It is well established that the class of recursive languages is strictly contained in the class of recursively enumerable languages (Rec $\ne$ RE). Any finite language is decidable and hence can not be RE-complete. My intuition is that an RE-complete language contains infinite number of (finite) strings (information) and can not be reduced to a finite language.The situation is different for the class NP since we can not rule-out finite NP-complete languages. If P=NP then there is some finite NP-complete language (under Karp reduction).Is there an intuition (or evidence) that explains why finite languages can not be complete for NP?I am looking for an intuition (evidence) that supports the conjecture that all NP-complete languages must be infinite (It should not assume anything about P vs NP). Different notions of completeness inside NP may have significant impact on the properties of complete languages inside NP. This was moved from a comment. Finiteness of complete languages shifts the focus on using the right notion of reduction to define completeness inside NP. The following post on CS Theory shows that defining completeness using injective Karp reductions would prove $P \ne NP$. The reason is  that SAT is infinite language and can not be reduced to a finite language using injective Karp reductions. 
Why can't we exploite finiteness to prove incompleteness in NP?
complexity theory;np;p vs np