SUO: Re: Expostulation
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Matthew,
Reverting to the un-anglish manner (sans ">").
New material goes unindented in the following.
Jon Awbrey
JA: It has begun to occur to me over the last few days that
the difference between our prespectives -- "prespective"?
hmm, that was a genuine typo, but prehaps it will turn out
to have a meaning that is telling in the present application --
arises more than anything else from divergent ways of seeing
the use of "formal or logical or mathematical" (FOLOM) models.
I am going to think about this a little more and maybe try to
write out a separate comment about it, but it takes us back to
a couple of pictures that we have seen here before, to a whole
array of issues that I myself have been thinking about for quite
some time, and over all to a problematic that is rather ancient --
Immanuel Kant's use of what he called "schemata" as intermediate
representations between realities and the mind is the first thing
that comes to mind, but I am sure that the topic goes back further
than that -- anyway, here are links to a few of the occasions that
I can find on which we broached this subject locally and recently:
http://suo.ieee.org/email/msg00657.html
http://suo.ieee.org/email/msg00671.html
http://suo.ieee.org/email/msg00676.html
http://suo.ieee.org/email/msg01251.html
http://suo.ieee.org/email/msg01293.html
http://suo.ieee.org/email/msg01350.html
http://suo.ieee.org/email/msg01772.html
http://suo.ieee.org/email/msg01969.html
http://suo.ieee.org/email/msg01973.html
http://suo.ieee.org/email/msg02005.html
http://suo.ieee.org/email/msg02123.html
http://www.bestweb.net/~sowa/ontology/
http://www.bestweb.net/~sowa/ontology/gloss.htm
http://www.bestweb.net/~sowa/ontology/causal.htm
http://www.bestweb.net/~sowa/ontology/mthworld.gif
JA: As I tried to follow this thread, it turned out to be
a lot more tangled than I thought, going in, it would be.
Since the fine old philosophical concept of "reification"
seems to be yet another one of those ideas that will soon
be rendered meaningless by the cargo cultists of the world,
MW: I don't understand this remark.
I am lamenting the late abuse that the fine old philosophical
term of "reification" has come to endure in our "modish" times.
I regret that its original meaning and usefulness, along with
its critical linkage to the crucially important concept of
hypostatic abstraction is now on the brink of vanishment.
If I'm shocked at this, it is only in a Casablanching way,
because I have seen it happen enough times before to know
that all the sea's children "will lean that way forever".
Just in recent memory, the once-fruitful "functionalism"
has already rotted on these new vines, so "sour grapes",
for a' that. This sot of thing frequently happens when
a crate'o'words from a foreign clime or remote discipline
washes up on the shores of any new island of consciousness,
and all the inhabitants of that shore run out to carry off
what they can, making up new uses, and thus new senses, for
what they can salvage of the designed and intended purposes.
I suppose that it would be inescapable and thus excusable if
this analogy to that familiar form of "cargo-cultism" really
did carry through, and the disciplines, new and old, really
were so cut off from each other, but when the very people
who have elected themselves -- in that new-fangled form
of election that our late lamented democracy on this
shore has deviced -- I say, appointed themselves to
the Web Mans's Burden of binding the world into one,
when it is those very pirateers of culture who fail
to read the treasure they are compillaging together --
well, like I said, I pine away in lamentation at the
utter'de'comp'o'site'o'tro'city'o'th'scene'o'err'all.
JA: if not by the flushed enthusiasts of the WW-WC,
MW: WW-WC is??
Silly joke. WWWC = W3C = World-Wide-Web-Consortium.
JA: if you catch my drift, I have tossed in a number of
classical references to the vast and now distant ocean
of good sense, of which our own humankind was long ago
the master on this score, to wit, the associated ideas of
abstraction and analogy that go into our once-evolved crafts
of hypostasis and modeling, in other words, reification and
simulation, as I knew them, once, to be in their glory days --
alas! those days are now gone and quite forgotten.
But I nostalgicize ...
MW: I've read ahead a number of messages,
and this is a summary of where I am
at present.
MW: In what you say below it seems that you are using
a different definition of what a relation and tuple
is to me (at least).
JA: I have been suspecting this for quite some time now, but
you have insisted on repeating the standard definition of
a relation as a set of tuples, even though you rarely ever
use this defintion when it comes down to cases.
MW: This is not what I meant. I may make mistakes sometimes
(sloppiness) but I really do mean a relation is set of tuples.
Okay, then we will persist in trying to develop
the logical annd practical consequences of this.
MW: To you it seems that any construct ...
