Tag Archives: Valid

Gotta stay positive

28 Aug

All Chocolate is satisfying

Ghirardelli is chocolate

Tf, Ghirardelli is not satisfying   

What???  That doesn’t make sense!

You’re right.  Our mind easily balks because Premise 1 and Premise 2 are both affirmative propositions, they are A statements.  And the senseless conclusion is a negative proposition, an E statement (No Ghirardelli is satisfying).

Below is the chart that shows the 4 kinds of propositions and their Quality (Affirmative or Negative)

Affirmative  Propositions                      Negative Propositions

in this column                                         in this column

A – All dogs are cuddly E – No dogs are cuddly
I – Some dogs are cuddly O – Some dogs are not cuddly

So, back to chocolate and the question of validity – We are continuing with our extended lesson of

  • “How to examine a syllogism and see if it’s valid”

There are 7 rules in our Validity Checklist that we must run down to determine if a syllogism is valid , that is, in the correct form.  Last time, we showed that NO conclusion whatsoever can be drawn from 2 negative propositions.  Today, we see from Rule # 6 that

  • if premise 1 & 2 are affirmative, then the conclusion MUST be affirmative as well.

So what happens if someone has asserted a negative claim about health care such as:

  • No costly plans are possible

and when you ask the person WHY??? (Whoever makes an assertion is required to back it up with reasons) he/she says:

Premise 1 – All government plans are possible

Premise 2 – All costly plans are government plans

They’ve JUST articulated two affirmative reasons for their NEGATIVE conclusion of “ No costly plans are possible”

Before you jump in (or down your conversation partner’s throat) and start giving YOUR reasons why you disagree, you have every right to encourage this person to explain what she has either

  • left out on purpose
  • left out because she is not THINKING

Remember, there is absolutely NO point in arguing about an invalid argument.  And a negative conclusion drawn from 2 affirmative premises is one of the 7 ways an argument can be deemed invalid.

An argument (syllogism) must win the ‘Good Logician’s Stamp of Validity ‘ to be considered ready to meet the next criterion – are the premises TRUE.

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!

Let’s get tough! Analyzing those arguments

12 Aug

Let’s imagine you’ve heard an argument that just doesn’t sound right,

but you can’t put your finger on the reason.  The major and minor premise are even

true statements!  So what could be wrong?

Formal Logic rules to the rescue!  Applying a few simple tests to an argument can help you determine if it is indeed ‘valid’, that is in the correct form.  (remember that formal logic doesn’t deal with the truth of propositions, but the structure of an argument)

Today we’re going to look at the first 2 of 7 rules that are easy to use in analyzing the structure of an argument.

Rule # 1 – Three and only 3 terms

       Some boys are strong

       My brother is a baseball player

       Therefore, my brother is strong

Let’s count the terms.  Remember that a term is the number of words necessary to describe a concept. Terms must contain at least one word and can have several (mint chocolate chip ice cream is one term containing 5 words).   

When we identify and label terms, we start at the bottom of the syllogism and label the terms in the conclusion

Our conclusion above is:     Tf, my brother (minor term) is strong (major term)

Next, we label the same terms elsewhere in the syllogism.  The unlabeled term will then be the middle term


As we look for that middle term, we see our problem, which term do we label as the middle term?  We have two remaining terms and they are different!

      Some boys ( ? term)  are strong (major term)

      My brother (minor term) is a baseball player ( ? term)

      Tf, my brother (minor term) is strong (major term)

You can see our problem: we have 2 terms, both different (boys, baseball player) so we don’t know WHICH one will be the middle term (the 3rd official term after we have identified the minor and major terms).

So we can say with assurance, this syllogism is NOT valid because it has 4 terms.

*

Rule # 2 – the middle term must not be in the conclusion

Again, we start to label ‘bottom up’. (this takes a while to become automatic for we are conditioned to start at the top and label down )

      Some baseball players are strong

      My brother is strong

      Tf, my brother is strong and a baseball player

We barely get started  labeling the conclusion and we see that we have a problem.  Not only are there 3 terms in that one proposition (brother, strong, baseball player), but we have a term, ‘strong’, that shows up 3 times.  That is the tip-off that our middle term strong’ is in the conclusion.  The entire syllogism is convoluted.  So we shout out: “INVALID!!”

Next time, when we look at Rules 3 & 4, we will measure how far an attribute or term extends.  We will be asking questions like,

  • Are we talking about the category or set of ALL baseball players?
  • Are we talking about the category or set of ALL that which is strong?

If we say ‘yes’, then we say that a term is ‘distributed’ – that the quality in question applies to ALL, or that we are addressing ALL the members of a set.

In the meantime, watch your words and how others use words.  We must strive to be precise with our language if we intend to communicate clearly and with as few words as possible.

Excessive and unclear verbiage is wearying!  

Using the either/or to argue to a conclusion

5 Aug

“Either you are pro-choice or you are anti-women” 

We ran into this statement as an example of how we need to frame an attribute/predicate as either A or non-A to determine more easily if a pair of statements were truly contradictory.

Framing a contradiction into an either/or hypothetical proposition is one way to argue. We call this a Disjunctive Proposition.

Today we are FIRST going to form a valid or correct argument and then we’ll look at the truth of the major proposition.

Consider the ‘formula’ where P and Q are different statements, called ‘disjuncts’.  On the left is the model syllogism; in the middle and on the right are two samples.

Either P or Q                   Either blue or red            Either she had a boy or a girl

Not  P                               Not blue                             She didn’t have a boy

Therefore, Q                   Tf, red                                 Tf, she had a girl

These arguments work; that is they are valid BECAUSE the major proposition that contains the disjunctive statement tells us that one of the 2 disjuncts is true. (we have to accept this as a given;  we’re NOT going to argue about the truth of that major premise YET.)   So if one disjunct (P or Q) is NOT true, then the other HAS to be true.

What happens, though, if in the 2nd premise, I AFFIRM one of the disjuncts? Can this kind of syllogism work the other way?  It would look like this:

           Either Susie travels to the UK or to France

          Susie travels to France (I’m AFFIRMING one of the 2 disjuncts)

          TF, she does not travel to the UK

No….this set up is INVALID for I have actually assumed MORE than the information given.  It could very well be that her journey takes her to BOTH France and the UK.  All we know from the major premise is that she AT LEAST travels to one of the 2 places.  It does NOT claim that if Susie travels to one, she does NOT then travel to the other.

Certainty exists ONLY if the minor premise (the proposition that denies or affirms one of the disjuncts) denies one of the disjuncts since we have as a given that ONE has to be so.

Either I had a salad for lunch or some soup.

I did not have soup

Tf, I had salad

Back to our original Disjunctive propositions:  Either you are pro-choice or you are anti-women.  Once we have determined that the syllogism is set up correctly, that it is valid, THEN we look at the truth of the major premise.

If you remember what we looked at last Friday, we talked about true dilemmas and the Fallacy of the False Dilemma.  So, is our disjunctive proposition a False Dilemma?

If you are willing, comment with your thoughts about how you would determine the truth or falsity of that proposition.  A lot is riding on your answer!

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.

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