Rewriting a logical statement

Question

Only lakers are irrational people.

I believe it technically should be translated as:

All irrational people are lakers.

Is there is any way at all to rewrite the above statement to mean the following and be logically correct:

All lakers are irrational people.

How would you justify it? (If it is possible)

Answer 1

All rational people are not lakers.

The opposite converse is equally valid.

The converse that you posit is not equally valid.

Answer 2

Indicating with $L$ the set of lakers $l$ and with $\Pi$ the set of irrational people $\pi$, the first statement is equivalent to

$$\forall \pi\in \Pi \quad \pi\in L$$

the second one is

$$\forall l\in L\quad l\in \Pi $$

which is not equivalent to the first one, indeed from this last one we could also have $\pi \not \in L$ for aome $\pi$.

Answer 3

Your initial translation is correct, though in standard form I would write

All non-rational people are lakers.

This is an Aristotelian A type statement, and A type statements have valid obverses and valid contrapositives. They do not have valid converses.

Obverse: No non-rational people are non-lakers.

Contrapositive: All non-lakers are rational people.

So the ultimate answer to your question is no, because you are trying to get the converse of an A statement to be true, which does not happen in general.

If you had an E or I statement, the converse would be valid.