Using the either/or to argue to a conclusion

5 Aug

“Either you are pro-choice or you are anti-women” 

We ran into this statement as an example of how we need to frame an attribute/predicate as either A or non-A to determine more easily if a pair of statements were truly contradictory.

Framing a contradiction into an either/or hypothetical proposition is one way to argue. We call this a Disjunctive Proposition.

Today we are FIRST going to form a valid or correct argument and then we’ll look at the truth of the major proposition.

Consider the ‘formula’ where P and Q are different statements, called ‘disjuncts’.  On the left is the model syllogism; in the middle and on the right are two samples.

Either P or Q                   Either blue or red            Either she had a boy or a girl

Not  P                               Not blue                             She didn’t have a boy

Therefore, Q                   Tf, red                                 Tf, she had a girl

These arguments work; that is they are valid BECAUSE the major proposition that contains the disjunctive statement tells us that one of the 2 disjuncts is true. (we have to accept this as a given;  we’re NOT going to argue about the truth of that major premise YET.)   So if one disjunct (P or Q) is NOT true, then the other HAS to be true.

What happens, though, if in the 2nd premise, I AFFIRM one of the disjuncts? Can this kind of syllogism work the other way?  It would look like this:

           Either Susie travels to the UK or to France

          Susie travels to France (I’m AFFIRMING one of the 2 disjuncts)

          TF, she does not travel to the UK

No….this set up is INVALID for I have actually assumed MORE than the information given.  It could very well be that her journey takes her to BOTH France and the UK.  All we know from the major premise is that she AT LEAST travels to one of the 2 places.  It does NOT claim that if Susie travels to one, she does NOT then travel to the other.

Certainty exists ONLY if the minor premise (the proposition that denies or affirms one of the disjuncts) denies one of the disjuncts since we have as a given that ONE has to be so.

Either I had a salad for lunch or some soup.

I did not have soup

Tf, I had salad

Back to our original Disjunctive propositions:  Either you are pro-choice or you are anti-women.  Once we have determined that the syllogism is set up correctly, that it is valid, THEN we look at the truth of the major premise.

If you remember what we looked at last Friday, we talked about true dilemmas and the Fallacy of the False Dilemma.  So, is our disjunctive proposition a False Dilemma?

If you are willing, comment with your thoughts about how you would determine the truth or falsity of that proposition.  A lot is riding on your answer!

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