Re: How is this collection called?
From: Laconic2 (laconic2_at_comcast.net)
Date: 04/08/04
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Date: Wed, 7 Apr 2004 21:46:44 -0400
Here's what Brown says in the preface to the first American edition of Laws
of Form:
<quote>
In ordinary algebra, complex values are accepted as a matter of course, and
the more advanced techniques would be impossible without them. In Boolean
algebra (and thus, for example, in all our reasoning processes) we disallow
them. Whitehead and Russell introduced a special rule, which they called
the Theory of Types, expressly to do so. Mistakenly, as it now turns out.
So, in this field, the more advanced techniques, although not impossible,
simply don't yet exist. At the present moment we are constrained, in our
reasoning process, to do it the way it was done in Aristotle's day. The
poet Blake might have had some insight into this, for in 1788 he wrote that
'reason, or the ratio of all we have already known, is not the same that it
shall be when we know more.'
Recalling Russell's connexion with the Theory of Types, it was with some
trepidation that I approached him in 1967 with the proof that it was
unnecessary. To my relief he was delighted. The Theory was, he said, the
most arbitrary thing he and Whitehead had ever had to do, not really a
theory but a stopgap, and he was glad too have lived long enough to see the
matter resolved.
</quote>
So, if the above is correct, it may be the Theory of Types, and not the
Laws of Form, that are irrelevant.
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