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felipec  unbelief  1yr ago (felipec.substack.com)   3251 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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I took the liberty of clarifying my position instead of answering the badly posed question. Naturally modular arithmetics is not the same as integer arithmetics.

"2+2=4" is true in both, only in one 2+2=0 is also true.

It's a yes-or-no question:

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

It's a badly posed question. You have been weaponizing ambiguity the whole time, I'm not accepting your framework without adding context.

If you want a question answered, state it clearly.

It's a badly posed question.

No, it's not. You are refusing to answer because the answer destroys your belief.

Are you denying that mathematical expressions exist?

It's a badly posed question because it's not fully specified, namely, you're not stating where (2+2=4) lives.

Normally this wouldn't be a problem, because we can assume it's the default if not otherwise noted, but a) we'e explicitly discussing multiple number systems here and b) you have already proven you can't be trusted not to omit relevant information.

Your question is ambiguously stated. Normally it wouldn't be, but have earned a reputation of communicating badly. 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 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.)

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