Assume that all possible hypothesis or theories (explanations in general) form part of an "explanation space." Some explanations are good (theories), some have no evidence (hypothesis) and some are false (we are riding a giant turtle). Given the number of false explanations, the overall space is infinite. Hypothesis spaces would be islands within the false explanation space, theories islands within hypothesis and the truth as a single point within one of those theory spaces.
The question is, does that mean that the theory space is infinite? If so, that would mean that it would be impossible to know that we've found the truth (as a single point within this infinite space) - we'd only ever be able to conclude that we've found a closer approximation. Scientists may never run out of work.
>The question is, does that mean that the theory space is infinite? If so, that would mean that it would be impossible to know that we've found the truth (as a single point within this infinite space) - we'd only ever be able to conclude that we've found a closer approximation. Scientists may never run out of work.
The theory space is definitely infinite, in either the interesting sense of something like "the space of all possible programs, treated as causal or directed-generative models" or in the trivial sense that you can take any simple, well-supported theory and come up with mathematical elaborations that don't change any of the pre-existing empirical predictions.
In a certain sense, "the truth" may constitute an infinitely small point in a space that's more continuous than discrete.
Your "explanation space" is almost certainly infinite and mostly empty.
The closer any model approaches reality, the more it is indistinguishable from the object being described. Like any map, it becomes unwieldy with increased accuracy. The model becomes the size of the universe. So, a universe-sized model inside of an infinite explanation space?
Assume that all possible hypothesis or theories (explanations in general) form part of an "explanation space." Some explanations are good (theories), some have no evidence (hypothesis) and some are false (we are riding a giant turtle). Given the number of false explanations, the overall space is infinite. Hypothesis spaces would be islands within the false explanation space, theories islands within hypothesis and the truth as a single point within one of those theory spaces.
The question is, does that mean that the theory space is infinite? If so, that would mean that it would be impossible to know that we've found the truth (as a single point within this infinite space) - we'd only ever be able to conclude that we've found a closer approximation. Scientists may never run out of work.