Tag Archives: Law of Non-Contradiction

Thinking about middle-schoolers, moral choices, and truth

29 Oct

 

The topic of the workshop focused on advisory programs run by many middle schools.  Ideally, no more than 6-10 students are assigned to a teacher who mentors these 11-to-14-year-olds during the turbulent years of their early adolescence.

Two skills the presenters emphasized as crucial for the development of youth were a) developing perspective and b) managing one’s emotions.  The overall premise was that social-emotional awareness and strengthening were foundational to and preceded academic success.

One or two barely perceptible groans slipped out of from among us attendees as the co-presenters ‘invited’ participants to leave their chairs and come forward to experience an activity designed to broaden perspective.

Here’s the scenario:  You’re on your way to work and you get into a minor traffic accident with another vehicle. Clearly, it’s the other driver’s fault.  She turns out to be a 95-year-old lady who pleads with you to ‘just exchange insurance information’ and NOT call the police.  For she is sure her license will be revoked.  Fortunately, no one is hurt, but your bumper is damaged.  What do you do?

We were directed to move to one side of the room or the other.  Those who would call the police stepped to the left and those who heeded the elderly woman’s plea chose the right.  As I stepped leftward, some of the others called out in jest, “heartless!”

The facilitator then called for a volunteer from the ‘compassionate’ side to explain his decision.  And then someone from the ‘cold-hearted’ side (my labeling) was invited to respond empathetically to the reasoning just articulated.

“I have an elderly dad and I know how significant it is to lose this last vestige of independence!” flowed one person’s reasoning.  Surely a compelling reason NOT to turn in this driver.

When it was the turn of someone on my side, one gal mentioned that although no one was hurt THIS time, someone very likely might be injured or even killed next time.  An equally compelling reason, for surely that elderly driver would not want to injure or kill someone.  A burden like that would be FAR worse than growing more dependent on others for help with running errands.

This activity was eye-opening and reinforced the notion that sincere people have very good reasons for their decisions.  I don’t dispute that at all.  But what the facilitators presented as the goal of the exercise caused me to ponder a possible unintended consequence, hence this post.

One of the gals reminded us of how middle-schoolers tend toward concrete, black and white reasoning.  The middle school years are when they need to learn that there are shades of grey.   She continued to say, “This is all part of growing more aware of differing perspectives, which grows compassion and empathy toward others.”

I completely agree that we must be open to the reality that others don’t think like we do.  And to expect the world to draw the same conclusions as I do is naive and self-centered.  Yet, I did wonder if our young teens might be led to the following kind of thinking:

  • Recognizing differing viewpoints means everyone has a ‘valid’ reason for why he or she thinks the way they do. (And ‘valid’ as a concept is often taken to mean ‘true’)
  • In fact, as long as I have a reason for what I am doing, this grounding is sufficient to stop YOU from telling me I’m wrong.
  • And if I am right and you are right, then maybe there is no such thing as ultimate rightness or wrongness.

Now are those conclusions what we want our young people to hold?  That just because we build an understandable and ‘reason’-able foundation for how we think and choose a course of action, no one can call us out on our decision?  I don’t think so.

For example: Not confronting a friend when you notice her cheating on a test  (or not telling the teacher confidentially) might be the choice you make as a student BECAUSE you think you could lose your friend. And that reasoning might be ‘valid’ because your guiding principle is to do anything to maintain a friendship. But the choice you have selected IS wrong.

Do you think it is plausible that if young teens are trained to acknowledge possible perspectives, they might ALSO think that there are possible ‘truths’, all of which emerge from one’s ideas of what matters most?

We might be aiming to grow our students from that pre-adolescent view that all of life is binary, but there are indeed some things that ARE binary.  The law of non-contradiction backs that up.  A and non-A cannot both be true in the same way at the same time.

