A quick review of the highlights so far, and then I’ll continue from the standpoint I indicated last time. As you recall, Dan Everett opened with the following problem.
- I am trying to represent two readings of the three juxtaposed sentences in English. The first reading is that the judge and the jury both know that Malcolm is guilty. The second is that the judge knows that the jury thinks that Malcolm is guilty.
Do these purported EGs of mine seem correct to you?
Dan’s initial question about logical graphs sent me further down memory lane than I usually go, to my first encounters with extensions vs. intensions in logic, intentional contexts, propositional attitudes, referential opacity, truth-functionality, and triadicity, puzzles about which my first logic prof sent me off to read Quine’s Ways of Paradox and a host of others.
I had been studying Peirce on my own through all my undergrad years and was fortunate at long last to find an advisor who was a fund of knowledge about Peirce and Pragmatism, not to mention the Ancients and philosophy in general. In several of our discussions from those days I can remember expressing my hunch the problems of intentionality were not due to a distinct modality or quality of propositions but a different quantity or dimension of relations. I did not get to Russell’s monographs of 1918 and 1913 until much later but when I did I was struck immediately by his use of graphs to represent relations, so like Peirce’s graphs for the logic of relatives.
To be continued …
- Bertrand Russell, “The Philosophy of Logical Atomism”, pp. 35–155 in The Philosophy of Logical Atomism, edited with an introduction by David Pears, Open Court, La Salle, IL, 1985. First published 1918.