Tag Archives: Invalid

Logical Gal and how kids can benefit from studying Logic

31 Jan

A friend of mine’s daughter has her doubts about the benefit of studying logic.  It’s a required course for 7th graders at her classical school.  The curriculum introduces informal logic in the 7th grade and formal logic in the 8th grade.

Informal logic consists in all the fallacies or bad arguments people use.  Formal logic is the study of GOOD argumentation: its form.

But back to this pre-teen’s question about the relevance of her course of study.  I hear it as a French teacher and I’m sure math teachers have learned to shut their ears to this perennial question:

When am I ever going to use THIS!!!!

Here is how the study of poor argumentation can help anyone, no matter his or her age.  Armed with the ability to identify the fallacies of others, you will be able to stop them in their tracks when they come at you with:

  • …because I said so (Argumentum ad Baculum – Big Stick) – often used by parents!!
  • …because anyone who is anybody does it (Argumentum Populum – Mob Appeal)
  • …because Justin Bieber said they were the coolest running shoes (Celebrity Transfer)
  • …because these puppies and kittens will die if you don’t donate (Appeal to Pity – avoiding looking at other reasons, but relying on emotions)
  • You shouldn’t vote Joe for class president because he’s a nerd (Ad Hominem Abusive- attacking the guy’s character instead of looking at his platform)
  • You can’t trust what the disciples said about Jesus.  After all, they lived with him for 3 years (Ad Hominem Circumstantial – they must be biased)
  • You can’t tell me not to smoke because YOU smoke (Tu Quoque – you do it, too!)
  • You can either clean up your room now or before dinner. (False dichotomy – there are other times) again, a favorite of parents.
  • If you don’t let me have a cell phone at age 12, then I’ll never have any friends! (Strawman – reframing someone’s position incorrectly)- a favorite of kids!

These are just a few of the more common poor arguments or fallacies that swirl around us all the time. Can you see how useful it will be in giving both the adolescent AND the adult the key to identifying manipulative reasoning?  Even if you don’t remember the name of any of them, once you understand the thinking behind each, they are super easy (and fun!) to spot.  All you have to do, when someone tries to lay one of these babies on you,  is come back forcefully with,

That’s a fallacy!  

Try your hand at spotting what’s wrong in this argument!

How did you do? At least you could probably FEEL that something was wrong.  It’s invalid because of the Fallacy of Equivocation.    In this case, the word ‘headache’ is used equivocally, that is – in two different senses, thus creating the fallacy.  Equivocal words refer to two different concepts.  Both a pain in one’s head and an annoying condition can be called a headache.

Finally, the one fallacy I, as a parent, would want my child to have down pat before launching out on his or her own would be the Fallacy of the Non Sequitor.

If you have a daughter, think of a guy trying to get her to indulge in casual sex with him.  He lays this line on her: “If you love me, you’ll sleep with me!”

That, my dear readers, is an example of something that does not follow, hence a NON SEQUITOR.

Or how about this: “Why not try these drugs, you’re only young once!”

In both cases, there is absolutely NO CONNECTION between the first premise and the second.  Our children need to know HOW to respond before they are faced with the absurd and sinful choices, which will surely be thrown at them.

Question: Which fallacies have you succumbed to?

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! 

Let’s get tough! Analyzing those arguments

12 Aug

Let’s imagine you’ve heard an argument that just doesn’t sound right,

but you can’t put your finger on the reason.  The major and minor premise are even

true statements!  So what could be wrong?

Formal Logic rules to the rescue!  Applying a few simple tests to an argument can help you determine if it is indeed ‘valid’, that is in the correct form.  (remember that formal logic doesn’t deal with the truth of propositions, but the structure of an argument)

Today we’re going to look at the first 2 of 7 rules that are easy to use in analyzing the structure of an argument.

Rule # 1 – Three and only 3 terms

       Some boys are strong

       My brother is a baseball player

       Therefore, my brother is strong

Let’s count the terms.  Remember that a term is the number of words necessary to describe a concept. Terms must contain at least one word and can have several (mint chocolate chip ice cream is one term containing 5 words).   