I’m not going to assume that the workshop presenters do NOT believe that some absolute truths do exist.  I am pointing out that we as educators and parents must be careful as we train the next generation to think clearly.  Yes, training in recognizing others’ perspectives IS important.  But we must not neglect to teach our kids that some decisions ARE right or wrong because some absolutes do exist.   A challenging endeavor, no doubt, in a culture where few ground values in God.

Logical Gal extols Excluded Middle Law

12 Mar

Excluded Middle

Tools are for the using.  And I was reminded yesterday, listening to a discussion, how helpful the laws of logic can be!

The conversation centered on the origins of the universe.  It seems that everyone has a theory or possible explanation for how our universe came into being or whether it has always existed. So how are we to judge?

First of all, to even hold a rational discussion presupposes that words have meaning.  And when we put words together we make truth claims that are either true or false. We all use and therefore at least implicitly rely on logic, whether we acknowledge it or not.  So to deny the laws that are present is folly.  Humans didn’t INVENT these laws, we simply have discovered them.  They are part of the universe.

rational v. irrational

And if they do NOT exist and if words hold no meaning that we can all agree on, then there is no point ever having ANY conversation.  We just end up sharing gibberish.

Back to the discussion I followed this week.  One man laid out a way of thinking about origins that relied on the Law of Excluded Middle.  This law states that there is no 3rd or middle option given A or nonA.  For example, a woman is either pregnant or NOT pregnant. There is no other possibility.

Regarding origins, the reasoning expounded proceeded this way:

  • The universe either had a beginning or it didn’t.
  • If it did have a beginning (and due to the articulation of the Big Bang Theory, most people accept that the universe is NOT eternal), something caused it or something did not.  
  • (If something did NOT cause the universe to begin, then it had to cause itself.  But that is irrational because then something would have to BE (to cause the universe) and NOT BE at the same time.  And that is impossible because of the Law of Non-Contradiction.

Law of Non-Contradiction

  • If something caused matter, time and space (MTS) to appear, it itself is MTS or it is not.  (If matter, time or space created the universe, then we are stuck with a problem of infinite regress, i.e what caused the PRE-matter, time and space that created the universe)
  • Whatever caused the universe to come into existence is either immaterial or it is nothing.
  • and finally….we are left with the conclusion that what caused the universe has to be immaterial, because nothing cannot create something.

Nothing produces nothing

The man pushing back against this line of thinking balked when pressed by this series of either/ors.  When the Law of Excluded Middle was articulated , all he could repeat was the assertion of a possible 3rd option.  I held my breath, curious to learn something I hadn’t previously considered.  But all he offered was that ONE DAY, scientists might come up with a different explanation.

I am VERY thankful for tools that help me sort out, categorize and think logically through complicated matters.

Question:  How does the Law of Excluded Middle help you?

Logical Gal and the Law of Non-Contradiction

19 Feb

Knowing how to use the Law of Non-Contradiction helps us think.  

This rule states that something cannot both be and not be in the same way at the same time.

My most favorite example addresses whether someone IS pregnant or is NOT pregnant.  A woman clearly cannot both BE with child and NOT be with child.

But many scenarios don’t present themselves as clearly as the above example.  We have to sort of ‘translate’ the situation into a ‘Kansas and not-Kansas’ fashion.

This morning I heard an apologist use the Law of Non-Contradiction in this more complicated way.  But because I have previously encountered the reason he was offering for an argument, I could recall how to set up the particulars.

He was in dialogue with another man about the 3 explanations for the origin of the universe.  Here were the 3 choices he mentioned.

Choice # 1:  The universe has already existed.

Choice # 2:  The universe had a beginning and therefore something or someone caused it.

Choice # 3:  The universe caused itself to come into existence.

It is this 3rd choice that is logically fallacious because of the Law of Non-Contradiction.  And that was all the apologist said.  It was left up to us, the listeners, to think through how that is so.

And this is the implication:  The universe would have to both BE and NOT-BE at the same time.  We’re imagining NON-SENSE for how can something both NOT exist and exist?

Furthermore, that scenario is  like…..MAGIC!  something from nothing.

