Notes and Quotes from Methods of Logic, 1.1

Notes:

Conjunction is associative, communitative, and idempotent.

Apparently to use "inclusive" can be misleading in certain circumstances when referring to nonexclusive alternation. I wonder what circumstances those are. I, trusting Quine, will adopt "nonexclusive".

We get 'V' as the or symbol from the Latin 'vel'. Apparently, to quote Quine, "Latin has distinct words for the two senses of 'or': vel for the nonexclusive and aut for the exclusive. IN modern logic it is customary to write 'V' reminiscent of 'vel', for 'or' in the nonesclusive sense: 'p v q'."

To logically represent the exclusive sense of 'p or q' just write 'p&-q V -p&q'

Alternation, too, is associative, communitative, and idempotent.

Note that -(p&q) is distinct from -p&-q.
These however are logically equivalent:
(-pV-q), -(p&q).
-(pVq), -p&-q.


Nice quotations/passages:

"Once we have an inventory of all the distinct componenets of a continued conjunction, no further details of the constitution of the conjunction need concern us" (11).

"In a metaphor from genetics, conjunction and alternation may be contrasted thus: in conjunction, truth is recessive and falsity dominant; in alternation, truth is dominant and falsity recessive" (13).

This is funny. In explaining his use of the dash rather than the tilde in notating negation: "Because in the present book there is much negating of single letters, I have here favored Pierce's bar for its compactness and perspicuity; and, given that, the dash in more in keeping than the tilde as negation sign for longer expressions" (15).