Re: All logic must begin somewhere Yes good point...
Godel made the interesting point that a conclusion of logic can only be of equal or less "weight" than the assumptions. IOW logic doesn't do anything aside from rearranging or discarding information in the assumptions.
Otherwise, we'd have some sort of analog to a perpetual motion machine, except with information, that is pulled out of thin air.
In popular opinion, assumptions are generally demonized as logic fallacies (for example the popular phrase "when you assume, you make an ass out of you and me"), but ultimately, logic is useless without them. Assumptions are actually necessary ... and even good to have.
The questions about evaluating the quality of assumptions should focus on subsets... to make as few as possible that maximize the overall weight of the deductions.
The approach shouldn't be that "assumptions are generally bad," but that that "simplicity is a virtue," since it's less likely two any two assumptions will turn out to contradict one another. |