Well, strictly speaking we don’t directly assume that 2+2=4. We have some basic assumptions about counting and addition, and it follows from these that 2+2=4. But that doesn’t really avoid the objection, it just moves it down the chain.
Can I change these assumptions? Well, firstly it bears saying that if I do, I’m not really talking about counting or addition any more, in the same way that if I define “beaver” to mean “300 ton sub-Saharan lizard”, I’m not really talking about beavers.
So suppose I change my assumptions about counting and addition such that it came out that 2+2=5. Would that mean that two apples added to two apples made five apples? Obviously not. It would mean that two apples added to two apples made five apples, where the starred words refer to altered concepts.
Well, strictly speaking we don’t directly assume that 2+2=4. We have some basic assumptions about counting and addition, and it follows from these that 2+2=4. But that doesn’t really avoid the objection, it just moves it down the chain.
Can I change these assumptions? Well, firstly it bears saying that if I do, I’m not really talking about counting or addition any more, in the same way that if I define “beaver” to mean “300 ton sub-Saharan lizard”, I’m not really talking about beavers.
So suppose I change my assumptions about counting and addition such that it came out that 2+2=5. Would that mean that two apples added to two apples made five apples? Obviously not. It would mean that two apples added to two apples made five apples, where the starred words refer to altered concepts.
That’s what I was trying to say, but I couldn’t find a decent way to put it and gave up.