Archive | July, 2013

“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!      

When a valid argument feels wrong – Logic to the rescue!!

29 Jul

So what do you do when someone’s argument is in the correct form, but you know that there’s still a problem?  

In a previous post I asked you to ‘draw’ out this syllogism:

All roads lead to Rome

Old Cabin Cove is a road

Therefore, Old Cabin Cove leads to Rome

Here’s what it should look like where BOTH the outer red square and the blue circle represent P1, and P2 is represented by the red X within the blue Roads circle.  We can CLEARLY see with our eyes that Old Cabin Cove is situated within the larger red square, “Things that lead to Rome”

Things that lead to Rome

As you can tell visually, the conclusion does not overreach the scope of the two premises P1 and P2. The syllogism IS, therefore, in the correct form and is considered VALID.  But our work does not end there.  You can FEEL that something else is wrong.

Anecdotally, I live on the gravel road, “Old Cabin Cove” in Western NC and I can attest that it does NOT lead to Rome.  It leads up a forested hill to our house and stops there!

What do we do then, with this valid syllogism?  We examine the truth of each of the 2 premises.

  • Let’s start with P2: Is ‘Old Cabin Cove’ a road?  YES! – no problem there.
  • Now for P1:  Do all roads lead to Rome?  NO!  Here’s the problem.  You already knew that, but what is illustrative in our simple example is this:  to DISPROVE an ALL or ‘A’ statement (also called a Universal Affirmative)  find ONE counter-example.  If there is JUST ONE single solitary road in the universe that does NOT lead to Rome, then the statement, “All roads lead to Rome” is false.
  • Why?  Thanks to the Law of Non-Contradiction which states that “A and non-A cannot both be true in the same way at the same time”.  Therefore we can’t say:  All roads lead to Rome and Some roads do NOT lead to Rome.
  • But we CAN say that Some roads lead to Rome and have that be a true statement.  (By the way, it takes only ONE road leading to Rome to make it true that ‘some roads lead to Rome’)

Back to our syllogism – if we want true premises, then we have to modify them to reflect reality:

P1   Some roads lead to Rome

P2   Old Cabin Cove is a Road

Tf……NOTHING!!!! –  we CAN’T conclude that Old Cabin Cove leads to Rome. It might and it might NOT.

Just like in our previous ‘cat and cuddly pets’ syllogism, our conclusion cannot reach further than P1 and P2, even if both of the premises are TRUE.  Here’s the sketch of what that would look like. We simply do not know where to place our X representing Old Cabin Cove.

Old Cabin Cove and Some roads

In our next post, I will share some real life examples of how knowing the Law of Non-Contradiction can help evaluate an argument you might read or hear.

Who’s allowed to make General Statements? It’s Fallacy Friday!

26 Jul

   

Mary Kaye women always wear pink!

Women from Dallas have big hair!

When I was growing up, my dad forbade me to make ‘general statements’ by disclaiming, “Maria – you are not a general, yet!”

It wasn’t until I was teaching logic that I realized other reasons for avoiding big broad, unsubstantiated pronouncements that were not backed up by enough data!

Welcome, again, to Fallacy Friday!  This is the day when we examine more examples of faulty reasoning.  Fallacies are shortcuts undertaken by either ignorant, lazy or devious people to convince you of the truth of their assertion!  But beware.

I just spent a week in Dallas, practicing new techniques in teaching second language acquisition.  Our group shared the hotel with 3 batches of Mary Kaye sales consultants, one after another.  In the elevators, in the restrooms, in the hallways bounced, minced & chattered well-coiffed, flawlessly made- up women, bedecked with sales awards.  

And no, contrary to my pre-conceived idea, Mary Kaye women DO NOT all wear pink.   That is a Sweeping Generalization.

All Mary Kaye women I have seen wear pink

Here are some Mary Kaye women

Therefore, they will be wearing pink

The problem is that the MK women I have experienced are too small a population size for me to come to my conclusion.  Hence I have just made a Sweeping Generalization.

