How to Think #11: Bocardo

The 11^th valid syllogism to study is called Bocardo. In symbols Bocardo looks like this:
Some M's are not P's
All M's are S's
Therefore, some S's are not P's

In words a Bocardo argument could come out like this:

Some people who act on their grievances against the government are not heroes
All people who act on their grievances against the government are protesters
Therefore, some protesters are not heroes.

Is that second line true? How do we define "protester?" That could be a weak point in this syllogism.

Here is another example:

Some people who break very minor laws are not deserving of jail time
All people who break even very minor laws are criminals
Therefore, some some criminals are not deserving of jail time.

Notice I changed the wording of the M term very slightly between lines 1 and 2. If I changed the meaning of the M terms in those two lines I have damaged this syllogism. I think the meaning is the same and the syllogism is good.

Notice that this syllogism is essentially making a distinction between different kinds of criminals – those who deserve jail and those who don't. A lot of thinking is just doing this – making distinctions. One of the clearest warning signs of a poor thinker is the inability to make distinctions. For poor thinkers everything gets a label and everything with the same label is the same. If you meet someone who thinks every Democrat and every Republican, every rich person and every poor person, every illegal alien and every terrorist, every person on welfare and every Syrian refugee is the same as everyone else in their group and deserves the same treatment – you're probably dealing with a poor thinker.

One caution, sometimes we use expressions like "All politicians seek power for themselves" as an emphatic way of saying "MOST politicians seek power for themselves." If they mean "most" ask them to say "most." If they mean all, you might be dealing with a poor thinker so start looking for counter-examples to disprove their statement.

Only use "all," as we do in syllogisms, when the subject is carefully limited and defined so that "all" is the right word to use and no counter-examples will shoot down the argument we are trying to make.

Copyright © 2016 by Joseph Wayne Gadway

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How to Think #10: Baroco

The 10^th valid syllogism is called Baroco and in symbols it looks like this:

1. All P's are M's

2. Some S's are not M's

3. Therefore, some S's are not P's

In words a Baroco argument might come out like this:

1. All philosophers are intelligent

2. Some philosophy professors are not intelligent

3. Therefore, some philosophy professors are not philosophers

Any valid syllogism with true premises and correctly defined terms has a true conclusion and is important for that very reason. My favorite syllogisms, though, have a little sting in the tail. They put ideas together in a surprising way, in a way we might not have noticed without the syllogism's help.

All good people are honest

Some police officers are not honest

Therefore, some police officers are not good people

All immoral acts are unnecessary

Some violent acts are not unnecessary

Therefore, some violent acts are not immoral acts

On this last one we could have very long debates about what "unnecessary" means. :-)

Copyright © 2016 by Joseph Wayne Gadway

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How to Think #9: Dimatis

Our ninth valid syllogism is named Dimatis and looks like this in symbols:
1. Some P's are M's
2. All M's are S's
3. Therefore, some S's are P's

You might notice this is identical to Disamis except that the terms in the first premise – the major premise – are reversed.

After we finish an introductory look at each of the valid syllogisms we'll talk about some important logical theory and then we'll go through the syllogisms again grouping them into "families" and also identifying the specific types of questions or truth each syllogism is especially suited to answer or illuminate.

In words a Dimatis syllogism could look like this:

1. Some buildings are works of art
2. All works of art should be preserved
3. Therefore, some of the things that should be preserved are buildings

Here is how – believe it or not - a Dimatis might pop up in casual conversation:

The person you are with says "I never waste my time with popular novels."

So you say, [Line 1] "Surely you must agree that SOME popular novels have deep philosophical insights."
They say, with a superior chuckle, "Well! There are so many of them, propagating like weeds! I suppose SOME of them must have deep philosophical insights."
So you say, [Line 2] "I suppose you would agree that anything containing deep philosophical insights is worth some of your time?"
They say, a little hesitantly, "Well... I suppose... perhaps... ok."
And then you conclude - with a casual air - as if it is the most obvious thing in the world, "It would seem then, that IF some popular novels have deep philosophical insights, and IF anything containing deep philosophical insights is worth some of your time, THEN [Conclusion] some of the things that are worth some of your time are popular novels."

And there they are, poor soul - entangled in the tentacles of a Dimatis syllogism, without ever having known that such a thing existed.

Copyright © 2016 by Joseph Wayne Gadway

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How to Think #8: Disamis

Now for our eighth valid syllogism. This one is called Disamis and in symbols it looks like this:

1. Some M's are P's

2. All M's are S's

3. Therefore, some S's are P's

If this one looks familiar there is a very good reason. It is exactly the same as Datisi except we have changed the first word of the first line from "All" to "Some" and the first word of the second line from "Some" to "All." The conclusion remains the same.

In words Disamis might come out like this:

1. Some police officers are criminals

2. All police officers get special treatment from prosecutors

3. Therefore, some people who get special treatment from prosecutors are criminals

Remember, syllogisms are intended to be true without doubt - if they are properly set up. Properly set up means: you use a valid syllogism, the premises are true, and the terms used in the syllogism have the same definition throughout.

So if you are making a syllogistic argument yourself make sure you set it up right. If your opponent makes a syllogistic argument and you disagree with the conclusion here is your line of attack: 1) check to see if the syllogism used is one of the valid forms, 2) check to see if the premises are true, 3) verify that the meanings of the terms used do not change from one line to the next.

If you find a mistake you may be able to refute your opponent's argument. If you can't find a mistake maybe you have found a new truth and will have to change your beliefs to accommodate it.

Copyright © 2016 by Joseph Wayne Gadway

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How to Think #7: Datisi

Here is our seventh valid syllogism which is named Datisi. In symbols it looks like this:
1. All M's are P's
2. Some M's are S's
3. Therefore, Some S's are P's

If this looks familiar there is a good reason for that. Datisi is exactly the same as Darii except the terms in the second premise are reversed.

Using words to construct a Datisi syllogism we might come up with this:

1. All medical doctors are well-educated
2. Some medical doctors are incompetent
3. Therefore, Some incompetent people are well-educated

Or this:

1. All medical treatments are beneficial
2. Some medical treatments are painful
3. Therefore, Some painful things are beneficial

For this last syllogism we might argue that the first premise is not as true as we would like it to be and I would certainly argue that the second premise – even though, in my experience, it seems to be true now - means we need to work harder to develop better, and less painful, treatments.

Copyright © 2016 by Joseph Wayne Gadway

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How to Think #6: Darii

For our sixth valid syllogism we look at Darii. In symbols Darii looks like this:
1. All M's are P's
2. Some S's are M's
3. Some S's are P's

If we substitute words for symbols we could come up with something like this:

1. All people who are cruel to children are evil
2. Some teachers are cruel to children
3. Therefore, some teachers are evil

Good syllogisms might lead to surprising results that make us stop and think about what we really do and do not believe. How about this example of Darii:

1. All intelligent people are worth listening to
2. Some terrorists are intelligent people
3. Therefore, some terrorists are worth listening to


Copyright © 2016 by Joseph Wayne Gadway

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