Archive | Constructing a Syllogism RSS feed for this section

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.

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!