[OT] "implies" (was Re: PEP-308 a "simplicity-first" alternative)

[Steven Taschuk]

Quoth Michael Hudson:
> Erik Max Francis <max at alcyone.com> writes:
  [...]
> > Not to nitpick into the ground, but the traditional symbol for
> > implication is an arrow with only one horizonal line.
> 
> In which context?  In my world, => is implication.  It's even
> $\implies$ in LaTeX, I think. -> is often used to denote a map.

Francis might be using "implies" to mean the material conditional,
which is common if not rigorous.  Afaik -> is customary in
symbolic logic for the material conditional, and => customary for
implication.

(The material conditional
	if 2 = 2 then Venus is hot
is true, but the implication
	"2 = 2" implies "Venus is hot"
is false.  As the quotes indicate, implication is about
statements, while the material conditional is about their truth or
falsity.  Quine, in _Methods of Logic_ (4th ed.), states the
distinction thus: "p implies q" means that "if p then q" is
analytic.)

> [...] Equivalent to is often <=>.

Likewise, afaik <-> is customary for the material biconditional
"if and only if", and <=> for equivalence (which is analyticity of
the material biconditional, following Quine).

-- 
Steven Taschuk           | Aral: "Confusion to the enemy, boy."
staschuk at telusplanet.net | Mark: "Turn-about is fair play, sir."
                         | (_Mirror Dance_, Lois McMaster Bujold)