My professor defines logical validity (in the English language) like so:
'An argument is logically valid if and only if there is no (uniform) interpretation (of subject-specific expressions) under which the premises are all true, and the conclusion is false.'
He contrasts subject-specific expressions (e.g., Donald Trump, Aristotle, chemical element, London), with logical expressions (i.e., if, not, if and only if, every, some). Logical expressions are not subject to re-interpretation; they keep their standard English meanings all the time.
My question is this: is the following argument valid?
P1: Santa Claus does not exist. C: Something does not exist.
Now, on the one hand, I'm inclined to say yes: if I replace 'Santa Clause' with any other noun, or I replace the property of not existing with any other property, the resulting argument is such that: if the premises are true, so too is the conclusion.
On the other hand, I'm hesitant to say yes: if I replace 'something' with, for example, 'a car', then the resulting argument seems to involve a true premise, and a false conclusion.
That said, I'd unhesitatingly say that the following argument is valid:
P1: Santa Claus does not exist. P2: Santa Claus is something. C: Something does not exist.
Could Santa Clause not be 'something'? From another angle: is 'something' a 'subject-specific expression'? I'm inclined to think it is not, but I'm not sure how to justify this thought. (My inkling is that it has something (lol) to do with the fact that 'something' is a pronoun, whilst 'a car' is a noun? Also, I'm aware that the argument in question involves a valid rule of inference in FOL. But I wonder if this is one of those cases where validity in FOL comes apart from more informal characterisations of validity in the English language (e.g., http://www.jimpryor.net/teaching/courses/intro/notes/leibniz-epist.html).)