Re: A Brief Note on Notation


Peter_Smith wrote:
> 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.)

the only metalogical text i've used used the threebar instead of =||=
for semantic equivalence--is this nonstandard? it seems like a waste of
valuable symbols to me...

>
> 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, \-/.

my impressoion is that philosophers tend to stick to things like &,
horseshoe, (x) and ~ tilde because a. they aren't using the
mathematical symbols that these are confused with and b. they read
older literature which uses these symbols more than mathemeticians do.

also, a note on & -- although i spoke (provisionally) in favour of
overloaded symbols, i think & should be saved for non-truth-functional
and, so we could say things like:

P(x&y)^Q(R)

(x and y are pious and r is quick)


>
> 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.

hmm, i haven't seen that particular trick (although i've seen the
inferences be an argument for the truth values, when it was already
assumed we would use the same symbol) but ok--it seems fine to use the
horseshoe in that very temporary setting--as the students will see it
in older literature anyway--but they should be specifically educated as
to how it is essentially set inclusion going the 'wrong way' to avoid
potential confusion, either then or on their future.

.

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