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Ben2 comments on How to Convince Me That 2 + 2 = 3 - Less Wrong

53 Post author: Eliezer_Yudkowsky 27 September 2007 11:00PM

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Comment author: Ben2 28 September 2007 07:11:19AM 2 points [-]

2+2=4 is a truth about mathematics. It is not a truth about the world.

Truths in the world have no bearing on mathematical truths. While we learn mathematics from observations about the world, it is not from observation that mathematics derive truth. Mathematicians do not test theories empirically; such theories would become the domain of physics or biology or the like. Thus, the only evidence one could infer 2+2=3 from would be misleading mathematical evidence.

Since 2+2=4 is so simple, there are not too many people who could be effectively mislead in this way, and Eliezer is most likely not one of them. One could probably convince someone to believe a false mathematical formula if it were sufficiently complicated for the individual to have trouble understanding it, and it had a sufficiently crafty explanation.

Basically, believing 2+2=3 to be true would require the evidence necessary to believe in married bachelors: evidence that confuses the hell out of you effectively.

Some people are arguing that mathematics is not a priori. If so, then the situation with putting two pairs of apples together and getting 3 apples would be the appropriate type of evidence. If mathematics is a posteriori, the answer is thus quite simple.

Sorry if this is overly redundant with previous posts.

Comment author: Skarey 19 February 2011 11:21:55AM 0 points [-]

There is an example that often floats around, where it is 'proven' mathematically that 1=2 (or some other such equality, by the principle of explosion it doesn't really matter). The trick is that at some step in the proof, a non obvious division by zero occurred.

Comment author: bigjeff5 03 March 2011 07:14:13PM 0 points [-]

I imagine it's the same proof that makes 2+2=5. There is a point in the proof where the correct result is obviously 0=0 (though never explicitly written), yet it continues as though it didn't happen.

It's an example of making the problems so complex that you make a mistake, it's not a valid proof.

The proof for 2+2=4, incidentally, is almost 400 pages long. The simplistic versions most use take for granted many things for granted (like + and = and 2) that the actual proof does not.