The argumentum ad populum is a second-order predicate argument that supports a value with a fact (2 pre VF).
ANALYSIS OF AN EXAMPLE
I am the world’s greatest writer of 140 character sentences, because many people have said so
The arguer states in the conclusion that something is the case and supports this claim by stating that many people believe the same. Since the argument fits the form q is true, because q is Z, it can be identified as a second-order predicate argument. In this specific case, q is instantiated by ‘that I am the world’s greatest writer of 140 character sentences’ and Z by ‘was said by many people’.
That I am the world’s greatest writer of 140 character sentences (q) is true, because that I am the world’s greatest writer of 140 character sentences (q) was said by many people (Z)
Second-order predicate arguments are further differentiated by identifying the types of statement in the conclusion and the premise. In this case, the former is a statement of (logical) value and the latter a statement of fact, which means that we are dealing with a second-order predicate argument supporting a value with a fact (1 pre VF).
The trivial name of second-order predicate arguments is derived from the characterization of the relationship between the predicates ‘true’ and Z. In this example, the argument is based on the idea that the fact that something was said by many people establishes its truth. We can therefore call such an argument an ‘argumentum ad populum’.