Rice's Theorem asserts that for any non-trivial property of partial functions, no effective method can decide whether an algorithm computes a partial function with that property. Essentially, there's no effective way to determine non-trivial properties of a function just by looking at its code.

Theorem (Rice's Theorem). Let P be a language consisting of Turing machine de- scriptions where P fulfills two conditions. First, P is nontrivial—it contains some, but not all, TM descriptions. Second, P is a property of the TM's language—whenever L(M1) = L(M2), we have (M1) ∈ P if and only if (M2) ∈ P.

Note the following: (1) Rice's theorem cannot be used directly to prove that a language is unrecognizable; only that it is undecidable. It can be used to prove unrecognizability indirectly, in conjunction with other results.