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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.

If all gals are pretty, then are all pretty people gals?

14 Aug

Being precise matters! “But Mom, ALL my friends get to do it….”

The question of how far a term applies is called the ‘distribution’ of a term.  Terms are either ‘distributed’ or ‘undistributed’.

And to answer the question – no – pretty is NOT JUST referring to gals, but to other members of the pretty set.

When we make a universal affirmative claim (an A statement) : All gals are pretty, we are talking about the subject term gals. And, YES, since we have the quantifier ‘all’ ,then gals IS distributed because…… we are talking about every single member of the set of gals.

What about the predicate term of pretty?   All gals are pretty

As you can see, it makes sense that there are other people/things that are pretty besides gals!  So pretty is undistributed in this A (all) statement.

If you scroll to the end of the blog you will see a chart that summarizes the nomenclature for both Subject and Predicate terms in each of the 4 propositions. Once I explain it, it’s much easier to just remember the pattern by its nickname.  Scatological references being the source of humor for 13 year old boys, my 1st crop of 8th graders called it the DUDUs and UUDDs chart.  And I have found that easy to remember and draw out myself.  

*

How about a particular affirmative claim, (the I statement)?  Are the S and P terms undistributed or distributed?

This one is easy – Some books are boring.

Since we are only talking about a partial group of books, then books is undistributed.  And just as obvious, there are other things besides books that are boring, so boring as the predicate term is equally undistributedSome books are boring

*

No guns are safe is our universal negative, (the E proposition).   According to our chart, the S term and the P terms are both distributed.  It’s easy to see why it if we draw it out.  No guns are safe

Are we talking about every single member of the gun category?  Yes, so guns is distributed.  Are we saying about the safe things category that all of them do not  (or none of them) apply to guns?  Yes – so safe is distributed.

*

Finally, let’s look at a particular negative (the O proposition): Some homework is not difficult.  Homework will be undistributed because  clearly we are not talking about every member of the homework class.  But what about difficult?  That is ‘more difficult’ to see in our mind’s eye, so let’s look at a drawing to understand why the predicate term difficult IS in fact distributed. Some HW is not difficult

We conclude that everything that belongs IN the set of difficult things has nothing to do with the ‘some HW’ that is shaded yellow.  You can see that we are making that predicate term distributed in this O proposition.

Next week we will use this concept of distributed/undistributed terms when we pick up with Rule # 3 for evaluating the validity of a syllogism.

Here’s our challenge – keep working on being precise with your language. In other words, “ Mean what you say and say what you mean!”

Here’s the infamous DUDUs and UUDDs chart: (warning – you have to remember to write the 1st vertical column of Quantifiers in the correct order:  A,I,E,O)

Subj Pred
A(all) D U
I (some) U U
E (no) D D
O (some…not) U D

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!