[Philo]

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You're missing Boro's (correct) point. Here's the prototype example:

Suppose you have a computer producing a string of output characters -- you don't know the program (input), but you do so far have the first 183,000 output characters. It just so happens that these 183,000 characters happen to be the first 183,000 digits of pi.

Now for the central question -- if you had to predict the next character (number 183,001), is it MORE LIKELY to be the next digit of pi, or a random character? What would you bet on, and why?

Keep in mind, there are plenty of possible programs that say "calculate the first 183,000 digits of pi, and then do something completely different," and given only the first 183,000 output characters, you can't distinguish between any of these and the much simpler program "calculate pi."

The fields of inductive inference, algorithmic probability, etc. were set up to answer this sort of question. And the answer turns out, not surprisingly, to be that "it is more probable that the next output character will be the next digit of pi." As such, they represent something of a rigorous justification for Ockham's razor, and makes Borodog's point -- that simpler explanations that fit the data equally well are typically more likely to be true.

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There are two points of disagreement here. The first was, what is the correct interpretation of OR? Is it an empirical claim which says that theories that are more ontologically parsimonious are more likely to be true? Or is it a heuristic principle that says something like, given two or more theories all of which are on an equal par with respect to the evidence and with respect to their explanatory power, choose the simplest. The right answer here is, OR is a heuristic principle, not an empirical one. The empirical claim that I just mentioned is a much stronger claim than OR. That's why OR is an interesting topic in the Philosophy of Science. If it was simply an empirical claim we could just test it against our actual results and see if it was right. That's of no special interest to philosophers. You can read about OR yourself to find out that this is true.

The second disagreement grew out of the first. The second one was, given two or more theories all of which are on an equal par with respect to the evidence and with respect to their explanatory power, is the simplest one more likely to be true? I say it's an open question whether or not ontological parsimony makes a theory more likely to be true. String theory is alive and well, despite requiring at least 10 space-time dimensions.

I think the analogy with the computer generated string of output characters is a poor one. It's an open question whether or not nature itself conforms to the principle of parsimony, such that the simplest theory is indeed more likely to be true, but even if it does your analogy would be a poor reason for thinking so. A computer program is written by human beings who have knowledge of pi, and if the string of digits through the first 183,000 matched pi, that would be the reason one would believe that the next digit is likely to be the next digit of pi. This says nothing about whether or not natural phenomena conform with the empirical claim that the more parsimonious theory is more likely to be true.