Archive | Syllogisms RSS feed for this section

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)

 

 

 

 

One false premise will lead you astray

29 Mar

A recent discouraging day and that of a friend (who texted me about the same kind of suffering) left me pondering from where such debilitating and energy-sapping thoughts arise.

Then our family’s daily trek through the Bible showed me the destructive power of a false conclusion.

The setting?  Moses is re-telling the history of the Hebrews’ 40 years of wandering.  The next generation is poised to enter and take the Promised Land.  This younger group of Wandering Jews was either NOT YET born when their parents left Egypt or they were babies and little kids.  Either way, they have no personal recollections of how God provided for their parents and grandparents in the midst of threatening situations.

Read Moses’ account of that first generation’s experience in sending tribal representatives to scout out the promised land in Deuteronomy 1: 23-28:

“This seemed like a good idea, so I chose twelve spies, one from each tribe.  They crossed into the hills and came to the valley of Eshcol, and returned with samples of the local fruit. One look was enough to convince us that it was indeed a good land the Lord our God had given us.  But the people refused to go in and rebelled against the Lord’s command.

“They murmured and complained in their tents and said, ‘The Lord must hate us, bringing us here from Egypt to be slaughtered by these Amorites.  What are we getting into? Our brothers who spied out the land have frightened us with their report. They say that the people of the land are tall and powerful, and that the walls of their cities rise high into the sky! They have even seen giants there—the descendants of the Anakim!’

 “But I said to them, ‘Don’t be afraid!  The Lord God is your leader, and he will fight for you with his mighty miracles, just as you saw him do in Egypt.  And you know how he has cared for you again and again here in the wilderness, just as a father cares for his child!’  But nothing I said did any good.

“They refused to believe the Lord our God  who had led them all the way, and had selected the best places for them to camp, and had guided them by a pillar of fire at night and a pillar of cloud during the day.

Their faulty conclusion was this:  Our God is not being good to us and means for us to be killed

Where did THAT come from?  Let’s look at the premises they uttered:

Premise 1:  The Land God is giving us is good (true premise)

Premise 2: The people of the land are huge and scary and we are weak and vulnerable (true premise)

Premise 3: If we face a dangerous situation, the only reasonable explanation is that God hates us (false premise)

Conclusion:  God means to kill us!

What makes the conclusion not true is the one false premise.

That same scenario was at the root of my discouragement last week and that of my friend’s.  Both she and I added a false premise to a true factual premise.  No wonder we arrived at false conclusions.

What was my situation?

My weight was NOT budging after 6 days of dieting. – TRUE PREMISE

FALSE PREMISE – This diet is not working

FALSE CONCLUSION – I’m doomed to weigh this amount. (cue in discouragement)

Any time you add a false premise to a true premise, you end up with a false conclusion. This is a law of logic. So it was with my friend Joyce:

Our dishwasher is broken, which is one more thing wrong with our house – TRUE PREMISE

FALSE PREMISE – God isn’t going to take care of all these problems we keep casting on Him

FALSE CONCLUSION – We’re stuck and there’s no way out (cue in discouragement)

So what did Joyce and I do when we each reached depressing conclusions?

We wallowed and went to bed.  The good news is that when we awoke to a new day we saw new mercies from God. The mercy He gave me was to read in next day’s Bible account the Hebrews error in logic leading to a false conclusion and detrimental punishment by God. Thank you, dear Father for the warning and review of Godly logic.

 

 

How do you know you exist?

13 Jul

Penseur  The math whiz and philosopher, René Descartes, sought to clarify his doubt and his knowledge.  So he pushed back as far as he could to what he could know for sure.  Most people can quote part of his argument:

I think, therefore I am

As many of you know, he left out the major premise.  No ‘doubt’ that it resided in his mind, but seemed too obvious to mention.  That’s the nature of an enthymeme, an unspoken premise or conclusion.

For example:

Sally pipes up with enthusiasm: I invited our neighbors to join us this Saturday for a picnic in the park!

