Last time we analyzed an argument by applying the 7^{th} 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:

- Has 3 and only 3 terms
- No middle term in the conclusion
- If a term is ‘distributed’ in the conclusion, it must be ‘distributed’ in one of the premises
- The middle term must be distributed once.
- No conclusion can be drawn from 2 negative premises
- If the 2 premises are affirmative, the conclusion MUST be affirmative as well
- 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 3^{rd} term (see rule 1) which is the M or middle term.

Until next time, keep thinking!

]]> **VERSUS …………. **

You, who pop a handful of carefully selected ‘food supplements’ SWEAR by the efficacy of these expensive pills. After all, how many sick days have YOU taken in the past five years?

But before you give her a piece of your mind, calm down and ask her to explain her claim. Remember that she who advances a proposition, a claim, a conclusion, an assertion MUST give her evidence, her reasons, her method of arriving at this thought. If you want some help, click on the link here for a resource by Greg Koukl. Great Book to Help who does what in an argument

After listening to your office mate, you realize that before you can even GET to thinking about the truth or falsity of her conclusion, you have to guide her in formulating her reasons. After some coaxing, here is what she has offered:

- Food provides enough vitamins and minerals to stay healthy
- No manufactured vitamins can provide the same quality of benefit found naturally in food.
- Therefore, taking vitamins is a waste of time and money

Your friend obviously needs some help in identifying her terms and organizing her argument into syllogisms that are built on 3 terms each.

But before you pull out your pencil and start sketching logic charts, we can just refer to Rule # 7 to show that her argument is invalid:

What is the quality of premise # 1 (‘food provides enough…’ )? It is** AFFIRMATIVE**

What is the quality of premise # 2 (‘no manufactured…’)? It is **NEGATIVE**

**Rule # 7 of the Seven Rules for Testing Validity** states that if one of the 2 premises is negative, then the conclusion MUST be negative. Your friend has NOT stated a negative conclusion but the AFFIRMATIVE statement that *‘Taking vitamins is a waste of time and money’*

Since the argument is invalid based on Rule # 7, you’re off the hook from giving your 2 cents worth. But spend some time helping her tease out her reasons and re-articulating them and then checking to see that is what she means. She’ll gain respect for you as a gentle friend and maybe SHE might see some holes in her reasoning.

Meanwhile play around with what YOU believe about vitamins and craft YOUR argument following the 7 rules.

Here they are in summary. Next time we’ll build an argument about vitamins that is VALID.

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

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

Keep thinking!

]]>**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.

** 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!

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