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Logical Gal and the ‘good’ life

6 Aug

Good Life - Rob Lowe Cigar Aficionado  “Good” – Once again we bump up against the importance of clarity in our language.

Rob Lowe, apparently, exemplifies someone enjoying ‘the good life’.  To wit, ‘Cigar Aficionado‘  even has a regular feature by that name. Just what IS the ‘good life’?   And what is meant by ‘good’?   The word good is one of those equivocal  terms that refer to different concepts.  The differences in meaning and usage range from-

  • the moral good – John always does what is good in the eyes of God
  • the effective good – This device is good for opening cans
  • the expedient good – What good timing, that John arrived in time to take the children home
  • the good player – John is good at tennis – skilled in a sport
  • the pleasing good – Your dinner tastes good;  the photo is a good representation of me
  • the thoughtful good – It was good of you to stop by with my mail

“Yes, well….what’s the big deal?” you say.  Good question!  (in this case, good means ‘appropriate’). The rub is the time one needs to clarify meaning.   Making distinctions takes time. It’s much easier for person A to be sloppy with terms or accuse person B of a contradiction or even portray person B’s view by means of a strawman fallacy.  (Distorting someone’s argument so you can knock it) Strawman Fallacy

I heard such an exchange the other day when a young Christian man announced that God had contradicted himself, citing several places in the Bible where God claims to show NO partiality:

  • For the LORD your God is God of gods and Lord of lords, the great God, mighty and awesome, who shows no partiality and accepts no bribes. (Deut 10:17)
  • ...because God does not show partiality. (Rom 2:11)

Yet, (the young man continued), God also says that He chooses some to love and some to hate.

  • Even as it is written, Jacob I loved, but Esau I hated. (Rom 9:13)

Perceptive young man, he was, but the key to unraveling a seeming contradiction was to clarify the term PARTIALITY. Fortunately for me (and the young man), the pastor reassuring us that there was NO contradiction was John Piper.  He clearly explained that partiality was discrimination based on irrelevant considerations.

For example, if I am hiring the most qualified person to teach French, but overlook someone’s clear lack of abilities and experience because her mother  is my friend, or due to her skill in baking goodies for the teachers’ lounge or because she and I both happened to be  born in Atlanta, then I am WRONGLY showing partiality.

But if God chooses people on whom to show His favor according to HIS wise and good criteria as opposed to how the world judges what is appropriate, then we can still say with assurance that God does not show favoritism.

Just look at how God saves people from every kind of :

  • social strata and
  • people group and
  • age bracket and
  • income level

..and people with differing levels of education and aptitudes and experiences

…and regardless of the crimes they have committed or societal good they have done

These examples surely point to the FACT that God IS impartial.

What good news for you and me.  All we have to do is act on His encouragement….

  • “Turn to me and be saved, all you ends of the earth; for I am God, and there is no other.” (Isaiah 45:22)

Jesus knocking at the door

Do you see the importance of taking the time to exercise correct thinking?  Deliberately parsing out meaning from the different distinctions is WORTH the energy.

Question: What is a seeming contradiction that the ‘world’ tends to showcase, whether in  the political, spiritual or educational arenas? 

Who gives a darn about distribution?

21 Aug

   Distribution of terms matters….

even if YOU don’t care about distribution, the logic police do!

If we want to be logical and hold others gently to the same standard, we have to follow some rules.  Today we are talking about Rule # 4 – the one smack-dab in the middle of all 7 rules for writing a syllogism in its correct form.

Here is a synopsis of the 3 previous rules

# 1 – Three and only 3 terms are allowed in a syllogism

# 2 – The middle term can’t be in the conclusion

# 3 – If a term is distributed (applies to all in the set) in the conclusion, then it must be distributed in the premises

Today we look at # 4 – The middle term must be distributed at least once.  Since this term connects both the major and the minor terms, then it has to be as ‘ broad ‘ as possible to apply to the major and the minor terms.  We follow the technical drill of labeling the terms in the syllogism. We visually check to see if the middle term is distributed at least once. If not……then we shout FUM!!! (aka – Fallacy of undistributed middle)

                   Some chocolate is dark

                   All yummy foods are dark

                   Tf, some yummy things are chocolate

Types of Propositions Subject Terms Predicate Terms
     
A D U
I U U
E D D
O U D

When we label terms, we start with the conclusion  ‘at the bottom’ and label up.  (the term IN FRONT OF the copula is the subject or minor term…..the term AFTER the copula is the predicate or major term)

Tf,  (an I statement) some yummy things (Su) are chocolate (Pu)

We spot  ‘ yummy things’, then we notice that it is in the ‘ subject position of the proposition’ and write S.  Looking at the chart, we see that for an I statement the term in the subject position is undistributed, hence we add a ‘ u’.  The term ‘ chocolate’ is located in the predicate position of this I proposition; we write P and seeing that in an I statement, a predicate term is ALSO undistributed, we add a ‘ u’ next to the P.

