Thread:
GR: http://permalink.gmane.org/gmane.science.philosophy.peirce/14086
JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/14122
GR: http://permalink.gmane.org/gmane.science.philosophy.peirce/14123
JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/14124
JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/14127
GR: http://permalink.gmane.org/gmane.science.philosophy.peirce/14128
JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/14129
SJ: http://permalink.gmane.org/gmane.science.philosophy.peirce/14133
Sung,
In order to pursue these questions with any degree of seriousness a person would
have to take the definition of a triadic sign relation and the definition of a
mathematical category seriously, and so far you haven't been doing that.
First off, you appear to be confusing a category with a single composition
triple of functions (f, g, h) such that h = f o g, and that is a serious confusion.
Next, you confuse a sign relation, a subset of a cartesian product O x S x I,
with a single triple (o, s, i) in a sign relation, and that is another serious
confusion.
Finally, you propose what amounts to saying:
• f maps o to s
• g maps s to i
• h maps o to i, where h = f o g
Functions are defined as mappings between sets, so we need to have names for the
sets of objects, signs, and interpretant signs that are under consideration in a
given discussion. Let's call those sets O, S, I, respectively. So what you are
saying, more properly stated, amounts to this:
• f : O -> S
• g : S -> I
• h : O -> I, where h = f o g
Functions are special cases of dyadic relations. So we have the following:
• f is a subset of O x S
• g is a subset of S x I
• h is a subset of O x I, where h = f o g
Right off the bat there is a problem. There is indeed a dyadic relation between
objects and signs that can be "projected" out of a triadic relation, but that
dyadic projection is not a function in general. Objects may have many signs
that denote them, and signs may have general reference or plural denotation,
just for instance. The same thing applies to all the other pairs of domains.
That is not the last of the problems, not by a long shot, but it's all I have
time for right now.
Regards,
Jon
--
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