Tag Archives: syllogisms

Assumptions surrounding logic

27 Jan

While listening to Al Mohler  (Link to his discussion here) explain the backstory to a recent Supreme Court decision affecting those on death row in Florida, I was struck once again about the importance of language.

supreme court

Words matter.

Obviously eight of the 9 justices in the photo assumed that as much. The wording of the 6th amendment to the US Constitution declares that a defendant is entitled to “….a public trial, by an impartial jury of the state….”.  The majority opinion of the Supreme Court argued that the words meant what they said.  The fact that Florida judges alone had the power to impose the death sentence (based on the recommendation of the jury) violated the sense of the language of the 6th amendment.

Al Mohler then drew the connection between how one reads the written text of the US Constitution and the Bible.  Either the words mean what they say or we open the gate to anyone’s interpretation.  And chaos ensues and words lose the power of meaning.

Language-based logic is the same.  Before we even examine and analyze a syllogism to determine whether it is sound, we have made an assumption:

Words matter!

Take the following sample syllogism:

Premise 1:All wood is a substance containing carbon

Premise 2: This stick is wood

Conclusion:  Therefore, this stick is a substance containing carbon

Logical Joe’s and Jane’s have to agree on what each term means.

  • Does ‘all’ unequivocally take in every member of the category of wood?
  • Does ‘wood’ represent the set of hard, fibrous materials that form the trunk of a shrub or tree*?
  • Is carbon only the chemical element represented by atomic number 6*?

*definitions based on Apple’s Mac dictionary

We ‘assume’ that words representing terms refer to a specific concept.  If that is not our starting point in logic, then we might as well abandon all reasoning.

But as my husband pointed out when we were discussing this necessary pre-supposition, another complication exists.  We can agree on the clear sense of a term YET once set in a proposition or even a clause, meaning grows complicated.

Take just a snippet from the Pledge of Allegiance:

“…with liberty and justice for all.”

Initially one can agree on individual concepts of liberty and justice in isolation. The term ‘all’ appears messier. Distinctions must be made, so we pose some clarifying questions:

  • does ‘all’ refer to all citizens or all those residing in the US?
  • and if all residing in the US are intended, do we need to differentiate between those legally residing and those who are not?
  • are we talking about all humans only?  Are the unborn included?  Are the mentally and physically dependent included?

Once we initially sort out terms, what happens next?  Other questions arise.  For instance, if we consider just one other term, the concept of ‘liberty’, what does the GUARANTEE of ‘liberty’ protect one against? How far does it extend and do I, who am included in the ‘all ‘, get to define liberty to suit my needs?

I’d love to say, “Let’s just go with the plain reading of the text!”  But I have to concede that a careful reading of any writing requires clear and focused thinking.  That’s why there will always be a need for diligent and thoughtful lawyers, judges, theologians and logical but ordinary men and women like us.

The challenge is great, but worthwhile.






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:


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!)

Logical gal takes on claim: “Truth is relative”

1 Nov

I teach a few precocious 8th graders who take pleasure in striking the contrary pose.  The other day a lively discussion erupted at the end of the period. What got us started was the conclusion in a simple French reader, “Il n’y a pas de familles parfaites”  – there are no perfect families.  One boy disagreed saying, ‘En fait’  /actually that there ARE perfect families!  I responded with incredulity, “Really?  for how long?”   He backed down and said that his family could be perfect for ……. half a day.  But when pressed to admit the enormity of 7 family members actually ‘being perfect’ with one another for that many hours, we slipped OVER into the bunny trail of TRUTH.

Since there were only 2-3 minutes left in class, I allowed us to converse en anglais in this French 1 class.

So, what was the connection between the concept of perfect and the concept of truth?  It all started when I asked the students how they defined ‘perfect’.  I think someone piped up about perfection being relative, like truth.  I then humorously asked, “So the Law of Gravity is relative?”

Class ended as the boys were affirming that “All truth is relative”.  Had we been able to pursue this chain of thinking, I would have led them to define truth.  Defining one’s terms is always the hinge on which statements or propositions rest.

As Bill Clinton might have expressed and Pilate thought, “It all depends on what truth means!

So if truth is defined as “that which corresponds to reality“, then relativity has NO bearing on the definition.  Truth doesn’t change according to the one who is looking at it.

For example: Terminating the life of a person or animal is the act of killing.

Whether that action is justified or not, is morally good or not is another question.  Good or bad, it is still killing due to how the term is defined.  It doesn’t matter that in some cultures people are exhorted to Love their Enemies where in other societies members are taught to Eat their Enemies.  Those are moral values which DO change according to how and in what/in whom they are grounded.

Back to truth. Truth either conforms to reality or it doesn’t.  The ‘discovered’  Law of Excluded Middle tells us as much. There is NO middle possibility.

Only pseudo-sophisticated modernists claim that Truth depends on the eye of the beholder.   And my 8th grade boys, as advanced as they are for their age, have yet to be  grounded in philosophy and critical thinking.   Nevertheless, I was encouraged to witness their grappling with important ideas.   Logical thinking can be found in all disciplines, even in French class!  It’s just part of ordinary life!

