Russel's paradox compared to Aristotle's logic

Question

How can we easily explain what Russel might mean about Aristotle's logic? Did I understand correctly that, loosely speaking, if we have a statement in Aristotle's logic for example:

No human being is immortal.

Then Russel's argument is that the above statement has no information about mortality whatsoever, the statement does not say that anybody is mortal though is makes me think that all human beings are mortal while in fact it does not say that human beings even exist.

Answer 1

The "standard" translation of the categorical proposition:

"No S are P"

is:

"do not exist x that are S and P.

In symbols: ¬(∃x)(Sx ∧ Px).

This is equivalent to: (x)(Sx → ¬Px).

With reference to your example, we have:

(x)(Human(x) → not-Immortal(x)),

i.e. "every human being is mortal".

As you correctly say, the above conditional is true whne there are no human being at all.

This was not Aristotle point of view; see Aristotle's Logic and he problem of existential import.