Aristotle's docrine of the soul is founded upon his notions of
matter and form, a basic understanding of which is henceforth presupposed. The
mind (interchangeable with
soul, for Aristotle) consists of pure form, capable of adoping any form its owner deems to
think about. A cornerstone of the human mind is the form of
rational animality, which gives us the capacity to think. It is a substantial form,
essential to the basic nature of the objects known as humans.
The nature of thought, inside Aristotle's model, is that it rests in the mind's ability to accept the forms of other objects. When a man sees a tree and accepts it as part of reality, the forms of the tree that he becomes aware of are reflected onto his mind. Neither thought, nor the mind can involve matter, for if the matter of the tree were reflected along with the form (or even if the form of the tree were to touch the matter of the mind), the matter and form would merge into a physical tree inside the thinker's head, which clearly doesn't happen.
Since the soul is pure form, it is eternal, and cannot be destroyed. However, the form of rational animality is a singularity, as are all forms -- it is matter which allows for there to be multiple instances of the same kinds of objects. When the body dies, there is no longer any distinction from the form and itself (clearly). So when someone asks Aristotle if the soul is immortal, he will respond that it is -- however, at the moment of body death, the soul merges with the universal soul from whence it came, a la Terence McKenna. So there is no personal immortality.
This set of theories conflicts drastically with the more popular modern beliefs on the nature of the soul. Most scientists will be quick to attack the claim that the mind contains no matter, calling attention to the textbook cases of selective brain damage. Many others may call to question the idea that there can be a singular soul which assimilates all dead souls, as this conflicts with their personal (often religious) definition of the soul. Many view the soul as the embodiment of the things that distinguish humans from one another on an unseen level: sense of humor, life experiences, cultural heritage, feelings of affection for certain others, etc.. In Aristotle's lexicon, the argument would be that the individual soul seperates each person from all others, and is itself a unique form.
Another objection deals with in Aristotle's conception of the nature of thought. The question arises: when a person thinks about, say, his pet goldfish, how is he able to think about that particular goldfish? Supposedly, the forms of the goldfish that he's aware of are reflected in his mind. But these forms are few: goldness, fishness, and life are the most important. These forms describe uncountably many goldfish around the world. But clearly, one is able to conceive of an individual goldfish without thinking about all goldfish. How is this possible?
To fit within the scope of Aristotle's theory, any given goldfish would have to have a specific combination of forms to be uniquely considered. One solution is that location in space at a given time singles out the object. But this kind of form calls the whole system into scrutiny. Is there a form for the location of every object in the universe? Taking into account the fact that every molecule of air has a seperate location, such a set of forms seems a bit extreme. But of course, Aristotle lived before it was well known that air consists of tiny particles, which are individual objects.
Another solution would be that each animal has, on a relatively small order of magnitude, distinctive markings which differentiate that animal from the rest of its species: fingerprints on humans, and stripes on zebras, for example. But if we allow seperate forms for each shape of fingerprint (as each shape is totally unique), we may as well allow a seperate form for each individual soul.