\documentclass[a4paper]{article}
\usepackage{amssymb}
\pagestyle{empty}
\hoffset=-40pt
\voffset=-20pt
\textwidth 15.3cm
\textheight 22cm % to fit our printers

\begin{document}

\begin{center}{\huge What Mathematical Truth Could Not Be-II\footnote{The
work from which this talk is drawn is a
 review of issues arising out of the author's ``What Numbers Could Not
Be'' ({\it Philosophical
 Review} 1965) and ``Mathematical Truth,'' (
 {\it Journal of Philosophy} 1973) but principally out
 of the latter -- hence the title (one version of
 ``What Mathematical Truth Could Not Be-I'' appears
 in {\it Benacerraf and his critics}, A. Morton and S.
 Stich, eds., Blackwells, 1996).}}\end{center}
\begin{center}{\large Paul Benacerraf}\end{center}
\begin{center}{\large Princeton University}\end{center}

\bigskip

\large In a recent paper, ``Must we believe in set
 theory?''\footnote{Forthcoming in a
 collection of his papers, {\it Logic, logic and
 logic}, J. Burgess and R.C. Jeffrey, eds.,
 Harvard University Press.} George Boolos declares
 that according to ZFC there  exists a cardinal
 $\kappa$, which is equal to $\aleph_{\kappa}$,
 and is the limit of the sequence
 $\left\langle\aleph_0,\,\aleph_{\aleph_0},\,
 \aleph_{\aleph_{\aleph_0}},\,\dots\right\rangle$.  That
 is (if it exists) $\kappa$ is the least ordinal
 greater than all of the $f(i)$, where
 $f(0)=\aleph_0$ and $f(i+1)=\aleph_{f(i)}$.  To go directly to the
 source: ``...if  $\kappa$ exists, there are at
 least as many as $\kappa$ sets.  {\it Are} there so
 many sets?'' Boolos asks.
  It is, of course, uncontroversial that ZFC is committed
 to the existence of $\kappa$, just as it is
 committed to the existence of $\omega$.  Boolos
 applauds the latter but seems to regard the
 former as an {\it over}commitment---a commitment
 with which he, personally, cannot go along.   Any
 theory committed to the existence of {\it as many as}
 $\kappa$  things is simply not to be believed, on
 that ground alone.  I take it that such a view is
 not uncontroversial---indeed that it is not even
 pellucid what the view {\it comes to}.  I try in this
 talk to examine the reasons Boolos offers for it
 and, through them, how we should interpret the
 view and how defensible it might be to hold it.
 My focus throughout is, of course, not the belief
 specifically in $\kappa$ itself, but how this case
 illustrates certain tensions in our view of
 mathematical truth, meaning, and belief.

\end{document}