I just bought the bestseller Why Does the World Exist: An Existential Detective Story by Jim Holt (New York, Liveright, 2012). The book looks great, but I haven’t read very far into it just yet. On page 1, the Prologue offers what is dubbed:
“A Quick Proof That There Must Be Something Rather Than Nothing, for Modern People Who Lead Busy Lives.”
Here is the proof:
Suppose there were nothing. Then there would be no laws; for laws, after all, are something. If there were no laws, then everything would be permitted. If everything were permitted, then nothing would be forbidden. So if there were nothing, nothing would be forbidden. Thus nothing is self-forbidding.
Therefore, there must be something. QED.
Again, I’ve yet to read beyond this page, but a quick glance revealed no immediate refutation of this proof. My daughter, a sophomore at a non-elite university, saw through the it immediately, pointing out that it employed equivocation on the word “nothing.” This does seem to be one way to describe what is wrong with the proof. With a few minutes to think and type I shall quickly attempt to explain.
Suppose there were nothing. OK, fair enough.
Then there would be no laws; for laws, after all, are something. Still good.
If there were no laws, then everything would be permitted. This no longer works, for in a state of total “nothingness” there would be no “everything” and no such thing as “permission.”
If everything were permitted, then nothing would be forbidden. Whatever. See the next line.
So if there were nothing, nothing would be forbidden. This sounds suspiciously like a prohibition or a law, which we have already been told, correctly, do not exist in a condition of absolute nothingness.
Thus nothing is self-forbidding. Wrong.
Therefore, there must be something. QED. Sorry. As explained, it doesn’t follow.
So, with all due respects to Jim Holt, whose book I intend to thoroghly enjoy, and with a quiet hope that he offers a similar refutation somewhere beyond page 1, I offer this alternative.
“An Even Quicker Proof That There Might Nothing Rather Than Something, for Modern People Whose Lives Are Still Busy”
Suppose there were nothing. Then nothing would exist, not even a prohibition against nothingness. Thus, there would truly be nothing, i.e., nothing at all. QED.
[Update on Nov 18, 2012: I’m very happy to say that the author goes far beyond such “proofs” as this. The book is very satisfying for those who like to read such things. The Quck Proof is a mere tongue-in-cheek introduction to an entertainingly written discussion of a long and serious subject.]