divisibility in Physics VI. I had been assuming at that time that
Aristotle's elimination of reference to the infinitely large in his
account of the potential inf inite--like the elimination of the
infinitely small from nineteenth century accounts of limits and
continuity--gave us everything that was important in a theory of
the infinite. Hilbert's paper showed me that this was not obviously
so. Suddenly other certainties about Aristotle's (apparently)
judicious toning down of (supposed) Platonic extremisms began to
crumble. The upshot of work I had been doing earlier on Plato's
'Third Man Argument' began to look different from the way it had
before. I was confronted with a possibility I had not till then so
much as entertained. What if the more extreme posi tions of Plato
on these issues were the more likely to be correct? The present
work is the first instalment of the result ing reassessment of
Plato's metaphysics, and especially of his theory of Forms. It has
occupied much of my teaching and scholarly time over the past
fifteen years and more. The central question wi th which I concern
myself is, "How does Plato argue for the existence of his Forms (if
he does )7" The idea of making this the central question is that if
we know how he argues for the existence of Forms, we may get a
better sense of what they are."
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