The other day a bizarre question popped into my mind: Is zero a number?  On one level, the answer is obviously yes.  Zero is not a letter, a flower, or a molecule.  It is in the class of things we call numbers.  While zero might be considered a number for classification purposes, does it truly exist in the real world?  While I can point to three eggs and say, “Here are three eggs,” I cannot point to some X and say, “Here are zero Xs.”  Zero does not correspond to anything in reality, because zero signifies the absence of reality.  To say one has zero eggs is just a mathematical way of saying one does not have any eggs.

Of course, the same could be said of negative numbers like -1, -5, or -100.  These numbers have no correlates in the real world.  You will never find -5 apples.  Negative numbers exist only in the mind.  Of course, the same could be said of all numbers.  While I can point to three eggs, five cows, or 17 cups, in none of these cases will I have located the numbers 3, 5, or 17.  I will have only found instances in which a specific numerical value is exemplified by particular objects.

Perhaps to be considered a real number, a mathematical symbol must have an actual value.  Since zero has no value, it is not a number.  But why think having a value is necessary to be a real number?  Is it special pleading to argue that the one numerical symbol that has no value is not a number simply in virtue of the fact that it alone has no value?  Would we be unjustly excluding zero from the realm of numbers simply because it is unique among numbers?  Perhaps.

What do you think?  Is zero a number?  Why or why not?

Advertisements