Thursday, December 5, 2013

Inclusive/Exclusive


Once again, listening to the radio during my commute this morning initiated this blog post.  There was a roundtable discussion on WAMC that concerned the city of Detroit’s bankruptcy issues.  Apparently the idea has been put forth that the city should sell its publicly held art collections (such as those in museums) in order to help pay its debts, most notably the pensions of public employees (such as teachers).  Alan Chartok immediately defended this as an obvious step to be taken, whereas other panelists adamantly disagreed.  Not only did they argue that this would be degrading to the art pieces, but also that the money brought in would be entirely disproportionate to the problem.  Chartok responded, saying it was a question of whether you see the art as more important than the teachers’ pensions, or vice versa.  He then interestingly described the problem in the form of this disjunction:

Either you sell the art collections, or you decide that the teachers won’t get their pensions.

I found this interesting because it seemed as though Chartok intended this disjunction in the exclusive sense.  However, the other panelists immediately responded that this was an unfair characterization, as it could well be the case that the art is sold and the teachers still don’t get their pensions.  Clearly Chartok’s disjunction is a ridiculous false choice.  But it also helps to show the importance of distinguishing between the inclusive and the exclusive “or.”

Wednesday, November 27, 2013

Thursday, November 14, 2013

Reflexive Logic


            I know that I blogged something similar to this before, but I have an hour commute that includes a lot of NPR and these things keep popping up.  The story had something to do with a recent effort in Germany to piece back together old shredded Stasi files from the Soviet days.  Again, I apologize that I don’t remember the details.  But they interviewed a young woman who was involved in the project and she explained her participation thus:  “If this work were not important, I would not be doing it.”

~Iè~D

            This seems like a perfectly reasonable thing to say, but my logic reflex kicked in and I immediately tried to discern her implicit premise and conclusion.  Is this an example of modus tollens, or the fallacy of denying the antecedent?

P:  ~Iè~D
P:  D
C:  I

            This works (with MT, DN), but seems strange:  “If this work were not important, I would not be doing it.  But I am doing it.  So, it must be important?”
           
            It seems more natural to say it the other way:  “If this work were not important, I would not be doing it.  But it is important.  So, that’s why I’m doing it.”

P:  ~Iè~D
P:  I
C: D

            But, alas, this is a clear case of FDA! Blasted logic! Perhaps the first formulation is not so strange after all, but it threw me for a loop.

Thursday, November 7, 2013

Wednesday's Challenge


So this is my best guess at the problem that we were struggling with in class on Wednesday.  I’m not sure if I’m using Material Implication correctly, but it seems to work as far as I can tell.  Also, I know that it is in the front cover of the book, but I did not think that we had actually been given MI as a rule of inference yet.  Can anyone point me to when that happened?

1.  ~(PçèQ)                                    Prem. / Therefore: ~(QçèP)

2.  ~[(PèQ) & (QèP)]         1, BE

3.  ~(PèQ)   ~(QèP)         2, DM
           
            4.  QèP                      Supp. CP

            5.  ~(PèQ)                 3,4, DN, DS

6.  (QèP) è~(PèQ)           4-5, CP

7.  ~(QèP) ~(PèQ)          6, MI

8.  ~[(QèP) & (PèQ)]         7, DM

9.  ~(QçèP)                        8, BE, QED

Thursday, October 31, 2013

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.     

Thursday, October 17, 2013

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?