When we identify and label terms, we start at the bottom of the syllogism and label the terms in the conclusion

Our conclusion above is:     Tf, my brother (minor term) is strong (major term)

Next, we label the same terms elsewhere in the syllogism.  The unlabeled term will then be the middle term


As we look for that middle term, we see our problem, which term do we label as the middle term?  We have two remaining terms and they are different!

      Some boys ( ? term)  are strong (major term)

      My brother (minor term) is a baseball player ( ? term)

      Tf, my brother (minor term) is strong (major term)

You can see our problem: we have 2 terms, both different (boys, baseball player) so we don’t know WHICH one will be the middle term (the 3rd official term after we have identified the minor and major terms).

So we can say with assurance, this syllogism is NOT valid because it has 4 terms.

*

Rule # 2 – the middle term must not be in the conclusion

Again, we start to label ‘bottom up’. (this takes a while to become automatic for we are conditioned to start at the top and label down )

      Some baseball players are strong

      My brother is strong

      Tf, my brother is strong and a baseball player

We barely get started  labeling the conclusion and we see that we have a problem.  Not only are there 3 terms in that one proposition (brother, strong, baseball player), but we have a term, ‘strong’, that shows up 3 times.  That is the tip-off that our middle term strong’ is in the conclusion.  The entire syllogism is convoluted.  So we shout out: “INVALID!!”

Next time, when we look at Rules 3 & 4, we will measure how far an attribute or term extends.  We will be asking questions like,

  • Are we talking about the category or set of ALL baseball players?
  • Are we talking about the category or set of ALL that which is strong?

If we say ‘yes’, then we say that a term is ‘distributed’ – that the quality in question applies to ALL, or that we are addressing ALL the members of a set.

In the meantime, watch your words and how others use words.  We must strive to be precise with our language if we intend to communicate clearly and with as few words as possible.

Excessive and unclear verbiage is wearying!  

Arguing about cuddly cats and ‘going TOO far’

25 Jul

Random question:   Is it true that some cats make good pets’?  This was a claim or CONCLUSION from last time when we were examining an argument.  We had started labeling & analyzing the argument about ‘roads that lead to Rome’ and got side-tracked by CATS! (see to the right:  ‘Spotting errors in arguments, beginning steps’

Your HW was to practice LABELING the following syllogism:

All animals that make good pets cuddle well

Some cats cuddle well

Tf, some cats make good pets  

 

Do you remember the steps?

1.   Put each proposition in ‘logical form’

All animals that make good pets are animals that cuddle well (needed a copula and we CLARIFIED terms)

Some cats are animals that cuddle well

Tf, some cats are animals that make good pets

2.   Start labeling the terms ‘bottom- up’, beginning with the Conclusion

–      Subject term is:   cats

–      Predicate or MAJOR term is:  animals that make good pets

–      Middle term (what’s left over) is: animals that cuddle well

 3.   Evaluate the terms with some quick questions

–      Are there 3 and only 3 terms?  YES

–      Is the Middle term in just the P1 and P2? (a rule new to you today) YES 

–      Is the Major/ Predicate term in P1? (the major premise -can’t be in P2) YES

 4.  Here’s a new step – draw out the syllogism to see if we have enough info to come to the conclusion legitimately

 cats as good pets

Because we have a question of where to place that subset of ‘cats that make good pets‘ (in the blue circle or out of the blue circle), we CANNOT legitimately reach the conclusion that Some cats are animals that make good pets.   Visually we can SEE that the syllogism is NOT valid…so there is no point in continuing  to debate with a cat/cuddly pet disputer whether the argument is true, because he/she has NOT correctly formed a syllogism.

Had the syllogism BEEN valid, then we would have continued on to examine the truth of Premise 1 and Premise 2.  There is a logic law that states, “In a valid argument, if the 2 premises are true, the conclusion MUST be true.”  That IF is the crucial two-letter word. Today’s argument was NOT valid, for there was insufficient information in the 2 premises to determine if in fact SOME CATS ARE ANIMALS THAT MAKE GOOD PETS.

So, for next time, practice with the argument from our previous post, the one below.  See if you can draw it out like I did with the cat argument.

All roads lead to Rome

Old Cabin Cove is a road

Therefore, Old Cabin Cove leads to Rome

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