Re: A Brief Note on Notation

For what it is worth, my sense is that notation has converged to a very
considerable extent since the 1950s, and particularly over the last
twenty years. The trend is towards ¬, ^, v, ->, <-> for the
propositional connectives, the use of \-/ for the universal quantifier.
(Also the use of box/diamond for modalities, single turnstile for a
syntactic proof relation, double turnstile for semantic entailment are
now pretty universal.)

One obvious reason for this is the use of LaTeX for most serious logic
typesetting, and the ready availablity of these symbols. Type in \neg
\land [for logical-and] \lor and \forall and you get [pretty versions
of] ¬,^,v, \-/.

However, let's not dump the horseshoe entirely. I think it is still
quite a nice practice (at least in introductory work with students) to
use the horseshoe for the connective defined by the truth-table, use
the arrow for the connective governed by the standard and
oh-so-plausible natural deduction rules, and then -- voila! -- it is a
perhaps initially surprising result that the two can be shown to come
to the same.

.