The "broken window fallacy" fallacy

A loyal MR reader wrote to me, complaining about Henry Hazlitt's Economics in One Lesson.  In particular, he noted that attacking the broken window fallacy does not much damage Keynesian economics.  I agree:

1. The broken window fallacy consists of claiming that destructive acts (say storms, hurricanes, or terrorist attacks) will improve economic welfare by occasioning repair expenditures and putting people back to work.

2. Measured gdp may rise but true real income will not.  After all, something has been destroyed.  In theory the extra spending flow could offset wage and price stickiness to such a degree that employment rises and the economy comes out ahead.  But a) this is unlikely, and b) you could get the positive effects, if indeed they are there, without breaking anything.  Better monetary and fiscal policies (for me especially the former but perhaps not for Keynes; do also note that raising taxes stifles work and innovation, an indirect breaking of windows) would be called for.

3. Appreciation of #1 and #2 does not much damage Keynesian arguments.  Keynesian doctrine argues that, under the right circumstances, stronger aggregate demand will stimulate output.  It affirms 2b without needing to contradict 2a, as stated directly above.

I am not a Keynesian, but this is one reason why I've never been persuaded by Hazlitt's critique of Keynes.  There is no a priori way to dispose of the possibility that a boost to nominal aggregate demand might increase employment; citing Say's Law doesn't do it either. 

Addendum: Alex points out that Keynes did, at least once, commit a version of the broken window fallacy.  Brad DeLong in turn criticizes Hazlitt.