Sam responds sourly: Great, now we can count on it raining this Saturday!

What’s the unspoken premise?

  • It always rains when we plan a picnic in the park!

Back to Descartes and his implicit assumption supporting ‘I think, therefore I am’

It has to be: All creatures that think exist.  So the complete syllogism would look like this:

P1 – All who think are

P2 – I think

C – Therefore, I am

What brought to mind Descartes’ foundation for knowing or epistemological basis for knowledge was a different origin for the assurance of one’s existence.

While listening to a podcast, I heard an African Christian talk about what anchors him in life. He talked about community as being this source.  He explained:

  • Because the community is the primary building block of humanity, each of us derives his or her own sense of self

His enthymeme would go like this: We are, therefore I am!

And by fleshing it out with the implicit major premise, we have:

P1: If there is a communal unit, then individuals can fully have their being

P2: There is a community in which I a recognized member

C: Therefore, I exist as a full human being

Thinking about and contrasting Descartes’ individualistic enlightenment view with this African brother’s sense of himself as part of a larger group strengthened my growing view that it is not good for man or woman to be alone.  After all, the one true God is a community of 3-in-1, a Triune Happy Godhead.  And if we are made in His image, then to feel fully alive and to function with health, we need to anchor ourselves in community with other people.

I need not be intimidated by famous thinkers and learned philosophers.  The simplest of men and women often are the wisest.

 

Responding to an attack posing as an argument

1 Jun

Illogical Lucy – You have no right to say that abortion is wrong!

Logical Joe – Why is that?

Illogical Lucy – You’re not willing to: 

  • adopt an unwanted child
  • take care of babies outside of the womb
  • bring the pregnant mom into your home

The presupposition of Illogical Lucy is that ‘Only prior action legitimizes one to make a belief statement/value judgment’

Is that true?  If it were, then the following convictions held by certain people would not be allowed into the arena of ideas for discussion:

  • The practice of 19th century American slavery was unethical (YOU 21st century American haven’t freed a slave or refused to buy a slave.)
  • Spouse and child abuse is wrong (Have you offered shelter to assault victims?)
  • Common Core curriculum usage should enforced by the federal government (YOU haven’t earned an advanced degree in education.)
  • Smoking is harmful to your health (You haven’t kicked the habit, so who are you to make such a judgment statement since you still smoke!)

The last rebuke of the anti-smoking belief is actually a known fallacy called Tu Quoque – or ‘you too?’  It goes like this:

If you participate in a bad action, you have no ground to stand on in order to claim that smoking is harmful.

Think about it, the person who can’t stop smoking but recognizes its detrimental side effects, is he or she not in an excellent position to call out and publicize the dangers?  I can imagine a man or a woman pleading with a teenager NOT to start smoking:

  • Young man, don’t start on the path of this foul and addictive habit.  I once was your age. Just like you I wanted to fit in, to look manly.  But boy do I regret it.  I’m a pack-a-day guy now and, you hear this cough?  – it’s not good.  My doctor keeps threatening me that I’ll die young from Emphysema like my Pa and his dad. Besides, my mouth stinks, my wife doesn’t like kissing me, my clothes reek, and I spend about $40 a week on this nasty addiction.

Here’s another tactical version of this ‘squash your opponent so his point of view can’t be voiced’:  Since you can’t possibly know what it’s like to be trans or unemployed or stuck with an unwanted pregnancy or hispanic or unemployed then……

  • Your view doesn’t count.  Your belief has no credibility.  Your opinion is wrong out of the gate.

Is that so?  That bullying tactic is actually a version of the Genetic Fallacy.  This maneuver draws strength from the false idea that the origin of the belief can de-legitimize the position.

Logical Joes and Janes KNOW that a premise, that is a belief, position, claim or view must stand or fall on the merits of the reasons backing it up.  It matters not at all WHO is putting forth the argument.  There are only 3 elements that must ‘pass muster’.

  1. Are the terms in each of the premises clear or ambiguous?
  2. Are the premises true or false?
  3. Does the argument or syllogism follow a valid structural flow?

