Tag Archives: Copulas

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.

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     

Whatta you sayin’? – or how to form a proposition

2 Jul
  1. Cats show affection.
  2. Ice cream makes me fat.

What you just read are ‘propositions’.  These statements or sentences are essential building blocks in a logical argument.

Who said anything about an argument?   Actually every time you assert something and give a reason for it, you’re making an argument.  The statements are the ‘propositions’.

Propositions comprise two terms.  One is the subject – what you’re talking about.  The other is what you are saying about the subject!  That term is the predicate.

So in our first proposition, ‘ice cream’ is the subject term and (a food that) makes me fat is the predicate term.

“Hold on a minute”, you say, “where did those 3 other words in italics come from?

Good question!  To look at a proposition clearly, we need to isolate the terms. Therefore, we rearrange it a bit and force a ‘copula’ to emerge.  The ‘copula’ is the neutral verb ‘to be’, but in one of 3 conjugated forms: IS, AM or ARE.

Dogs bark becomes Dogs are animals that bark.

Boys stink becomes Boys are kids who stink.

I sing becomes I am a person who sings.

How do you figure out the word after the copula?  Just ask what kind of set or category of ‘things’ your subject term might belong?  You can choose from several appropriate categories.

Ice cream is a……. food/dessert/snack/treat/concoction/item……. that makes me fat. YOU pick what you think communicates effectively, given the context.  Some fancy logicians might say, “Ice cream is THAT which makes me fat” (Whatever works!)

Something else to consider when looking at propositions – we need to add something to our subject term for accuracy.

Let’s go back to our example – Cats show affection.

  1. 1.   First – add the copula (the ‘is, am, are’ form of the verb TO BE) Cats are animals that show affection.
  2. 2.   Now – ask yourself this:  do ALL cats show affection?  Do SOME cats show affections?  Do NO cats show affection or do SOME cats NOT show affection?

What I’m asking you to discern is called the quantifier.  Too often we inaccurately misrepresent someone, a group or something by asserting falsely, “All teens text while driving.”    

-do we truly mean ALL?

-how do we know that EVERY SINGLE teen in the universe texts while driving?

Unless we can document that claim, we owe it to our audience to pull back and say SOME teens text while driving.  That is truthful.  As long as we can prove that ONE SINGLE INDIVIDUAL teen somewhere DOES indeed text while he or she drives, then we are safe to use the quantifier SOME.

Your homework for the week:

1)    Practice ‘translating’ statements/sentences into propositions with a copula (is/ am/ are)

2)    Question yourself when putting FORTH a proposition without a quantifier.  Can you spot how misleading that communication could be?   As my dad used to say, “You can’t make a general statement, you’re not a General!”  He had the correct intention, but not the correct reason.