FOM: Re: First-order logic -- a query

[Michael Thayer]

Joe Shipman asks the question:


>Kanovei reminds us that set theory is the "official" foundation for
>mathematical *objects* and "classical mathematical logic" is the foundation
for
>mathematical *reasoning*.  But what exactly is "classical mathematical
logic"?
[...]
>So why would one use higher-order logic instead of Z or ZF or ZFC?
>

While we are at it, may I ask why use of Z or ZF or ZFC instead of NF, NFU,
NFC or the Church systems?
While Joe's question goes to Kaonvei's point about mathematical *reasoning*,
mine is more related to his point about mathematical *objects*.

Name: Michael Thayer
Position: Director
Institution: T & S Software Associates
Research interests: Foundations of computation and performance of algorithms