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How recognizing a fallacy helps sniff out a poor argument

10 May

All cows have four legs

My dog Fido has four legs

Therefore, Fido is a cow

Pastor John Piper explained in a rebroadcasted sermon how high school geometry had grounded him in clear thinking.  Mathematical laws, one leading to a next, trained him to use deductive reasoning.  With practice in drawing valid and true conclusions, he developed a ‘nose’ for truth, as he put it.  The practical effect for him has been to alert him to ‘fishy’ conclusions that stink, that is they don’t add up, given the premises provided.

Looking at the syllogism above, we notice something and we ‘smell’ something:

  1. Premises 1 & 2 are in fact TRUE – cows have 4 legs and dogs normally do as well
  2. But we know that the conclusion is FALSE.  Our dog Fido is NOT a cow.

For me, the quickest way to explain why our sense of ‘fishiness’ is spot on, is to draw out each premise.

Take All cows have 4 legs.

Step 1:  draw a circle – label it Creatures with 4 legs.

2 cirlces

Step 2: draw a smaller circle somewhere inside the first circle.  This represents ALL COWS.  Every cow that ever WAS, IS, WILL BE  is in that circle.  (assuming no handicapped cows)

Step 3:  Mark an X in the big circle called, Creatures with 4 legs.

Circles with X

Do you spot the problem?  We don’t know where to place Fido.  Does he belong in the circle of cows? or out of the circle of cows?  From the information given, the 2 premises, that cannot be determined.

Therefore, the conclusion is false.  Why?  Because the new premise that ‘Fido is a cow’ assumes too much.  It might be, but it might not be.

There is of course, a technical way of categorizing the validity of the syllogism.  But for me, just sketching it out is simplest.

When I taught in a classical Christian school in Yorktown, Va, logic was a mandatory class for 7th and 8th graders.  I instructed the younger students in the joy of spotting fallacies (much to the annoyance of their parents who thereafter had to be on their guard!).  The 8th graders were at the perfect age to begin to understand how to analyze and formulate good arguments.

I believe that this tool in clear thinking is invaluable to young teens AND adults.  This kind of knowledge is powerful and builds confidence when they head out into a world such as ours:

Woe to those who call evil good, and good evil: who substitute darkness for light and light for darkness; who substitute bitter for sweet and sweet for bitter!  Woe to those who are wise in their own eyes and clever in their own sight!  Isaiah 5: 20-21 (NASB)

 

 

 

 

Prayer logic

4 Jan

You do not have, because you do not ask.  James 4:2c

I’ve been listening to archived John Piper sermons on prayer.  The Bible’s stunning truth about prayer hit me afresh this morning.

We don’t understand WHY the all-powerful God, the One who created every visible molecule in the universe as well as everything that is invisible, says He waits on us to ask. Only that He DOES…command that we pray, that we ask Him for what we need and want.

Note to Maria – Don’t spend any energy chewing on the bone of how come – just revel in it. The fact that He who created all things at His command should invite us to participate with Him should STUN us!

After we pick ourselves up off our face, we should then focus on the truth that James announces.

But an obvious question emerges if we try to formulate James’ truth claim into a syllogism in order to think it through. Do we apply James’ statement universally (ALL versus SOME) or as referring to a particular group of people?  Here’s what it looks like when I write it as a universal truth.

Premise 1: ALL people who lack something are people who don’t ask God for that item

Premise 2: You are a person who doesn’t have something

Conclusion:  Therefore, you are a person who doesn’t ask God

Hmm, does that logic square with how you have experienced reality so far?  Are there situations in which you have prayed to God and have yet to receive?  Or conversely, has God given you gifts for which you didn’t ask/pray?

I think all of us can attest to circumstances when despite LOTS of prayer God has not supplied the healing, the job, the baby, the money, the spouse or the resolution. As well as times when He ‘out of the blue’ graced us with a surprise blessing, both unanticipated and unasked.

In analyzing the above syllogism, we would say it is logically valid, that the premises are laid out in a correct order, but the conclusion is not true. Why?  because the subject in Premise 1 falsely includes ALL people in the world.

