Academic

Carlson on Legal Positivism & Russell's Paradox

By Lawrence Solum

David Gray Carlson (Yeshiva University - Benjamin N. Cardozo School of Law) has posted Russell's Paradox and Legal Positivism on SSRN. Here is the abstract:

In 1902, Bertrand Russell overturned set theory, which aspired to reduce all sets to their rules of recognition. These rules were to have logical priority to empirical sets posited by empirical human beings. As a result of Russell's Paradox, set theory gave up the hope of theorizing sets. This paper claims Russell's Paradox can be applied directly to jurisprudence. The result is that legal positivism (carefully defined as the claim that law can be reduced to rules of recognition) is invalid and must be abandoned. The corollary to this proposition is that law cannot be entirely separated from morality.

I really enjoyed reading this, but I am afraid I think is utterly wrong.  If you are unfamiliar with Russell's Paradox--follow this link for an excellent introduction.  The paradox is generated by the set of all sets that are not members of themselves.  Is that a set a member of itself?  If it is, it's not & if it's not, it is!  Hence the paradox.  There are various solutions in set theory/formal logic.  One set of solutions restricts what is called the Comprehension Axiom--which says that any propositional function (P(x) where x is a free variable, can determine a set: the idea is to restrict the ways in which sets can be determined so as to rule out Russel's paradox.

So Carlson imagines that positivists are committed to the idea that the rule of recognition can have any content and that this can lead to paradox's that are similar to Russell's paradox.  The example that Carlson uses is the following (RoR = Rule of Recognition):

RoR: Any statute enacted by parliament law.

Statue S: No statute enacted by parliament is law.

S is both law and not law.  Carlson concludes that there must be some restriction on RoRs so as to avoid this paradoxical possibility, and that restriction, according to Carlson would be a moral principle (because it is given by reason).

There are many possible lines of response to Carlson.  I'm going to leave comments open.  Feel free to contribute yours.  I'll post mine over the weekend.

Full post as published by Legal Theory Blog on March 11, 2009 (boomark / email).