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Philosophy 103: Introduction to Logic
Syllogistic Fallacies: Affirmative Conclusions from a Negative Premiss

Abstract:  The Fallacy of the Affirmative Conclusion From a Negative Premiss is explained and illustrated.  

I. The following argument illustrates another one of our syllogistic fallacies.
"Some laborites are democrats, because All blue collar workers are laborites, and some blue collar workers are not democrats.
A. When we set up this argument in a standard form and order syllogism, we obtain ...
Some [blue-collar workers] are not [democrats].
All [blue-collar workers] are [laborites].
Some [laborites] are [democrats].
1. The Venn diagram shows this argument to be invalid. Diagram of an OAI-3 Syllogism
2. The mnemonic mechanism of the syllogism suggests why this argument is invalid. We can't make the affirmative link between S and P. Diagram of the Mechanism of Affirmative Conclusion From a Negative Premiss
B. Intuitively, most of us think that if a conclusion is negative, then one premiss must be negative as well, and if the conclusion is affirmative, neither premiss could be negative in a valid argument. This intuition is correct.
II. The second quality rule is if either of the premisses of a valid standard form syllogism is negative, then the conclusion must also be negative.
A. Reason: If an affirmative conclusion is entailed, then both premisses must be statements of class inclusion. Since class inclusion is only obtained by affirmative statements, if the conclusion has one class is partly or wholly contained in the other, then the premisses must assert that the middle class is contained by the minor class and contained in the major class.
B. The Fallacy of Drawing an Affirmative Conclusion from a Negative Premiss is the resultant fallacy, if the rule does not hold.
C. Note: the syllogism does not have to be in standard form for use to be able to spot this fallacy. All that we need to see is the mood. Test your understanding by trying the following problems.

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