Consciousness of Abstraction
December 26, 2003
I'll begin by describing a number of levels or types of abstracting.
The first four of these more-or-less correspond to Levels or perspectives on the use of
language. Because general semantic levels involve nervous systems, I
will then describe the neurological process of abstraction. And because
language is our focus, I will then particularize the neural abstraction process
to the context of words, so we can get to verbal levels. Once these are
presented, I will then be able to illustrate the complexity and the additional
requirements needed to illustrate abstracting between verbal levels.
Lexical abstraction.
- A large set of sentences.
- Selecting some of these sentences to represent the set or a subset.
Logical abstraction
- A large set of sentences of propositional form.
- A set of valid rules of inference
- Constructing more sentences using (1) and (2)
- Selecting some of the resulting sentences to represent the set or a
subset.
Semantic abstraction.
- A large set of words and sentences
- A collection of objects
- A mapping function from objects and sets of objects to words
- A set of rules for determining "well formed sentences".
- A set of valid rules of inferences applied to well formed sentences.
- Constructing more sentences using (4) and (5).
- A process for determining if any sets of objects "satisfy" a
well formed sentence.
- Selecting some of the resulting sentences to represent the set or a subset
of well formed sentences.
Note: Lexical, logical, and even semantic abstraction can be performed by (properly
programmed) computers. In 1963 a theorem proving program rediscovered a
more simple and elegant proof of the Euclidean geometry theorem that an isosceles triangle
(a triangle with two equal sides) has two equal angles. Research showed that the
relatively unknown proof had originally been discovered around 300 AD by Pappus,
but it had apparently been largely forgotten, especially in educational
contexts.
General semantic abstraction
- A large set of words and sentences
- A collection of objects
- A mapping function from objects and sets of objects to words
- A set of rules for determining sentences.
- A set of rules of inferences applied to well formed sentences.
- Constructing more sentences using (4) and (5).
- A process for determining if any sets of objects "satisfies" a sentence.
- A set of nervous systems to observe and respond to (1) through (8) and
other nervous systems.
- Selecting some words to represent the set or a subset of words, objects,
rules, process, nervous systems, and responses of nervous systems. (Note the absence of both the "valid" and "well formed"
criteria at this level.)
Neural abstraction underlying general semantics abstraction.
Korzybski's highly abstract model describes this using only three levels -
event, object, and verbal.
Our current model of the process is significantly more complex.
- An energy source in the environment.
- A medium to conduct energy (with losses [=abstraction])
- A sensory interface that can detect (some of) (some kinds of) energy.
(electromagnetic, vibratory, chemical, pressure, etc.)
- (Multiple) sense cells that undergo an electro-chemical cascade reaction
in response to various of the energy presences (with minimum threshold
levels of energy for activation -each responding to different kinds of
energy)
- Synapses
that allow one nerve cell to trigger (or inhibit) another.
- Neurons that respond to sensory cells and trigger (or inhibit) other cells
(nerve, glands, muscles)
- Collections of neurons that selectively respond to different combinations
of sensory cell responses.
- "Organs" within the brain that communicate via nervous process
with each other, with sensory input paths, with motor control functions,
with glandular functions, etc.
- Specialized muscle groups that move limbs for releasing pressure energy (
making marks on paper, tapping keyboards, pushing people, etc.) and
vibratory energy (grunts, growls, speech, etc.), as well as organs for
releasing chemical energy, (pheromones, hormones, etc.), both internally and
externally to the person.
In this process each of us has learned to "identify" certain marks
and sounds as "letters" and "words".
Neural abstraction to verbal levels process.
Assume light (electromagnetic energy) reflected from certain
"marks" are the input to the above process. It then expands as
follows:
- Light reflected from marks strikes a person's retina. Light is
transduced into nerve firings
- The retina abstracts from the billions of cells responding into millions
of nervous processes, sending a continuous stream of nerve impulses into the
optic centers of the brain. Nerve firings are transduced to
neurotransmitters and neurotransmitters induce some and inhibit other nerve
firings in a multiply repeated sequence of processes.
- The structure of the connections process various combinations of retinal
patters into distinct areas of the brain.
- Connections to other parts of the brain stimulate different regions to
interact with the incoming patterns. Patterns are "recognized"
and associations are brought forth from memory.
- Other parts of the brain are stimulated to
interact with the resulting patterns. Various centers respond to the
patterns, responses, and associations - centers that have been identified as
"emotional", "cognitive", "verbal",
"spatial", etc. (and many others whose functions we have no
understanding of).
- Here we have a significant gap in our model, because no allowable
instrumentation has yet been devised to observe in detail any particular
part of a brain functioning when an individual is presented with a visual
stimulus that we might call a particular word. We presume that there
are, perhaps highly individualized to each individual, combinations of brain
structures, neural firing patterns, synapse distributions, and specific
chemical changes that we could, in principle, sometimes be correlate to
particular visual or auditory patterns that we would call a
"word". These presumed structural-functional
processes could be labeled that person's "semantic
reaction".
- A small portion of any person's "semantic
reactions" could, theoretically, with the advent of appropriate
non-invasive instrumentation (Star-Trek like) be independently correlated to
specific marking and auditory patterns (which we might call specific words).
These "identifications" are learned, and they are necessary for
time-binding.
