The Principle of Uniform Solution (of the Paradoxes of Self-Reference)
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This paper responds to Graham Priest's 'The Structure of the Paradoxes of
Self-Reference' (MIND 103 1994 25-34) in which Priest (i) argues that all the
paradoxes of self-reference, both semantic and set-theoretic, have the same
structure: all instantiate what Priest calls 'Russell's Schema'; (ii) advances
the Principle of Uniform Solution (PUS): paradoxes of the same kind should have
the same kind of solution; and (iii) concludes that all the orthodox solutions
to the paradoxes are inadequate, because each solves only one sort of paradox:
semantic or set-theoretic.  I argue against (iii).  Priest shows that the
paradoxes are alike at a certain level of abstraction, i.e. have the same
structure.  At a more concrete level the paradoxes are distinct: Russell's
Paradox concerns sets, not truth; the Liar Paradox concerns truth, not sets;
etc.  Thus the fact that the orthodox solutions are distinct at the more
concrete level---some concern truth and solve the Liar Paradox but not
Russell's Paradox, etc.---is, contra Priest, no cause for criticism.  For PUS
to be respected, the solutions need only be as alike as the paradoxes, i.e.
alike in structure---and indeed they are: considered at the more abstract
level, all are Russell's Schema-circumventers.