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 Philosophy 103: Introduction to Logic
Reducing the Number of Terms
Abstract: Translation techniques, including
immediate inferences, are discussed and used for syllogistic inference.
- Arguments in ordinary language need to be translated into
standard-form categorical syllogisms before they can be tested.
Standard-form translations often require a number of special
techniques.
- First, the argument must be set up in standard form.
- The first sub-step is to find the conclusion.
- Use the techniques outlined in the tutorial notes on
diagramming arguments. The
conclusion can occur anywhere in a passage, although most
often it is the last or first sentence. The conclusion is
often the "topic" sentence of the paragraph.
- If you can not easily determine the conclusion from
the use of common premiss and conclusion
indicator words, then
the conclusion can be found to answer the question you ask
of the passage: "What's the point"? or "What are you (i.e.,
the author of the passage) trying to prove?"
- The second sub-step is to reduce the classes to three in number, and place
the major premiss first and the minor premiss second so that
the argument is transformed into standard order. (Most ordinary
language syllogisms do not have all of the same terms of the syllogism expressed
in exactly the same words.)
- Finally, before testing, each proposition in the argument is translated in
standard-form and order.
- Second, the argument is tested for validity by means of Venn
Diagrams and the Syllogistic Fallacies.
- When the terms of a syllogism do not match exactly, resist the tendency
to proclaim the fallacy of four terms. It may well be that by translating to
a synonym or suitable paraphrase, the syllogism can be transformed into a valid
argument. Let us consider two ways the reduction of terms can be accomplished..
- If the same term is not expressed in exactly the same words, then we
translate one of them to match the other so that only three classes in toto
are used.
- When complementary classes are present in the original argument, often
we can reduce the number of terms by using obversion or, less often, contraposition.
- Consider the following example illustrating the use of both techniques:
- "Not all Americans are religious people, but some are invariable fond of
the out doors. It is not surprising, therefore, only some nonreligious people
are nature lovers."
- To analyze this syllogism, we can begin by identifying the conclusion,
which, in turn, enables us to identify the major and minor premisses. The
stepwise process is subject to some common
procedures.
Major Premiss: Some Americans are religious people and some
Americans are not religious people.
Minor Premiss: Some Americans are people invariably fond of
outdoors.
Conclusion: Some nature lovers are nonreligious people. (The result
from the given exclusive proposition).
- Since the major premiss is a compound statement, a syllogism corresponding
to each premiss is constructed. If either syllogism proves to be valid, the
original argument is said to be valid.
- The first argument is ...
Some Americans are religious people.
Some Americans are people invariably fond of outdoors.
_______________________________________
Some nature lovers are nonreligious people.
The classes "nature lovers" and "people invariably fond of outdoors"
can be considered paraphrases, so we can collapse the minor term to
one or the other.
We can match our major terms by obverting the conclusion to yield the
following:
Some AmericansU are religious peopleU.
Some AmericansU are nature lovers.
_______________________________________
Some nature lovers are not religious peopleD.
Hence, this argument is shown to be invalid by illicit major as
well as fallacy of the undistributed middle.
- We now can try the second argument...
Some Americans are not religious people.
Some Americans are people invariably fond of outdoors.
________________________________________
Some nature lovers are nonreligious people.
Once again, the classes "nature lovers" and "people invariably fond of outdoors"
can be considered paraphrases, so we can collapse the minor term to
nature lovers."
We can match our major terms by obverting the conclusion to yield the
following:
Some AmericansU are not religious people.
Some AmericansU are nature lovers.
__________________________________________
Some nature lovers are not religious people.
Hence, this argument is shown to be invalid as well by the fallacy
of the undistributed middle term.
- Since neither syllogism is valid, the original argument is invalid.
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