You used the word instantiation without knowing what it meant.
Again you avoid any
detailed reply that is related to how
instantiation is used by me.
The needed
details of this usage and its impact on my reasoning, are given both in
http://www.internationalskeptics.com/forums/showpost.php?p=11285851&postcount=1535 and in the following corrected part of post
http://www.internationalskeptics.com/forums/showpost.php?p=11286596&postcount=1539:
What you are doing is this:
"{} = {}" is a tautology.
"{X}$X OR {X}~$X" is a tautology.
Since tautology = tautology, "{} = {}" is indistinguishable of "{X}$X OR {X}~$X".
This is a trivial way of reasoning.
A non-trivial way of reasoning enables to distinguish between "{} = {}" and "{X}$X OR {X}~$X" as follows:
"{} = {}"
can't be used in order to define optional (non-essential) properties of mathematical objects, according to their relations with each other.
"{X}$X OR {X}~$X"
can be used in order to define optional (non-essential) properties of mathematical objects according to their relations with each other, where
http://www.internationalskeptics.com/forums/showpost.php?p=11285851&postcount=1535 is a concrete example of such non-trivial reasoning.
What you call
instantiation is simply another name to force {X} to be a successor of X by using the wff "Y$Z <=> Y = {Z}", as if being a successor is an essential (non-optional) property of {X}.
Between these two posts I asked you to provide your view about
instantiation, and your hands-waving reply (that does not supply any
details about
instantiation) was:
Without understanding the meaning of the term, you boldly provided links to multiple posts wherein you claimed instantiations were provided? Is this your preferred method of building credibility? It is not working.
By the way, instantiation is a common enough term in Mathematics. You asked about it once before, and I told you what it meant once before.
So I ask you for the second time, more precisely:
jsfisher, please be more informative about your use of
instantiation, by providing
in details all what you think is needed in order to discuss about
instantiation and its usage among the issue at hand.
A given reply of "By the way" style
By the way, instantiation is a common enough term in Mathematics. You asked about it once before, and I told you what it meant once before.
is
not a sufficient reply for further discussion about the the issue at hand.
Also
http://www.internationalskeptics.com/forums/showpost.php?p=11284073&postcount=1525 clearly exposes the weakness of your reasoning about the issue at hand.
--------------
So I am waiting for your
detailed reply, that may be enables a fruitful basis for further discussion about the issue at hand.
In case that you are missing it, it is about the distinction between optional (non-essential) and non-optional (essential) properties of mathematical concepts.
--------------
EDIT:
Some analogy:
If we use Symmetry for better understanding of the issue at hand, then non-optional (essential) properties of mathematical concepts, are invariant under different points of view (for example, a ball shape is not changed under different points of view), where optional (non-essential) properties of mathematical concepts, are variant under different points of view (for example, a cylinder shape is changed under different points of view).
"{} = {}" is equivalent to ball shape, by this analogy.
"{X}$X OR {X}~$X" is equivalent to cylinder shape, by this analogy.
