Udayana, Ibn Sina and Leibniz: three arguments for a first cause that do not need a beginning
People often assume that arguments for a first cause depend on the universe having a beginning. I want to compare three that don't, from three traditions.
Udayana (Nyāya, eleventh century). In the Nyāyakusumāñjali he gives a series of inferences for Īśvara, starting from effects: things like the earth are products, and products, like pots, need an intelligent maker who knows the materials. Note that Nyāya held the world is created and dissolved in beginningless cycles. Īśvara is needed for each arrangement, not for a first moment.
Ibn Sina (died 1037). Things whose essence does not include existence are possible in themselves and need something to make them exist. A chain of such things, even an infinite one, is still, taken as a whole, possible in itself, so it needs a cause outside the chain that is necessary in itself. No beginning required; Ibn Sina in fact held the world to be eternal.
Leibniz (1714). Even an infinite series of states of the world, each explained by the one before, leaves unexplained why the series exists at all. So the sufficient reason must lie outside the series, in a necessary being.
What interests me is that the Indian argument is causal-and-design rather than about contingency, and that it met fierce opposition at home: the Mīmāṃsakas and the Buddhist logicians both rejected Īśvara. I'd like to hear how these arguments look side by side, and whether the opponents' objections travel.