Why isn’t mathematics sensitive to experimental scrutiny?

Posted: February 9, 2012 by alephnaughty in Philosophy, Science
Tags: , ,

Suppose I have two containers, both full of (what I believe to be) a single fluid. Each container’s volume is 500 mL. I then empty the contents of the two containers into a third, the volume of which is 1000 mL. To my surprise, the container is only 75% full–it holds just 750 mL of the fluid. How should I revise my beliefs in light of this discovery?

Among my presumptions was that volume is additive when mixing a single fluid. One conclusion that suggests itself is that the two containers in fact contained different fluids. Another is that volume is not necessarily additive.

A third conclusion, however, does not suggest itself: 500 + 500 = 750. Why not? What is it about 500 + 500 = 1000 that justifies my willingness to concede that the fluids were different, or that volume is not necessarily additive, but not that 500 + 500 = 750? The surprising outcome of my experiment shows that at least one of my presumptions is incorrect, but it does not indicate which. What is it about this experiment that prevents it from lending support to the hypothesis that 500 + 500 = 750?

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