[FOM] Tennant's (Prawitz's) rule of generalization

Michael Kremer kremer at uchicago.edu
Fri Sep 10 07:05:45 EDT 2004

Note that the rule of generalization described by Neil Tennant, in which 
only closed sentences are used, does place one requirement on the language 
-- for the rule to be complete there have to be infinitely many individual 
constants in the language.  (If there are only n individual constants one 
won't be able to prove (forall x1)...(forall xn)(for all xn+1)(x1 = x1 & x2 
= x2 & ...& xn+1 = xn+1).)

This is not a criticism, just something worth remembering, since it is not 
always assumed in constructing first-order languages.

--Michael Kremer

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