- The circular argument, in which the proof of some proposition presupposes the truth of that very proposition
- The regressive argument, in which each proof requires a further proof, ad infinitum
- The dogmatic / foundationalist argument, which rests on accepted precepts which are merely asserted rather than defended.
These all tend to rub us the wrong way.
Addressing the trilemma
Changing the logic
This is a problem for classical logic in particular.
It could be addressed by introducing nonmonotonic logic: e.g. default and challenge approach to justification where some claims (e.g. first person observations) come with a default justification (which is not based on the justification of other claims). Yet they must be defended when challenged.
Challenging the meaning-theory distinction
The pervasive ideology of analyticity leads us to think that the meanings of our commitments are determined prior to deciding which claims are justified. Rejecting this is to say we cannot be clear about the contents of our expressions prior to determining their inferential realtions. So we cannot be in the original predicament we thought we were in.
- Also called Münchhausen trilemma.