*

Now about my second pronouncement about hair – a true Hasty Generalization:  I’ve actually only met ONE woman from Texas who had big hair, Beth Moore.  I think what compounded my idea was that some people make fun of Texan women by talking about their hair.  For me to conclude, from ONE data point + hearsay, that all women from Texas have big hair is even worse than my Mary Kaye pre-conceived idea!  

So what do we do with those traditional sayings that get passed along?  Is there NO truth in them?

Just be more specific.  Instead of claiming “ALL this or that”….or even worse…. leaving off a quantifier altogether – (i.e. claiming “Mary Kaye women….Texan women….without the words – all/some/no/some…not), BE SPECIFIC and use that honest 4-letter word “SOME”.

Consider these assertions that are MORE honest if they can be backed up by at least one example:

  • ·         Some capitalists are dishonest.
  • ·         Some conservatives are not compassionate.
  • ·         Some liberals resort to name-calling.
  • ·         Some teens talk back to their parents.
  • ·         Some mothers-in-laws criticize constantly.
  • ·         Some Americans are not fat.

Your HW for the coming week is this – try practicing awareness of your own thoughts or speech:

          What Sweeping or Hasty Generalizations do you tend to make routinely?

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     

Welcome to Fallacy Friday – the Genetic Fallacy

19 Jul

  

We’ve been dipping into some initial areas of formal logic by considering terms and propositions.  On Fridays, I’d like to look at what is called ‘informal’ logic.

By the way, ‘Formal’ logic does NOT refer to thinking in fancy dress or tuxedos, but studying the FORM of an argument.  Informal logic refers to poor, lazy thinking, that is to say faulty or fallacious ways of arguing, hence:  “fallacies.”

People often unwittingly resort to fallacies as shortcuts because they don’t want to take the time (or they sense the impatience of their opponent) to present a sequentially thought-out case for why they believe what they do.  Let’s look at a snippet of a typical conversation taking place at a county fair.

Old-timer: Carolina barbecue is the best in the country!

City-slicker:  You’re just saying that because you grew up in Appalachia!

Our Old-timer (OT) just made an assertion and he should be willing to offer proof.  But the City-clicker (CS) is not being fair to assume that the OT has no reasons to back up his claim.  It could very well be that OT DID grow up in Appalachia AND that Carolina barbecue IS the best per some culinary standard.

The likelier case is that neither wanted to take…. the…. time to investigate the reasons.

But the argument regarding the superiority of Carolina-style Barbecue does hang on reasons.  Where our Old-timer grew up is immaterial or irrelevant to his claim.  We should never dismiss an assertion due to the background of the one making the claim.

When we default to that kind of retort or response to a statement/conclusion, we are using the Genetic Fallacy.  Genetic is reminiscent of our word for origins, or ‘genesis.’

Where the person making the claim comes from should have no part in the argument.   They MIGHT be prejudiced toward something related to their background, but they might just as equally have stacked the deck against the very thing.  We have an adage about that, “Familiarity breeds contempt!”

In summary, clear thinking people who correctly use the tool of logic rely on REASONS to support their case and they ask others to show evidence to support their claims as well.

However, as you know, most public conversation we observe barely rises above the swamp of snarkiness. Look at the kinds of retorts that fly back and forth, whether in the Press, on TV or just in every day conversation:

“You’re just saying that because you’re………..

·         a westerner

·         racist

·         a woman

·         against women

·         over 40

·         a teen

·         against the establishment

·         vegetarian

·         an agnostic

·         a Christian

·         against having fun

·         rich

·         Democrat

·         ….and ad nauseum…….”

 All those circumstances MAY be the case, but we need to look at the naked argument.  A claim and its reasons need to stand on their own.  Period.

So what do you do when someone makes what sounds to you like an outrageous claim?  Challenge them gently by asking them why they think that!

