I'm most of the way through George Englebretsen's Something to Reckon With: The Logic of Terms. I hadn't read a book on logic for a while, but, sure enough, it has me thinking.
It's largely about Fred Sommers' system of symbolizing Aristotelian logic, in which "Some dogs are black" is represented as:
And "all dogs are mammals" gets transcribed as:
You can then arrange this into a symbolic syllogism:
Yes indeed, some mammals are black.
It's actually a somewhat complicated system. Well, any worthwhile system of logic has to be somewhat complicated. I've read 2 books that went into it before. One was Fred Sommers' original Logic and Natural Language. That's out of print. The other book was David Kelley's old version of The Art of Reasoning: Expanded Version with Symbolic Logic. The current version, while an excellent book, no longer includes this positive and minus letters stuff.
Anyway, I think I've almost gotten it, finally. I found it useful to refer back to David's discussion. His is nicely compact. He defines a "canonical form" for the method, and also includes helpful practice quizzes - with answers in the back!
The form that still has me thinking is the one for disjunction. "All dogs are good or bad" becomes:
Kelley, at least, concedes this is a bit unwieldy.
While searching Amazon for the above links, I just found out there is a new (2005) book on the subject, an anthology, The Old New Logic, from MIT Press. Very exciting. I may understand this stuff yet.
All dogs certainly should
But every dog I've had,
Was sometimes bad.
I won't try to turn this into abstract letters.
I'll just tell my dogs: Act better!