The development of the paradigm of Granular Computing as a framework for processing of information abstractions has raised an interesting question whether the computational power of the multi-resolution information processing is higher than that of a Universal Turing Machine (UTM). There are good reasons to believe that this is so. The UTM is essentially a state machine that acts on a recursively enumerable input. This is why it is unable to evaluate functions that are either partial or non-recursive. These limitations of UTM are well known and Turing has proposed the augmentation of UTMs by oracles OTM (which are essentially look-up tables). Although, theoretically such an augmented Turing machine can overcome the problems with evaluation of halting functions but it does so at the cost of requiring infinite resources to implement oracles. However, as Turing has shown, even using the OTM the famous Hilbert's Entscheidungsproblem is not computable (the statement, T is in the set of theorems provable from axioms A, can be solved by computation, but the problem of showing that T is not provable cannot). Similarly, the set of all truth of elementary number theory is not computable (it is not recursively enumerable - which is what Goedel's Incompleteness Theorem says). Nevertheless, both of these problems can be solved by human thought processes that are not confined exclusively to computing. For example one can start by asserting the negative answer to the Entscheidungsproblem as a first approximation and then proceed with checking whether the theorem T is in a set of theorems that are provable from the axioms A (this is an OTM computational process). If such a theorem can be found the initial answer is changed from negative to positive (this change of mind contradicts the definition of computations but it captures what human reasoning is like). Such a two-trial approach to achieving hypercomputational powers has been suggested by Kugel, 1986, and subsequently developed by other researchers. What is promising with Granular Computing in this context is that it provides a formal basis for such mind changing that reflects human analysis of complex problems at various levels of abstraction (granularity).