Demonstrations and dialectical arguments are both forms of valid argument, for Aristotle.
However, he also studies what he calls contentious (eristikos) or sophistical arguments: these he defines as arguments which only apparently establish their conclusions.
In fact, Aristotle defines these as apparent (but not genuine) dialectical sullogismoi.
They may have this appearance in either of two ways:
– Arguments in which the conclusion only appears to follow of necessity from the premises (apparent, but not genuine, sullogismoi).
– Genuine sullogismois the premises of which are merely apparently, but not genuinely, acceptable.
Arguments of the first type in modern terms, appear to be valid but are really invalid.
Arguments of the second type are at first more perplexing: given that acceptability is a matter of what people believe, it might seem that whatever appears to be endoxos must actually be endoxos.
However, Aristotle probably has in mind arguments with premises that may at first glance seem to be acceptable but which, upon a moment’s reflection, we immediately realize we don not actually accept.
Consider this example from Aristotle’s time:
– Whatever you have not lost, you still have.
– You have not lost horns.
– Therefore, you still have horns
This is transparently bad, but the problem is not that it is invalid: the problem is rather that the first premise, though superficially plausible, is false. In fact, anyone with a little ability to follow an argument will realize that at once upon seeing this very argument.
Aristotle’s study of sophistical arguments is contained in On Sophistical Refutations, which is actually a sort of appendix to the Topics.
To a remarkable extent, contemporary discussions of fallacies reproduce Aristotle’s own classifications. See Dorion 1995 for further discussion.