In Phaedo, Plato (and this dialogue certainly seems to be platonic and not socratic) argues for the transmigration of the soul, in part with a cyclical argument:
Let us consider the question whether it is inevitable that everything which has an opposite be generated from its opposite and from it only. For instance, when anything becomes greater it must inevitably have been smaller and then have become greater. (70d)
He then goes on to suggest that these opposites are generated from each other:
- Weaker and stronger
- Slower and quicker
- Worse and better
- More just and more unjust
- Being awake and sleeping
And ends with the idea that death comes from life and life comes from death.
My sense of this line of reasoning is that Plato draws his conclusions from the way we make definitions of these abstract concepts. For instance, Google's definition of awake as an adjective:
Not asleep
Modern definitions of asleep don't define it as "not awake" (probably to avoid needlessly circular definitions), but it's easy to imagine defining each of the opposites in terms of its pair. So if we define death as not being alive and being alive as not dead, it follows that there is a cyclical relationship between them in the same way as sleep and wakefulness cycle.
Does that capture the sense of Plato's argument or am I missing something?