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Lee_B 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: Lee_B 28 September 2007 01:01:54AM 20 points [-]

I am confused by this discussion. Are we talking about integers or things?

Analytic truths may or may not correspond to our situations. When they don't correspond, I guess that's what you all are calling "false." So, if we're engineers working on building a GPS system, I might say to you, "Careful now, Euclidean geometry is false."

Similarly, quantum physicists on the job might say, "Watch out now, two and two isn't necessarily four."

I'm thinking of this excellent blog post I came across last week:

...Consider a basket with 2 apples in it. Now toss in 2 more apples. Examine the basket, and you will find (surprise!) 4 apples. However, you cannot prove a priori that there will be 4 apples in the basket. It is an empirical question, albeit a trivial one, whether baskets of apples (which are physical things) behave in the same manner as the non-negative integers under addition (which is an abstract logical construct).

This distinction might seem hopelessly pedantic at first, but you can easily go astray by ignoring it. For example, many people naively expect photons to behave in the same manner as integers under addition, but they don’t. “Number of photons” is not a conserved quantity in the way that “number of apples” is; photons can be created/destroyed, one photon can be split into two, et cetera....