The domain of the science of heredity

I more-or-less take it for granted that:

• We should have a science of heredity;
• That this science should be called "genetics";

There seem to be a fair number of people who think that the term "genetics" is best reserved for the study of nucleic-acid-based heredity - but that seems like an extremely parochial and out-dated perspective to me.

Nor do there seem to be other sensible proposals for the name of a science of heredity. In my "Against Replicator Terminology" essay, I propose "replicatology" as the name for a possible alternative science of heredity. However, it doesn't seem very likely that "replicatology" will get anywhere. We already have a science of heredity. It's called "genetics".

This post is about another topic, namely: what is the proper domain of the science of heredity. If you look up "genetics" you'll see that it is often defined as the science of heredity in living organisms. This would make it part of biology. However, heredity, like evolution, is not confined to living things. Both of these concepts apply to all kinds of things that are not conventionally considered to be alive - electrical discharges, drainage basins, propagating cracks - and so on.

Do we really need a science of heredity for living things - and another science of heredity for non-living things? I am sceptical. I'm pretty sure that the domain of the proposed science of heredity should not be limited to things that are alive. This proposal means that genetics would not be a sub-discipline of biology.