You might feel you’re way over your head when it comes to scientific discussions.  But being able to spot when someone breaks the Law of Non-Contradiction is a tool that will at least empower you to ASK the one advancing the assertion to stop and think.  That in itself is useful!

Question:  Where has someone tried to use the Law of Non-Contradiction on you?

“That’s a contradiction!” – are you sure?

30 Jul

So…how does knowing the Law of Non-Contradiction help in real life?

Remember we said that according to this DISCOVERED law (it’s built into the fabric of our universe by God as opposed to invented by culture):

 A & non-A cannot both exist at the same time and in the same way.

Consider this pair of statements:

  • ·         Susie is pregnant
  • ·         Susie is not pregnant 

Now we have to be careful and not automatically ASSUME that this is a contradiction. Two propositions that LOOK contradictory could in fact be explained…….

1.    If we mean that Susie Jones is pregnant, but Susie Smith is NOT pregnant (2 different Susies)

2.    Or if we mean that Susie is pregnant with many good ideas, but Susie is NOT pregnant with child (pregnant as an analogous term – referring to different but related concepts)  

But if we are talking about the one and only Susie Smith and we understand the predicate term ‘pregnant’ to indicate about to have a baby, then….

·         They cannot both be true OR false at the same time and in the same sense.

In Christianity this law of logic helps me sort out my theology.

My favorite attribute of God is His sovereignty.  When we say that God is sovereign, we understand God to be 100 % in charge of all that happens, the good and the bad.  I’m not saying that I understand this characteristic of God, but I am comforted by it!  (If God allows suffering and evil, then He must have a good purpose for it even if I can’t see that…yet!)

Therefore, because of the Law of Non-Contradiction, when I assert that God is always sovereign I cannot say:


God is sovereign

But

God had no control over that deadly train accident in Spain.     

That would be saying:  God is sovereign over all/ God is NOT sovereign over all

Either God IS sovereign or He is not, if I take sovereign to mean that He controls all molecules in the universe.

What we have to do when hit with confusing statements that seem irreconcilable is to ‘translate’ them, if possible, into A and non-A forms.  Then we can evaluate them clearly.

I say, ‘if possible’ with this caveat in mind – you might run across an either/or claim –

·         God is either all-loving or He is a God of wrath.

·         You’re either pro-choice or you are anti-women.   

If you can’t ‘translate’ the 2 predicates into an A and a non-A term, then you might be facing the Fallacy of Bifurcation (aka ‘false dilemmas’).  We’ll talk about that on our next Fallacy Friday!

Back to the above assertions – If we wanted to deal with that first claim, we’d have to re-frame it and then discuss terms.

·         God is either all-loving or He is not all-loving

·         You’re either pro-women or not pro-women

 Your HW for the next few days is to keep an ear out for ‘either/or’ claims and try to determine if they are in fact contradictory or perhaps examples of the False Dilemma fallacy or actually TRUE!      

What is Truth?

9 Jul

You don’t have to work so hard!

I’m talking about how to show that someone’s ‘big fat general statement’ is false.

Last time we talked about the beauty of the Law of Non-Contradiction.  Simply stated, 2 contradictory propositions can’t both be true or both be false AT THE SAME TIME and IN THE SAME WAY.

For example:

           All MacDonald restaurants look similar.

To ‘prove’ that this proposition is false, all we have to do is offer ONE counter-example:

           Some MacDonald restaurants do not look similar

(In fact, the other day on a trolley tour of Asheville, North Carolina, the guide pointed out a MacDonald’s sporting a grand piano and the strict architectural façade of Biltmore Village.  I had to do a double take. Was there REALLY a grand piano in a fast-food place!!!!  Yep! )

Today, I want to address the OTHER contradictory pair affected by the same Law of Non-Contradiction, the E/I pair.

What am I talking about with these capital letters?

Propositions are different, one from the other, based on their quantifier (how many of the subject.)

