[FOM] Classical logic and the mathematical practice

[Timothy Y. Chow]

Harvey Friedman wrote:

> Let me address just one small aspect of these questions. This concerns 
> "safer".
>
> There are many results of the following form. Let T be one of the 
> standard formal systems based on classical logic. Let T' be the 
> counterpart based on intuitionistic logic. Then
>
> T is consistent if and only if T' is consistent.

Perhaps by "safer," Moshe David was worried not about inconsistency per 
se, but about the danger of being "fooled" into saying "either A or ~A" 
when A turns out to be undecidable in ZFC?

I agree with Jeremy Clark that a large part of the answer is sociological. 
But also, it is common in "ordinary" reasoning to argue that either X 
happened or it didn't happen (where X is some real-world event), even if 
there might not be any way of proving which one is the case.  It generally 
takes considerable philosophical education before someone seriously 
entertains the notion that if there is no way to decide whether X happened 
or not, then maybe X neither happened nor didn't happen.  So classical 
logic gets a boost from common sense (until one reaches the requisite 
level of philosophical sophistication, by which time one may already be 
irrevocably prejudiced).

Tim