Tag Archives: Universal statements

If all gals are pretty, then are all pretty people gals?

14 Aug

Being precise matters! “But Mom, ALL my friends get to do it….”

The question of how far a term applies is called the ‘distribution’ of a term.  Terms are either ‘distributed’ or ‘undistributed’.

And to answer the question – no – pretty is NOT JUST referring to gals, but to other members of the pretty set.

When we make a universal affirmative claim (an A statement) : All gals are pretty, we are talking about the subject term gals. And, YES, since we have the quantifier ‘all’ ,then gals IS distributed because…… we are talking about every single member of the set of gals.

What about the predicate term of pretty?   All gals are pretty

As you can see, it makes sense that there are other people/things that are pretty besides gals!  So pretty is undistributed in this A (all) statement.

If you scroll to the end of the blog you will see a chart that summarizes the nomenclature for both Subject and Predicate terms in each of the 4 propositions. Once I explain it, it’s much easier to just remember the pattern by its nickname.  Scatological references being the source of humor for 13 year old boys, my 1st crop of 8th graders called it the DUDUs and UUDDs chart.  And I have found that easy to remember and draw out myself.  

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How about a particular affirmative claim, (the I statement)?  Are the S and P terms undistributed or distributed?

This one is easy – Some books are boring.

Since we are only talking about a partial group of books, then books is undistributed.  And just as obvious, there are other things besides books that are boring, so boring as the predicate term is equally undistributedSome books are boring

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No guns are safe is our universal negative, (the E proposition).   According to our chart, the S term and the P terms are both distributed.  It’s easy to see why it if we draw it out.  No guns are safe

Are we talking about every single member of the gun category?  Yes, so guns is distributed.  Are we saying about the safe things category that all of them do not  (or none of them) apply to guns?  Yes – so safe is distributed.

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Finally, let’s look at a particular negative (the O proposition): Some homework is not difficult.  Homework will be undistributed because  clearly we are not talking about every member of the homework class.  But what about difficult?  That is ‘more difficult’ to see in our mind’s eye, so let’s look at a drawing to understand why the predicate term difficult IS in fact distributed. Some HW is not difficult

We conclude that everything that belongs IN the set of difficult things has nothing to do with the ‘some HW’ that is shaded yellow.  You can see that we are making that predicate term distributed in this O proposition.

Next week we will use this concept of distributed/undistributed terms when we pick up with Rule # 3 for evaluating the validity of a syllogism.

Here’s our challenge – keep working on being precise with your language. In other words, “ Mean what you say and say what you mean!”

Here’s the infamous DUDUs and UUDDs chart: (warning – you have to remember to write the 1st vertical column of Quantifiers in the correct order:  A,I,E,O)

Subj Pred
A(all) D U
I (some) U U
E (no) D D
O (some…not) U D