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Re: How is this collection called?

From: Laconic2 <laconic2_at_comcast.net>
Date: Wed, 7 Apr 2004 21:46:44 -0400
Message-ID: <z-ydndt0z4FBM-ndRVn-uA@comcast.com>


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. Received on Wed Apr 07 2004 - 20:46:44 CDT

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