[OT] "implies" (was Re: PEP-308 a "simplicity-first" alternative)
Steven Taschuk
staschuk at telusplanet.net
Wed Feb 12 20:58:58 CET 2003
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)
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