“Modal Diamond Box” « Search Results

Saturday, July 30, 2022

Modal Diamond Box

Filed under: General — m759 @ 10:54 am

A mnemonic from a course titled
“Galois Connections and Modal Logics“—

“Traditionally, there are two modalities, namely,
possibility and necessity. The basic modal operators
are usually written (square) for necessarily
and (diamond) for possibly.
Then, for example, diamond P can be read as
‘it is possibly the case that P .'”

See also Intensional Semantics , lecture notes
by Kai von Fintel and Irene Heim, MIT,
Spring 2007 edition—

“The diamond ⋄ symbol for possibility is due to C.I. Lewis, first introduced in Lewis & Langford (1932), but he made no use of a symbol for the dual combination ¬⋄¬. The dual symbol □ was later devised by F.B. Fitch and first appeared in print in 1946 in a paper by his doctoral student Barcan (1946). See footnote 425 of Hughes & Cresswell (1968). Another notation one finds is L for necessity and M for possibility, the latter from the German möglich ‘possible.’”

Barcan, Ruth C.: 1946. “A Functional Calculus of First Order Based on Strict Implication.” Journal of Symbolic Logic, 11(1): 1–16. URL http://www.jstor.org/pss/2269159.

Hughes, G.E. & Cresswell, M.J.: 1968. An Introduction to Modal Logic. London: Methuen.

Lewis, Clarence Irving & Langford, Cooper Harold: 1932. Symbolic Logic. New York: Century.

For less rigorous remarks, search Log24 for Modal Diamond Box.

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Saturday, October 23, 2021

From the Powder-Room of the Muses

Filed under: General — Tags: Mythspace — m759 @ 5:25 pm

The above title is from Northrop Frye —

"Is it possible* that understanding the nature of clarity and order
can cast suspicion on the very ideas of clarity and order?"

— Douglas Sadao Aoki, University of Alberta, "The Thing Never
Speaks for Itself: Lacan and the Pedagogical Politics of Clarity,"
Harvard Educational Review , Vol. 70, No. 3, Fall 2000,
Copyright © by President and Fellows of Harvard College.

Related scholarly citation by Aoki —