Friday, July 12, 2013

Why prefer simple and elegant theories?

Why should we prefer simple and elegant theories, the empirical evidence being equal? There are two standard answers (besides the answer that no, we shouldn't):

  1. truth: beautifully simple theories are more likely, all other things being equal, to be true
  2. pragmatic: simple theories are easier to work with.
Here's a fun alternative to (2):
  1. aesthetic: just as it's better to hang around beautiful places, it's better to hang around beautiful theories.
This is mainly a tongue-in-cheek suggestion. I definitely think, in part for theistic reasons, that truth is the right answer.

But I think there is a bit of truth to the aesthetic suggestion. When you have multiple equivalent formulations of the same theory, why not spend more time with the more beautiful ones, simply because they are more beautiful? Of course, this could be defeated by more pedestrian pragmatic concerns, because a more beautiful formulation can be harder to actually work with. (Actually, that last point suggests that (2) can't be the whole story about preference for elegant theories.)


Gorod said...

Metaphysically, we say that God is absolutely simple, and we look for added simplicity as we climb up the ladder of being.

We were also expecting this to be the key to the physical world: it was fun discovering that all matter could be explained with a few elements on the periodic table... and hey, it seemed they were ALL made up of just protons, neutrons, and electrons. Great!

Except that modern physics is turning all this upside down, and when we look inside the atoms we find more complexity. The Standard Model is quite hard to understand, with lots of different particles, and more yet to be discovered.

So, my question is: how correct are our expectations that there should be simplicity "at the bottom of" all things? It MUST be so metaphysically, regarding God, but what if the material world is made differently?

Holopupenko said...

Why? Because beauty--like truth and goodness--are transcendentals, which means they are ontologically one in beings. To the extent a being exists, it it good and beautiful and true... ONTOLOGICALLY. Or, where there is truth, there is also beauty and goodness. None of these transcendentals are formal or proper objects (subject matters) of any of the modern empirical sciences, but are presupposed. Dirac was attracted to the beauty of his mathematical formalisms for electrons because their beauty (partly displayed in symmetry) also reflected the truth, i.e., their correspondence to the reality described... and hence, they are good. None of these can be separated from any real thing (except logically in the mind as a person reflects upon and analyzes them) because they are co-extensive with being.