Wittgenstein’s Language-Games and Gödel’s Incompleteness Theorems As the Foundation of Law

14 Pages Posted: 18 Oct 2019

Date Written: October 9, 2019


Incompleteness specifically refers to the fact that given any system of symbols, there will always be questions that can be formulated in that system that cannot be answered using just the symbols of that system.

An example would be that if a person had a box of objects that person was holding, and an interrogator asked to show the objects in the box which cannot be shown. That would be a paradoxical question with no possible answer.

Those sorts of questions can always be formulated, and this shows that there are some propositions that will be unresolvable no matter what the premises are of a system.

So, if one wanted to judge an axiomatic system — as David Hilbert did at the turn of the last century — by whether it could have an answer for any question one could ask of it, then one will not be able to make that judgement of some system being more thoroughly 'complete' (able to answer questions asked of it) relative to another.

Can, this, then can be applied to law and moral judgements? If one perceives law or morality as a propositional system then, yes, it would be applicable to moral judgements. Many pragmatists do not perceive law as such a propositional system, though. Some of the quotes I have collected refer to such pragmatists with that different approach.

Morality cannot be approved and everything is subjective intent including law. So, in the same way that in the early 1900s Bertrand Russell’s attempts with mathematics were approved futile in Principia Mathematica. Are the philosophical foundations of law proved futile?

How is Gödel's incompleteness theorem as being a problem for morals? Nobody has "true" premises to go from? Therefore — it can be said — all our conclusions are subjective. Is this accurate?

Suggested Citation

Lincoln IV, Charles Edward Andrew, Wittgenstein’s Language-Games and Gödel’s Incompleteness Theorems As the Foundation of Law (October 9, 2019). Available at SSRN: https://ssrn.com/abstract=3466594 or http://dx.doi.org/10.2139/ssrn.3466594

Charles Edward Andrew Lincoln IV (Contact Author)

University of Groningen, Faculty of Law ( email )


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