How to Think #4: CELARENT

As I said earlier there are 256 syllogisms and 24 of them are valid. Nine of the valid ones however are controversial. How can a valid syllogism be controversial? We'll get to that later.

For now, here is the third non-controversial valid syllogism which is named Celarent.

In symbols Celarent looks like this:...

1. No M's are P's
2. All S's are M's
3. Therefore: No S's are P's

Using words instead of symbols we could come up with something like this:

1. No college professors are rich
2. All the attendees at a scientific conference are college professors
3. Therefore: no attendees at a scientific conference are rich

Compare Celarent to Barbara and you will see they are close relatives. Kind of opposites in a way.

One more example of Celarent:

1. No government employes are trustworthy
2. Police officers are government employees
3. Therefore: No police officers are trustworthy

My examples are intended to show valid syllogisms. I do not claim that my premises are always true!

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Copyright © 2016 by Joseph Wayne Gadway

How to Think #3: CAMESTRES

By the most common method of counting them there are 256 deductive syllogisms. These were all identified and discussed by Aristotle more than 2300 years ago. Only 24 of these syllogisms are valid! If you use any of the other 232... you are making a mistake!

The second valid syllogism we will cover is called Camestres. In symbols it looks like this:
1. All P's are M's.
2. No S's are M's.
3. Therefore, No S's are P's.

If we replace symbols with words we could come up with something like:
1. All people with malaria have a fever
2. No people in my traveling party have a fever
3. Therefore, no people in my traveling party have malaria.

Camestres is a valid syllogism so if the premises are true the conclusion MUST be true. The first premise above about malaria is a bit questionable but if it, and the second premise, are both true, than the conclusion MUST be true.

One more example of Camestres:
1. Good managers try to promote the careers of their subordinates.
2. Managers at Company X do not try to promote the careers of their subordinates.
3. Therefore, managers at Company X are not good managers.

Notice in this last example I modified the wording a little bit but I think you can see it still matches the pattern of Camestres.

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Copyright © 2016 by Joseph Wayne Gadway

How to Think #2: BARBARA, Cont.

Let's cover a couple more points about syllogisms using Barbara before we move on to the next one.

First, here is another example of Barbara:

1. All politicians tell lies
2. All presidential candidates are politicians
3. Therefore, all presidential candidates tell lies.

Now look at this one:

1. All college professors are intelligent
2. Doctor Smith is a college professor
3. Therefore, Doctor Smith is intelligent.

This second example looks different from the first because the second line is about one person rather than "all" the members of a group. But that's OK. Whether the second line is about a group or an individual, the syllogism is still Barbara and still valid.

As we have already stressed, if the premises of a valid syllogism are true, then the conclusion MUST be true. But if the premises are false that does not prove the conclusion is false. It just means we don't know.

One more thing to watch out for. Sometimes people get confused when a conclusion is true and assume that the syllogism must prove the conclusion.

But consider this:

1. Everything Joe owns is a car
2. A Toyota Camry is one of the things Joe owns.
3. Therefore a Toyota Camry is a car.

Now we may believe that it is true that a Toyota Camry is a car but this syllogism does not prove it. The syllogism is an example of Barbara so we know it is valid. But the first premise is not true so the syllogism is not sound and does not prove its conclusion. We may know through some other means that a Toyota Camry is a car but this particular argument is a failure.

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Copyright © 2016 by Joseph Wayne Gadway

How to Think #1: BARBARA

Deductive arguments are one of the five major types of arguments. The other types of arguments are inductive, abductive, based on testimony, or based on authority. The three-line arguments called syllogisms are one of the major types of deduction. In this series of posts I will describe, and give examples of, the valid syllogisms.

I will also link to some great books you can read to learn more about how to think!

There is a valid syllogism called Barbara! It is called Barbara for theoretical reasons we will get to later. For now, this is how Barbara looks in symbols:

1. All M's are P's
2. All S's are M's
3. Therefore, All S's are P's.

This is a "valid" syllogism, meaning that, if the premises are true, then the conclusion MUST be true.

Replace the symbols with words and you could get something like this:

1. All mammals have four-chambered hearts
2. All squirrels are mammals
3. Therefore: All squirrels have four-chambered hearts.

These premises are true so this syllogism is both "valid" and "sound."

One more example of Barbara:

1. All Democrats are Liberals
2. All the people in Massachusetts are Democrats
3. Therefore, all the people in Massachusetts are Liberals.

Now this is Barbara so we know the syllogism is valid, but in this case both of the premises are false so the argument is not "sound." The conclusion might still be true, but it is not supported by the premises because they are NOT true.

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Copyright © 2016 by Joseph Wayne Gadway