No! :-) Statistic is just the first step, it is a first step becuase you get relevant result.

It ought to depend on how you use the statistical models. If you use them to analyze/generalize a whole bunch of inputs, yes, that is flawed, as there are human behaviours that do not depend on a large set of inputs, but something more like an internal model. This is basically Chomsky's point, and he's right to the extent that learning approaches which depend on aggregation of data like this are not a good clue to human behaviour. However, that is not the only way you can use statistics. If you look at Anderson's ACT-R model, for example, it is firmly rooted in statistics but at a memory chunk level not at a stimulus level. This is both neurally relatively plausible and capable of modelling complex human behaviours, such as problem solving.

I'm not sure Norvig's points are helpful, either. ACT-R is sort of algorithmic modelling, but it really does make claims of correspondence to the processes in human psychology. That's why it's really cognitive modelling. For some time, artificial intelligence and cognitive science have gone their separate ways. Chomsky's critique of artificial intelligence as not saying much about human language is reasonable in this respect, but that doesn't undermine the use of statistical modelling in disciplines which do care about understanding the processes in human psychology.

There are a number of valid ways to model human behavior and get equivalent results. In the end it is not about whether it can be done in a certain manner but whether you know how to use a particular technology to get the results you desire. As Stuart pointed out, extracting a set of rules or a more fundamental understanding of human behavior from some of these models is harder with some than with others.

Using statistical modeling, I believe, is not the best way to go if the result you want is to distill out a simplified model. It's not clear that simplified models are even meaningful. It's a bit like looking at the behavior of many vaguely related computer programs and trying to make a general determination about program behavior. Generalizations can be made but they are usually not deep. As Noam has pointed out, humans are not axiomatic systems so there are no human lemmas to be discovered. Humans are basically pattern matching and transformational neural networks so we are, by training, artificially intelligent. What we are modeling, in some manner, reflects our education and environment. The arrangement of these neural networks also vary significantly from one individual to another making it easier for some individuals to learn language skills, math skills, etc.

You will need to use a mix of things to "solve all our problems" -- if they are solvable at all!! Statistical is useful since it provides a real grounding -- learning or inferencing is happening with trace of what has actually happened, and not on a model -- but guiding statistical models is needed for the approach to stay manageable. And for realistic problems, the data size requirement is huge. Bring other models -- represented human knowledge -- and you get a size that is manageable, something inspectable, and something you can reason with. But, we dont know models for most of the interesting problems. Statistics need to fit here.

Plus, statistics can provide a mechanism to adapt your system with changes taking place over time, as it is data driven.

I can see statistics as a tool, and not the whole package to solve every problem. When the problems are purely logic driven than data driven, statistics would not have a major role. Even granted the fact that certain logic or reason is data driven, it does not preclude that statistics to be a solution. In addition, statistics can be misleading at times, especially on problems where the data is sparse and few!.

their are lots of methods that can be in problem solving, then you can select form those methods depending on the research methodology, and the problem types.

Statistics is a sciences of collection,presentation, analysis and interpretation of the results generated from the study. Yes, statistics may be considered as the initial steps in solving in most of our problems. As Ismail Romi indicated that the correct statistical methodology do depend highly on the problem. Statistic is just a tool and it can be used to solve many problems but it can also be the cause of the human problems...

It appears to me that statistics is no doubt a scientific method that can be fruitfully applicable to solve many of our problems but obviously not all. Mainly, the problems associated with logical senses as well the problems related to continuous asymmetric changes, it very difficult to apply proper statistical operations.