[FOM] Inference Avoidance?
silver_1 at mindspring.com
Mon Oct 9 12:24:40 EDT 2006
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
This is just my opinion, and I hope I won't have to argue for it.
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