We can’t understand the pre-modern beliefs about soul before understanding that they saw the term as uncontroversial from being obvious. A soul was whatever a living thing had that its corpse did not, or what pigs had that pork didn’t. Speaking about “proving the existence of soul” would have been the same thing as proving that some things are alive. It was not something that would divide the nowadays dualist and materialist; and no one was compelled by soul-talk into imagining ecoplasm or gaseous vertebrates pushing bodies around.
Aristotle defined soul as form, and what was just said about soul extends to form. Form is initially the totality of the characteristics that make a thing be, or whatever makes a thing be by belonging to it.* Speaking about a proof for forms in this sense would be proving that things had characteristics; denying the existence of forms is denying there are any characteristics. Again, no one is compelled by form-talk into imagining ghostly line drawings that float about and slam themselves into pinkish goo (prime matter!) in order to make sparrows and spam. Form was a placemarker word for a larger research project of speaking about how various things are intrinsically made to be, and what characteristics they shared with others.
We refine the account of form by refining what it means to be, which happens not by dividing a genus by differences but by dividing the diverse ways of being. Thomas gives us a list of these ways in c. 11 of his Fallacies:**
For being is per se or per accidens, by which we get the fallacy of the accident; it is perfect or imperfect by which we get the fallacy of secundum quid and simpliciter. By being opposed and non-opposed we get the fallacy of ignorantio elenchi; by it being the same or different we get the fallacy of begging the question; by it being prior and posterior we get the fallacy of the consequent; by it being a cause or caused we get not-cause-as-cause; by it being one and many we get the fallacy of many-questions-as-one.
[N]am ens aliud est per se, et aliud per accidens: et secundum hoc accipitur fallacia accidentis. Item secundum perfectum et imperfectum accipitur fallacia secundum quid et simpliciter. Secundum autem oppositum et non oppositum est fallacia secundum ignorantiam elenchi. Secundum vero idem et diversum est fallacia petitionis principii. Secundum vero prius et posterius est fallacia consequentis. Secundum causam et causatum est fallacia secundum non causam ut causam. Secundum autem unum et multa est fallacia secundum plures interrogationes ut unum.
All of these divide up the different modalities or measures of being, and their clarification and order is what the Aristotelian tradition calls the analogy of being.
Being per se is substance and accidentally is accident, which is the first division of form. As perfect or imperfect form is either actual or potential, which in turn will lead us to divide matter from form as a subject of change. The most well-known dispute about forms was how to understand the relation between forms-in-minds and forms-in-things. Both uncontroversially are forms since both things and ideas have characteristics (like “being physical” or “being correct”) but the dispute between Platonists and Aristotelians was over how the two were the same or different, with Platonism claiming they were the same object and Aristotle claiming they were the same logos or ratio. Nominalism seems to be the denial that there is any unity among the two at all, and that ideas (of themselves?) correspond to nothing at all.***
Thomas does prove that soul is not a body but the form of a body, but a close look at his proof show that he proves that soul is a substantial form ≠ the substantial form making something a body, or that a thing is made living by a substantial form that cannot be identical to another substantial form making something a body, since, were it so, then obviously every body would be alive.
*We’ll have to divide form from matter at some point, but this helps to explain why Aristotle so often would identify the form and the thing. Under the initial account of form, form is the thing.
**The text, yet untranslated, was proven authentic by Busa, in spite of now being listed as one of the dubia at corpusthomisticum.org
***We can get get to the heart of the differences if – leaving aside divine ideas and divine being – we see platonism as saying that forms in things and forms as known are the same in essence and mode of existence; Aristotelianism as saying that forms have one essence in different modes of existence, and Nominalism saying that the two forms are diverse both in essence and existence; or share no common essence or existence (though nominalism has more than one way of denying common essences.)