What is Truth?

9 Jul

You don’t have to work so hard!

I’m talking about how to show that someone’s ‘big fat general statement’ is false.

Last time we talked about the beauty of the Law of Non-Contradiction.  Simply stated, 2 contradictory propositions can’t both be true or both be false AT THE SAME TIME and IN THE SAME WAY.

For example:

           All MacDonald restaurants look similar.

To ‘prove’ that this proposition is false, all we have to do is offer ONE counter-example:

           Some MacDonald restaurants do not look similar

(In fact, the other day on a trolley tour of Asheville, North Carolina, the guide pointed out a MacDonald’s sporting a grand piano and the strict architectural façade of Biltmore Village.  I had to do a double take. Was there REALLY a grand piano in a fast-food place!!!!  Yep! )

Today, I want to address the OTHER contradictory pair affected by the same Law of Non-Contradiction, the E/I pair.

What am I talking about with these capital letters?

Propositions are different, one from the other, based on their quantifier (how many of the subject.)

Logicians use 4 letters to represent the 4 possible propositions:

A = All S is P (where S is the subject term and P is the predicate term)

I = Some S is P

E = No S is P

O = Some S is not P

These 4 letters come from Latin:

·         Affirmo (the A and the I)

·         Nego  (the E and the O)

Thus we get: A, E, I, O. One pair is: A & O and the other comprise the E & I propositions.  This pairing tells us what we have to do to show a statement to be true or false.  If from real life, we can come up with the contradictory partner to what someone has said, then we KNOW that their original statement cannot be true simply because of the Law of Non-Contradiction.  Here’s a table to show the color-coded pairs:





On to our E and I pair:

I just read in our local paper an emotional letter to the editor.  The author lashed out with a statement to this effect.

          No one should tell women what to do with their bodies

Let’s put that in logical form so we can see the terms.

No people are people who should tell women what to do with their bodies.

This is an E statement:  No S is P (we can tell from the NO)

The subject term is people and the predicate term is people who should tell women what to do with their bodies.

According to the Law of Non-Contradiction, the above proposition is in fact true unless we can find a counter-example that is an I statement. (its contradictory partner)

So, if we can think of at least ONE person who should be allowed/able to tell women what to do with their bodies, then the original statement is false.

If we can’t (or if there are none), then we have to reason that her E statement is likely true.

So, I toss the ball in your court, is the writer correct?

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