I consider it a disservice when Mayr, in "What Makes Biology Unique", equated his organcist notion of emergence with Bohr's reference to water, as this tore at my own reading of the same literature.
It is hard for me to imagine that you have captured some sufficient and necessary understanding of the term beyond Mayr.
What makes the notion (emergence) difficult, for me, and it should send up flags at least for others, is that actual infinity in the sense that the parts equal the whole and yet the whole is more than the sum of the parts if applied without contradiction (others simply assume without evidence that that must be in this case) covers the place emergence seeks to carve out linguistically and yet it might still argue against reductionism nonetheless. There is no recognition of this in the literature and yet the lit. goes lightly over the original discussion of upward and downward causation given by Campbell.
Thus Russell(Principles of Mathematics page 145),
quote:
If a unity is infinite, it is possible to find a constituent unity, which again contains a constituent unity, and so on without end. If there are any unities of this nature, two cases are prima faciepossible. (1)There may be simple constituents of our unity but these must be infinite in number.(2)There may be no simple constituents at all, but all constituents, without exception, may be complex; or to take a slightly more complicated case, it may happen that, although there are some simple constituents, yet these and the unities composed of them do not constitute all the constituents of the original unity. A unity of either of these two kinds will be called infinite.
It is through the differences of upward and downward causation that implicate the possibility. We tend to polarize around the dualism instead. Reframing evolutionary space in terms of
Ackerman functions(see link to WolframScience here) (I have not thought this yet) seems to offer up a way to cognize the possibility raised logically by Russell but conflated in Mayr's notion of emergence.
It is possible there is no actual infinity through upward causation, in which case we would only have empirically the second of Russell's categories. Current thinking on emergence constrains scientists to logically stay restricted to a part/phrase of the second clause. That is why infinite creationism is sometimes a fresh breeze or a snowflake. Emergence keeps one away from this notion of infinity of Russell.
That's how I think it. I think you could have asked your question without bringing emergence into it.
Edited by Brad McFall, : wrong word
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