Friday, March 11, 2011

Adding and multiplying

Two oranges plus three oranges equals five oranges. Two oranges times three oranges equals...? That just sounds malformed. One can add objects but one can't multiply them, it seems.

I suppose one could do a Cartesian product of sets, though, and say that two oranges times three oranges equals six pairs of oranges. If you're a mereological universalist, the "pairs of oranges" might be genuine though unnatural objects; otherwise, you might take them to be abstracta. So addition is either more concrete or more natural than multiplication.

Is there a point to these observations? Not really. They just struck me.


Mike A Robinson said...

I’m just glad I don’t read your blog right before I go to sleep; your work is always fascinating and enriching, but this post may make it harder to count sheep while I try to fall asleep.

loudogg said...

"One can add objects but one can't multiply them"

For the mathematical realist who believes numbers are objects, wouldn't multiplication of numbers (just as oranges) suffer from the same problem?