If an argument contains clear terms within true premises, which lead to a ‘rule-abiding’ conclusion, then we say that the argument is both valid AND true and deserving of being considered SOUND.

And a sound argument, my friends, is golden.

Let us stand our logical ground with courage and courtesy and follow the same principles ourselves!

Q: So where are you being bullied in the marketplace of ideas today?

 

 

 

 

Gospel logic

18 May

God is able to make all grace abound to you that always having all sufficiency in all things, you may have an abundance for every good work. 2 Cor 9:8

I sometimes struggle with feeling as though I have SUFFICIENT time to do what I want to do – read during a period of the day when I am most alert.

So anytime I hear mention of the concepts of ENOUGH or SATISFACTION, which both can be described as contentment with the current supply, my ears perk up.

The other day, I was thinking about how  I might logically frame my feeling of sufficiency. Here is an initial attempt:

Premise 1: If I have all sufficiency in money, time and health, I am content

Premise 2: God has said that He is able to provide me with complete sufficiency

Conclusion: I should be content because I have access to my sufficiency by asking Him regularly for what I need

If the above reasoning is true, then why might I still struggle with a sense of lack or not enough?

Immediately the Holy Spirit reminded me of the PURPOSE for which God promises to provide me sufficiency.  Not primarily (so it might seem) simply to please myself, but instead to do the work that HE has planned for me to undertake.  In Ephesians, Paul reminds us that we are raised from the walking dead to being alive in Christ to undertake and carry out the works that God has planned for us.

For we are His workmanship, having been created in Christ Jesus for good works which God prepared beforehand that we should walk in them. Eph 2:10

(an aside, the Greek word for workmanship is poiema which some have rendered as ‘poetry’)

Okay – so when God gives us grace that translates into sufficiency, He says that it is not for our good pleasure (my reading), but to do the work that He has pre-ordained for us.

Hmm…is that disappointing?  Well, ça dépend! (that depends, as the French say).

Jesus said: My food/meat is to do the will of God who sent me and to accomplish His work – John 4:34  And food is the Greek word broma which means:

  • aliment which refreshes, delights or truly satisfies the mind

It seems that God is VERY efficient.  He has so created work both to accomplish His purposes AND to refresh me. I can be assured that looking to God the Father for what will ultimately satisfy me involves letting HIM assign and organize the work I am to do.

Left to please myself, I might think what I crave for restoration are the time and energy to READ.  But I am beginning to see that maybe I am not wise enough as the created being to know what is best for me.

I’m slowly learning to depend on my Maker to know what kind of high-grade octane nurtures, protects and optimizes my spiritual engine.

high octane

Trotting out the Credential

4 Nov

Sometimes when a person has no solid argument to back his viewpoint, he’ll invoke his status as member of a privileged elite.  Such credentials might be based on education or experience or one’s lofty position in an organization.

But those considerations should carry no weight, as they are irrelevant to one’s position or reasoning.

Here’s a comical example taken from the Book of John in the New Testament.  The set up is this:

  • consider the Pharisees, those ruling religious leaders trying to hold on to limited power granted them by the Roman occupiers
  • then there is Jesus, threatening the status quo with his unorthodox teaching and miracles
  • add to the mix the masses, growing more and more intrigued and swayed by this new rabbi

The Pharisees dispatch a posse of soldiers to arrest Jesus and bring him back to them for questioning.

Let’s pick up with the dialogue upon their return, empty-handed:

pharisees

The officers then came to the chief priests and Pharisees, who said to them, “Why did you not bring him?”  The officers answered,“No one ever spoke like this man!”  The Pharisees answered them, “Have you also been deceived?  Have any of the authorities or the Pharisees believed in him?  John 7: 45 -48

John doesn’t add their response, but I would have loved to be a fly on the wall back at army headquarters!

