[FOM] paradox and circularity
twilson at csufresno.edu
Sun Sep 15 17:36:23 EDT 2002
On Fri, 13 Sep 2002, Stephen Yablo wrote:
> For each integer n, let G_n be the set of well-founded sets of type (n-1).
> On the one hand, each G_n must be well-founded, because an infinite
> descending membership chain starting from it would include an
> infinite descending membership chain starting from one of its
> members, and its members are one and all well-founded.
> On the other hand, if each G_n is well-founded, then it belongs to
> the set of well-founded sets one level up, that is G_n belongs to
> G_(n+1). Since n here ranges over the integers this gives us an
> infinite descending chain: each G_k contains G_(k-1) contains G_(k-2)
Well, what are the sets of type -1, -2, ...? Presumably, types start
at 0, in which case there is no infinite descending chain.
Todd Wilson A smile is not an individual
Computer Science Department product; it is a co-product.
California State University, Fresno -- Thich Nhat Hanh
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