How do I translate 'no philosopher student admires any rotten lecturer' into quantificational logic formula?

Question

Let's assume that $Fx=x$ is a philosophy student, $Rx=x$ is a rotten lecturer, and $Mxy=x$ admires $y$.

My translation of the sentence was $\forall x(Fx\supset\neg\forall y(Ry\supset Mxy))$, but my logic textbook translated it as $\neg\exists x(Fx\wedge\exists y(Ry\wedge Mxy))$.

As far as I know, no philosophy student admires any rotten lecturer means the same as every philosophy student doesn't admire every rotten lecturer. But, the textbook's author seems to understand it as every philosophy student doesn't admire some rotten lecturer. How do I wrap my mind around this?

Answer 1

The trip-up is that the usage of "any" when inside a negated clause refers to "some" rather than "every".

Hence "No F admires any R" translates as "there does not exists an F that admires an R."

$$\neg\exists x~\Big(F(x) \wedge \exists y~\big(R(y)\wedge M(x,y)\big)\Big)$$

Which is equivalent to $$\forall x~\Big(F(x)\to ~\forall y~\big(R(y)\big)\to \neg M(x,y)\big)\Big)$$

Or in PNF: $$\forall x~\forall y~\Big(\big(F(x)\wedge R(y)\big) \to \neg M(x,y)\Big)$$

Answer 2

I realized that no philosophy student admires every rotten lecturer cannot possibly mean the same thing as no philosopher student admires any rotten lecturer. It is the same thing as no philosopher student admires some rotten lecturer.