An interesting problem that arises from logic is the Münchhausen Trilemma. This applies in most situations when we are arguing to support a particular proposition (justificationism). A problem arises when we ask where do the axioms of a logical argument come from? This is expressed in the three “horns” of the Münchhausen Trilemma:

  • The circular argument, in which theory and proof support each other. A because B. B because A. e.g. “The Bible is true because the Bible says so.” Since anything can be justified by a circular argument, it is considered absurd to use this as a valid logical argument. It is also can involve tautology.
  • The regressive argument, in which each proof requires a further proof. A because of B, B because C, C because D, to infinity. If every proposition is supported by other propositions, there is no “foundational axiom”. Since there is no foundational axiom, we cannot even try to assess if our basic assumptions are true. Therefore we cannot know if our conclusion is true or false. This is classically seen in some versions of the cosmological argument.
  • The axiomatic argument, which rests on accepted precepts. This is problematic for the philosopher, as how can we know our axioms are true? Hume, among others, have pointed out the impossibility of a priori knowledge of a posteriori experience. We also can use the argument from obviousness, but this can be countered by claiming “nothing is obvious”, Descartes evil dæmon, Plato’s cave, etc. Also, if there is a disagreement on the truth value of an axiom, there is no way to verify it – this allows possibly any axiom to be claimed as “obvious” and we are back to absurdity. Mathematics rests on axiomatic assumptions but this is acceptable for an abstract field of knowledge. But outside a-priori knowledge, certainty of axioms seems impossible.

    “I shall begin with observing, that there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. […] I propose this argument as entirely decisive, and am willing to rest the whole controversy upon it.” Cleanthes in David Hume’s Dialogues Concerning Natural Religion

Given the objections and doubts of all possible logical justification, we are forced to conclude that no certainty in a-posteriori knowledge is possible! This leads us to fallibilism, the belief that all knowledge could, in principle, be mistaken. I do not go as far as claiming knowledge is impossible (for one thing, that statement might be considered “knowledge”).

Another way of analysing justification of logical argument is Fries’s trilemma. This ignores circular arguments (since they are worthless) and splits Münchhausen’s “axiomatic argument” into two futher divisions.

  • Dogmatism – we can just assume the truth value of axioms. This is usually unacceptable to philosophers. It also opens the door to possibly false statements.
  • Infinite regress – again, a problem.
  • Psychologism – defined by Popper as “the doctrine that statements can be justified not only by other statements but also by perceptional experience.” Remember that this too abandons certainty in knowledge, due to the variability in interpretation of perceptions. This highlights the need for philosophy to be aware of psychology.

Given the apparently inescapably of fallibilism, anyone who claims to be certain of something is “a question mark concerning his wisdom”. We need modesty in what we know. But I don’t think most people would be comfortable with the idea that everything they know could be false…

Anti Citizen One

PS Simpsons Quote: Moe: “It’s po-mo! [blank stares from all] Post-modern! [more staring] Yeah, all right — weird for the sake of weird.”

PPS Looks like the UK government was in on the US’s torture and rendition antics the whole time.