Not to drag this further... as the original post asked if animals have souls...
I keep seeing a lot of "what is a soul?"
I take my understanding of soul from Socrates and Plato. I thus consider a soul to be the essence of a person or being. The essence is incorporeal, eternal occupant of our being. As bodies die the soul dies and is reborn into the essence of the world and its beings.
The Platonic soul comprises of three parts:
1. Logos (mind)
2. Thymos (emotion, spirit)
3. Eros (desire)
These three parts are easy to understand, except the third part clashes with what we perceive desire to be. If we break it down:
1. Mind - brain and its functions both psychological and biological
2. Spirit - the inhuman essence and energy
3. Desire - greed, motivation, and that 'push' that makes us do things
Broken down like that shows that all humans have souls. We all have a mind, a spirit, and we desire things (even if you're Buddhist!) Animals too display these 3 parts. Animals have a brain, they have a spirit (you know your dog looks at you mean when you kick him off the bed), and their desire is primitive (love me, feed me, stay off my property, gotta do some excretion, and sleep).
Thus, animals do have souls.
~Sorry, I went all philosophical.