Your linkage of Mendel and Cantor is a good start, but baby, you've got a long way to go!
We are in the midst of a renaissance in the historiography of set theory--Grattan-Guinness, Ferreiros, Garciadiego.
You are going to have to revisit your fundamental mathematical ideas if you are ever to say anything about Mendel and Cantor. Above all, you have to decide where you stand on constructivist mathematics. This involves, in Cantor's case, deciding whether he has anything at all to say which has logical content, or whether he is simply blithering.
I think he is simply blithering. And on that score, please immediately read A. Garciadiego, BERTRAND RUSSELL AND THE ORIGINS OF THE SET-THEORETIC 'PARADOXES."
Now, where Mendel makes his constructivist intervention in his argument, is interesting, but remember, Mendel has to be saying something which has sufficient logical content (he's not simply pulling letters out of a bag) for there to BE a constructivist intervention.
Compare Godel. It is clear now that Godel was such a sloppy investigator and the issues were so devoid of logical content, that there are no such things as Godel's theorems--they are drivel, they don't have sufficient logical content for one to claim they are arguments, much less faulty arguments. You have to confront this issue in Mendel too.
Needless to say, we have begun a new era in our intellectual history, in which a lot of sacred cows are being slaughtered. Good.
By the way, it may well be that Mendel is not so much a Cantorian mathematician, as that BOTH Mendel AND Cantor are simply using the same constructivist b.s. math which dates back to Aristotle, who developed the notion because he felt that Zeno's "paradox" had somehow to be avoided. Well, Zeno's "paradox" has no logical content and is letters pulled out of a bag.
Constructivism has no program--it has no job to do. Therefore, it should be no surprise that it is b.s., and all arguments using it are b.s.
Good luck revisiting your settled opinions! It's difficult!
SSRN-Paradox, Natural Mathematics, Relativity and Twentieth ...Apr 18, 2006 ... Ryskamp, John Henry, "Paradox, Natural Mathematics, Relativity and Twentieth-Century Ideas" . Available at