Tag Archives: Middle Term

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! 

Spotting errors in arguments – beginning steps

23 Jul

All roads lead to Rome

Old Cabin Cove is a road

Therefore, Old Cabin Cove leads to Rome

Our Gravel Road in NC

We just moved to Western North Carolina.  We live on an unmarked gravel road.  Believe me; it does NOT lead to Rome.

So if the conclusion is not true, what went wrong?  And where do we even start to determine that?   Tell you what – if we analyze the three lines, we can determine where the hole in the thinking is.  And believe me, the process is actually FUN!

The 3 propositions or sentences in red above constitute a SYLLOGISM.  It’s easier to examine this argument or syllogism if we rewrite & label it. The 1st proposition we’ll label P1 for Proposition # 1, the 2nd will be P2 and the 3rd proposition is the conclusion, hence C.

And remember that each proposition is made up of a Subject, a Copula (is/am/are) and a Predicate.  Making these parts explicit or obvious will help.

To figure out which term is the Subject term and which is the Predicate, we start with the conclusion and label ‘bottom up’.  The simple rule is this:

  • In the conclusion of a syllogism, the term before the copula is ALWAYS the Subject term and the term AFTER the copula is ALWAYS the Predicate term.
  • Once you identify them IN the conclusion, they STAY labeled S and P no matter where they are in Premise 1 or Premise 2
  • The ‘left-over’ or 3rd term that remains to be identified is called the M term or Middle Term

*

P1 – All roads (M) are roads that lead to Rome(P)

P2 – ‘Old Cabin Cove’(S)  is a road (M)

C – Therefore, ‘Old Cabin Cove’(S) is a road that leads to Rome(P)

Some rules for a proper syllogism:    

  • We can only have 3 terms…and if you notice, each one shows up twice in the syllogism.  If you have fewer or more than 3 terms, the syllogism/argument is considered INVALID.
  • Nota Bene…..the plural term of ‘roads that lead to Rome’ is the same term as the singular term  ‘road that leads to Rome’. (not TWO separate terms)
  • The 1st proposition listed has to be the one that contains the Predicate term – it’s called the Major Premise because that predicate term is considered the Major Term ………….. hence the premise that contains the major term is the major premise – (this is not ROCKET SCIENCE!!) . If you see a syllogism with that Predicate or Major term in the 2nd premise, the argument is in the wrong form and you should SHOUT, “INVALID!”

So, can YOU spot what might be wrong?  Our syllogism SEEMS to be in the correct order and it DOES have the correct number of terms.  Yet we know that the conclusion is NOT correct.  Something else is in play here!

Next time we’ll look at the truth of each premise and to determine if we can spot the faulty reasoning.

Your HW – look at this syllogism and write it out in logical form and label it!  It’s tricky!

All animals that make good pets cuddle well

Some cats cuddle well

Tf, some cats make good pets