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Tom_Breton 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: Tom_Breton 28 September 2007 09:41:47PM 1 point [-]

There are really two questions in there:

  • Whether the Peano arithmetic axioms correctly describe the physical world.
  • Whether, given those axioms and appropriate definitions of 2 and 4 (perhaps as Church numerals), 2 + 2 = 4.

One is a question about the world, the other about a neccessary truth.

The first is about what aspect of the world we are looking at, under what definitions. 2 rabbits plus 2 rabbits may not result in 4 rabbits. So I have to assume Eliezer refers to the second question.

Can we even meaningfully ask the second question? Kind of. As David Deutsch warns, we shouldn't mistake the study of absolute truths for the possession of absolute truths. We can ask ourselves how we computed whether 2+2=4, conscious that our means of computing it may be flawed. We could in principle try many means of computing whether 2+2=4 that seem to obey the Peano axioms: fingers, abacus, other physical counters, etc. Then we could call into question our means of aggregating the computations into a single very confident answer and then our means of retaining the answer in memory.

Seems a pointless exercise to me, though. Evolution either has endowed us with mental tools that correspond to some basic neccessary truths or it hasn't. If it hadn't, we would have no good means of exploring the question.