List, John:
Comments inserted within text:
> On Dec 22, 2017, at 9:38 AM, John F Sowa <s...@bestweb.net> wrote:
>
> On 12/22/2017 7:50 AM, g...@gnusystems.ca wrote:
>> for instance, you can say that a dicisign has subject(s) and predicate, but
>> in late Peircean semeiotics, the analysis into these “parts” is somewhat
>> arbitrary, and in some cases, so is the choice of whether it has one
>> “subject” or several.
>
> But that doesn't answer the question whether a sign has parts.
>
> A sign is a triadic relation. But it's not clear whether
> you can or should say that a relation has parts. For example,
> consider the dyadic relation greater-than or its symbol '>'.
>
> If you write "7 > 2", that statement has three symbols,
> and it expresses a relationship between 7 and 2.
> But those three symbols aren't parts of the relation.
>
Well stated!
But, this is traditional mathematical usage because of the role of
well-defined, separate, clear and distinct symbols of the orderly display of
numbers that must be aligned in sequence along a one-dimensional geometric line.
The formation of collections of pairs of atoms generates relations that depend
on symbols as parts of the molecule (Mereology). This is essential to the
emergence of the whole, as in the formation of chiral centers. The alignment of
the parts of the chiral molecule are in space. This proven by well-defined
emanations necessary for the patterns of x-ray diffraction of the sinsign.
In the material world of the chirality of molecular genetics, the symbols where
A is the symbol for adenosine and G is the symbol for guanosine, the three
symbols,
A > G
makes no logical sense.
In other words, the mathematization of symbols is dependent of the symbol
system under inquiry.
(A few days ago, John referenced the paper by Church on semantics and syntax
which is highly relevant to this discussion.)
> That particular relationship has 7 and 2 as parts, but the
> relation named greater-than can "have" infinitely many
> relationships. And as Aristotle observed, "have as part"
> is only one of many ways of "having”.
A chemical example of this is the abductive set of isomers of a given molecular
formula, such as was discussed for Pastuer's chiral forms of tartaric acid.
>
> One might say that the *extension* of greater-than is an
> infinite set of pairs. But that does not imply that
> greater-than has infinitely many parts.
Agreed.
>
> The *intension* of greater-than is defined by axioms
> (several statements with multiple symbols). But those
> axioms aren't considered "parts" of the relation.
Agreed.
Abstractly, this is one component of the “alphabetic” sign system for chemical
notation. The composition of the names of the parts (as names of atoms)
generates a new name for the molecule that is the "difference that makes a
difference” between atoms and molecules. The new name must give an exact
accounting of the spatial organization of the parts, as with tartaric acid and
virtually all other biochemicals.
>
> In summary, I would avoid using the word 'part' to
> describe any relation, including the sign relation.
Agreed.
>
> If anybody asked me "Do relations have parts?",
> I would say "What do you mean? Why are you asking
> that question? What would you do with the answer?”
Very well stated from the CSP spirit of inquiry perspective!
>From my perspective, I would suggest that John assertions are closely tied to
>the general problem of taxonomy / categorization / classification / order and
>organization which are intrinsic to the mathematization of natural sorts and
>kinds, as well as a host of other problems associated with the bare
>grammatical usage of the term “part” in the context of philosophy and public
>rhetoric.
Cheers
Jerry
>
> John
>
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