More Stats… & a Question

Two more recent views of the rise of statistics:

1) the positive from Marie Davidian here, ending with, "Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write" (supposedly a quote from HG Wells):

http://www.huffingtonpost.com/marie-davidian/2013-the-international-ye_b_2670704.html

and 2) a somewhat cautionary take (regarding "big data" and how it leads to increased spurious claims) from the usually irascible, often provocative, always wary, writer Nassim Taleb here:

http://www.wired.com/opinion/2013/02/big-data-means-big-errors-people/

And on a complete side note a simple question I'm curious about:

The prior post (Monday) referred to the "pigeon-hole principle" and caused me to wonder just how mathematical "principles" and mathematical "axioms" or "postulates" are distinguished by formal definition in math? … both represent (it seems) strong underlying intuitive assumptions. From googling around a bit, it appears to me that axioms/postulates may be a sub-category of "principles," which are specifically implemented to derive theorems through logical steps (while "principles" are a broader category of assumptions that also lead to other results, but not restricted to theorems). Am I on the right track, or if I'm not can someone set me straight with the correct, precise distinction?