Tag Archives: Distribution of terms

Do you take vitamins? Creating an argument in support

4 Sep

Food supplements – to take or not to take, voici la question!

Last time we analyzed an argument by applying the 7th rule for checking a syllogism’s validity.  We showed that if one of the 2 premises is negative, then the conclusion MUST be negative as well.

I asked you to think of how you would argue FOR the position that taking vitamins makes a qualitative positive difference in one’s health.  If we are to formulate an argument in its correct form, we need to comply with ALL 7 rules for validity.

Here they are again in a summary list:

Every syllogism to be valid (that is correctly formed), must abide by all seven rules:

  1. Has 3 and only 3 terms
  2. No middle term in the conclusion
  3. If a term is ‘distributed’ in the conclusion, it must be ‘distributed’ in one of the premises
  4. The middle term must be distributed once.
  5. No conclusion can be drawn from 2 negative premises
  6. If the 2 premises are affirmative, the conclusion MUST be affirmative as well
  7. If one of the 2 premises is negative, then the conclusion MUST be negative as well.

On to constructing OUR argument.  Remember, that when we formulate a syllogism, we start with our conclusion and work backwards.

Here is our hypothetical conclusion in ordinary language:

  • Therefore, taking supplements improves one’s health

Before we go any further, we have to add a quantifier and rewrite the proposition so that a copula appears.  First we reflect  – Do we  intend to defend the assertion that ALL taking of supplements improves one’s health or just SOME taking of supplements?

To be on the safe side, it is more truthful and easier to defend an I proposition, or SOME taking of ‘vits’.  After all, some vitamins might be so poorly made NOT to be efficacious.

Next , in order to uncover the copula, we need to ‘tweak’  our second term resulting in:

Therefore, some taking of supplements is a habit that improves one’s health

Now 2 of the allowed 3 terms pop up clearly.

We can label them and determine the distribution based on our ‘DUDU & UUDDs’ chart.  Remember that a term IN FRONT of the copula is in the subject position and a term which FOLLOWS the copula is in the predicate position.  We determine the TYPE of proposition by the quantifier (All, Some, No, Some…not)

Type of Proposition Subject position Predicate position
A (All) D U
I (Some) U U
E (No) D D
O (Some….not) U D

Another reason for starting to create or analyze a syllogism ‘bottom up’, that is to say WITH THE CONCLUSION, is that the minor term (represented by S FOR THE ENTIRE SYLLOGISM) is always the term that precedes the copula in the conclusion and the major term (represented by P FOR THE ENTIRE SYLLOGISM)  always follows the copula in the conclusion.

Here is our conclusion properly labeled:

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

So as we end this discussion, we have the following information about our syllogism:

S term = taking of supplements

P term = a habit that improves one’s health

Next time, we will come up with our 3rd term (see rule 1) which is the M or middle term.

Until next time, keep thinking!

Who gives a darn about distribution?

21 Aug

   Distribution of terms matters….

even if YOU don’t care about distribution, the logic police do!

If we want to be logical and hold others gently to the same standard, we have to follow some rules.  Today we are talking about Rule # 4 – the one smack-dab in the middle of all 7 rules for writing a syllogism in its correct form.

Here is a synopsis of the 3 previous rules

# 1 – Three and only 3 terms are allowed in a syllogism

# 2 – The middle term can’t be in the conclusion

# 3 – If a term is distributed (applies to all in the set) in the conclusion, then it must be distributed in the premises

Today we look at # 4 – The middle term must be distributed at least once.  Since this term connects both the major and the minor terms, then it has to be as ‘ broad ‘ as possible to apply to the major and the minor terms.  We follow the technical drill of labeling the terms in the syllogism. We visually check to see if the middle term is distributed at least once. If not……then we shout FUM!!! (aka – Fallacy of undistributed middle)

                   Some chocolate is dark

                   All yummy foods are dark

                   Tf, some yummy things are chocolate

Types of Propositions Subject Terms Predicate Terms
     
A D U
I U U
E D D
O U D

When we label terms, we start with the conclusion  ‘at the bottom’ and label up.  (the term IN FRONT OF the copula is the subject or minor term…..the term AFTER the copula is the predicate or major term)

Tf,  (an I statement) some yummy things (Su) are chocolate (Pu)

We spot  ‘ yummy things’, then we notice that it is in the ‘ subject position of the proposition’ and write S.  Looking at the chart, we see that for an I statement the term in the subject position is undistributed, hence we add a ‘ u’.  The term ‘ chocolate’ is located in the predicate position of this I proposition; we write P and seeing that in an I statement, a predicate term is ALSO undistributed, we add a ‘ u’ next to the P.

Having identified the Major and Minor terms (also called the Predicate & Subject terms), the ‘ leftover term’  in the syllogism defaults to being the Middle Term (labeled M).  We can now finish labeling Premises 1 & 2.

P1:  (an I statement) Some chocolate (Pu) is dark (M u)

P2: (an A statement) All yummy foods (Sd) are dark(Mu)

So the whole syllogism looks like this:

        Some chocolate (Pu) is dark (Mu)

        All yummy foods  (Sd) are dark(Mu)

        Tf, Some yummy things (Su) are chocolate (Pu)

Is the middle term distributed at least once?  NO!!!

Therefore, we can say to the person making the argument:

“ We can’t even DISCUSS whether your case is sound until your syllogism is in the correct form!  And your middle term of ‘ Dark’ is not distributed even once!  Your conclusion assumes too much, given the data in premises 1 and 2.  You have committed…..FUM – the Fallacy of the Undistributed Middle Term.

  Off to Logic Prison with you!         

How is this useful?  I find that knowing the 7 rules of validity is a quick way to assess a syllogism when I sense that something isn’t quite right. The logic error emerges quickly when I run the argument through this checklist.

Keep an ear open for a conclusion that seems far-reaching and let me know if you’re stumped.  We’ll practice together.