Having identified the Major and Minor terms (also called the Predicate & Subject terms), the ‘ leftover term’  in the syllogism defaults to being the Middle Term (labeled M).  We can now finish labeling Premises 1 & 2.

P1:  (an I statement) Some chocolate (Pu) is dark (M u)

P2: (an A statement) All yummy foods (Sd) are dark(Mu)

So the whole syllogism looks like this:

        Some chocolate (Pu) is dark (Mu)

        All yummy foods  (Sd) are dark(Mu)

        Tf, Some yummy things (Su) are chocolate (Pu)

Is the middle term distributed at least once?  NO!!!

Therefore, we can say to the person making the argument:

“ We can’t even DISCUSS whether your case is sound until your syllogism is in the correct form!  And your middle term of ‘ Dark’ is not distributed even once!  Your conclusion assumes too much, given the data in premises 1 and 2.  You have committed…..FUM – the Fallacy of the Undistributed Middle Term.

  Off to Logic Prison with you!         

How is this useful?  I find that knowing the 7 rules of validity is a quick way to assess a syllogism when I sense that something isn’t quite right. The logic error emerges quickly when I run the argument through this checklist.

Keep an ear open for a conclusion that seems far-reaching and let me know if you’re stumped.  We’ll practice together.

Illicit logic

19 Aug

Now that I have your attention, on with validity!

Last time we chatted about ‘distribution’ of terms.  If a term is distributed, then what we mean is that we’re referring to ALL members of the subject or ALL those the predicate could possibly address.

For example in the proposition No carrots are sweet, we are saying something about ALL carrots and something about ALL ‘sweetness’ as a predicate.  So carrots and sweet are both distributed. 

If we posit……. Some boys are strong, then the terms boys and strong are undistributed because we are talking about only some of the set of boys and only some of the set of strong things.

Why do we care whether a term is distributed or undistributed?  I’m glad you asked!

Remember that we must be precise with our words.  We must not give the impression of ALL if we mean only SOME.  To say that ALL pre-teens get to stay up until midnight is a lot different than SOME do.  Since terms and their quantifiers build propositions which in turn build arguments, accuracy is important.

Often people over-generalize in order to make a point.  We, the recipient of the argument, need to be aware of quantifiers (the all, some, no, some..not) or we’ll be HAD!!!

On to rule 3 of how to test whether a syllogism (argument) is valid (i.e. in the correct FORM):

Rule 3 – if a term in the conclusion is distributed (applies to ALL of a term) , then it also must be distributed in the premises.  This prevents over-reaching conclusions.

To determine whether a term is distributed/undistributed we label our terms by the position they occupy in each of the 3 propositions and in the syllogism itself.  Here is our ‘DUDUs and UUDDs’ chart again from last time.

Subj

Pred

A(all)

D

U

I (some)

U

U

E (no)

D

D

O (some…not)

U

D

 

Some satisfying relationships are happy

Some satisfying relationships are marriages

Tf, all marriages are happy

 

Labeling our terms, starting ‘bottom up’ with the conclusion, we get:

 

Premise 1 –     Some satisfying relationships(Mu) are happy (Pu)

Premise 2 –     Some satisfying relationships (Mu) are marriages (Su)

Conclusion –   Tf, all marriages (Sd)  are happy(Pu)

 

S = subject term is marriages

P = predicate term is happy

M = middle term is satisfying relationships

U = undistributed

D = distributed

 

Rule # 3 states that if a term is distributed in the conclusion, then it has to be distributed in the premises.  We find that marriages IS distributed in the conclusion; however, where the subject term marriages is located in P2, it is NOT distributed because Premise 2 is an “ I” statement (see chart above).

Therefore, we say that the syllogism is INVALID because it violates rule # 3 (of 7 altogether), committing the Fallacy of Illicit Minor (one can violate the minor or the major term.)

Just pronounce the word ‘illicit’ in a class of 8th-graders and you have their instant attention as they wait to hear about SEX!!! 

So I have explained to my rapt class that the term ‘illicit’ means NOT allowed or unlawful.  What we are NOT allowed to conclude is that every single marriage is happy JUST because SOME satisfying relationships are happy and marital ones.   That conclusion goes FARTHER than the information given in premise 1 and premise 2.

Next time we will talk about a fallacy called FUM, where the middle term is undistributed.

In the meantime, as you read and listen to arguments, ask yourself if the conclusion drawn is valid or invalid according to Rule 3.   If you run across an egregious and interesting example, please share! 

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.  

*

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

*

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.

*

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