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by **Forest_Dump** on September 16th, 2008, 11:43 am

Certainly math, as a language, is self-contained and allows for a degree of concreteness. In fact, as far as I know, math is the only branch of science for which there is an unambiguous definition of "proof". Computer simulations and models are also, as you say, deterministic and ultimately simply extensions of pure math. Consequently, since these things are deterministic, pure deduction, etc., applies.

Where this all starts to weaken is when there are attempts to link these things with "the real world". It may well be that, for example, one ion of sodium plus one ion of chloride equals to ions still or, alternately, one molecule of salt. The problem is that, for quantification to work and tell us things, we need to start being careful about what is being quantified (and then manipulated mathematically, etc.), how it is being quantified, etc. Mathematical and computer simulations and models are simplifications of the "real world" so that we can say some things about that real world. We can and do try to make these models more accurate by adding in more factors, more data, more algorithms, etc., but ultimately it is not the computer or the equations, etc., that decides what goes into all of this, it is the individual researcher, relying on judgement, etc., who decides what counts as appropriate date, how it fits in, decides on the appropriate formulas, etc. And then that researcher (hopefully) tests that data against the real world observations, designs tests which ideally employ independent factors which in turn may be different simplifications of the real world, etc. Math may well be a rigorous application of a specific language and structure but it is individuals who decide what numbers and formulas to use etc.