7 Jan
2022
7 Jan
'22
7:14 p.m.
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?
7 Jan
7 Jan
11:15 p.m.
New subject: Imprecise Probabilities
<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
11:42 p.m.
New subject: Imprecise Probabilities
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.
On Fri, Jan 7, 2022 at 2:15 PM Jon Awbrey <jawbrey(a)att.net> wrote:
<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
8 Jan
8 Jan
12:21 a.m.
New subject: Imprecise Probabilities
By "calculus of relations" are you referring to the work of Tarski? (which
I suppose will answer my previous question) Do you have a reference for
"complex events, contingency tables, ..." with reference to Peirce in
particular?
On Fri, Jan 7, 2022 at 2:42 PM Peiyuan Zhu <garyzhubc(a)gmail.com> wrote:
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.
On Fri, Jan 7, 2022 at 2:15 PM Jon Awbrey <jawbrey(a)att.net> wrote:
<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
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