I believe that I many years ago read that Leibniz discarded belief in reincarnation on something like the grounds that there is no difference between not having an earlier life and having a previous life while not remembering it. Did Leibniz express such an opinion on reincarnation, and if so can you provide quotations?

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He did dismiss it, at least for the purposes of ethics. Oddly enough, it is not aimed at ancient or Oriental metempsychosis, but comes in passing in a polemic against... Descartes and his substance dualism. Here is from Leibniz's Letter on Cartesianism (to an unknown correspondent):

"I say, then, that the immortality of the soul, such as Descartes establishes it, is useless, and cannot console us in any way. For let us suppose that the soul is a substance and that no substance is completely destroyed; that being so, the soul will not perish, as indeed nothing will perish in nature. But like matter, the soul will also change in a way, and just as the matter which composes a man has at other times composed plants and other animals, this soul will also be able to be immortal in fact, although it will pass through a thousand changes and have no memory of what it was. But this immortality without memory is completely useless for ethics, as it overturns all reward and punishment.

What would be the use, Sir, of becoming the King of China on the condition that you forget what you have been? Would this not be the same thing as God creating a King of China at the same time as he destroyed you? This is why, in order to satisfy the hope of humankind, it must be proved that the God who governs all is wise and just, and that he will allow nothing without administering reward and punishment; these are the great foundations of morality. But the doctrine of a God who does not act for the good, and of a soul which is immortal without memory, serves only to deceive simple folk and to corrupt spiritual people.

It is interesting that modern Buddhists find Leibniz's irrelevance objection to be serious enough to warrant a response, see e.g. Perry, Reincarnation.

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    An excellent answer but it can be supplemented by later material. In 1991 Fichant published a booklet containing inedit Leibniz writings pertaining to the Eternal recurrence. Leibniz uses combinatorial arguments in commenting the revival of Origenes ideas by Johann Petersen. His stance on reincarnation is prudently ambiguous. (see a summary in NResher's Leibniz's quantitative epistemology in Studia Lz 2004).
    – sand1
    Commented May 11, 2019 at 9:58

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