[AndrewC]

Now, back to your post, it’s not a theorem if it has no proof, as above. Without proof, it’s a conjecture. Unless you are assuming it to be axiomatic, which wouldn’t surprise me.

In the strictest sense of theorem you are right. In the more colloquial use which you point out, it is a "theorem". But unless you can name one of the objects which does provide a means for "information" to arise spontaneously and can rigorously prove it, it seems entirely reasonable to accept the "theorem".

[Buck W.]

My comment and challenge to the use of the term was meant to shed some light on the paucity of rigor and absence of logical process in the original document.

[GodGunsGuts]

Apparently, the word theorem has a slightly different definition with respect to science:

“There are also “theorems” in science, particularly physics, and in engineering, but they often have statements and proofs in which physical assumptions and intuition play an important role; the physical axioms on which such “theorems” are based are themselves falsifiable.”

http://en.wikipedia.org/wiki/Theorem#Theorems_in_logic