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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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I suppose your larger point is true, but not particularly meaningful.

Are you 100% certain of that?

So a statement that seems easy and clear to interpret can actually be misleading when your interlocutor is deliberately trying to confuse and deceive you by omitting key information?

This is a loaded language claim, a rhetoric trick. You are intentionally adding the word "misleading" to prompt an emotional response.

Consider this exchange:

  1. If you don't denounce Russia's illegal war of aggression, that makes you a Putin apologist, that's as unequivocally true as 2+2=4

  2. Actually, 2+2=4 is not unequivocally true

My claim (2) is not "misleading", and I'm not "deliberately trying to confuse and deceive" anyone, it's the other person who made a false claim (1). The sole objective of me bringing up this abstract algebra notion is to increase doubt on the original claim about Russia sides. The factoid 2+2=4 is not used by me as an end, it's used by somebody else as a means to an end. 2+2=4 is often used as a tool to demonstrate 100% certainty, and it can be dismantled.

Your loaded language claim doesn't apply in this example. We can get rid of the loaded language and make a much more fair, generous and neutral claim:

"A statement that seems easy, clear to interpret, and is obviously 100% certain to be true can actually be not necessarily true when an unrealized assumption is present."

How is this more generous claim not correct?

  • -10

Statement 1 is debatable but not because 2 + 2 ≠ 4, so it's pointless to argue that point. A few of the deficiencies:

  1. “Illegal war of aggression” is begging the question.

  2. “That makes you a Putin apologist” is a nonsequitur: a refusal to denounce someone's actions does not equal an endorsement of the perpetrator. Has your Muslim neighbor denounced Islamic terrorism recently? Does that make him an ISIS-apologist?

  3. Finally, and most importantly, law in general and international law in particular is much less clearly defined and broadly agreed upon than simple arithmetic over the natural numbers. Even if you believe that 2 + 2 = 4 isn't objectively true, it's undeniably more well-established than jus ad bellum.

The point is that the fact that statement 1 is false doesn't make statement 2 any more (or less) true.

To give a different example, if I say “Waffles are better than pancakes, that's as clear as the sky is blue”, would you start arguing that the sky isn't always blue? Or would you agree that the two clauses here have no logical relation to each other, and to disagree with the first doesn't require you to argue against the second?

And yes, you could argue that sometimes the sky is black or red or that the color blue is ill-defined etc., but if I put a gun to your head and asked you “What color is the sky?” I'm sure you know exactly what word you need to utter to save your life. But if I asked you about waffles vs pancakes instead, the correct answer would be a lot less obvious, proving that the truth of these statements isn't equally clear.

Finally, and most importantly, law in general and international law in particular is much less clearly defined and broadly agreed upon than simple arithmetic over the natural numbers.

This supports my argument. If I demonstrate that a rational agent should doubt something very "clearly defined" such as 2+2=4, then it logically follows that something much less clearly defined should be doubted as well.

if I say “Waffles are better than pancakes, that's as clear as the sky is blue”, would you start arguing that the sky isn't always blue?

Yes. I start with the claims that are more easy to dismantle because I know that people virtually never doubt their beliefs in real time. It would be very hard for me to convince that person that waffles are not necessarily better than pancakes, but it would be easy to dismantle the auxiliary claim.

This person may attempt to find another more unequivocally true auxiliary claim, but I would easily dismantle that too. And sooner or later this person would be forced to realize that it's not easy to find an unequivocally true claim. And if it's not easy to find an unequivocally true claim, perhaps the unequivocally true claim that waffles are better than pancakes is not so unequivocally true.

If a person says "Bob is as racist as Alice", and I show that Alice is not racist, then says, "OK. Bob is as racist as Mary", and I show Mary is not racist, "OK. Bob is as racist as Linda", Linda isn't racist. Wouldn't it make sense to doubt whether or not Bob is actually racist?

Using metaphors to tackle deep philosophical problems isn't even fringe. The notion of a black swan is nowadays common in order to explain that the fact that something has never happened before is not a valid reason to think it will never happen in the future. It tackles the deep philosophical problem of induction.

