Comment by seanhunter

That physical representation argument never made any sense to me. Like say I have a rock. I split it in two. Do I now have 2 rocks? So 2=1? Or maybe 1/2 =1 and 1+1=1.

What about if I have a rock and I pick up another rock that is slightly bigger. Do I now have 2 rocks or a bit more than 2 rocks? Which one of my rocks is 1? Maybe the second rock, so when I picked up the first rock I was actually wrong - I didn’t have one rock I had a little bit less than one rock. So now I have a little bit less than 2 rocks actually. How can I ever hope to do arithmetic in this physical representation?

The more I think through this physical representation thing the less sense it makes to me.

OK so say somehow I have 2 rocks in spite of all that. The room I am in also has 2 doors. What does the 2-ness of the rocks have in common with the 2-ness of the doors? You could say I can put a rock by each door (a one-to-one correspondence) and maybe that works with rocks and doors but if you take two pieces of chocolate cake and give one to each of two children you had better be sure that your pieces of chocolate cake are goddam indistinguishable or you will find that a one-to-one correspondence is not possible.

To me, numbers only make sense as a totally abstract concept.