Form:
Any form of categorical syllogism with an affirmative conclusion and at least one negative premiss.
Example:
The indeterminist believes that no caused acts are free, that some human acts are uncaused, and hence, some human acts are free.
Source: A philosophy exam, University of Miami, 4/4/1975.
Counter-Example:
No cats are marsupials.
Some mammals are not cats.
Therefore, some mammals are marsupials.
Venn Diagram:
This diagram represents both the Example and Counter-Example, and shows that neither is valid, since the conclusion, "Some S is P", is not shown to be true, for the asterisk might be in the portion of S outside of P.
Syllogistic Rule Violated:
All validating forms of categorical syllogism which have one negative premiss also have a negative conclusion.
Source:
Irving Copi & Carl Cohen, Introduction to Logic (10th Edition), (Prentice Hall, 1998), pp. 277-8.
Analysis of the Example: The indeterminist's argument is given as follows:
No caused acts are free.
Some human acts are not caused.
Therefore, some human acts are free.
This is a categorical syllogism, and both premisses are negative, specifically, the first premiss is an E-type categorical proposition and the second is an O-type. In contrast, the conclusion is affirmative, specifically, an I-type proposition. Thus, the argument commits the fallacy of Affirmative Conclusion from a Negative Premiss.
Acknowledgment: The example is taken from: Howard Pospesel, Introduction to Logic: Predicate Logic (1976), p. 178.
