This is a reply to Jerry (***):
>Let us discuss the concepts of "element", "number", "size", "quality" and
>such in more depth and detail.
>The word "element" can be understood both in a set-theoretical and in a
>chemico-logical sense. The concept goes back to the Greek a-tomos (not
>divisible).
***The concept of a number (in mathematics) is a unique abstraction - it
signifies a unique position in an endless sequence of unique
positions. Peano named these successor relationships within a
defined group of axioms over one hundred years ago.
Now I extend this definition by saying: "The concept of a number includes -
above signifying its position in an endless sequence of positions cf.
Peano - a statement about the fragmentation of the entity this number
describes. A number is a description of an extent AND concurrently a
statement about the integrity of that extent. A value - matched to the
number - does not imply the integrity of the underlying concept."
Difference Peano - Javorszky:
Peano understands under "5": "This is an extent, signifying an extent
between the extents 4 and 6."
Javorszky understands under "5": "This is an extent, signifying an extent
between the extents 4 and 6. Furthermore, it signifies that the underlying
interval is not segmented. Possible other ways of writing '5' as a value are
:1+1+1+1+1, 1+1+1+2, 1+1+3, 1+2+2, 2+3, 4+1. These descriptions are
Peano-equivalent, Javorszky-distinct."
The concept of a chemical element is also unique and it also occupies
a position. However, the notion of "successor" is radically
different in chemistry. Roughly speaking, the combining capacity of
a chemical element is unrelated to the successor relation. Same
terms, but very very different meanings in the two disciplines. Was
it not B. Russell who introduced this semantic trick in an attempt to
justify his logistics of "atoms" of logic? A similarity of meaning
exists but it certainly is not an semantic "isomorphorism" that
builds a bridge between chemical logic and mathematical logic.
The concept of understanding is to translate unspoken experiences into the
public language. That chemistry has so far not been understood by
mathematics is a marketing chance. If there were no subjective abysses
between the concepts: "set of understandable, logical relations" and
"chemistry", there were no progress possible. Imagine how the situation was
before trigonometry was discovered. There were things you could count,
reckon and calculate and then there were distances and heights. There was
of course no isomorphism between bushels of grain, gold pieces and the
height of towers.
Progress is possible. Progress shows itself by being all of sudden
able to calculate something one was not able to calculate before.
>It is basically a tactile experience. If you can touch it and it
>is of minimal extent, we call it "object", "element", "idealised thing" and
>such. If you cannot touch it and it is of a minimal extent, we call it
>"force", "space", "relation", "logical principle" and the like.
*** The tactile experience is indeed important component of
distinguishing "real" stuff from abstractions, ideas and the like.
None the less, the concept of a chemical element also includes an
abstract component by virtue of its relations with other
abstractions. Chemistry is thus a "bridging" discipline in which it
functions in both the world of ideas and concepts as well in the
world of sensory perceptions.
Yes. Chemistry occupies itself both with the stable, static concept of an
"atom" or "molecule" or "complex" and as well with derived concepts like
"valence" and "affinity" and "aggressiveness" and "nobility" (in German,
they say The noble gases because they have no desires towards others)
This point we have complete meeting of minds, or have I not understood your
injunction?
>As we play with cards, we distinguish the cards as physical things we can
>bite on and sensually experience and the ways of playing (with) them which
>we cannot sense by older regions of the brain. Experiences we make before
>having learnt to speak we treat differently to experiences we store in such
>parts of the brain the lexicon is in connection with.
>So, we have avoided mixing (linking) the two levels up: the set of objects
>and the set of their relations. Yet, it is a great difference if we speak
>of a set, whether we mean the number of "Sachverhalte" (Wittgenstein: ~
logical facts) or the number of tactile things.
*** In chemistry, this is unavoidable. The meaning is determined from
the context. When I use the word "benzodiazapine", the reference may
be an abstraction as a set of atoms arranged in a pattern or it may
mean a drug for human consumption.
Yes. Now we begin to see eye to eye. The idea is to look more into the
connection between what a thing is and how its possibilities to appear in
context are. ("Ueber das Ding und die Moeglichkeiten seines Vorkommens in
Sachverhalten") This is what the song goes about. Absolutely right. Now we
beign to discuss, how many contexts are there if one uses n things.
This is the right approach. In how many distinct contexts can n things
appear? And how many of the n are distinct (within/among themselves)? Yes,
this is it! Now we talk about the same question.
>My approach integrates the Kant concept of the thing as such and the
>Wittgenstein concept of the (number of) ways of being included in
>Sachverhalte (logical relations). My starting point is to investigate:
>"How many logical relations are there per object AND which fraction of
thing
>is needed to represent a logical relation with?". These symmetric questions
>touch the information carrying ability of carriers, therefore have some
>relevance.
*** In chemistry, the logical relations are not a mathematical variable
in the sense that you are using the term, rather a property of the
element with respect to other elements as well as the circumstances.
The logical combining of chemical elements is highly dependent on the
reaction partner as well as the circumstances of the conjoining
environment. This is one of the critical components of the endless
diversity of unique chemical substances. This endless diversity of
chemical structure is also the source of living systems.
Right. The question therefore is: "a property of the
element with respect to other elements as well as the circumstances." - how
many of these are there?
Maybe we should rethink the usage of the word "endless". You will no doubt
have seen satellite-made images of the Earth. We will agree that on this
planet no thing can exist in an endless quantity. So please let us drop the
term and the concept of endless. The question is: how many? We shall have
to dwell on this point until we agree that the usage of the term "endless"
in these 2 sentences is false:
"This is one of the critical components of the endless
diversity of unique chemical substances. This endless diversity of
chemical structure is also the source of living systems."
and, after that, reformulate the question with "how many" instead of the
obviously irrelevant and non-fitting term "endless".
In short, both chemical mathematics (reactivity, selectivity) and
biochemical mathematics (reactivity, operations, selectivity) are
highly irregular compared to the natural numbers or to such
mathematical structures as groups.
So the task is to find such a way of presenting natural numbers that the
pattern we observe will be reflected in the way we look at the natural
numbers. This task has been attempted by me (and with no small success, may
I say.
*** I will not comment on the issues of your languaging of "partitions"
and choice because I do not understand how your work relates to the
Mobius inclusion exclusion principle and related general methods for
identifying unique subsets. I feel that your explorations are being
developed as our conversations continue.
As I don't know what Mobius meant, I cannot comment further. I agree that
as people talk they will find out if and how far they understand each other.
Best regards
Karl
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Received on Fri Jul 11 13:21:22 2003
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