Re: A Brief Note on Notation


George Dance wrote:
> adamgolding@xxxxxxxxx wrote:
> > George Dance wrote:
> > > IMO, when it comes to notation logic today is much like mathematics 500
> > > years
> > > ago. To me, that's a negative; I'd like to see a common notation, and
> > > I think that one worthy goal of logic lists like this would be to agree
> > >
> > > on and work towards adoption of, a common notation.
> >
> >
> > i agree. for starters let's rally against the 'horseshoe'
> > operator--it's too easily confused with set inclusion--the single
> > arrow, ->, is preferrable. accordingly we should use the <-> for
> > material equivalence.
>
> Agreed. Both also have the big advantage of being reproducible at the
> keyboard (unlike the horseshoe, or the triple bar for equivalence).

well, i my office autocorrect settings i have )- and -( for the horse
shoe operators--sort of a curved turnstile.. it cases where humans can
figure it out, a well spaced ) can be used. that being said, i
would only do that if i actually meant set inclusion.

> I
> could go with > for conditional,

i would only do that if you use arithmetic symbols generally (* + >
etc.)

> but <> is confusing (I'd prefer that
> as the sign for possibility)

yes!! along with []. (and [#] for the filled-in box).

> so one needs the tail there; in which case
> it's consistent to add one to the conditional as well.
>
> also, i would like to see more use of the
> > reverse arrow, <- -- it often is disallowed entirely but to me allows
> > for a greaty fluidity in constructing formulae
>
>
> Well, OK - I don't see exactly how one would use it, but I see no
> reason not to so long as it's strictly defined (I assume, as:
> A <- B =df. B -> A).

indeed--i often write logical symbols at ANY angle, since if i'm using
logic to problem solve in something more difficult, i.e analysis, i
might write sets of strings in circles on the page, with various arrow
operators joining them at various angles, for exampe. thus to me ->
and <- are actually the same operator, along with infinitely many other
angles of arrow which instantiate 'the arrow'. for this reason rules
about commutativity i think could almost be done away with with rules
about reading wffs in either direction--commutative symbols are
symmetrical for a reason. (the only complication would be using
'symbol variables' until an operator is proved commutative)

(this almost makes be want to reject upside-down T for F, but that's
silly--then i would have to reject -] and \-/ as well ... the
direction can be assumed constant in a single string, and we need F for
predicates)


>
> > i'm also against the (x) for universal quantification--it doesn't mix
> > well in mathematical contexts, so we should use \-/, since it works in
> > all contexts.
>
> I've always used (x) (because it's keyboard-friendly), but I'm starting
> to come around to Ax and Ex - easier to type, less brackets to worry
> about, stuff like that. I suppose that using those requires a
> convention to *not* use A or E as predicates, as that would be
> confusing as well.

i would hate to be unable to use A and E for predicates--i'm very picky
about the letters matching the english. \-/ can be snappy with
practice, since there's no shift button involved. (x) could be VERY
confusing in mathematical contexts. \-/ also has the added benefit
that high school math students don't have to unlearn the idea that a
symbol's meaning is unchanged when you put brackets around it. (that
teachers and texts rarely point out that (x) violates this pattern kind
of boggles my mind)

>
> > i like both ^ and * for and, but * makes complex formulas easier to
> > read, IMO, although the ^ v symmetry is good for deMorgan's rule...
>
> I like ^ and V for the same reason (and that symmetry would also be a
> reason to use > for the conditional and < for your backwards
> conditional, BTW)

how do <- and -> lack that symmetry?

> while I don't like * (for your reason, that's it
> could easily be confused in some math contexts).

except that AND and multiplication are identical if we see truth values
as integers. i, for one, don't fully understand why
logicians/mathematicians can't agree to use what are called
'overloaded' symbols in java--operators whose meaning changes depending
on the operands. they *already* have this situation with things like
set equality, vector equality, etc. why not have ^ be conjunction for
numbers and intersection for sets? similarly, if you *reverse* the
horseshoe operator the analogy to set inclusion is obvious.

this makes the analogies involved stronger, and (also, this greatly
reduces the numbrer of symbols--which is good for typists!

(i even have a text that lists the reversed horeshoe as an alternative
symbol for material implication--does anyone know th ehistory of this?
it looks like they started out wanting it like set inclusion, but some
dullards changed the direction to make it more 'like an arrow' ... ??)

.