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>3) Finitists have drank the realist koolaid that math must be "physically" real, rather than simply platonically existentAgain this is not true. Most of the finitists I know about have been platonists, myself included, in the sense that we recognize the abstract validity of the number 2, for example, independent of its implementation. I highly doubt it's even possible to be a mathematician without also being a platonist when it comes to MEANINGFUL concepts in mathematics, like rational numbers.
Since there are many possible implementations of rational numbers, which are equivalent, these implementations must have something in common, which is not any particular implementation, but rather the abstract, PLATONIC concept of the rational number. It is only such a platonic view that allows mathematicians to see the appropriate equivalence of the implementations and abstract concepts needed to see the uniformity in actions about the implementations such as addition. If you weren't a platonist of some sort or another, you would not recognize the validity of adding two numbers in the abstract sense, since the action of addition looks different for different numbers you add, and you would not be able to recognize the uniformity between these different operations which can be unified under the single banner of "addition".
Numbers themselves are NOT physically real. However, statements about them can be translated into statements about definite states in the real world, which is what makes them meaningful. For example, once I have the implementation of natural numbers using python, the abstract statement about abstract, platonic entities, that "2+4=6" is translated to the concrete statement about the definite state of reality, which is that "If I go to my computer, pull up python, and ask it to evaluate the truth value of the proposition "2+4==6", the output will be "True"".
> Why? Sell me on Finitism. 
