Joseph Ransdell wrote:
Jean-Marc says:
I am surprised that you are claiming that the classes can be traversed
by a unique, "natural", ordered sequence from 1 to 10 while at the same
time you claim to have come up with a structure similar to a lattice,
these are contradictory assertions.
REPLY:
I made no such claim, I said there is an order and there is, most assuredly,
an order, and that is not a matter of convention. It is an order of
presupposition -- or, from another perspective, of internal complexity --
and it can be read from top to bottom in the lattice representation.
Whether or to what extent it can be filled out further is something that has
to be worked out laboriously by actually thinking the conceptions through,
as distinct from manipulating graphical representations containing the names
for the classes, If the word for the structure is not "lattice" please
supply the correct one. I am referring to what Merkle calls by that name in
his representation of Merrel's and Marty's versions of it. The one I came
up with is identical with that one. I'll send it along in a separate
message. The only important difference is that I gave the classes nicknames
of my own.
Joe Ransdell
the numbers on the boxes (1, 2, 3, ...) that you wrote are purely
conventional. since when you are calling a class '5' and another one '3'
you imply that "5 is bigger than "3", which in a lattice it is not.
you have to write 3-3-1, 3-3-2, 3-3-3, 1-2-3... to be correct. Check
Marty's work for a correct presentation.
/JM
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