FOM: Universal Generalisation (No Aribitary Objects)

Neil Tennant neilt at
Fri Feb 15 22:15:46 EST 2002

On Fri, 15 Feb 2002, Dean Buckner wrote:

> UG is one of four rules used in logic to move between statements using
> constants
> and statements using variables.  What does this rule mean?
> I looked at a number of academic websites, all of which give broadly similar
> accounts of this rule.

I invite you to look instead at

for universal introduction, and at

for existential elimination.

These are the two rules that usually invite informal talk of arbitrary
objects. They are formulated so as to avoid talk of arbitrary objects
altogether. Instead, the formulation simply clarifies what syntactic
conditions must be met by the instantiating parameter in relation to 
other salient sentences in the deductive context. These syntactic
conditions capture exactly the otherwise semantic-looking gist of talk
about arbitrary objects.

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