Logicians use 4 letters to represent the 4 possible propositions:

A = All S is P (where S is the subject term and P is the predicate term)

I = Some S is P

E = No S is P

O = Some S is not P

These 4 letters come from Latin:

·         Affirmo (the A and the I)

·         Nego  (the E and the O)

Thus we get: A, E, I, O. One pair is: A & O and the other comprise the E & I propositions.  This pairing tells us what we have to do to show a statement to be true or false.  If from real life, we can come up with the contradictory partner to what someone has said, then we KNOW that their original statement cannot be true simply because of the Law of Non-Contradiction.  Here’s a table to show the color-coded pairs:

A

E

 I

O

On to our E and I pair:

I just read in our local paper an emotional letter to the editor.  The author lashed out with a statement to this effect.

          No one should tell women what to do with their bodies

Let’s put that in logical form so we can see the terms.

No people are people who should tell women what to do with their bodies.

This is an E statement:  No S is P (we can tell from the NO)

The subject term is people and the predicate term is people who should tell women what to do with their bodies.

According to the Law of Non-Contradiction, the above proposition is in fact true unless we can find a counter-example that is an I statement. (its contradictory partner)

So, if we can think of at least ONE person who should be allowed/able to tell women what to do with their bodies, then the original statement is false.

If we can’t (or if there are none), then we have to reason that her E statement is likely true.

So, I toss the ball in your court, is the writer correct?

True or false: Bananas are the most popular fruit.

8 Jul

Well, what do you think? Can you even say?  (yes, you can!)  Isn’t that being….. narrow or intolerant to say?  Besides who are YOU to say that!  Horrors!

Most Westerners in the 21st century don’t like to come right out and make categorical statements.  They are afraid of being labelled the J-word!  judgmental

Put your mind at ease:  saying that something IS or IS NOT is perfectly logical!

**

We’ve looked at terms, one or more words used to describe a concept (something one can either see or picture in one’s mind) and discussed how terms are either CLEAR or UNCLEAR.  (not T/F, not  logical/ illogical not  right/wrong)  This is the Question you should be asking as you choose your terms:  Does your language recipient understand what you mean, you the originator of the spoken or written term?  That’s clarity.

Next in constructing a logical argument come the propositions.  A subject term, a copula (is/am/are) and a predicate term are the parts of a proposition.  There are 4 possible propositional forms:

  • All S is P  – All girls (subject)  are people who wear skirts(predicate)
  • Some S is P – Susie is a person who wears a skirt or  Some girls are people who wear skirts  (1 or more exemplars of your subject , but not all)
  • No S is P – No boys are people who wear skirts
  • Some S is not P –  Some girls are not people who wear skirts

What all these have in common is that they are either True or False statements/sentences.

That is how we evaluate propositions.

For example:   All killing is condemned by God   (as in, ‘Thou shall not murder.)

We can’t say:  That statement isn’t logical….that statement isn’t clear.  But we CAN say:  That statement is true or it’s false.

So how do we prove the proposition true or false? :  All killing is condemned by God.

This is what is so cool.  All we have to do is find ONE SINGLE SOLITARY CASE where a killing is NOT condemned by God. That one case will make our proposition false.  What we DON’T have to show is:  No killing is condemned by God.   That is TOTALLY and extravagantly unnecessary.  Let’s take just one example of God-approved killing, say defending your family. THAT would render the proposition false.  The proposition that IS true, i.e that corresponds to reality  would be this:  Some killing is condemned by God.  (or equally true:  Some killing is NOT condemned by God)

This principle is called the Law of Non-Contradiction.  It goes like this:  Contradictory statements cannot both be true or both be false at the same time and in the same way.  This specific stipulation means that you can’t equivocate (change the meaning) of the term, “Killing”.  You have to be referring to the exact same concept in both propositions.  (All killing is condemned by God and Some killing is NOT condemned by God)

Truth (aka ‘reality’) is so clean and precise, if you handle it correctly. 

PS:  there is one other contradictory pair – and we’ll talk about that next time.

HW: Listen for and notice a ‘general statement’ that are not true and see if you can come up with the counter-example that proves it false.