Denying a Conjunct
Alias: The Fallacy of the Disjunctive SyllogismType: Fallacy of Propositional Logic
| Forms | |
|---|---|
| Not both p and q.
Not p. Therefore, q. |
Not both p and q.
Not q. Therefore, p. |
| Similar Validating Forms (Conjunctive Argument) | |
| Not both p and q.
p. Therefore, not q. |
Not both p and q.
q. Therefore, not p. |
| Example | Counter-Example |
| It isn't both sunny and overcast.
It isn't sunny. Therefore, it's overcast. |
It isn't both raining and snowing.
It isn't raining. Therefore, it's snowing. |
Exposition:
Negating a conjunction—"not both", which is sometimes abbreviated as "nand"—means that at least one of the conjuncts is false, but it leaves open the possibility that both conjuncts are false. So, if we know that one of the conjuncts is true, we may validly infer that the other is false (by Conjunctive Argument). In contrast, if we know that one of the conjuncts is false, we cannot validly infer from that information alone that the other is true, since it may be false as well (Denying a Conjunct).
Exposure:
Presumably, it is the similarity between these two argument forms that is the psychological source of the fallacy. However, Denying a Conjunct is likely to seem more plausible when we have independent reasons for thinking that at least one of the two conjuncts is true. Suppose that we add to Denying a Conjunct the further disjunctive premiss:
Either p or q.
The resulting argument form is validating. So, when it reasonable to suppose that the corresponding premiss has been suppressed, the argument will be a valid enthymeme, rather than fallacious.
Sources:
- Howard Pospesel, Introduction to Logic: Propositional Logic (Third Edition) (Prentice Hall, 1998), p. 67
- William L. Reese, Dictionary of Philosophy and Religion (Humanities, 1980).
