What is the theory behind Bishop's Opening, Philidor Counter-Attack? What is the theory for this opening for black?

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]

1. e4 e5 2. Bc4 c6


I've started playing the Bishop's Opening because it is something different, but I had not seen this counter play before.

It seems weak, because--although it has the advantages of an opening like Caro-Kann by grabbing control over the center--black immediately loses defense of his king pawn (Nc6 is unplayable). Despite this, it seems a solid opening for black.
Black cannot play Nc6 at the moment, that is true. However, it doesn't look like White can exploit this immediately, either. 

Black will answer 3 Nf3 by ...d5, gaining tempo on the Bc4 that he can then use to either defend e5 (d7 is open for the knight, at the very least) or counter-pressure e4 (which is equally weak as e5). The whole motive is similar to the classical center attack in the Italian (c3 + d4).

Trading the pawns (4 exd5 cxd5) opens c6 for the knight again and doesn't look very attractive as it yields the center to Black. 5 Bb5+ is toothless, Black will reply ...Bd7 and then take back on d7 with his knight (or simply play Nc6 if the white bishop retreats now). Immediately retreating (by 4 Bb3) doesn't look very good either, Black will gain the initiative.

Of course, White has other options for his third move. 3 d4 is a similar attempt to attack e5. Black can reply 3...d5 again, which leads to a very complicated position. But again, e4 is just as weak as e5 and swapping away e4 opens c6 for the knight. No clear advantage for any side.

Against 3 Nc3 (prevents 3...d5, but doesn't attack e5), Black has time to play 3...Bc5 , followed by 4...d6 (e5 is safe) and he will achieve something similar to a Giuoco Pianissimo Reversed - which is not too bad, really.

So, yeah: Totally playable in my opinion.

Disclaimer: I'm not an actual expert in this opening.