.0001% of people think 2+2=4?

It's very clear what you said:

  1. Most people think 2+2=4 is true

  2. The existence of modular arithmetics makes 2+2=0 another representation of the same statement

  3. 2+2=0 (mod4) is not the same statement as 2+2=0

There are facts. I'm not misrepresenting anything you said.

If by 2+2=0 you didn't mean 2+2=0, but 2+2=0 (mod 4), then that contradicts your initial claim that most people think 2+2=4 is true, because to be the same statement it would need to be 2+2=4 (mod 4).

So either your claim (2) is false becase 2+2=0 (mod 4) is not another representation of 2+2=4, or it's unrelated to claim (1) because 2+2=4 (mod 4) is not the same as 2+2=4.

Either way your argument is invalidated.

But it's pretty clear that you meant 2+2=4, not 2+2=4 (mod 4), because the former is what most people think is true. You are trying to antagonize me to distract from the fact that your argument has been blown up to bits.

You're trying to cut out the context, which makes it a misrepresentation of me. Retract and apologize.

You know what you tried to do, and now you are trying to hide it. Even when one tries to be as charitable as possible, there's only one likely conclusion: you are arguing in bad faith.

You are trying to distract from what you said

No, I'm trying to explain what I said, because you keep removing the context:

  1. 2+2=0 (mod4) is not the same statement as 2+2=0

I said 2+2=4 in standard arithmetic is not the same statement as 2+2=0 (mod 4). I insisted on making this explicit, because it came up on the context of mod 4. And because I suspected you were trying lead me to a contradiction, so I made sure to speak clearly, proofing myself against it.

So if you cut out the important context, and then try to construct a contradiction that doesn't work with the context included, you're misrepresenting me.

Retract and apologize.

(Assuming here you meant to write 4 instead of 0, but otherwise it would just be an even worse misquote, so I'm charitably assuming it's a typo.)

But it's pretty clear that you meant 2+2=4, not 2+2=4 (mod 4), because the former is what most people think is true.

I meant "2+2=4", "in Z/4Z" omitted, as in your original setup*. When it's about people's reaction to the statement, formulation is important.

*But in my case it was available from context, whereas in your example it was deliberate misdirection.

People think it's true, while they're denied the context. But given the full context, which changes the meaning, it's still true.

It's also quite peculiar that you're doing what you're accusing me of: I pointed out you were contradicting yourself, you tried to weasel away, and when I nailed you down, you tried to ignore it. Do you stand by the statement

(2+2=4 (mod 4)) exists, which is not the same as (2+2=4), and you finally accept that they are two different things.

?

I said 2+2=4 in standard arithmetic is not the same statement as 2+2=0 (mod 4).

You keep omitting the context of your own statements, you clearly implied that "more than 0.0001% people think 2+2 is necessarily 4", obviously you meant in standard arithmetic, since very few people know that 2+2=4 (mod 4) even exists. And you also accepted 2+2=4 (mod 4) is not the same statement as 2+2=4, therefore it's entirely possible for more than 0.0001% people to think that 2+2=4, and less than 0.0001% people think that 2+2=4 (mod 4).

you clearly implied that "more than 0.0001% people think 2+2 is necessarily 4", obviously you meant in standard arithmetic, since very few people know that 2+2=4 (mod 4) even exists.

Obviously I meant "with unspecified context", because that was the example we were talking about. Yes, people don't know you're sneakily talking about modular arithmetic - but "2+2=4" is still true, so people are giving the correct answer, despite the confusion.

And you also accepted 2+2=4 (mod 4) is not the same statement as 2+2=4

Can you just fucking stop misrepresenting me? That would be great, thanks.

And you also accepted 2+2=4 (mod 4) is not the same statement as 2+2=4

Can you just fucking stop misrepresenting me? That would be great, thanks.

False. I'm not misrepresenting you, you literally said they are not the same statement right here.

Do you believe that (2+2=4) and (2+2=0 (mod 4)) are "the same statement"?

But just for the record, the answer is no then.

It took you 5 comments where you tried to misdirect, but you finally accepted it, and because now it's clear that admission dismantles your whole argument, you are trying back down from it, but you did accept it.

You cut out the part where you specified (2+2=4) in standard arithmetic before I answered. That's the misrepresentation.

Since you seem to have hard time understanding context, I'll repeat my actual statement with the context explicit:

(2+2=4 in standard arithmetic) and (2+2=0 (mod 4)) are not the same statement.

With that cleared up, any further questions?

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