Theories that require additional premises are less likely to be true, according to the eternal laws of probability. Adding premises like “Odin created everything” makes a theory less probable and also happens to make it longer; this is the entire reason why we intuitively agree with Occam’s Razor in penalizing longer theories. Unfortunately, this answer seems to be based on a concept of “truth” granted from above -
Not to me it doesn’t. (Though I may not understand what you mean by “truth” here.) Bayesian probability theory as I’ve come to understand it deals with maps directly and with the territory only indirectly. It purports to describe how logic, or the laws of thought, apply to uncertainty. So we can describe in some detail how these laws demand a lesser probability for a compound hypothesis, without ever mentioning the reality you want this hypothesis to address. In that sense the math doesn’t care about the content of your theories.
(I started to add a silly technical nitpick for something else on the site. Suffice it to say that numerical probabilities serve as maps of other maps, or measures of the trust that a ‘rational’ mind would have in those maps.)
So should we trust our ‘logical’ map-evaluating software in this respect? Well, it seems to work so far. As I understand it our mindless evolution created the basics by trial and error, after which we created more mathematics by similar methods. (We twisted our mathematical intuitions into strange shapes like “the square root of minus one” and kept whatever we found a use for.) Bayes’ Theorem as we know it emerged from this process. So we can imagine discovering that probability or logic in general has misled us in some fundamental way. Perhaps the most complex possible theory is always correct and we just can’t imagine said theory (or, indeed, a way for it to exist). But our internal software tells us not to expect this. ^_^
Not to me it doesn’t. (Though I may not understand what you mean by “truth” here.) Bayesian probability theory as I’ve come to understand it deals with maps directly and with the territory only indirectly. It purports to describe how logic, or the laws of thought, apply to uncertainty. So we can describe in some detail how these laws demand a lesser probability for a compound hypothesis, without ever mentioning the reality you want this hypothesis to address. In that sense the math doesn’t care about the content of your theories.
(I started to add a silly technical nitpick for something else on the site. Suffice it to say that numerical probabilities serve as maps of other maps, or measures of the trust that a ‘rational’ mind would have in those maps.)
So should we trust our ‘logical’ map-evaluating software in this respect? Well, it seems to work so far. As I understand it our mindless evolution created the basics by trial and error, after which we created more mathematics by similar methods. (We twisted our mathematical intuitions into strange shapes like “the square root of minus one” and kept whatever we found a use for.) Bayes’ Theorem as we know it emerged from this process. So we can imagine discovering that probability or logic in general has misled us in some fundamental way. Perhaps the most complex possible theory is always correct and we just can’t imagine said theory (or, indeed, a way for it to exist). But our internal software tells us not to expect this. ^_^