So, long story short, I'm supposing my father knew what he was doing when he took the power saw to the sink.
The less short story: Apparently, the seal between the sink and the garbage disposal took to leaking. I hadn't noticed since I don't use the garbage disposal much --- mostly, I finish eating stuff, after all --- and it was only earlier this year I got a handle on just how to start it on purpose. It's turning on the wall switch and turning the water on and twisting on a cap on the machine. The twisting of the cap was the thing I couldn't get right, although it's not a bad design scheme for avoiding accidents. I also hadn't looked underneath the sink to where the leak presumably was, since my mother had got rid of the recycle and trash bins from under the sink, so I never have need to look under there.
My father warned that he'd need my help getting the disposal loose, since he hasn't got the strength he had before his heart surgery. This is a point he reminds me of about four times per day, and I should point out, it doesn't really show in his activity outside complaints about how he hasn't got the strength he used to have. I was fine trying to twist the disposal out of its spot, except that the disposal wasn't going along with the twisting. Some of this was the complex of hoses and cables feeding into it, but with every one of them taken out, the remainder wasn't any more loose.
Finally my father identified the problem as the metal ring holding the unit up to the sink, which had turned into a solid sheet of rust. We tried a spray of WD-40 on it, and that didn't get anything anywhere. So that's when my father took out the power saw and hacked the old ring out of the sink.
It's a two-basin sink, so, we had kitchen sink abilities despite the removal. The dishwasher would be out of service, though.
Trivia: England's King Charles II granted to the Royal African Company, organized after the disbanding of the Royal Adventurers into Africa in 1672, the exclusive right to trade with Africa for a thousand years. It lost its monopoly a decade after the Glorious Revolution of 1688. Source: A Splendid Exchange: How Trade Shaped The World, William J Berenstein.
Currently Reading: Wrestling With Moses: How Jane Jacobs Took on New York's Master Builder And Transformed The American City, Anthony Flint. I was not aware Jane Jacobs had dabbled in writing science fiction, though I would have to imagine james_nicoll posted a double-blind what-if about it at some point.
PS: Dense Places I Have Lived: I have a vision for a set of articles on a particular topic and I hope not to annoy anyone living west of the Appalachians.