If we exchange the universal quantifier ‘ALL’ for the particular quantifier ‘SOME’, then we might get closer to the Truth.  Let me show you what that looks like and then we’ll talk about it:

Premise 1: Some people who lack are those who don’t ask God to provide what they need/want

Premise 2:  You are someone who doesn’t have what you want

Conclusion:  Therefore, you are someone who hasn’t asked God to provide

Again, that conclusion is not true in every situation.  To wit, I have repeatedly asked God to give me a different job.  And He hasn’t, YET……

So just using one circumstance in my life as a counter-example, I can prove that the conclusion in this second syllogism is not true.  It’s also not valid.  Why?  Because the conclusion overreaches the facts given in Premises 1. This first or major premise describes only one of two categories I’m going to call ‘LACKERS’ – those who haven’t prayed.  There is the category of ‘LACKERS’ who have indeed asked God for what they want.  So even though Premise 2 is true (you don’t have what you want) we can’t be sure which group of ‘LACKERS’ you fall into.

Bottom line?  I don’t know why God hasn’t answered my many prayers, YET.  But I do believe the Bible is authoritative.  I know that God commands us to pray.  I also know that He is good.  So there I rest AND I will continue to pray. What about you?

Logical Gal and when making sense is not enough

21 Jan

Makes sense

That makes sense to me!

Have you ever heard that comment or uttered it yourself?  It sounds so innocent, doesn’t it!  Don’t we want to make sense of the world around us – especially in light of all the horrors and issues that DON’T make sense?

It’s human nature to try to identify, draw associations and categorize all the information that cascades into our consciousness, moment by moment!

But, we must not forget that just because something makes sense, that detail does NOT make it true!

I ran across a useful example of this faulty thinking the other day.  While listening to a radio program broadcast by the organization Stand to Reason, the host discussed how to deal with the possibility that scientists might very well indeed find a gene marker held in common by some gay men and women.  The presupposition explored by the host is this:

Whatever makes sense is right or must be true.

The caller who holds to the above assumption suggested the following opening to an argument based on that assumption:

  • If there is a ‘gay gene’, then it is natural for those with that gene to want to/ need to engage in what is ‘natural’

After having suggested that line of thinking, he finished his explanation with the comment, “Makes sense to me!”

The host, Greg Koukl, reminded listeners that JUST because something makes sense, that doesn’t make it true or right.   An argument based on the faulty assumption could be stated like this:

P1 – All that makes sense is right

P2 – Doing what is natural makes sense

C – Therefore, doing what comes natural is right

And going on, one can continue:  Given a ‘gay gene’, then it is only natural that those with this gene engage in the behavior that is part of their inherited disposition.

However in the above argument, although it may be rational and correctly formed, it can still be faulty if one or both of the premises are FALSE.  Take a look at the following obvious example of a valid, but unsound syllogism:

P1 – All things with 4 feet are alive

P2 – This table has 4 feet

C – Therefore, this table is alive

Why is this argument valid?  Because it follows the rules of formal logic.  It makes sense, we could say. But you don’t have to be a rocket scientist to tell that something is WRONG!!!

Bingo!  The faulty premise is the very first one.  NOT all things that have 4 feet are alive, only SOME.  So the universal statement needs to be changed to a particular statement to be true.

P1 – Some things with 4 feet are alive

P2 – This table has 4 feet

C – Therefore, this table is alive

Soundness Venn diagram

Let’s get back to the possible research into gene markers and whether doing what is natural makes sense.

  • Besides the unsoundness of the argument due to the faulty 1st premise..
  • Besides the false nature of the underlying presupposition that What makes sense must be so,

There is ALSO the assumption that could be debated:  We should engage in what comes naturally!

Really?

Question: Which ‘natural’ scenarios come to mind that raise a red flag?

tantrums

 

Logical Gal and Communicating via symbols

4 Jun

Today is our middle school end of year celebration where we recognize high achievers in character and scholarship and fête the 8th graders who are moving up to high school.

As I was dressing this morning, I fastened my small cross necklace around my neck.  I was thinking what I would say if someone were to ask me what my cross means.  It’s a good question.

cross necklace

Part of being a Logical Joe or Jane is being able to think carefully about the content of one’s knowledge and beliefs and then to articulate them clearly and in a way that connects with one’s listener.

So here goes:

  • I wear a cross because it reminds me that I belong to a ‘Loser’.…..at least that’s how the world viewed Jesus of Nazareth at the time.  Execution by crucifixion was the ultimate in shame and degradation.   Rome had mastered this method of torture and capital punishment to dispatch slaves and criminals.
  • I wear a cross so I won’t fall into thinking that there is something ‘better’ or more ‘moral’ about me.  Christianity is a religion FOR losers.  And we are all losers.
  • I wear a cross so I won’t forget that Christianity is not about what WE do, it’s about what was done FOR us.  This places Christianity in a completely different category.  For in each of the other religious communities, it’s spiritual power from a person or force PLUS one’s works.  Grace and/or faith PLUS deeds or  letting go or mindfulness or....

