I had a question about the motivation behind this definition provided in Katz and Lindell's cryptography book. I copied the paragraph in question along with the definition of the experiment.
    
   

> Perfect (adversarial) indistinguishability. We conclude this section
> by
>     presenting another equivalent definition of perfect secrecy. This 
>     definition is based on an experiment involving an adversary passively observing a 
>     ciphertext and then trying to guess which of two possible messages was encrypted.

[![From Katz and Lindell Chapter 2][1]][1]

In the text, this is supposed to be an experiment where the adversary is *passively* observing a ciphertext and then trying to guess. My question is that in this game, it seems as if the adversary is choosing the two messages. Isn't this not simply an *eavesdropping* adversary, but rather one that can choose the messages being encrypted? I tried reading more about this, but I couldn't find anything regarding motivation behind this particular definition. 

Rather than letting the adversary choose two messages, why not consider for any two arbitrary messages from the message space, sending an encryption of one of them to the adversary along with the two messages? More formally stated:

$$\forall (m_0, m_1) \leftarrow M^2,\; [m_0, m_1, E(m_0)] \approx_c [m_0, m_1, E(m_1)]$$

In this way, the adversary does not have a choice in what was encrypted, which seems more in line with the original definition.

Thank you in advance for the help. 

  [1]: https://i.sstatic.net/kVDsL.png