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Philosophy 103: Introduction to Logic
Strategies for Uniform Translation: Mechanizing Translation

Abstract: An inductive strategy for mechanizing translation is illustrated.

1. 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

2. 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:

1. Identify the conclusion and premisses.

2. Put the syllogism into standard order as best you can.

3. Supply the suppressed statements, if any.

4. Reduce the number of terms to three per syllogism.

5. Translate the statements to standard form.

6. Test for validity

3. 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."

1. 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."

2. 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.

3. Had Neill omitted the word "only" from his argument, the argument could have been logically acceptable

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