FOM: second-order logic is a sterile myth

Charles Silver csilver at
Tue Mar 23 05:47:57 EST 1999

	I quote some of Steve's remarks in response to Randall Holmes, in
order to request again that some of the inference rules for second-order
logic be spelled out.  (I believe it was Pat Hayes who indicated that
there were some nice ways to extend first-order rules to second-order

On Tue, 23 Mar 1999, Stephen G Simpson wrote:

>  Regardless of what a hypothetical philosopher might say,
> logic is still the science of correct inference.  Second-order logic
> is not logic in this sense, because it lacks rules of inference. 

	Ok.  I'm jumping on the last sentence.  I got the impression--was
this wrong?--that there are some inference rules for second-order (though
of course not *all* the rules that would be desirable).  I'd like to see
some of them spelled out.  What occurs to me is that there are obvious
second-order counterparts to first-order rules, but how far do they go?
What do they miss? 

Charlie Silver

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