Question As commonly understood and reinforced here, 2 + 2 = 4 is taken as meeting the test for absolute certainty. This appears to be true in a formal or symbolic sense but is it true in reality? When we count two things as being the same and add them to two other same things do we really get four identical things? Perhaps, perhaps not; it may depend on one's identity theory. Do we know with absolute certainty when we have one thing and not two? What am I missing?

Accepted:
November 10, 2008

Comments

I don't myself have a view on whether 2+2=4 is absolutely certain. I suppose it's as certain as anything is or could be. But the question here is different. It's whether that certainty is undermined by doubts about what happens empirically.

As Gottlob Frege would quickly have pointed out, however, the mathematical truth that 2+2=4 has nothing particular to do with what happens empirically. It might have been, for example, that whenver you tried to put two things together with two other things, one of them disappeared. (Or perhaps they were like rabbits, and another one appeared!) But mathematics says nothing of this. That 2+2=4 does not tell you what will happen when you put things together. It only tells you that, if there are two of these things and two of those things, and if none of these is one of those, then there are four things that are among these and those. It's hard to see how one's theory of identity could affect that.