Five deep questions in computing (2008) [pdf]

I don’t think questions two and four are asking for a definition, but rather talking about classification based on established definitions within specific field of mathmatics. In that context the questions should be read to mean something like "How can we know what things are and are not computable/information."

If something is computable, that means it’s solvable within a particular model of computation such as a Turing machine (Turing computable). The most common question of computability found in applied computer science is “is there programmable algorithm to solve this problem”

Information, in this context, just means meaningful signal, as opposed to random noise. “What is information?” could be expanded to ask “How do we differentiate information for randomness and noise, and how do we extract information from noisy systems?”

Question three does seem a bit vague, but I think it’s intended to be something along the lines of “What systems and algorithms give rise to human intelligence.” But yes, intelligence itself is hard to define. I still think you could find an acceptable answer to this, at least a partial one. If you could directly design and create a system that presents a human level of general intelligence, then you would have necessarily defined some part of the systems/structures/algorithms that give rise to such an intelligence.

I’m honestly not sure what specific question 5 is alluding to, I think this is touching on Complexity Theory, but that’s a topic I am not at all versed in. I wonder if someone more familiar with that field could weigh in.

All that being said, I agree this particular article does not do a good job of posing the questions in a clear and well defined way, and the 3-word versions of the questions makes them ambiguous without further context and background. I think the purpose of this very short article is just to present the questions as "curiosities" as a way to spark the reader's interest and prompt them to seek out other resources with more detailed and context/field specific explanations.

Contrarily, I'd say that these questions were picked precisely because the author understands the profound difficulty we've encountered in the pursuit of formalizing them. Also, at least one of the other questions has a very precise formulation (number 2).

I don't get why these questions are posed as "problem-lists"; the questions don't seem related (or perhaps by coincidence through the answers). Is it that if we answer these questions, the entire field is "solved" somehow?

As @aaachilless point's out, question 2 is quite precisely formulated. But anyway, what is wrong with fishing for definitions?

Right now, no one can come up with a really satisfactory definition of either "intelligence" and "information". By trying to do so we can learn more about what we would want from such a definition. Better yet we might learn that definition can't exist for some reason: i.e. that those concepts are ill-posed.

Reading through the article I got the impression that these questions were posed because they lead to more interesting questions. In fact, the last paragraph fittingly sums it up. "I pose these questions to stimulate deep thinking and further discussion."

Here's an example from the text of what she means: "In order to answer what is computable, we must consider the underlying machine (abstract or physical) that is the computer. Consider the Internet as a computer. What is a universal machine model for the Internet? Consider a molecular computer, a DNA computer, a nano-scale computer, or even a quantum computer. What problems can and cannot be solved through them?"