ONT Re: Differential Logic & Dynamic Systems
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Howard,
I continue with the inspection of your Para-Hertzian picture,
interspersing new remarks along the way and then continuing
from where I left off last time.
Howard Patee wrote (HP):
Jon Awbrey wrote (JA):
JA: I will pick up this Hertz-lichen picture once again and
keep on trying to get a clearer picture of what it means.
HP: | EXTERNAL OBJECTS ____ WE FORM FOR OURSELVES ____ IMAGES, SYMBOLS, OR PICTURES
| | / [SIGNS, BRAIN STATES, WHATEVER]
| | / |
| | / |
| [NATURAL LAWS] . . . SUCH THAT . . . / [LOGICAL, MATHEMATICAL MODEL]
| | / |
| | / |
| | / |
| NECESSARY NATURAL /___ ARE THE SAME AS THE _____ LOGICALLY NECESSARY
| CONSEQUENTS CONSEQUENTS OF THE MODEL
HP: Let me elaborate. The only formal part is in the right vertical column. All the rest is
a kind of epistemological diagram indicating the necessary conditions for an empirically
verifiable formal model to successfully represent our experience. An important aspect
of Hertz's statement, emphasized by the diagram, is that the horizontal lines represent
the observer's (or agent's) semantic interaction with the world (i.e., detection, pattern
recognition, observation, measurement), the right vertical column represents the syntactic
or formal (usually sequential) manipulations of the observer, and the left vertical column
represents the part of the world (space, time, energy, and matter) that we choose to model.
The separation of semantics (measurement of particular events) from syntax (the formal model
of universal laws) is essential for physical theory.
JA: I thought at first that I recognized this picture,
but a lot of the things that you have said in the
meantime have muddled my sense of what the sundry
headings and labels on its several parts may mean.
Maybe the problem is in the translation, the word
"consequent" is especially problematic, and seems
to have a punning sense in the way you explain it.
Dewey was fond of a punning parse when it came to
the word "con-sequence", so perhaps I am missing
some cosmic joke here. It wouldn't be the first
time, for sure.
JA: The words "logically necessary" did seem pretty clear to me, once,
unless you wish to retract them now, and to recuse yourself from
further association with that not-to-be-trusted name of "Logic".
Once again I fear that the problem here is that we attach all
sorts of different connotations to the word "Logic", and this
promises to be ongoing problem due to our historical setting.
We have just been through a period of a hundred years or more
of a "decline in logical literacy" (DILL), itself due in part
to a "degeneration of logically operative realism" (DOLOR) that
beset us from the beginning of the Late Great 20th Century out of
that "Foist Order Logic, Self-Conceived Analytic Philosophy" (FOLSCAP)
that a certain following of "Principians" had set up in their own images
and their own imaginations as the one true "Logic As God Wrote It" (LAGWI).
Well, I understand how anybody would get the wrong idea about logic from that,
but, myself, I have gotten other ideas, from sources that I trust just a bit more.
JA: Oh well, let me get down off the soapbox and get back to the picture.
You next said some things about "'following' in a temporal sense" that,
once again, I thought I grasped at first:
| HP: Hertz's "consequent" means only "following" in a temporal sense.
| It does not imply a "consequence" which means two things.
| Logically it means "derived from" and
| physically it means "caused by", often
| a source of confusion, as you warn us.
But it appears that I was only grasping at straws here,
given the things that you said after that:
| HP: For "logical" a physicist would mean "mathematical" (they don't trust logic).
| For example, one mathematical consequent of Dirac's image of electrons
| (the relativistic wave equation) are states with negative energy.
| At the time this was considered nonsense, as well as contradictory
| to experience, and some thought, even to logic. However, this
| mathematical consequent of Dirac's image turned out to be
| an image of the consequent of high-energy collisions
| (pair production, the creation and annihilation of
| particles and antiparticles ). Physicists believe
| that in the long run experience (our images of
| natural consequents) will always supervene what
| we call logic or even nonsense.
JA: That left me at an utter loss. I seem now to have three different senses of "following" --
the number three is not a problem, but I just cannot follow what you mean by any of them --
perhaps it has something to do with e-lecturons traveling backward in time?
Given the accumulation of these and further explanations of how you intend
the phrase "LOGICALLY NECESSARY CONSEQUENTS OF THE MODEL" to be interpreted,
together with what I will guess is meant by "NECESSARY NATURAL CONSEQUENTS",
my updated hypothesis would have to be that you are referring to what I might
call the "properties" or the "qualities" of an object, except that maybe you
are (unnecessarily) restricting yourself to "formally provable" properties
on the right. So let me redraw an approximate sketch of this scene in the
manner to which I've become accustomed, and that makes me more comfortable
from a hierarchical perspective, with properties placed above their objects:
| Natural Property Model Property
| o---------------------------->o
| ^ ^
| | |
| | |
| | |
| o---------------------------->o
| Natural Object Model Object
I take this sort of commutative diagram as nothing more or less than
a pictorial representation of what we mean when we intone the jingle:
"The picture of a quality is a quality of the picture".
Now, if I need to be more careful about it, I will probably be forced
to utter things like "object in the model" and "property in the model",
but let's not go there, just yet. I can think of some problems already
with such a rough approximation, but maybe this bit will do for a start.
Maybe I should stop here, and wait until we can discuss this fraction of it.
Jon Awbrey
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