Open thread, Dec. 29, 2014 - Jan 04, 2015

MrMind

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If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should be posted in Discussion, and not Main.

4. Open Threads should start on Monday, and end on Sunday.

From what I understand, there is a debate in epistemology / philosophy of science regarding the concept of simplicity ("Occam's Razor"). Some hold that there is a justifiable basis for the concept in the sense that it is an indicator of which of a set of possible theories is more likely to be true. Others dispute this and say that there is no justified basis for simplicity arguments in this sense.

In a recent conversation I made the following assertion (more or less):

Those who say that simplicity arguments are unjustified are actually saying that we can never really know the truth about any theory at all, since there are always an infinite number of alternative and more complex theories that account equally for the data. The best we can do is to falsify a theory (as Karl Popper proposed), but beyond that we can never say anything about whether a theory is true.

So (I said), we have only one of two choices. We can either allow for simplicity arguments, or we can give up on ever saying anything positive about the truth (beyond falsifying a few of the infinite possible theories).

Is this correct?

Why can't there be other criteria to prefer some theories over other theories, besides simplicity?

1ChristianKl11y

You don't have to go that road, you can also say: "The map is not the territory" and stop looking for true maps but rather value maps based on accuracy or usefulness.

6passive_fist11y

Adding to Vulture's reply (that you can not make absolute positive statements about truth), the modern view of "Occam's razor" (at least in Bayesian thought) is the minimum description length (MDL) principle (http://en.wikipedia.org/wiki/Minimum_description_length), which can be rigorously formalized. In this formalism, it becomes a prior over models. Multiplied with the likelihood over models (derived from data), this gives you a posterior. In this posterior, if you have two models that make exactly the same predictions, the simpler one is preferred (note that the more complicated one isn't completely rejected; it's just given lower posterior probability). There are very deep fundamental theoretical considerations for why MDL is a very good way of assigning a prior to beliefs. If someone wants to reject Occam's razor, they would have to give an alternative system and show that under the assumptions of MDL it gives better long-term utility. Or that the assumptions of MDL are unfounded.