Tag Archives: Venn Diagrams

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

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.

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

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.

How to hold onto your money, using logic

3 Jul

Advertisers count on the fact that we don’t understand basic logic! 

They appeal to our desire to be like the ‘beautiful people’. And we fall for their offer to transform our ordinary lives into something more exotic, like the people we admire.

Take for instance the lucrative business of make-up.  What woman DOESN’T want to look better?  So we fall for emotional appeals to browse Sephora or use a product, convinced that if we do, we’ll look more like our favorite model/actress.

Here’s what these companies count on.  They make a statement like:

·         All models use La-di-dah Lipstick

What goes unstated explicitly (but they count on you to implicitly absorb it) is the false corollary:

·         All women who use La-di-dah Lipstick (just might end up being gals who…) are models

In symbolic form that is saying

·         All S is P……All P is S         where  S = Women who use LL   and             P = Models

But one CAN’T just interchange the subject and the predicate and have the converse be true.
Let’s suppose that Cindy wants to look like her favorite model who uses La-di-dah Lipstick.  She believes the advertising and emotionally responds with the belief, ” If I buy and use La-di-dah Lipstick, maybe I’ll be a model too!”

Unfortunately, the advertisers have NOT given Cindy enough information in their claim for her to know if this is true.

Here’s what the first proposition (claim)  and our dilemma look like:

All models use LLAnswering that question in the above diagram: “No, we do NOT know to which group Cindy belongs if she uses their product L.L.”

 You can easily see for yourself that the two propositions are not equivalent if you just switch the S and the P

  All women who use LL are modelsThis drawing shows that all women who use La-di-dah Lipstick are in fact models.  Remember, the diagrams are different and the marketing claims are different.  ( in fact – our advertisers will NOT state the latter, that All women who use their product will be models – they can’t guarantee that at all!)

But as I said above, marketing  managers want to by-pass your rational mind and get  right at your emotions in order to pry your fingers off of your hard-earned money and invest it in your pipe-dream, courtesy of their product!

Your homework for the week – watch for and see if you can spot the implicit lies bandied about in commercials, either on TV or in print.  Let us know of a particularly blatant one!