Instead of saying "as clear as the sky is blue", people in the past used to say "as impossible as a black swan". To say "actually, the fact that we haven't seen a black swan doesn't necessarily mean black swans don't exist" is not pedantry, it's in fact valid reasoning, a deep philosophical notion (problem of induction), and something that should have made people doubt their 100% certainty on "impossible" events.

If a person says "Bob is as racist as Alice", and I show that Alice is not racist, then says, "OK. Bob is as racist as Mary", and I show Mary is not racist, "OK. Bob is as racist as Linda", Linda isn't racist. Wouldn't it make sense to doubt whether or not Bob is actually racist?

Okay, but if someone says "Bob is as racist as a KKK grand wizard", it would still make sense to doubt it. Conversely, if they say "Bob is as racist as Alice, because he's the author of the bobracial supremacy manifesto", pointing out Alice isn't racist just distracts from the point at hand. Yes, it's a bad metaphor, but the point stands.

Compare this discussion. I have refuted your argument that 2+2=4 is not unequivocally true, but I'm still willing to discuss the point you were trying to make without forcing you to come up with a new example.

Conversely, if they say "Bob is as racist as Alice, because he's the author of the bobracial supremacy manifesto", pointing out Alice isn't racist just distracts from the point at hand. Yes, it's a bad metaphor, but the point stands.

Yes, but the premise of this line of thought is precisely the opposite: it's not easy to prove Bob isn't racist, other other hand it's extremely easy to prove Alice isn't racist.

I have refuted your argument that 2+2=4 is not unequivocally true, but I'm still willing to discuss the point you were trying to make without forcing you to come up with a new example.

But discussing is not accepting. You are arguing that Bob is a racist, but you are nowhere near accepting the possibility that he might not be.

You are not willing to accept that Alice might not be a racist, and Bob even less. Which proves my point.

Yes, but the premise of this line of thought is precisely the opposite: it's not easy to prove Bob isn't racist, other other hand it's extremely easy to prove Alice isn't racist.

That's my exact point. If you prove Alice isn't racist, you haven't proven anything relevant. You're just nitpicking. The actual relevant question of whether Bob is racist is unaddressed.

But discussing is not accepting. You are arguing that Bob is a racist, but you are nowhere near accepting the possibility that he might not be.

I'm accepting the possibility Bob might be racist to the degree I'm required to: I'm listening to the supporting case and engaging with your arguments.

Your arguments that Bob is racist just aren't convincing. You're mainly arguing he's as racist as Alice and I happen to know she isn't. And instead of leaving it at that until you make a better argument, which I could, I'm trying to work out why you think Alice is racist and how it applies to Bob, and arguing against that.

You are not willing to accept […]. Which proves my point.

No, I'm not accepting your point because it's false. You don't get to twist opposition to your argument into support for your point.

If you prove Alice isn't racist, you haven't proven anything relevant. You're just nitpicking.

In your opinion, which isn't infallible.

I'm listening to the supporting case and engaging with your arguments.

This is not enough. Open debate requires an open mind: you must accept the possibility that you might be wrong.

If you don't even accept the possibility that you might be wrong about anything, then there's no point in debating, not about Alice, not about Bob, not about anything. All you are doing is wasting the time of your interlocutor.

This in my view is arguing in bad faith. If there's absolutely no way you can be convinced otherwise, then what am I even doing?

You're mainly arguing he's as racist as Alice and I happen to know she isn't.

Therefore it's impossible for you to be convinced of anything (about Alice and even less of Bob), and there's no point in me even trying.

In your opinion, which isn't infallible.

Is that supposed to be a counterargument?

This is not enough.

Yes it is. Listening to your case and engaging with your argument will make me change my mind if your case is convincing enough.

Therefore it's impossible for you to be convinced of anything (about Alice and even less of Bob), and there's no point in me even trying.

No, it's still possible for me to be convinced of true things.

You'e right there's no point trying to convince me of a false statement about math. Instead you should let yourself be convinced by me.

Listening to your case and engaging with your argument will make me change my mind

No it won't.

No, it's still possible for me to be convinced of true things.

Obvious circular reasoning. You believe X is false, and you say it's possible for you to be convinced that X is true if X were true, but X is false, because you believe X is false. Could not be more obvious.

Do you accept the possibility that X may be true? Yes or no.

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