Skitch comparison of Christianity & all other religions

One of the conclusions to be drawn from a religion whose founder the world viewed and views even today as a Loser is this:

Premise 1: If the leader is mocked, persecuted and even killed, then his followers will likely be treated the same

Premise 2: Jesus was mocked, persecuted and murdered

Conclusion: Therefore, His followers should not be surprised when they are mistreated by the world

If...then statements

The above syllogism is the classic  ‘Conditional Hypothetical Syllogism‘. The 1st or major premise is the If/Then statement. And the argument is considered VALID if the 2nd or minor premise either AFFIRMS the antecedent (what precedes the ‘then’) or DENIES the consequent (what follows the ‘then’).

Back to the symbolism.  Wearing a cross also reminds me of another way that Christianity is different. It represents a counter-intuitive system of thought.  Jesus’ helplessness on the cross and His willing submission to His Father shows how God is different.  Jesus saved sinners, aka LOSERS by His seeming passivity.  God prevailed through allowing His Son to suffer and not help himself.  When Jesus was raised, His resurrection to life WAS substantiation of God’s ways and His approval and pleasure with this beloved Son.

We don’t EARN God’s approval by anything we do.  God is pleased with us to begin with, before we were born. Then He rescues us and trains us to walk in the School for Losers also calledLife with God as His adopted child’.

When I fasten that little cross around my neck and look in the mirror, that is what I am reminded of.  I need to practice articulating what I believe FIRST for my benefit and THEN for anyone who might ask me.

Question:  What symbol do you display in or around your home, on your car or on your person?  Can you clarify what it means?

Tatoo - Hope and anchor

It’s biblical!

23 Sep

“Unlike the welfare state, prostitution is biblical!” –

 

This final jab by a local newspaper reader’s letter to the editor was meant to snarkily shut down a Republican columnist.  The government minimalist had explained that many conservatives advocate the Bible’s pattern of family and faith communities support for the poor rather than depending on the state to provide benefits.  

The premise ‘prostitution is biblical’ is actually an enthymeme. Remember them?  Those are informal arguments that are missing one or two premises. Usually the parties to a conversation know the missing claims, so the proponent feels that to articulate the obvious would be a waste of breath or ink.

 One sibling to another:  What’s for dinner? 

The response:  It’s Tuesday!   

 What goes unsaid is the following:  ‘Mom always serves meatloaf on Tuesdays, so if today is Tuesday, then we’re having meatloaf!”

In the case of the premise:  “It’s biblical” we can’t be sure of the rest of the argument.  It would be helpful to actually engage with the one who advanced the statement.  But if the proponent is not around to enlighten you, you have to consider what he or she might have meant.

Here’s how one context could be construed:

 All practices in the Bible are commendable behaviors

“Prostitution is a biblical practice” (the comment by the letter writer)

Tf, prostitution is a commendable behavior

The above syllogism IS valid.  But is it true?   

Not at all!  Just because something is in the Bible, does NOT mean that God endorses it.  David committed adultery and arranged a murder.  Abraham passed his wife off as his sister – twice!! – to save his skin.  Jewish religious leaders manipulated the Roman officials to eliminate by execution a problem teacher – Jesus!  Peter turned coward and denied Jesus!  A Jewish man throws his concubine to a frenzied crowd who rapes & kills her; the man then callously cuts her into 12 pieces and sends a piece to each of the 12 tribes of Jacob.  The Bible is, in large part, the history of humankind’s sinful mistakes and the account of how a loving God planned and executed our rescue!  So just because accounts of dishonesty, rape, murder and pillage are biblical, i.e. IN THE BIBLE, that does NOT mean God condones them.  Au contraire!  (They actually offer credibility to this holy book – if YOU were going to make up a religion and its teachings, would you show the seamy side of your followers?)

Here’s the takeaway: when you are ‘bestowed’ an enthymeme, simply ask politely for clarification.  Just what does the argument-advancer have in mind when he or she pronounces what turns out to be an argument only partially articulated?  Make them turn that enthymeme into an explicit argument.

 

Vitamins DO make a difference – creating our first valid syllogism

9 Sep

So, have you taken your vitamins yet?  Are you convinced that some taking of supplements is a habit that improves one’s health?

Last time we set out our conclusion by identifying 2 of the 3 necessary terms.  And we narrowed down our quantifier to SOME vitamin taking, not ALL.

Today we need to finish fleshing out the syllogism by adding a 3rd term.

