I'm studying cryptography for my university course, but some doubts arose from reading a book. In this book the author says: "Now we present another equivalent definition of perfect secrecy. This is base on an experiment involving an adversary $\mathcal{A}$ and formalizes $\mathcal{A}$'s inability to distinguish the encryption of one plaintext from the encryption of another." referring to the eavesdropping indistinguishability experiment. Then he concludes saying that an encryption scheme is perfectly secure if $Pr[PrivK^{eav}_{\mathcal{A}, \Pi} = 1] = 1/2$.
In other pages, he says "Any scheme that has indistinguishable encryptions under a chosen-plaintext attack clearly also has indistinguishable encryptions in the presence of an eavesdropper."
My doubt is: if an encryption scheme is indistinguishable from an eavesdropper but it is weak against a chosen plaintext attacks, so how can the scheme be considered still perfectly secure?
Another doubt: "eavesdropping indistinguishability" and "perfectly secure" are both referred to information-theoretically secureness?
