FOM: Book recommendation

[Stephen G Simpson]

Dear Joe,

 > Please take a look at "Extensions of First Order 
 > Logic", by Maria Manzano (Cambridge Tracts in 
 > Theoretical Computer Science 19, Cambridge
 > University Press 1996, ISBN 0-521-35435-8, xxii+388 
 > pages).

Thanks very much for telling me about this book by Manzano.  I spent
some time looking at it, and I am amazed at the wealth of detail about
higher-order logic, modal logic, dynamic logic, etc.  In a way, there
is more detail here than I really want.  Of course I am delighted by
Manzano's point about first-order logic subsuming the other systems.
But the basic point seems obvious to me.  I guess I am a believer in
what Martin Davis (Mon, 22 Feb 1999 14:36:21 -0800) called "Hilbert's
Thesis", in the "second-order logic is a myth" thread last year (FOM,
February-March 1999).  Manzano's remarks are obviously relevant to
that thread.  They are also relevant to the polylogism thread (FOM,
March 1999).

Best regards,
-- Steve