[FOM] Logic moving from philosophy to mathematics

[Daniel Crosby]

Apologies in advance if this is not the appropriate forum, but I think 
it is a question of interest to FOM.

It seems to me that "logic" as a subject moved from being the interest 
of some philosophers -- in the early 19th century, and maybe later -- 
to the interest of some mathematicians, by the early 20th century, and 
maybe earlier. Philosophers still study logic, of course, but they now 
study mathematical logic. Everyone that I've talked to about this 
agrees that this has happened, but I have not been able to find a 
secondary source analyzing this important shift.

Can someone point me to such a source? Or correct my characterization 
of (or the existence of) this change?

Dan Crosby