# “We use it because it works” is one thing; as a heuristic, models are helpful. I tend towards Pragmatism – it’s in my culture (American) and I comprehend its value.

Yes, I think you’ve identified strongly one of the possible dangers of a Pragmatist philosophy. [take your pick of the pragmatists, from Scottish Realism or before or on up to today]

“We use it because it works” is one thing; as a heuristic, models are helpful. I tend towards Pragmatism – it’s in my culture (American) and I comprehend its value.

But then we run into the danger of our analogies for reality REPLACING reality in our minds. An analogy turns into a substitution. The Universe is Math is one of my favorite ones to pick on as of late.

I love recommending: http://www.lhup.edu/~dsimanek/scenario/analogy.htm for this reason. The most relevant passage:

Mathematical analogies.

Can we teach physics without ever using analogy? Let’s not forget that mathematical models are analogies. And even these carry some dangers, for mathematical models are inevitably incomplete, incorrect and only as good as the data that went into them. Albert Einstein recognized this, when he said,

Insofar as mathematics is true, it does not describe the real world. Insofar as it describes the real world, it is not true.

Yet the mathematical analogy is the safest, and the prefered analogy for physics. It is quite free of emotional baggage, and it is adaptable to any situation that might arise. To be fair, we must note its dangers.

Mathematical equations suggest or imply a false sense of precision and accuracy. The equation for a law or principle, presented without disclaimers and qualifications, fails to convey the limitations of scope and precision that apply.
Equations alone don’t distinguish quantities that are directly measurable and observable, such as mass, length and time, and those that are useful invented concepts, such as energy, momentum, field strength, wave function, etc.
Students often fail to recognize “unphysical” consequences of an equation. Any of the equations for fields such as inverse square fields “blow up” to infinite values at r = 0. Any limit taken by calculus methods obviously can’t be taken all the way to zero values of dx or dt at the quantum level.
Mathematical expressions of fields and wave functions tempt students to think of these things as having a “real” existence on a par with macroscopic quantities like mass or distance.

These misconceptions are not the fault of mathematics, nor the fault of physicists. Physicists are fully aware of these facts, and in a full treatment of theory they are all dealt with properly. It is only when the physics is diluted, simplified or dummied down for popular consumption, that important qualifications and disclaimers are left on the cutting-room floor.