Vitamins DO make a difference – creating our first valid syllogism

9 Sep

So, have you taken your vitamins yet?  Are you convinced that some taking of supplements is a habit that improves one’s health?

Last time we set out our conclusion by identifying 2 of the 3 necessary terms.  And we narrowed down our quantifier to SOME vitamin taking, not ALL.

Today we need to finish fleshing out the syllogism by adding a 3rd term.

You will most likely think that our syllogism doesn’t communicate a strong and complete case in support of the conclusion.  You will be right!  This syllogism is just a 1st step.  The 2 premises that we write will simply show your thinking process, how you are arriving at that first conclusion.  An entire argument involves a series of syllogisms.  By focusing on just this ONE LITTLE step, we are staying ‘ honest’ in our reasoning.        

Think about Math Teachers whose litany rings in our memories, “You must show ALL your work to get full credit!”  

Here is our conclusion from last time, properly labeled:

I statement – Therefore, some taking of supplements (Su) is a habit that improves one’s health (Pu)

By the end of our session, we had established the following information about our syllogism:

  • S term of the syllogism (aka Minor Term)  = taking of supplements
  • P term of the syllogism (aka Major Term)  = a habit that improves one’s health

Today we have to come up with our 3rd term (Rule 1), which will be the M or middle term.  This term will LINK the other two terms (major & minor terms), enabling a conclusion.

After playing around with some terms to determine the IDEAL one, I think I found the one that can link the other ideas.  What we are talking about are those daily activities that make a difference in one’s health.   Thus I chose the following for a Middle Term:

Doctor-endorsed daily practices

Next I had to choose the affirmative quantifier.  Did I intend the term to be UNIVERSAL as in ALL or particular as in SOME?

For argument’ s sake, let’s suppose that I happen to think that ALL doctor-endorsed daily practices are habits that improve health (we’ll talk about TRUTH later)

Here is what our syllogism looks like:

All  doctor-endorsed daily practices (Md)  are habits that improve one’ s health (Pu)

Some taking of supplements(Su)  is a doctor-endorsed daily practice(Mu)

Tf, some taking of supplements (Su) is a habit that improves one’s health (Pu)


Let’s go through our checklist to see if the syllogism is at least valid.  Remember that we haven’t even addressed the truthfulness of each premise.

1. 3 and only 3 terms? YES
2. Does the Middle term illicitly show up in the conclusion? NO
3. If a term is distributed in the conclusion, is it Distributed at least one other place NA (both terms in the conclusion are Undistributed)
4. Middle term Distributed at least once? YES (in Premise # 1)
5. Are Premises 1 & 2 negative? NO
6. If Premises 1 & 2 are affirmative, is our conclusion also affirmative? YES
7. If either of the 2 premises negative, is the conclusion also negative? N/A

Therefore, we have written a VALID syllogism!  Yay!

Once you have a valid syllogism, THEN you can look at the truth/falsity of each premise.  But that’s another discussion!

The takeaway?   Those little quantifiers REALLY make a difference.  Be precise with your words.

Two negatives make NOTHING!

26 Aug

         No boys like me

                                        Some of my best friends don’t like me

                                        Tf, my life is awful

What’s wrong with this argument?

-besides being the lament of a ‘too-introspective’ teen girl

-besides consisting of more than 3 terms (violates Rule # 1 of the Valid Argument test)

Here’s what’s wrong – You can’t draw ANY conclusion WHATSOEVER from 2 negative premises.

That’s Rule # 5  for “Evaluating the validity of a syllogism” in a nutshell.

Rules 1 to 4 have focused on

  • the number of terms in a syllogism
  • the occurrences of each term (Major, Minor and Middle) in a proper syllogism
  • the ‘distribution’ of each term, that is –  the reach or how many ‘members in a set’ to which each term applies

With Rule # 5 (there are seven in total), we look now at what is called the QUALITY of  the premises in the syllogism.  Quality refers to whether a proposition is affirmative or negative.

Both common sense AND logic inform us that you can’t get ANYTHING positive out of a negative.  And if you can, then there is more ‘back’ argument that needs to be flushed out (unarticulated pre-suppositions or other propositions).

Imagine someone stepping outside of his office cubicle and shouting seemingly à propos of nothing…..

-the picnic is not going to happen!   

-there is no pizza in the freezer!

– therefore, I’m happy

We’d conclude that this guy was nutty!

So what do we do when we run across an argument in a letter to the editor that is drawing an affirming conclusion from a bunch of negative ‘facts’ – that is, when their premises are either E or O statements?     

(E – No pizza is in the freezer; 0 – Some picnics are not going to happen)

First of all, since we are equipped with logic as a tool, we know to ask for more information.  Their claim, constructed from 2 negative premises, can’t stand on its own.  There HAVE to be affirmative propositions (A  – All food is what makes me happy; I – Some meals are better than no meals).

Don’t be afraid to gently push back against an argument-maker by asking questions.  After all, the burden of proof is on him who makes the claim.

And by the way, this is an easy way out of an argument you might not want to tackle.  If you can point out gently that someone is basing their argument on negative premises, you don’t even HAVE to consider the conclusion – it’s irrational to begin with!