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