Affirmative Conclusion from a Negative Premiss
Taxonomy: Logical Fallacy > Formal Fallacy > Syllogistic Fallacy > Affirmative Conclusion from a Negative Premiss
Any form of categorical syllogism with an affirmative conclusion and at least one negative premiss.
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)1
No cats are marsupials.
Some mammals are not cats.
Therefore, some mammals are marsupials.
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. Note that this diagram does not show every instance of the fallacy to be invalid, since other instances may have different forms, and a single Venn diagram can represent only one form.
Syllogistic Rule Violated:
All validating forms of categorical syllogism which have at least one negative premiss also have a negative conclusion.
Inferring an affirmative conclusion in a syllogistic argument that has at least one negative premiss is a formal fallacy in the logic of categorical syllogisms―for a short introduction to categorical syllogisms, see the entry for syllogistic fallacy. This is because all validating forms of categorical syllogism that have at least one negative premiss also have a negative conclusion, which can be shown by inspection since there are only 256 different forms of categorical syllogism. However, it's intuitive that a negation in the premisses should lead a validly drawn conclusion to also be negative.
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. As if that weren't enough, it also commits the fallacy of Exclusive Premisses, since both premisses are negative. This is a doubly bad argument!
- Howard Pospesel, Introduction to Logic: Predicate Logic (1976), p. 178
- See, also: Irving M. Copi & Carl Cohen, Introduction to Logic (Tenth Edition, 1998), p. 277-8