## The Münchhausen Trilemma

9 Oct, 2021 at 15:15 | Posted in Theory of Science & Methodology | 2 Comments

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The term ‘Münchhausen Trilemma’ is used in epistemology to stress the impossibility to prove any truth (even in logic and mathematics). The term was coined by Albert in 1968 in reference to Popper’s Trilemma of dogmatism vs. infinite regress vs. psychologism.

1. My German is not up to it, so I consulted https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma . This does not go so far as your ‘even in logic and mathematics’. As a mathematician it seems to me that your extension is reasonable as regards logic and mathematics as widely understood by economists and other social scientists. But what about the ‘real deal’?

My own view is that the whole of mathematics proper is conditional on some logic, and hence should always be understood as ‘either this theorem is true or the logic that it relies on is false’, and such claims can be proved relative to their logic. This leaves open the question as to whether or not the logic applies in a particular case, to which the trilemma applies.

As an example, mathematics has various theories of geometry, calculus and probability that are widely used by economists (and others). They seem to me ‘proven’ in a way that escapes the trilemma but always questionable and too often false in the way they are sometimes thought to be universal truths.

Alternatively, some people hold that all logics are social constructs, in which case societies seem all at sea, unless they can construct something more suited to their debates than we have at the moment. Any advance on propositional logic?

• 《mathematics has various theories of geometry, calculus and probability that are widely used by economists (and others). They seem to me ‘proven’ in a way that escapes the trilemma》
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Open, standing question: Why does the quadratic formula give results that, operationally, you throw out?
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When I sight measure a tree diameter and use the quadratic formula to solve the Biltmore equation for the actual tree diameter, why is the math only 50% correct? Why does the theory produce one nonsense result for every correct one?
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《in which case societies seem all at sea》
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Does pretending you are on land make you feel better?