Relationships

Rules for valid categorical syllogisms

What we are going to reason through now is how to discover good thinking and bad thinking (otherwise known as fallacious thinking).

Before we do, we need to introduce "The Choir." These are birds that have flown in, to accompany the page with their with tweeting and song.

The birds have various characteristics, and, as we move along, we'll get to know them a lot better. To know them is to love them.

 RULE 1 A syllogism can only have three terms, each used exactly two times. Breaking this rule is the "Fallacy of four terms."
Example:

Baby pink flamingo sings soprano.
The big pink flamingo sings bass.
So, baby duck sings soprano.

If the second premise had mentioned something about a relation between babies singing soprano, there might be movement from premise 1 to premise 3 through premise 2. But, as we have it here, we cannot make any valid conclusion. Maybe baby ducks have wider throats and sing alto. Flamingos are the topic in the first two premises, but the conclusion deals with ducks - wholly unrelated to the Flamingo class.
Another Example

The chubby little blue-headed Blue Jay sings tenor.
The parrot has blue on top of his head.
Therefore, the parrot sings tenor.

At first it seems like the above syllogisms have only three terms used two times. But let's diagram the logic.

In the case above, a fourth term is a subgroup of one of the three terms. There is a lack of inference even though the premises may be totally true. The example below shows that you can go from the truth of the first to the conclusion without the second.

Another Example

The birds in the choir are beautiful to hear and to behold.
The choir is singing Handel's Messiah.
The mallard duck has a beautiful voice and handsome in appearance.

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