What Did Epicurus Say About Whether Humans Have A "Soul"?
Short Answer: Epicurus definitely held that there is no such thing as an eternal or supernatural soul, because nothing is eternal in Epicurean physics other than matter and void, and nothing is supernatural - period. On the other hand, Epicurus devoted considerable attention to explaining the phenomena that is generally called "soul" or "spirit" as referenced in the cites below.
Long Answer:
In his letter to Herodotus, Epicurus wrote that the “soul” is composed of a particularly fine type of atoms of a unique type which themselves have no sensation apart from the body, but which carry the potentiality of sentience in combination with the body. Neither these particles, nor any other particles, can combine except according to the laws of Nature: “Next, keeping in view our perceptions and feelings (for so shall we have the surest grounds for belief), we must recognize generally that the soul is a corporeal thing, composed of fine particles, dispersed all over the frame, most nearly resembling wind with an admixture of heat, in some respects like wind, in others like heat. But, again, there is the third part which exceeds the other two in the fineness of its particles and thereby keeps in closer touch with the rest of the frame. And this is shown by the mental faculties and feelings, by the ease with which the mind moves, and by thoughts, and by all those things the loss of which causes death. Further, we must keep in mind that soul has the greatest share in causing sensation. Still, it would not have had sensation, had it not been somehow confined within the rest of the frame. But the rest of the frame, though it provides this indispensable conditions for the soul, itself also has a share, derived from the soul, of the said quality; and yet does not possess all the qualities of soul. Hence on the departure of the soul it loses sentience. For it had not this power in itself; but something else, congenital with the body, supplied it to body: which other thing, through the potentiality actualized in it by means of motion, at once acquired for itself a quality of sentience, and, in virtue of the neighborhood and interconnection between them, imparted it (as I said) to the body also. Hence, so long as the soul is in the body, it never loses sentience through the removal of some other part. The containing sheaths may be dislocated in whole or in part, and portions of the soul may thereby be lost; yet in spite of this the soul, if it manage to survive, will have sentience. But the rest of the frame, whether the whole of it survives or only a part, no longer has sensation, when once those atoms have departed, which, however few in number, are required to constitute the nature of soul. Moreover, when the whole frame is broken up, the soul is scattered and has no longer the same powers as before, nor the same notions; hence it does not possess sentience either. For we cannot think of it as sentient, except it be in this composite whole and moving with these movements; nor can we so think of it when the sheaths which enclose and surround it are not the same as those in which the soul is now located and in which it performs these movements. There is the further point to be considered, what the incorporeal can be, if, I mean, according to current usage the term is applied to what can be conceived as self-existent. But it is impossible to conceive anything that is incorporeal as self-existent except empty space. And empty space cannot itself either act or be acted upon, but simply allows body to move through it. Hence those who call soul incorporeal speak foolishly. For if it were so, it could neither act nor be acted upon. But, as it is, both these properties, you see, plainly belong to soul. If, then, we bring all these arguments concerning soul to the criterion of our feelings and perceptions, and if we keep in mind the proposition stated at the outset, we shall see that the subject has been adequately comprehended in outline: which will enable us to determine the details with accuracy and confidence.
We have a further explanation of these matters in Lucretius. In Book III, Lucretius wrote (translation by HAJ Munro):“Therefore, again and again I say, you are to know that the nature of the mind and the soul has been formed of exceedingly minute seeds, since at its departure it takes away none of the weight. We are not however to suppose that this nature is single. For a certain subtle spirit mixed with heat quits men at death, and then the heat draws air along with it; there being no heat which has not air too mixed with it: for since its nature is rare, many first beginnings of air must move about through it. Thus the nature of the mind is proved to be threefold; and yet these things all together are not sufficient to produce sense; since the fact of the case does not admit that any of these can produce sense-giving motions and the thoughts which a man turns over in mind. Thus some fourth nature too must be added to these: it is altogether without name; than it nothing exists more nimble or more fine, or of smaller or smoother elements: it first transmits the sense-giving motions through the frame; for it is first stirred, made up as it is of small particles; next the heat and the unseen force of the spirit receive the motions, then the air; then all things are set in action, the blood is stirred, every part of the flesh is filled with sensation; last of all the feeling is transmitted to the bones and marrow, whether it be one of pleasure or an opposite excitement. No pain however can lightly pierce thus far nor any sharp malady make its way in, without all things being so thoroughly disordered that no room is left for life and the parts of the soul fly abroad through all the pores of the body. But commonly a stop is put to these motions on the surface as it were of the body: for this reason we are able to retain life. Now though I would fain explain in what way these are mixed up together, by what means united, when they exert their powers, the poverty of my native speech deters me sorely against my will: yet will I touch upon them and in summary fashion to the best of my ability: the first-beginnings by their mutual motions are interlaced in such a way that, none of them can be separated by itself, nor can the function of any go on divided from the rest by any interval; but they are so to say the several powers of one body.
In Book II Lucretius had previously written:
“Wherefore the bodies of the first-beginnings in time gone by moved in the same way in which now they move, and will ever hereafter be borne along in like manner , and the things which have been wont to be begotten will be begotten after the same law and will be and will grow and will wax in strength so far as is given to each by the decrees of nature. And yet we are not to suppose that all things can be joined together in all ways ; for then you would see prodigies produced on all hands, forms springing up half man half beast and sometimes tall boughs sprouting from the living body, and many limbs of land-creatures joined with those of sea-animals, nature too throughout the all-bearing lands feeding chimeras which breathed flames from noisome mouth. It is plain however that nothing of the sort is done, since we see that all things produced from fixed seeds and a fixed mother can in growing preserve the marks of their kind. This you are to know must take place after a fixed law . …. To come to another point, whatever things we perceive to have sense, you must yet admit all composed of senseless first-beginnings: manifest tokens which are open to all to apprehend, so far from refuting or contradicting this, do rather themselves take us by the hand and constrain us to believe that, as I say, living things are begotten from senseless things. …Therefore nature changes all foods into living bodies and engenders out of them all the senses of living creatures, much in the same way as she dissolves dry woods into flames and converts all things into fires. Now do you see that it is of great moment in what sort of arrangement the first-beginnings of things are severally placed and with what others they are mixed up, when they impart and receive motions? Then again what is that which strikes your mind, affects that mind and constrains it to give utterance to many different thoughts, to save you from believing that the sensible is begotten out of senseless things? Sure enough it is because stones and wood and earth however mixed together are yet unable to produce vital sense.”
Discussion of this question is here.