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Author Topic:   Gregor Mendel and Georg Cantor
Brad McFall
Member (Idle past 5033 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 1 of 3 (52838)
08-29-2003 10:37 AM


I am REviewing the Harvard University Press "Experiments in Plant Hybridisation" by Gregor Mendel here, the copy foreworded by PC Mangelsdorf. If anyOne learns anything from this threaD I will add aNNotations to the Mendel Web accordingly. Please try to keep the color commentary to a minimum as colour is the topic this book artificially covers. And good luck.
I will start with the claim that Mendel was working with a notion akin if not identical to Cantor in near-by Central Europe of cardinal and ordinal numbers but that this did not show up not because of the existence in this time of philosophy of Science in Darwin's circles and philosophy of Math as it reached an international stage but because no practical use of Transfinite EXPONETIATION. I will metadata this review to the final effect that when Mendel wrote (p34 in this reproduction) "If it be accepted that the development of hybrids follows the lw which is valid for P i s u m, the series in each seperate experiment must contain many forms, since the number of the terms, as is known, increases, with the number of the differentiating characters, as the powers of three."he ~Mendel~ meant but was not using a transfinite exponential number that Cantor's most read work? basically concludes conceptually with. I contend that Mendel was using the concept of cardinal and ordinal numbers between the copy-pages-17-19 and that connotations of cardinality are denotationally genetic out the space between periods "If the numbers in which the forms beloning to these classes appear be compared, the ratios of 1,2,4 are unmistakenably evident. The numbers 32, 65, 138 present very fair approximations to the ratio numbers of 33, 66,132." and for ordinals at the space between the two periods of "All constant combinations which in Peas are possible by the combination of the said seven differentiating characters were actually obtained by repeated crossing. Their number is given by 2^7=128."
THE BURDEN OF THIS VIEW IS UNDBOUBTEDLY ON ME but I feel as confident as the cost of Cornell degree that such is the case whether upper or lower for I find the issue of the ordinals of ordinals dealt with in the classical genetic difference of transmission vs physiological genetics and Mendel's possible use of Newton's "black body" in the see color. With nanotechnology this implies that one may indeed scientifically transform one species into another by ARTIFICAL FERTILIZATION else this notion of seed will not hold up generalized to any taxogeny as the color relations will not hold up the biogeography of reciprocation. The conclusion in the conceptual retension is that bioloigcal change IS NOT remanded primarily within evolutionary theory at all as is the dominant popular teaching and rightly criticisable by "creationist" groups. I need only think of what the "reciprocal cross" is in Lichens and I already have problems as deep as Haldane's dillema or Provine's refusal to legally act as MENTOR in my education finished. Watch in for the word "series".
The only remaing question for me is whether any proposed statistical refinement tends more in the data base to that tagged as genetypic vs pheonotypic as the quibble between which type is typed as what biologically into the computer will remain as well an issue of pure math the philosophy of science that has been growing academia since this time is framed by Mendel in this work as well. Perhaps biology and computers will show that some other sign-symbol-formalism be taught be we can not grasp the score of this nature untill more than the classes being taken as Croizat's phllotatic symbols which are NOT mathematical and perhaps only I understand my own short hand.
I will discuss any thing directly if it is by quote within this text till learning my point shows other threads that engage the thought whether in line with the same sequence of concepts or not.
[This message has been edited by Brad McFall, 08-29-2003]

  
jrysk
Junior Member (Idle past 5691 days)
Posts: 2
Joined: 08-28-2008


Message 2 of 3 (479599)
08-28-2008 1:52 PM


Cantor, Mendel and New Set Theory Historiography
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

  
bluegenes
Member (Idle past 2477 days)
Posts: 3119
From: U.K.
Joined: 01-24-2007


Message 3 of 3 (479612)
08-28-2008 4:42 PM


Twins?
There's two of them?
Well I'll be blowed. It took five years, but old Brad's finally got a dialogue going.

  
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