Radio Logic

I was listening to NPR on my drive home today, and there was a story concerning a community that has been attempting to rebuild after Superstorm Sandy.  I don’t remember the specifics, but that’s beside the point.  During an interview, one community member made the following comment in regards to why they were helping out:

“If this had happened anywhere else, I wouldn’t be here.”

My initial knee-jerk reaction was to point out that, admirable as the sentiment is, this is a fallacious comment.  In my mind, I assumed the rest of the “argument” was implied to go as follows:

1.  If this had happened anywhere else, I wouldn’t be here.

2.  It did not happen anywhere else. (It happened here.)

C:  Therefore, I am here. (DN)

This looks like a clear example of the Fallacy of Denying the Antecedent.  However, upon giving it a bit more thought, I noticed that it could be understood differently:

1.  If this had happened anywhere else, I wouldn’t be here.

2.  I am here.  (DN – I’m not not here)

C:  Therefore, it must not have happened anywhere else.

This actually works, although it seems a bit stranger.  More than likely the comment was not actually meant as an argument at all, so much as an explanation.  But this is what Logic class will do to you.     

Take 2

Just as a continuation of last week, I think that Brett makes a good point.  I was having trouble seeing how the two statements could be different, seeing as how, in both, having A, B, and C leads to D.  However, it does seem to be significant that the consequent of the first formulation is the conditional relationship between C and D, whereas the consequent of the second is simply D.  If we declared these equivalent, then couldn’t we translate the second formulation into several forms, all of which would have to be equivalent as well?  For example if:

[(A&B)&C]èD

can be restated as

(A&B)è(CèD),

then can’t we also turn it into

(A&C)è(BèD)

or

(B&C)è(AèD)?

Looking at it this way, I am less inclined to declare the statements to be equivalent.  However, I am by no means certain.  Any further thoughts?

Logically Equivalent?

A problem that we did in class last week left me with an interesting question.  There seemed to be two ways of translating an argument into symbolic form, and I was wondering if they were logically equivalent.  It seemed to me that, according to language of the argument, there was an overall compound conditional, the antecedent of which was a conjunction of two statements, and the consequent was itself a conditional statement:

(A&B)è(CèD)

But some people wanted to read it as:

[(A&B)&C]èD

It seems to me that the two formulations are actually logically equivalent, but I was wondering if anyone could give a reason why they would not be.  I suppose I could easily look this up, but I thought it would be an interesting blog topic.

How Logic Saved the Day

This morning I awoke to my dog wishing to be let outside to go to the bathroom (so to speak).  So I thought to myself, (1) if I do not let her outside, she will have an accident in the house.  (2) I certainly want her not to have an accident in the house.  Therefore, (3) I should not not let her outside (1, 2, MT).  Which makes more sense if I say that (4) I should let her outside (3, DN).  At which point I did just that, all was well, and I promptly thanked my new logical insights for helping me avert certain disaster.