JA: I think that we may have to pause at this point and discuss
what is meant by "construct", no doubt as used within various
dialects, and if we fail to find a common meaning then we may
need to look for a way to dispatch the word without portfolio.
MW: (data) Construct, an assemblage used to represent something,
e.g., a relation, a tuple, a constant, a variable, a set,
a predicate.
Okay, in general, I would call these "mathematical objects",
but when I employ them as mental pegs on which to hang data,
then I think that I also call them "constructs" or "models",
at least, in some senses of these latter words. I may have
to resort to a technical dictionary, however, if the matter
gets any more critical than what is fitting for this moment.
MW: To you it seems that any construct
that has to involve at least three
things to be valid is necessarily
a 3-adic relation.
JA: I try to take you at your word, but I honestly never know for sure
when you are using the word "relation" to mean "relation" and when
you are using the word "relation" to mean "relation instance", as
seems to be required to make sense of what you go on to predicate.
JA: If I try to read this straightforwardly,
I must amend it to read a bit like this:
| To you it seems that any construct
| that has to involve at least three
| things to be valid is necessarily
| [a (>= 3)-adic relation instance].
JA: Can you clarify for me what you mean in this instance?
MW: I was thinking at the set level, like Chris M's signature,
e.g., gives involves a giver, a receiver, and a given.
Let me go back to what you said:
| MW: To you it seems that any construct
| that has to involve at least three
| things to be valid is necessarily
| a 3-adic relation.
Problem. What "construct" do you mean here?
1. The construct of a set, at the "set" level,
involves many things, namely, its elements,
which happen in this case to be 3-tuples.
2. The construct of a 3-tuple, at the "tuple" level,
involves exactly three components.
Why is there any waffling here about "at least three"?
JA: In order to continue without going totally bats,
I will have to substitute in your text below,
in square brackets, the changes that I need
to make sense of what you say. Please let
me know if these are not agreeable to you.
MW: The problem with this is that a 3-adic relation [instance]
requires EXACTLY 3 components, not at least 3 components,
and that these three components are necessary for identity.
JA: I do not know what the last clause, about identity, means here.
MW: That without all 3 elements, in this representation form,
you cannot identify the object uniquely.
But the 3-tuple is a "construct", a mathemetical object,
that is "constructed" precisely to bear this character.
It is an object, an object of discussion, at least, if
and just so long as we discuss it with any consistency,
but it is not, of course, in general, "the object" of
primary interest to us in our present applied setting,
which types of object we last saw under the signature
of x in X.
MW: Relatively few things [relation instances?] in real life meet
the criterion of exactly 3 components, and though I agree that
the example you have used of logical operators is one of them,
activities [activity instances?] generally are not.
MW: My sloppiness, I should have said activity classes.
That only makes it worse. We simply have to exert ourselves to
distinguish two levels of existence, mathematical or otherwise:
1. Relations, activity classes, transaction types.
2. Tuples, activity instances, transactions proper.
JA: You must try to remember whose team you are on --
it is not my fault that you keep throwing me all
of these interceptions! My team is the one that
keeps on saying that there are things in reality,
the activities of communicating, giving, learning,
and thinking, just to name a few, whose inherent
complexities -- the full measure of which no doubt
goes beyond our meagre mortal abilities to render
effable, effectively describabel, f-able, or even
formalizable at all -- are such that they require
relational models whose arity is at least three
in order to represent them with anything like
the requisite adequacy.
MW: Actually I am arguing that many 3-adic relations (or
higher) are inadequate for modelling these situations
adequately. This is because 3+adic relations imply
constraints that are just no true of the wolrd in many
cases, particularly in the cases of the examples given
above. I am also arguing that even for those where a
3-adic relation is valid, as in your logic example, it
is possible to replace it with a set of binary relations
that convey the same information.
JA: Your team is the one
that keeps on saying that it just ain't so,
that anything that can be talked to death
can be talked to death, without loss of
adequate descriptive power, solely in
the reduced medium of 2-adic relations.
Every now and then, you appear to want
to switch sides, and yet without having
your move be counted a foul of the game
in play, as if to say that references to
realities more complex than 3-adic should
count on the side of 2-adic reductionists.
I do not understand this sort of thinking.
MW: Perhaps because I (my team) is trying to discover
the truth rather than argue a point. Further, I
assume that there is something in what you say,
and I would prefer to understand what it is,
rather than just dismiss it because I don't
understand.
JA: The game-theoretic aspects of argument, inquiry,
and logical reasoning are commonly accepted and
go well beyond being just a colloquial metaphor,
but if you do not wish to acknowledge that you
are arguing for a particualr position, then
this will only delay the day of clarity.
