How many (peer reveiwed) journals are there?

["Joseph J. Esposito" <espositoj@gmail.com>]

In a conversation with a client recently, I made the offhand 
remark about "the 24,000 peer-reviewed journals."  She said, Not 
so fast!  That number is suspect; the actual number is both 
bigger and smaller.  The number is smaller, in her view, because 
only a subset of journals have a careful peer review process; and 
it is larger in that the number of journals continues to grow, 
but the review process is often sketchy at best.  (As far as I 
know, none of this has anything to do with whether a journal is 
open access or toll access.)

Clearly there are matters of definition at issue here:  What must 
peer review consist of in order for it to earn the use of the 
name? And while we are at it, what is a journal anyway?

I would appreciate hearing from anyone who has some thoughts on 
this topic.

How many journals are there?

Joe Esposito