From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Mon Jan 30 2006 - 11:12:00 MST
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.
http://www.google.com/search?q=material+implication
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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