How is it possible that he had past lives and how did he know they were his? What defines them as his?
How is it possible that he had past lives?
Because until he became the Buddha he hadn't eliminated craving. Craving leads to clinging, clinging leads to becoming, becoming leads to birth.
how did he know they were his? What defines them as his?
Do you remember your childhood? If so, why do you call it your childhood? Because your current existence(assuming you are an adult now) is conditioned by how the child behaved. In the same manner, if your mind had the power to go further back in time, even before your birth, you would see what actions you performed in your last life to condition your present birth. In that sense, it makes it your past life.
But here we are merely talking about a causes and effect relationship. Such a relationship does not require an existence of a soul. A mango seed does not require a soul to result into a mango tree. It rather requires sunlight, water, fertilizer, air etc. Water does not require a soul to turn into steam. It requires heat.
In order for something to qualify as a soul, it has to be under your total control. Which means, it shouldn't be existing without your consent, it shouldn't be changing without your consent, it shouldn't be dying without your consent. Can you find anything in your mind or body that meets those conditions? Could the child have stayed as a child if he/she didn't like to become an adult?
There is no independent soul, there is no independent self. Everything depends on something.
Buddha's past life depends on his past deeds.
Thus there are souls and self but they are dependent on past causes
In Maha-sihanada Sutta: The Great Discourse on the Lion's Roar
section of Ten Powers of a Tathagata.
- "Sariputta, the Tathagata has these ten Tathagata's powers, possessing which he claims the herd-leader's place, roars his lion's roar in the assemblies, and sets rolling the Wheel of Brahma. What are the ten?
(8) "Again, the Tathagata recollects his manifold past lives, that is, one birth, two births, three births, four births, five births, ten births, twenty births, thirty births, forty births, fifty births, a hundred births, a thousand births, a hundred thousand births, many aeons of world-contraction, many aeons of world-expansion, many aeons of world-contraction and expansion: 'There I was so named, of such a clan, with such an appearance, such was my nutriment, such my experience of pleasure and pain, such my life-term; and passing away from there, I reappeared elsewhere; and there too I was so named, of such a clan, with such an appearance, such was my nutriment, such my experience of pleasure and pain, such my life-term; and passing away from there, I reappeared here.' Thus with their aspects and particulars he recollects his manifold past lives. That too is a Tathagata's power...
(9) "Again, with the divine eye, which is purified and surpasses the human, the Tathagata sees beings passing away and reappearing, inferior and superior, fair and ugly, fortunate and unfortunate, and he understands how beings pass on according to their actions thus: 'These worthy beings who were ill-conducted in body, speech and mind, revilers of noble ones, wrong in their views, giving effect to wrong view in their actions, on the dissolution of the body,  after death, have reappeared in a state of deprivation, in a bad destination, in perdition, even in hell; but these worthy beings who were well-conducted in body, speech and mind, not revilers of noble ones, right in their views, giving effect to right view in their actions, on the dissolution of the body, after death, have reappeared in a good destination, even in the heavenly world.' Thus with the divine eye, which is purified and surpasses the human, he sees beings passing away and reappearing, inferior and superior, fair and ugly, fortunate and unfortunate, and he understands how beings pass on according to their actions. That too is a Tathagata's power...
the original question is about "jathaka Katha".My dear friends,there is huge discrepancy with doctrine of no soul(what the Buddha thought by Walpola Rahula thero) with Jathaka katha is mislead people towards continuous conciseness.so i think jathaka katha belongs to Buddhist literature.