- 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?
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 …
- Peirce’s 1870 “Logic of Relatives” • Overview
- Peirce’s 1870 Logic of Relatives • Part 1 • Part 2 • Part 3 • References