Friday, February 20, 2009

An Improved Deductive Argument

An extraordinarily astute observer -- an anonymous Cardozo colleague (who very probably wishes to avoid the embarrassment of being associated with my blogs) -- points out that the proposed inference in the below argument is valid only if it is assumed that Hs must prefer either L or ~L; Hs cannot be in the position of having no preferences about L.

For your convenience, the argument in issue is:

Stipulation: All Hs prefer P or ~P [Hs prefer P or ~P but not both]
Premise 1: if H prefers P --> H prefers L
Premise 2: if H prefers ~P --> H prefers ~L
Premise 3: (H prefers L) is True
[Therefore]: The inference, or conclusion, [(H prefers P) is True] is valid
So let's restate the argument this way:
Stipulation 1: All Hs prefer P or ~P [Hs prefer P or ~P but not both]
Stpulation 2: All Hs prefer L or ~L [Hs prefer L or ~L but not both]
Premise 1: if H prefers P --> H prefers L
Premise 2: if H prefers ~P --> H prefers ~L
Premise 3: (H prefers L) is True
[Therefore]: The inference, or conclusion, [(H prefers P) is True] is valid
So now we have a better deductive argument, apparently an ironclad one. But this will just go to prove that a perfectly good deductive argument can get you into a lot of trouble.

&&&

Flash!: My astute colleague makes the further point:

If you are going to add the assumption that either H prefers L or H prefers -L but not both, I think you can drop premise 1. You just need H prefers -P to imply H prefers -L.
I think my colleague is correct. But at the moment I will proceed on the assumption that logical overkill is not always a bad thing. Besides, since I want to get his basic point out in a hurry and since I am slow on the uptake, I will leave the modified argument (above) unchanged for the moment.

the dynamic evidence page

coming soon: the law of evidence on Spindle Law

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