Tag Archives: Premises

Logical Gal and why your major premise matters

20 Jan

Premise 1 – All exercise benefits the body

Premise 2 – Stretching is an exercise

Conclusion – Therefore, stretching benefits the body

The major premise is the first one listed above, in this example:  All exercise benefits the body

The way deductive logic works is this: if the major and minor premises are TRUE and if the syllogism conforms to rules for correct formation (validity), then the conclusion is both predictable and true. Without going into any further discussion about validity, I want to focus on WHY one’s major premise, in general, can have a weighty effect on one’s conclusions.

Consider a married couple who trust each other.

Let’s imagine a situation where it’s reported to the husband (Bob) that his wife has been seen having some tête-à-tête discussions with a man.  The implication is that maybe the wife (Sue) is having an affair.

Depending on Bob’s major premise about his wife and their marriage, his conclusions will be different.

Possibility # 1:

Overarching presupposition or major premise:

Premise 1:  (overarching major assumption) My wife is faithful to her word and her commitments and loves me completely

Premise 2: (the circumstances) – But she has been seen with another man

Conclusion: since I know that she is a faithful gal and loves me, there must be a good explanation for who that other man is.

Here’s the other major premise and subsequent conclusion

Premise 1: My wife might not be totally committed to me or to our marriage

Premise 2: She’s been spotted talking with another guy

Conclusion: She probably is cheating on me

Do you see how what we do with new information depends on the contexts we hold?  Same circumstance in both cases – the wife is seen meeting with another man.  The conclusions vary due to the original major premise or pre-supposition.  Sometimes we are not even aware ourselves of the assumptions we carry with us.  They are implicit, subconscious.  But they powerfully affect our lives!

Just for fun, what could be possible scenarios that would explain Sue’s conversations with a strange man? Maybe she was talking….

  • with a craftsman to plan a special birthday gift for her husband
  • with a potential care-giver for her aging father
  • with their son’s new soccer coach about his skills

If we move into a more spiritual plane, how might our pre-suppositions about God affect our reactions and conclusions to disappointment, illness or acts of violence we encounter in life? Have you ever met someone who claims that God must not be good or all-powerful if He lets evil happen?

Their major premise probably goes something like this:

God is good and almighty if He answers my prayers according to my desires

Question: Have you ever drawn a conclusion about someone or something that turned out wrong? How did your assumption or major premise impact your conclusion?

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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!  

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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     

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