You will most likely think that our syllogism doesn’t communicate a strong and complete case in support of the conclusion.  You will be right!  This syllogism is just a 1st step.  The 2 premises that we write will simply show your thinking process, how you are arriving at that first conclusion.  An entire argument involves a series of syllogisms.  By focusing on just this ONE LITTLE step, we are staying ‘ honest’ in our reasoning.        

Think about Math Teachers whose litany rings in our memories, “You must show ALL your work to get full credit!”  

Here is our conclusion from last time, properly labeled:

I statement – Therefore, some taking of supplements (Su) is a habit that improves one’s health (Pu)

By the end of our session, we had established the following information about our syllogism:

  • S term of the syllogism (aka Minor Term)  = taking of supplements
  • P term of the syllogism (aka Major Term)  = a habit that improves one’s health

Today we have to come up with our 3rd term (Rule 1), which will be the M or middle term.  This term will LINK the other two terms (major & minor terms), enabling a conclusion.

After playing around with some terms to determine the IDEAL one, I think I found the one that can link the other ideas.  What we are talking about are those daily activities that make a difference in one’s health.   Thus I chose the following for a Middle Term:

Doctor-endorsed daily practices

Next I had to choose the affirmative quantifier.  Did I intend the term to be UNIVERSAL as in ALL or particular as in SOME?

For argument’ s sake, let’s suppose that I happen to think that ALL doctor-endorsed daily practices are habits that improve health (we’ll talk about TRUTH later)

Here is what our syllogism looks like:

All  doctor-endorsed daily practices (Md)  are habits that improve one’ s health (Pu)

Some taking of supplements(Su)  is a doctor-endorsed daily practice(Mu)

Tf, some taking of supplements (Su) is a habit that improves one’s health (Pu)

 

Let’s go through our checklist to see if the syllogism is at least valid.  Remember that we haven’t even addressed the truthfulness of each premise.

1. 3 and only 3 terms? YES
2. Does the Middle term illicitly show up in the conclusion? NO
3. If a term is distributed in the conclusion, is it Distributed at least one other place NA (both terms in the conclusion are Undistributed)
4. Middle term Distributed at least once? YES (in Premise # 1)
5. Are Premises 1 & 2 negative? NO
6. If Premises 1 & 2 are affirmative, is our conclusion also affirmative? YES
7. If either of the 2 premises negative, is the conclusion also negative? N/A

Therefore, we have written a VALID syllogism!  Yay!

Once you have a valid syllogism, THEN you can look at the truth/falsity of each premise.  But that’s another discussion!

The takeaway?   Those little quantifiers REALLY make a difference.  Be precise with your words.

Gotta stay positive

28 Aug

All Chocolate is satisfying

Ghirardelli is chocolate

Tf, Ghirardelli is not satisfying   

What???  That doesn’t make sense!

You’re right.  Our mind easily balks because Premise 1 and Premise 2 are both affirmative propositions, they are A statements.  And the senseless conclusion is a negative proposition, an E statement (No Ghirardelli is satisfying).

Below is the chart that shows the 4 kinds of propositions and their Quality (Affirmative or Negative)

Affirmative  Propositions                      Negative Propositions

in this column                                         in this column

A – All dogs are cuddly E – No dogs are cuddly
I – Some dogs are cuddly O – Some dogs are not cuddly

So, back to chocolate and the question of validity – We are continuing with our extended lesson of

  • “How to examine a syllogism and see if it’s valid”

There are 7 rules in our Validity Checklist that we must run down to determine if a syllogism is valid , that is, in the correct form.  Last time, we showed that NO conclusion whatsoever can be drawn from 2 negative propositions.  Today, we see from Rule # 6 that

  • if premise 1 & 2 are affirmative, then the conclusion MUST be affirmative as well.

So what happens if someone has asserted a negative claim about health care such as:

  • No costly plans are possible

and when you ask the person WHY??? (Whoever makes an assertion is required to back it up with reasons) he/she says:

Premise 1 – All government plans are possible

Premise 2 – All costly plans are government plans

They’ve JUST articulated two affirmative reasons for their NEGATIVE conclusion of “ No costly plans are possible”

Before you jump in (or down your conversation partner’s throat) and start giving YOUR reasons why you disagree, you have every right to encourage this person to explain what she has either

  • left out on purpose
  • left out because she is not THINKING

Remember, there is absolutely NO point in arguing about an invalid argument.  And a negative conclusion drawn from 2 affirmative premises is one of the 7 ways an argument can be deemed invalid.

An argument (syllogism) must win the ‘Good Logician’s Stamp of Validity ‘ to be considered ready to meet the next criterion – are the premises TRUE.