 Alcmaeon developed the first argument for the immortality of the soul, but the testimonia concerning it differ slightly from one another, and it appears to have been taken over and developed by Plato, so that it is very hard to determine exactly how to reconstruct Alcmaeon’s own argument. Barnes (1982, 116–120) and Hankinson (1998, 30–3) provide the most insightful analysis. Alcmaeon appears to have started from the assumption that the soul is always in motion. At one extreme we might suppose that Alcmaeon only developed the simple argument from analogy, which Aristotle assigns to him (De An. 405a29). The soul is like the heavenly bodies, which Alcmaeon regarded as divine and immortal (DK, A1, A12), in being always in motion, so it is also like them in being immortal. This is clearly fallacious, since it assumes that things that are alike in one respect will be alike in all others. The version in the doxographical tradition is more sophisticated (DK, A12). Alcmaeon thought that the soul moved itself in continual motion and was therefore immortal and like to the divine. The similarity to the divine is not part of the inference here but simply an illustrative comparison. However, Mansfeld has recently pointed out that the doxographical report in Aetius is just a paraphrase of Aristotle’s earlier report with the significant addition that the soul is self-moving. Examination of the context in Aetius shows that the self-motion of the soul, which is attested independently for Plato and Xenocrates, was projected back on Pythagoras and Thales, who are very unlikely to have held such a view. This context and Aristotle’s failure to assign self-motion to Alcmaeon makes it likely that the same projection occurred in the case of Alcmaeon, who thus is likely to have assigned continual motion but not self motion to the soul (Mansfeld 2014b, see also Laks 2018). The core of the simpler argument is the necessary truth that what is always in motion must be immortal. This is the assumption from which Plato starts his argument for the immortality of the soul at Phaedrus 245c, but how much of Plato’s analysis of what is always in motion can be assigned to Alcmaeon? Plato makes no mention of Alcmaeon in the passage. There are still serious questions for Alcmaeon, even on the more sophisticated version of the argument. We might well recognize that things with souls, i.e. things that are alive, are able to move themselves, and conclude that it is souls that bring this motion about. We might also conclude that the soul, as what moves something else, must be in motion itself (the synonymy principle of causation).  But why did Alcmaeon suppose that the soul must be always in motion?  (Hankinson [1998, 32] provides two possible answers and discusses the difficulties with them.) Horn argues that there is no obvious meaning to the idea that the human soul is in continual motion so that Alcmaeon must be talking about a world soul, which has the continual motion of the heavens (2005, 157–8). However, Mansfeld rightly argues that Aristotle’s report on Alcmaeon’s view of the soul is clearly about the human soul; since the soul being discussed is said to be similar to the heavenly motions it has to be distinct from them (2014a). Finally, what sort of motion is being ascribed to souls? The natural assumption might be that the soul’s motion is thinking, but, at this early point in Greek thought, Alcmaeon was more likely to have thought that, if the soul is going to cause motion in space, it too must be in locomotion. Plato describes the soul as composed of two circles with contrary motions, which imitate the contrary motions of the fixed stars and the planets, so that the soul becomes a sort of orrery in the head (Timaeus 44d). It has been suggested that this image is borrowed from Alcmaeon (Barnes 1982, 118; Skemp 1942, 36 ff.).