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Thanks karalee for posting a new link to Boole’s ‘Investigation’!
Chapters 2 and 3 are the essentials of Boolean logic that Dennis used in
TROM. Boole wrote that the most important law was x(1-x) = 0, in other
words a thing either exists or it doesn’t. The only values of x that
satisfy this equation are 1 and 0, hence the system of binary arithmetic
where these are the only numbers. We can recognise this equation now as
the boundary between sanity and insanity, and as Dennis said in the
Insanity Lectures it is also valuable in explaining the perceived
solidity and mass of the physical universe. x(1-x) = 0 can also be
written as x squared = x, or a thing cannot be more itself than it
already is. Dennis (and Aristotle, long ago) wrote this more simply as
as x = x.
In chapter 4 Boole writes about two classes of propositions in logic:
primary (concrete) propositions, about actual things; and secondary
(abstract) propositions about propositions. I think there’s some
parallel here with what we’d now call two classes of postulates.
There are postulates that a thing exists or not. On the other hand there
are bonding postulates about the relation between two things.
The later chapters in Boole’s Investigation are interesting but might
be less helpful. Chapters 5 to 12 develop his basic principles to
manipulate logical equations with algebra. He shows how all the terms in
a problem or a philosophical argument can be symbolized by letters and
written as a series of logical propostions, and the conclusion of these
propositions found by manipulating them as algebra, with examples of
this in chapter 13. Then he goes on about probabilities.
In the Investigation, Boole only uses lowercase letters for variables,
representing qualities or attributes that define classes of things. He
had previously (in The Mathematical Analysis of Logic, 1843) used
uppercase letters as well to stand for actual things. He considered this
simplification was a breakthrough, like a language that had eliminated
nouns and needed only adjectives. He also noted in this book that we
really only need one verb – the verb ‘to be’, since all other
verbs can be expressed by a word modifying this one. So he may well
have been on the way toward Dennis’ concept of be known/ know.
I read somewhere (it might be in Wikipedia) that Boole at 17 had a big
cognition that everything converged on one-ness. He connected this to
the Hebrew concept of one God, and at first wanted to convert to Judaism
and study theology. A wise Rabbi pointed him in the direction of
mathematics instead. Boole remained a Christian - but a Unitarian.
As Dennis wrote, to run TROM you don’t need to study Boolean logic in
any more detail that he gave ... unless you want to, of course.
Personally I think it's much, much more fun than games like football.
Kind regards,
David Cooke
https://adarsajnana.wordpress.com
On 27/12/2016 7:20 am, The Resolution of Mind list wrote:
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A bio: https://plato.stanford.edu/entries/boole/#LawTho185 [1]
The book which Dennis undoubtedly read:
http://www.eng.auburn.edu/~agrawvd/COURSE/READING/DIGITAL/15114-pdf.pdf
[2]
Links:
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[1] https://plato.stanford.edu/entries/boole/#LawTho185
[2]
http://www.eng.auburn.edu/~agrawvd/COURSE/READING/DIGITAL/15114-pdf.pdf
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