[FOM] Inference Avoidance?

[Charles Silver]

On Oct 8, 2006, at 2:35 AM, Harvey Friedman wrote:

> Can one identify any basic inference rule which is not used in actual
> mathematical practice? Or at least whose use is particularly rare?

(I'm speaking only of Natural Deduction rules below.)

	My own opinion is that every "basic" rule of inference but one in  
first-order logic (f-o) is an exact reflection of reasoning in  
mathematics.   The single exception, which I know is arguable, are  
all variants (I'm familiar with) of Existential Instantiation (EI).   
In other words, I do not think that the various ways that EI are used  
in f-o are true reflections of the same sort of reasoning in  
mathematics, though they're close.
	I'm fairly sympathetic with Fine's non-standard characterization of  
EI in _Arbitrary Objects_, in the sense of it reflecting mathematical  
reasoning.   However, Fine's EI does not seem completely accurate to  
me either.

	This is just my opinion, and I hope I won't have to argue for it.

Charlie Silver