Hi Jon, Thanks for your reply. I found this one of his writings not very accessible. Has anyone tried to put this in a more modern language of modern algebra and probability? For example, for Boole I found David Miller and Theodore Hailperin have done good annotations of Boole, Michael Brady also has written interesting paragraphs on how to start reading Keynes's follow up on Boole.
<QUOTE Peiyuan Zhu:>
I’m studying imprecise probabilities which initially works as
an extension in Boole’s Laws of Thoughts. It seems like Boole
was solving a set of algebraic equations for probabilities where
some of the probabilities do not have precise values therefore
need to be bounded. Has anyone studied Boole’s algebraic system
of probabilities? Is Peirce extending Boole’s algebraic system in
his Logic of Relatives?
</QUOTE>
Dear Peiyuan,
Issues related to the ones you mention will come up in the Selections and
Commentary I'm posting on Peirce's 1870 Logic of Relatives, the full title
of which, “Description of a Notation for the Logic of Relatives, Resulting
from an Amplification of the Conceptions of Boole’s Calculus of Logic”, is
sufficient hint of the author's intent, namely, to extend the correspondence
Boole discovered between the calculus of propositions and the statistics of
simple events to a correspondence between the calculus of relations and the
statistics of complex events, contingency matrices, higher order correlations,
and ultimately the full range of information theory.
But it will take a while to develop all that ...
Regards,
Jon