any philosophy/belief system that is descriptive (as opposed to prescriptive/normative) will be _apodictically_certain_ to the extent that it is free from internal contradictions. in simple cases we can examine the ideas and be very confident that there are no internal contradictions.
for example: given "A implies B" and "A" then we can conclude "B".
essentially any time you formalize definitions to the point that a statement of equivalence becomes obvious as a tautology, then you have an idea you can be certain about.
rejection of the principle of identity leaves one at the point where no further intersubjective dialogue is meaningful. which is why Avicenna said that anyone who denies the identity should be beaten until he acknowledges that "to be beaten" is not the same as "to not be beaten" and he should be burned until he acknowledges that "being burned" is not the same as "not being burned." [1]
I'm very interested in any corrections, comments, or other replies. I'm also aware that there are other approaches to logic besides the aristotelian approach I have tried to convey above. an example of a non-aristotelian attempt at communicating would be e-prime [2].
[0] https://en.wikipedia.org/wiki/Syllogism
[1] https://en.wikipedia.org/wiki/Law_of_noncontradiction#Avicen...
Oh, absolutely. I was merely suggesting that there is a difference between a lack of doubt for all practical purposes, and a lack of doubt in principle. This difference may not be terribly helpful or pertinent, of course.
Can you give some examples?