Attacks against Arguments: Rebutting and
Undercutting
An argument can be attacked in any of three ways: by attacking its
premises, by attacking its conclusions, or by attacking the support
relation between premises and conclusions. Conclusive arguments can only
be attacked by challenging their premises, since, if the premises are
accepted, then the conclusion must also be accepted. So, for instance,
if we accept that Fido is a dog and that all dogs are mammals, we must
also accept that Fido is a mammal (as soon as we are aware of the
logical connection between premises and conclusion). In fact, it may
also be possible to attack the conclusion of the argument—i.e., to
deny that Fido, who is a robot in the likeness of a dog, is a
mammal—but then we must also reject the premise that Fido is a dog (if
we exclude that dog-like robots count as dogs), or alternatively, we can
deny that all dogs are mammals (if we also include dog-like robots among
“dogs”).
By contrast, a defeasible argument can also be attacked by denying its
conclusion, even if its premises are not questioned. For instance, let
us assume that Fido is not only a pet dog but also a Doberman, and that
Dobermans are presumably (normally) aggressive. Then, as shown in Figure
5 we can build an argument that attacks the previous argument by
contradicting its conclusions (attack is expressed by the jagged arrow).