From: Chris Capel (pdf23ds@gmail.com)
Date: Tue Jan 31 2006 - 13:06:55 MST
On 1/30/06, Eliezer S. Yudkowsky <sentience@pobox.com> wrote:
> Philip Goetz wrote:
> > On 1/28/06, Eliezer S. Yudkowsky <sentience@pobox.com> wrote:
> >
> >>The way to explain logical "if" to humans is to rephrase "P => Q" as "~P
> >>or Q" which is mathematically equivalent and makes much more human sense
> >
> > The problem is that the word "implies", as we use it in real life,
> > cannot be reduced into a Boolean truth table. The difficulty people
> > have in understanding Boolean "implies" shows the poverty of Boolean
> > logic, not the poverty of human reasoning.
>
> It shows that you have to do some extra work to translate Boolean logic
> into English. Humans, when we hear "if...then", tend to hear evidential
> implication or counterfactual implication, not material implication;
> these are all distinct structures. And, yes, only material implication
> has a Boolean truth table, but that doesn't make it useless.
> To use the connective of material implication in human discourse, one
> should, I suggest, say "~P or Q". If/then has a quite different meaning
> in English. We do not say, "If the moon is made of green cheese, then I
> have four arms" or "If birds fly, then I have two arms" or "If I have
> four arms, then I have two arms". By contrast, "I do not have four
> arms, and/or I have two arms" makes perfect sense in English.
Interestingly, (if I have all this straight,) there are a few
idiomatic English phrases using "if" in which the correct
interpretation is material implication. The one I just noticed is "I'm
damned if I'll do that."
But, of course, you're right in general. That meaning is specific to
those idioms.
Chris Capel
-- "What is it like to be a bat? What is it like to bat a bee? What is it like to be a bee being batted? What is it like to be a batted bee?" -- The Mind's I (Hofstadter, Dennet)
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