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 Philosophy
103: Introduction to Logic
Strategies for Uniform Translation: Mechanizing Translation
Abstract: An inductive strategy for
mechanizing translation is illustrated.
- We have at this time a kind of "took kit" to work on syllogisms.
Our tools include:
obversion, conversion, and contraposition
Venn diagrams
logical analogies
rules and fallacies
various techniques for reducing the number of terms
translation strategies
- The following inductive technique can be used for mechanizing translation
by isolating the steps for testing the validity of a syllogism. The steps can be
itemized as follows:
- Identify the conclusion and premisses.
- Put the syllogism into standard order as best you can.
- Supply the suppressed statements, if any.
- Reduce the number of terms to three per syllogism.
- Translate the statements to standard form.
- Test for validity
- Let us conclude by evaluating a complex example from A.S. Neill's
Summerhill (New York: Hart, 1960) 94.
"If Summerhill teachers had urged, "Come on lads, get on the field!" sports
in Summerhill would have become a perverted thing because only under freedom to
play or not to play can one develop true sportsmanship."
- First, let's do steps 1 and 2
Major Premiss: All instances where true sportsmanship develops are
times where one has the freedom to play or not play. (Note the reversal of
terms due to the nature of the original exclusive proposition.)
Minor Premiss: . . . . . . . . . . . . . . . . . . .
. . . . . . . . . .
Conclusion: No occasions at Summerhill are instances where sports becomes
a perverted thing.
Once we notice that "instances where true sportsmanship develops" in
context is the
complementary class of "instances where sports becomes a perverted thing," then
we can match our classes by obverting the conclusion to obtain "All
playing times at Summerhill are instances where true sportsmanship
develops."
Next, we can supply the missing minor premiss with the classes "playing times at
Summmerhill" and "times where one has the freedom to play or not play."
- The resultant argument now becomes...
Major Premiss: All instances where true sportsmanship is developed are
times where one has the freedom to play or not play.
Minor Premiss: . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . .
Conclusion All playing times at Summerhill are instances where true
sportsmanship is developed.
The minor premiss contains the minor term "playing times at Summerhill' and the middle
term "times where one has the freedom to play or not play." For validity, the
middle term must be distributed (otherwise the fallacy of the undistributed middle
term would occur), and the statement must be affirmative (otherwise the fallacy of
drawing an affirmative conclusion from a negative premiss would occur).
Hence the minor premiss would have to be...
"All times where one has the freedom to play or not play are playing times at Summerhill,"
but this statement is false.
The true statement "All playing times at Summerhill are
times where one has the freedom to play or not play" makes the syllogism invalid by the
fallacy of the undistributed middle term. Hence, Neill's argument is not sound.
- Had Neill omitted the word "only" from his argument, the argument could have
been logically acceptable
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