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felipec  unbelief  2yr ago (felipec.substack.com)   3612 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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And in plain arithmetic, which is what more than 99% of all uses of those symbols occur in, 2 + 2 = 4 is a true statement.

Perhaps a better analogy would be if you throw a random French word that sounds identical to a different English word into an otherwise English sentence, and trick people with the double meaning. It's a language that exists, it does mean that thing to some people in some contexts, but you've deliberately placed it out of context and in order to deceive the audience. This can be great as the setup to a pun/joke, but not so much for making educational points.

The statement "in normal arithmetic 2+2=4" is true, but "2+2 is always 4" is false.

You can dismiss semantics all you want, but the meaning of the statements we make matter, and the certainty we have about the meaning of the statements other people make do matter.

Just this week I debated a person who was 100% certain he knew what anti-Semitism was (he didn't), what a dictionary was (he didn't), and what all the words in the definitions I presented to him meant (he didn't).

In my view 100% certainty is a problem.

I believe questioning the meaning of 2+2 might help some people question other unquestionably true beliefs.

Are you 100% certain it's impossible for this to happen?

The map is not the territory.

If you hold constant the referents, then 2+2 is always 4. That is, the number 2 in the integers/real-numbers, added to the number 2 in the integers/real-numbers, deterministically always yields the number 4 in the integers/real-numbers.

The symbol "2" does not always refer to integers/real-numbers, and "+" does not always refer to addition in the integers/real-numbers, and "=" does not always refer to equality in the integers/real-numbers, so the string of symbols "2+2=4" does not always refer to a true statement, but that's only if it refers to an unusual statement other than the standard referent of the string.

So I would say that "2+2=4 is always true" is true, because when I say 2+2=4 without additional context I implicitly mean the integers/real-numbers. I will concede that " "2+2=4" always refers to a true statement" is false, but consider this vacuous, because literally any string can be redefined to refer to any true or false statement. So when somebody says "2+2=4", I am not 100% certain that the statement they intend with their words is true, but I am 100% certain that the statement in my mind induced by those words is true, and am 99.99% sure that the true statement in my mind would be the same statement created in the minds of the majority of people who have at least 1 month of mathematics education using Arabic numerals, so am not at all worried about considering this to be the default interpretation unless otherwise specified.

You didn't answer my question.

I am not 100% certain it's impossible for someone (including myself) to be mistaken about the definitions or meanings of commonly used words or mathematical symbols. It's technically possible with nonzero but very very small probability, especially for very commonly used stuff like 2 and +. But that's true of literally every fact, and there is not enough time in the human lifespan to thoroughly interrogate all of them, so 2+2 is not a wise choice to focus on. I think that the assumption of common knowledge of words is incredibly useful when used appropriately, so sowing doubt and being pedantic about it is likely to cause more harm than good if done unstrategically. Your goal is potentially useful, but pedantry is not the way to accomplish it, you'd do better targeting more ambiguous words that don't have the force of mathematical logic and precision behind them.

I am not 100% certain it's impossible for someone (including myself) to be mistaken about the definitions or meanings of commonly used words or mathematical symbols.

That was not my claim. Please read my claim and then answer my question.

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