See if you can recognize the Genetic Fallacy during the next few days.  Ask yourself, instead of addressing the claim, what accusation are they making against the person advancing a point of view?   Or catch yourself falling into the same rut of laziness argumentation!

 

 

 

Of Bouncers and Secret Servicemen

16 Jul

What do bouncers do?  I’ve never been to a skanky private nightclub guarded by a big burly bouncer, but I’ve seen them in the movies.

The function of a bouncer is to let in ONLY those authorized to enter – same job description of the President’s Secret Service.

We started to define ‘meal’ last time when our imaginary Susie opined, “It’s not healthy to eat between meals!”

We identified a GooD definition as one having a clearly identified genus or a broad category (think family) that contains different members easily distinguished one from another.  If you can picture a Venn diagram, then the boundary of the diagram delineates the genus and individual points within the genus circle are the differentia.

We thought deeply and decided that meals belong to the genus that WE called,

“Food prepared for human consumption”

And besides meals, we proposed other ‘family members’ such as –

  • a single edible item like a CARROT that is seasoned, cooked, cut or arranged in such a way as to have been ‘prepared’
  • a potable drink that is either poured from a container or created from ingredients or seasoned or heated/iced

So now the question is, are we done?  If we include ‘meals’, we have 3 participants in our category.  Are we ready to finish describing and distinguishing a meal?

Almost, but not quite:   We need to run our genus through a grid to insure a complete & accurate definition.

Consider this question –

  • Does our genus contain ALL possibilities?  Can we say, that with our 3 described differentia, we have exhausted ALL possibilities?  (I AM aware that we have YET to describe the differentia that separates ‘meals’ from its other 2 ‘siblings’.)  The way to answer this is to think of any and all ‘foods prepared for human consumption’ and see if they fit into one of the 3 sub-groups.

How about a container of yogurt that I buy at the store – Where does that fit?

Is it a ‘single food item that is seasoned, cooked, cut or arranged’?  NO!!!

Woops, then we need to add another member to the food category.  How about

  • Food or drink that comes pre-packaged, ready to be consumed.

Now we ask our 2nd detailed question “Is there any ambiguity or possible confusion among our differentia?  Could a potential member be assigned to more than one of our differentia?” If so, then we have to be more specific in limiting/ describing the differentia.  If we can’t think of any possibilities, then we can say with confidence that our definition is:   ‘mutually exclusive’.

Let’s return to our Bouncer/ Secret Servicemen analogy.  Imagine two different functions occurring at the White House on the same night.  One might be a reception welcoming the National Spelling Bee finalists and the other a state dinner for UN ambassadors.   The President is going to mingle and congratulate the young people before going into the international soirée.  Invitees to both are filing through security under the scrutiny of Secret Service and Protocol officials.  You can be sure that the lists for each event are VERY detailed.  And I doubt that any of the ambassadors and their spouses are good enough spellers in English OR young enough to be on the elite guest list of Spelling Bee-ers and family.  The 2 lists ARE mutually exclusive.  There will be no confusion.

And if those are the only 2 events hosting outside guests, the two lists are also ‘ jointly exhaustive’.  They take care of ALL guests that night.  In summary, there ARE no other possibilities, there IS no confusion, no one admitted to the White House can be on both lists or on NEITHER list.  Protocol has done its job correctly.

So must we be as accurate when we define a term.

Let’s return to our term ‘meal’.  If we look at the other 3 differentia, I think we can confidently define a meal as:

A food prepared for human consumption that is composed of two or more edible/potable items previously packaged and/or presently seasoned, cooked, cut or arranged.

Food genus

Whew !  So what’s the point of all that?   Well, there’s no sense in engaging in a discussion with Susie UNTIL we reach agreement WITH her on what constitutes a meal.  Once we all accept the definition of terms, then we can turn to the propositions and evaluate whether they are true or not and then examine the deduction that Susie undergoes to arrive at her conclusion.

Your ongoing assignment is to pick a term and draw it out, placing it in its larger family or genus.