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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Notes -
You can do equally annoying semantic tricks with pretty much anything, it's just harder to get away with it with when it isn't math:
Ie, "The Sun is smaller than a pebble" - - (Pebble is an alternate name I made up for the Milky Way)
"Grass isn't green" - - (I've defined Green to be 00FF00 in Hexadecimal, and this grass here is 28CF0E, which I have named "moss", so the colors aren't equal)
etc.
When you say things without rigorously defining every word ahead of time, there is an implicit promise that your words mean approximately what they usually mean in that language. Most words and concepts have reasonably well understood meanings, or such can be inferred via context. And this is almost always a good thing because it enables people to have conversations without carrying dictionaries around, not some close minded thing that needs to be challenged and abused with pedantic tricks and deception.
Except arithmetic isn't a semantic trick, and modern algebra is an important field of mathematics, not something I invented.
Using non-standard definitions without denoting them beforehand is a semantic trick.
And if you want to do math, you absolutely need to rigorously define things.
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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+2is always4" 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+2might 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.
That was not my claim. Please read my claim and then answer my question.
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