Examples just from Alan's own "adulthood", speaking chronologically only, of course, show the prevalence of double dip recessions.
The two recessions in 1969-70 & '73-75 and the two in 1980 & '81'82 were double dips, while the 1990-91 & 2000-01 recessions were unusual in not being doubles, although there was a slowdown in '94 & the Dow did double bottom in Oct 2002 & Mar 2003. The wars in '90-91 & '03 may have prevented double dipping.
A true, vicious double dip, with the second blast almost as bad or worse than the first would also depress EPS as well as lowering P/E. Why does everything have to be explained to you, no matter how simple & basic?
When money flees stocks, it lowers P/Es across the board. Some sectors take bigger earnings hits than others.
A double dip recession could cut PFE's earnings to two bucks from present $2.24 & drop its P/E to five from 9.26, for a price of $10. Hardly one in a 1000 odds stuff.