MW: However, even with logical operators it is possible
to represent these without using 3-adic relations, ...
JA: No, it is not.
MW: T'is so :-o) (sticks tongue out)
JA: Jon eschews the classical response.
MW: although I agree that this does not remove
the three-ness of what is represented.
JA: ???
MW: I am quite happy that in a "giving" that ontologically there
are necessarily at least 3 things involved, at least one giver,
at least one given and at least one receiver.
Here, you appear to talking about an instance of what you call "giving".
MW: However, I do not agree that there is at most one giver,
at most one receiver and at most one given, and this is
what is implied by a 3-adic relation.
Here, you appear to be talking about a 3-adic relation, which would needs
correspond to a class of instances of the activity that you call "giving".
I will not engage you in the discussion of giving,
as you long ago mutated the subject into P-TRANCE,
or something, which nobody who understands giving
acknowledges to be the same notion, and until you
see the difference, there is no meeting of minds
to be found in this arena. Back to maths, then,
where the nuts'n'bolts can be laid out in view.
MW: I have demonstrated this.
JA: No, you have not.
MW: Then you have to explain what is wrong (and don't give me
stuff about (and a b c d) since this can easily be replaced,
and is strictly not necessary anyway, since the simple set of
relations -- since they are enumerated -- is all that is required.
Let us tackle this back on the other strand,
as I do not have all of the details to hand.
For the moment, all that I can do is to say,
again, that a set and a list are two rather
different constructs, and that 1-1 and 1-24
are two manifestly different manifoldnesses
of correspondence.
MW: You claim (elsewhere) that I have only presented tuples,
but in fact I have presented fully enumerated relations.
JA: And by this "enumerated" to say that you changed the subject from
a 3-adic relation to a 4-adic relation. "Changing the subject"
appears to be the solecism of choice in regard to this matter.
MW: What do you mean here by "changed the subject"?
We began by talking about a particular 3-adic relation,
with a question to resolve about its precise properties.
You then changed the subject to a 4-adic relation, whose
properties are very different from the properties of the
initial subject. This is a recognized logical fallacy,
going by the classical name of "changing the subject".
MW: My interpretation is "changed the identifier".
In your 3-adic relation, all 3 elements are
needed in order to identify any particular row.
There are really no "rows", much less numbered rows,
in the relation, because -- you guessed it!? -- the
relation is a set, not a list. There is not a whit
about bits'o'twine that might be wound around these
distinct tuples, indices, keys, labels, mark-up tags,
paper-clips, post-it-notes, rows, thumbtabs, thumbtacks,
nor any other brands of accidental office accessories to
find in the definition of a set, and the introduction of
them only amounts to changing the subject in an arbitrary,
capricious, and information-theoretically irreversible way.
MW: I have started by adding a "row id" which alone
is capable of representing the same object.
This is quite a legitimate move, even when
it isn't necessary.
It is not legitimate to change the subject in this way,
and I told you this from the beginning of this exercise.
It is not exactly cheating that you keep wishing to take
a few "warm-up practice swings" (WUPS) at the ball in play --
it is only accounted cheating when you omit to enter their
number on the scorecard -- to keep trying to get away with
this is "just not g o f" -- and it is a very good analogue
of this that you do when you try to reconstruct a 3-adic
relation in terms of other relations, some of which are
clearly 3-adic, but then to say that those do not count.
MW: Finally, there is still the issue of your claim that things can be
reduced to triads. You have however singularly failed to provide
the solution to this for the measurement example I presented for
those who think this can always be done without violating the
constraints that you wish to impose on others as to what
adacity is. I note the continued failure to respond
to this.
That was a long time ago, and I cannot even remember if I was
an active participant in that discussion, so maybe you could
find me a few links to the Archives as to where it left off.
You must understand that these are utterly textbook cases,
and although, pack-rat that I am, I have a hoard of old
textbooks still tucked away here and there about the
house, it is almost useless for me to read off this
info to you, since you always find a way to dismiss
those whom you have not elected to be your authority.
I sympathize with the difficulties incumbent on your
choice, as many of those sources probably clued in to
their initial mistake a while ago, and simply lack the
due consideration that it takes to save you any further
inconvenience in the matter, but I cannot have any direct
impact on your choice, nor on the actual consequence of it.
MW: I'm going to write two brief papers:
1. The transformation of a ternary relation into
some set of binary relations (and vice versa)
2. The use of relations to represent the world about us,
practice and limitations.
MW: These should at least put in one place where I stand currently.
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