I realize Data is a fictional character, but, even so, I wish that the spirit of Data would infuse the actor who played him and drive out the Malibu-inspired woo that has apparently lodged itself into his brain.
Naturally, thus leads me to the question of why we assume Data would be woo-free. Given that he is free of emotional responses and uses logic alone to formulate his world, will that suffice to keep woo out of Data's understanding of the world? What role does logic play in the separation of superstition from fact? I will give my impressions and understandings below the fold.
First, I want to briefly reiterate what logic is: a formal system of combining definitions, and operations in a well-defined manner to derive results based on those axioms, definitions, and operations. In classical Western logic we accept certain fundamental notions and classification as the starting points. For example, that propositions can be meaningfully discussed, that every proposition must be assigned a value of True or False, that you can invert the truth value of a proposition by negating it, what it means for one proposition to imply another, etc. All of these assumptions are needed just to form the calculus of logic, the well-defined manner we use to derive true propositions from other true propositions. Then, we need to throw into the mix our undefined objects and axioms. We need undefined objects because you have to have a starting point. The alternative is that if you try to define everything, at some point you will be using term A to define term B, when A has already been defined in a manner that B is important to the definition of A. So, we avoid this circularity by allowing some term to be undefined. Axioms now have a key role to play: they describe the behavior of the undefined objects. We can then define other objects based on the undefined objects. As an example, in a typical geometry class, I note that there are four undefined notions: a point, a line, a plane, and space. We describe what we intend these things to represent, but you can formally define them with using circular terminology. Then, we introduce axioms like Line Creation (there will be one line connecting any two points) to describe one of the relationships between lines and points. We introduce definitions based on these concepts (rays, line segments, angles, etc.). We generate theorems to show what other statements our axioms and definitions imply under the accepted logical calculus. So, logic can be used to show what you accept has additional consequences you may not have realized.
However, one thing (among many) that logic is not is a validation system in any but the barest sense. Sure, logic can occasionally be used to produce contradictions that derive from a given set of axioms. That's really not saying very much. First, to be effective at all as a means of persuasion to change the axioms involved, there has to be a prior commitment to make a change when a contradiction is reached. However, real life is full of situations that seem contradictory and yet persist, saying that are both accepted as true when saying the opposite. For example, the advice offered by "haste makes waste" is seemingly opposed to "a stitch in time saves nine". We have ways of resolving those pieces of advice, of course. However, this skill gets carried into other types of contradictions as well. So, producing contradictions, the only form of validation logic is capable of, is not protection against accepting all sorts of outright nonsense. Indeed, many people who accept axioms like "Properly understood, every word of the Bible is completely true" are skilled at using logic to defend their positions, because logic can be used in cause of woo just as easily as in the cause of skepticism.
This means I don't see Data necessarily having a special protection from woo by virtue of his thought proceeding from a logical calculus only. Whatever skeptical traits Data would possess would be a matter of programming. The more his programming was set to look for, find, and act upon patterns, the more likely Data would have wooish beliefs. One example is the show where the Enterprise-D is stuck in a time loop where it keeps blowing up at the end. Data uses the occurrences of a highly unlikely aggregation of 3s appearing to decide to follow the suggestions of Riker, who has three buttons on his collar, as opposed to 2.5 for Data. Data was eager to find a sign or symbol, and made A rapid, spur-of-the-moment pattern connection with no evidence that the connection is causal in any way. What could be wooier?