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felipec  unbelief  2yr ago (felipec.substack.com)   3600 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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It's a badly posed question because it's not fully specified, namely, you're not stating where (2+2=4) lives.

Really? Wasn't your entire argument relying on the fact that if the arithmetic wasn't specifically specified, then certain arithmetic was always assumed?

Your question is ambiguously stated.

Which was my entire point.

Normally it wouldn't be

So you are accepting it: normally 2+2 is not 0, but I didn't ask if normally that was the case, I asked if it was always the case.

For the record, when I ask ChatGPT if it's always necessarily the case, it answers "no". It says that's not the case in other arithmetics. Weird that it interprets math like me, not like you.

Define whether (2+2=4) in your question is integer arithmetics or (mod 4) (or something else) and I'll answer your question.

It's not any modular arithmetic, it's standard arithmetic (the one you claimed should always be assumed).

Really? Wasn't your entire argument relying on the fact that if the arithmetic wasn't specifically specified, then certain arithmetic was always assumed?

It has been specified beforehand:

in Z/4Z, 2+2=0 and 2+2=4 are the same statement.

If in response you talk about standard arithmetic without clearly denoting it, that's just you communicating badly again, which is why I made you add a clarification.

For the record, when I ask ChatGPT if it's always necessarily the case, it answers "no". It says that's not the case in other arithmetics. Weird that it interprets math like me, not like you.

You can get ChatGPT to tell you all sorts of bullshit, including self-contradictions. It's not an authority for anything.

it's standard arithmetic

That makes it a derail, since we were talking about modular arithmetics. But just for the record, the answer is no then.

It's not an authority for anything.

That's a straw man fallacy. Nobody said it was an authority.

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

Finally, it only took you 5 comments to answer my very simple question.

It merely makes 2+2=0 another representation of the same statement.

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

No

Therefore you are contradicting your previous claim: (2+2=4) is not another representation of (2+2=0 (mod 4)): they are different statements. (2+2=4 (mod 4)) might be the same statement as (2+2=0 (mod 4)), but not (2+2=4).

I claimed that virtually nobody understands that (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.

(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).

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