If we formulate a syllogism based on the Pharisees’ last question, we get this:

  • Premise 1 –  All (only) beliefs held by the Pharisees are valid and officially sanctioned beliefs
  • Premise 2 –  The belief that Jesus is special is not held by the Pharisees
  • Conclusion – Therefore, the belief that Jesus is special is NOT a valid, officially sanctioned belief

We need to be able to spot quickly, to sniff out the misuse of a credential to bolster a weak or non-existent argument

One clue that never fails to tip us off is when someone sidesteps the issue completely.  Of course there are many ways to do that, all of them Fallacies of Relevance.  Sometimes they work, however, as many a parent will attest.

(Why, Daddy?  Because I said so!)

Could Dilbert’s ‘mean’ robot be logical?

2 Sep

Dilbert Robots Read News

You never know where or when you’re going to bump into a logical syllogism. Or shall I say an ATTEMPT at a logical syllogism.

I scan the daily paper, including the comics, for interesting and challenging blog topics. I chuckled recently when I read Scott Adams’ Dilbert cartoon featuring a news anchor robot that sports a bad attitude.

Panel # 1 reads:

The Supreme Court ruled that engineers cannot be found guilty of murder

When I encounter a statement like that, my logical antennae tend to perk up. Why? Because I’ve just met a CONCLUSION. Now I need to hunt for the argument, also known as the reasons. Scan on with me!

Panel # 2 reads:

Lawyers argued that any good engineer knows how to get away with murder, so getting caught is proof of innocence. 

This statement appears to be an argument in itself. The telltale two-letter word, SO, often introduces a conclusion. Yet when I tried to tease out the assumptions lurking in this complex sentence I got bogged down.

Part of cartoonist Scott Adam’s humor resides in his deliberately obtuse attempts at logic. Here’s what I came up with as I struggled to make heads or tails out of these tangled words:

  • All engineers who are ‘good’ at being engineers are engineers who know how to conceal their guilt
  • No engineers who are caught in a murder are engineers who are guilty

But then the questions that arose gave me pause; as well they should when anyone advances a belief!  I wondered,

  • How is ‘good’ being defined?
  • And who is doing the defining?
  • Is there a hidden assumption that a good engineer might actually commit murder but be capable of concealing it so that he can’t be charged as ‘guilty’?

Then I saw something troubling in the clause after the comma (‘…so getting caught is proof of innocence’). I would have expected the ‘bad robot’ to have concluded rather:

  • So getting caught is proof that the accused is NOT a good engineer

Since this logical workout comes from a ‘tongue-in-cheek’ comic strip, we mustn’t take it very seriously. But I did attempt to represent it with a Venn diagram.

The red annotation reads: “Set of all engineers who are innocent of murder”

The blue label shows: All ‘good’ engineers

The black set comprises: All engineers who don’t commit murder

Dilbert Engineer Venn Diagram

There is not enough information given in the 3-panel cartoon strip to know how to portray the non-good engineers.  Are they engineers who commit murder and get caught?  Or does the concept of ‘good’ engineer include any other talents than the ability to get away with murder? How and where do I draw THAT set?  Where are there intersections of sets?

I’m not too bothered that I didn’t dissect it to the satisfying point of seeing how it worked. Why not?  Too many fallacies and problems that I don’t have the energy to sort out!  So I’ll call it ‘a day’ and lay aside my cartoon logic analysis.

Nonetheless, I’m grateful for the 30 or so minutes I invested in playing around with Scott’s wording. Actually, the process of drawing different category sets and subsets helped me think. And thinking is never a waste of time. So what if I had to conclude that I was dealing with some crazy robot’s irrational news reporting!

Oh, and in case you couldn’t make out the wording Scott Adam’s concluding cartoon square, here’s

Panel # 3:

The ruling was unanimous because no one could figure out which side was the liberal one.

Maybe I spent my energy on the wrong parts of the cartoon!  Oh, well.  I enjoy challenging myself to think through assertions, whether encountered in conversations, in my reading or in movies. Wanting to grow wiser, my goal is to become quicker to think and reflect and slower to share my views. Join me in being on guard, with a nose ready to sniff out poor reasoning and irrational statements.