Wednesday, January 23, 2008

Missing types 7

To be uneducated is a great misery. Today I discovered De Morgan's eight types of categorical propositions (in "Syllabus of Proposed System of Logic"), which match my types, even if he seems not to have recognized the same natural language expressions for new types. His notation is interesting:

Universal propositions:
[-X+Y]: X))Y All Xs are some Ys
[-X-Y]: X).(Y All Xs are not (all) Ys
[+X+Y]: X(.)Y Everything is either some X or some Y (or both)
[+X-Y]: X((Y Some Xs are all Ys

Particular propositions:

(+X-Y): X(.(Y Some Xs are not (all) Ys
(+X+Y): X()Y Some Xs are some Ys
(-X-Y): X)(Y Some things are not either (all) Xs nor (all) Ys
(-X+Y): X).)Y All Xs are not some Ys

'X)' and '(X' is read '(all) X'
'X(' and ')X' is read 'some X'
'.' is negative copula
'X' is positive term, 'x' negative.

For me, this notation would be clearer, if dot would always mark particular proposition. Then the meaning of symbols would be almost iconically given. E.g.:

Universal propositions:
X))Y All Xs are only Ys
X)(Y All Xs are not any Ys
X()Y Only Xs are not only Ys
X((Y Only Xs are any Ys

Particular propositions:

X(.(Y Some Xs are not any Ys
X(.)Y Some Xs are some Ys
X).(Y Some things are neither any Xs nor any Ys
X).)Y All Xs are not some Ys

He calls this notation spicular, borrowing the name from Sir Hamilton, who characterized it as "horrent with mysterious spiculae."