All living things have souls. For most Ur-Platonists (which includes nearly all orthodox Christians, Muslims, Jews, and pagan Greek and Roman philosophers/theologians until the Enlightenment), the soul is:
* what makes a thing what it is (it's form/eidos/essence/universal/nature)
* what makes a thing a living thing at all
* what unifies and coheres the many disparate parts of a living thing
The relevant difference between those of us with human natures and those beings who lacked human natures is that our human nature (i.e. our souls) has the power to come to know universals/natures/forms themselves (albeit imperfectly), whereas other beings do not. For a dog, their senses are acquainted with many instances of cats, but they never are able to go from these individual sense impressions to the form/nature/universal of cat, or ficus carica, or what have you.
* what makes a thing what it is (it's form/eidos/essence/universal/nature)
* what makes a thing a living thing at all
* what unifies and coheres the many disparate parts of a living thing
The relevant difference between those of us with human natures and those beings who lacked human natures is that our human nature (i.e. our souls) has the power to come to know universals/natures/forms themselves (albeit imperfectly), whereas other beings do not. For a dog, their senses are acquainted with many instances of cats, but they never are able to go from these individual sense impressions to the form/nature/universal of cat, or ficus carica, or what have you.