Paradox of Self-Amendment by Peter Suber [T]hese secondary rules are all concerned with the primary rules themselves. They specify ways in which the primary rules may be conclusively ascertained, introduced, eliminated, varied, and the fact of their violation conclusively determined. Nor does Hart explicitly deny the necessity of tertiary rules, or ever use the term. But his repeated expressions of the adequacy of his theory, without tertiary rules, imply denial. Hart did not apparently see the mutability, justiciability, or recognizability of the secondary rules as a problem. Because these four theories are unsatisfactory at least as explanations of the actual change of rules of change, let us examine the other horn of the dilemma, the horn affirming self- applicability in the face of apparent paradox. We shall reserve the right to return to these theories if the other horn turns out to be just as implausible. Notes 1. H.L.A. Hart, The Concept of Law, Oxford University Press, 1961, pp. 79, 92. 2. See the discussion of Gerber and Benditt, cited in Section 3, note 12. 3. The theory of types was devised by Bertrand Russell in order to avoid the contradiction in his paradox of set theory (see text at Section 1, note 4) while preserving as much set theory and mathematics as possible. Basically the theory forbids self-reference and structures a substitute method of reference that preserves most of what had formerly been accomplished through self-reference. For example, under the theory it is simply meaningless to speak of a set being or not being a member of itself, although it is quite meaningful and important to speak of a set of level or type 2 being or not being a member of a set of type 1. Under the theory of types there simply is no set corresponding to the description, "the set of all sets that are not members of themselves". The theory adds one more grammatical or syntactic rule to the group of rules that determine whether a string of symbols is well-formed: no reference may refer to any entity of the same or higher level or type. The hierarchy of levels is admittedly metaphysical and cumbersome, but it does eliminate self-reference and most (but not all) the need for self-reference. See Bertrand Russell, "Mathematical Logic as Based on the Theory of Types," American Journal of Mathematics, 30 (1908) 222-62, reprinted in an anthology of Russell's essays, Logic and Knowledge, ed. Robert C. Marsh, Capricorn Books, 1956, pp. 57-102. The hierarchy of types postulated by Russell should be distinguished from both the logical (Hartian) hierarchy of primary, secondary, tertiary...rules, and the legal hierarchy rising through adjudications and statutes to constitutional rules. I am not denying the legal hierarchy in any sense (but see Section 21.C). I am assuming the Hartian hierarchy throughout the essay to test its coherence and extend it. And I am merely considering the Russellian hierarchy in this part of this section. Hart's hierarchy may well be a two-tier theory of types, but to call it that without inquiry begs the question at issue, whether secondary rules may apply to themselves. No rules in a proper theory of types could apply to themselves. 4. See Section 3, notes 13 and 14. 5. Hart, op. cit. at 92, emphases added; see also 79, 93, 94, 97, and 108. 23