Philosophical Nothingness Argument - Jim Holt

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I recently received Why Does the World Exist by Jim Holt. I haven't gotten around to reading anything but the first chapter, but the book opens with a rather interesting paragraph:
A Quick Proof That There Must Be Something Rather Than Nothing, for Modern People Who Lead Busy Lives

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.

QED

The book then starts on a completely different note, and from my skimming it doesn't seem to treat this introduction with any length.

I, however, am stuck on this.
It seems to me to be a rather concise proof of what it tries to accomplish, but I cannot believe it is as simple as it appears.

Can anyone point out a flaw in this argument? Or a place of weakness?

Thank you.

I'll note that an initial qualm was over the use of 'nothing' both as a noun and as meaning 'the lack of a noun' but it seems to me that even with this considered, this paragraph makes a daunting argument.
 
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