Empricism with a Formalist Face: A Platonic Dialogue by MC Complete

Stewart: Enough of epistemology.  Let’s get down to brass tacks.  What is a number?

Daniel: A number is the outcome of a measurement.  Take the expression “7 + 5 = 12”.  This expression is an empirical prediction (or, if you are a hard core skeptic, an empirical generalization).  I could test it by putting seven apples and five oranges in a basket and counting them.  Counting is an empirical process that yields the result, 12.  The assumption that I started with -- that there are seven apples and five oranges -- means that when I count the apples I get 7, and when I count the oranges I get 5.

Stewart: Hmmm.  Interesting, but doesn’t that just beg the question?  You said “I get 12” -- but what *is* 12?  What do you get?

Daniel: 12 has a written form and an auditory signature, which vary, of course, according to language.  It’s a linguistic token.

Stewart: But that’s formalism.  I thought that you were an empiricist regarding math.

Daniel: It’s formalism with an empiricist heart, or maybe empiricism with a formalist face.  Numbers are linguistic tokens that are the return value of an empirical procedure.  Linguistic tokens are sense data, among other things.

Stewart: Interesting that you drew on deductivism in your last post, which is a branch of formalism.  I see how you’re advocating a compromise position between formalism and empiricism.

Daniel: Compromise?  I prefer to call it The Great Synthesis.