[FOM] substitutional quantification, counterfactuals and ontological commitment

[paul at personalit.net]

I was recently talking with a colleague, who teaches logic and 
philosophy of science using Copi-style rules only, about an advantage of 
substitutionalist quantification over objectualist quantification.

An objectualist accepts the inference from |- (Ex)Fx to |- Fa by 
assuming that 'a' refers. Not so for substitutional quantification, for 
which this inference requires two names 'a' and 'b'.  This is 
advantageous when 'Fa' is not equivalent to 'a=a' because it requires 
application of a rule of detachment, like =-elimination, to infer |- Fa 
from |- (Ex)Fx.  And applying =-elimination in this case requires 
assuming the non-trivial identity 'a=b'.

Therefore, substitutional quantification is advantageous because the 
negation of 'a=b', '~(a=b)' is amenable to counterfactual reasoning, 
while the negation of 'a=a', '~(a=a)', is not, except in the case of an 
"impossible possible world."

To me, this expresses a distinction between objectualist and 
substitutionalist interpretations of quantification, while remaining 
agnostic about ontological commitment, the question of whether 'a' and 
'b' refer.  The substitutionalist supports non-trivial counterfactual 
reasoning, but not the objectualist.

I'm curious as to any feedback from FOM.

Cheers,

Paul Hollander