2

What kind of argument (if it does count as an argument) would this be?

All men are mortal
Therefore, if Socrates is a man then Socrates is mortal

It's not a syllogism as far as I'm aware, so what is it?

4

It is a syllogism "in disguise".

The "standard" form is :

All men are mortal;

Socrates is a man.

Therefore, Socrates is mortal.

If we consider its logical form, it is :

P,Q ⊨ R

that is equivalent to :

P ⊨ Q → R.

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