- Hypothesized highly individualized semantic reactions
are abstracted from ongoing process and stimulate other parts of the brain
to interact with various organs and motor control areas. Of the many
sensory experiences in combination with evoked associated memories
(including prior responses), and subsequent neural processing (including
devising new responses), a limited abstraction is selected to activate motor
neurons to effect physical gestures and or the emission of audible
vibrations.
- Some of these motor actions coordinated with physical objects produce
additional marks.
And the above process repeats over and over throughout the life of the
individual
- Assume that, in principle, the correlation presumed by (7) above has been
done for the population of a specific language and culture for all the
individual words accepted by the members of that culture, and that each time
a person learns a new word, his or her brain is mapped by the hypothesized
process to his semantic reaction to that word. Moreover, assume that
this culture has in place a process to keep the individual mappings between
individual semantic reactions to words up-to-date.
With this information at hand, we are in a position to define "verbal
level" in relation to neurological level. Whenever a person is
experiencing the particular semantic reaction associated with a word, we can
choose to focus our attention on the semantic reaction (neurological level) or
the associated word (verbal level). With this connection established, we
can now refer to the "marks on paper" as "words", because we
have a process of abstraction going from the energy emitted by the marks through
the sense organs, into the brains, to the semantic reactions of persons, which
because of our constantly up-to-date map, we can then say what the words
are. Note that the 9 step process from seeing words to writing words has a
branch, like an antenna sticking up on a little remote control toy, at the 7th
level of abstraction that performs an identification to bridge the gap
from neurological to "verbal" levels.
Of course, using Korzybski's three level model is much simpler, but it is
disastrously so, because it completely leaves out the fact that any verbal
semantic reactions we have are not simple abstractions from the
object level. Our semantic reactions include our prior experiences - our
memories.
Now consider what is involved in abstracting from one "verbal"
level to another. For lexical, logical, or even semantic abstraction the
process is very simple, as a review of the above processes shows, however a
"general semantic" abstraction from one "verbal" level to
another involves much more.
The starting point is the marks on paper that have been associated with and
identified by the cultural mapping of words to semantic reactions.
- First, the person involved must go through the first 7 steps in the
process to develop his or her semantic reactions to the set of words that we
will call the baseline verbal level.
- Second, the person must undergo "subsequent neural
processing (including devising new responses)"
- Third, the subsequent neural processing resulting from combining the
responses to individual words (mapped as semantic reactions) stimulate areas
of the brain, some new, some re-stimulated, generating additional semantic
reactions.
- Next, from these composite semantic reactions, the person must select
(abstract) which of his or her many ongoing neural processes (aka semantic
reactions) that have been identified with words need to be emitted.
- These selected reactions in turn stimulate the motor responses that result
in the writing of new marks (words).
Evaluating whether the words emitted at step 11 "constitute" a
"higher level of abstraction", in any conventional sense of the term,
requires that we have additional structure not yet described. We need, in
addition to words, sentences, rules of inference, and rules of composition,
objects, and reference rules, a dictionary, and general knowledge.
A dictionary is a set of sentences that identify a word with a set of other
words, usually in the form of either a synonym or other sentences, but may also
include "negative" defining by using antonyms and explanations of what
the word does not "mean". A dictionary specifies a
"definition" of a word in terms of other words, or processes using the
names of objects. Sometimes a dictionary also includes non-verbal
illustrations of objects for which the words stand in semantic relation to.
General knowledge includes, for our purposes, relations between words and
objects, ways of describing in words relations among objects, relations among
words, and relations among words and objects, as well as ways of responding to
objects or words, and the ability to specify, in words, appropriate actions,
(and other things too).
Both dictionaries and knowledge are highly individualized for each person.
Moreover the absence of the requirement for "valid reasoning" or
"well formed sentences" together with the interaction in step 5 of the
neural levels to verbal levels process with emotional and other portions of the
brain can result in semantic reactions not logically consistent or even
linguistically well formed.
Evaluating whether the words emitted at step 11 constitute a "higher
level of abstraction" (in the conventional sense) requires that the person
performing the evaluation have at his disposal the dictionary for all the words,
and the knowledge associated with the words and sentences forming the basis
level. In doing so, process step (9) may require a significant amount of
processing.
Because of the highly individualized nature of dictionaries and knowledge, as
well as the similarly individualized response patters, vis-a-vis cognition,
emotion, etc., there is no way to guarantee that any two individuals will arrive
at the same evaluations regarding whether or not, between two sets of
statements, one is at a higher level of abstraction than the other.
A high degree of consistence in the acculturation process regarding
definitions of words, and the associated knowledge is required for agreement to
be possible, and this is where time-binding comes in. The greater the
"enforcement" of standard dictionary definitions and the acquisition
and sharing of knowledge, including valid reasoning, well formed sentences, and
the appropriate proportion of emotional, cognitive, and other responses, the
more effective time-binding is.
Evaluating the relative level of abstraction between sets of verbal
statements with any degree of reliability requires consistency of use of terms,
agreement on definitions, the use of valid reasoning, well formed sentences, and
the primacy of conditioning of brain function to give primacy of valid reasoning
over emotional responding. There is nothing in the neurological to verbal levels
that provides any mean for processing between verbal levels of
abstraction. The evaluating of the relative levels of abstraction between
different verbal statements depends entirely on the culturally shared
definitions of the words involved, the knowledge associated with these words,
and the emotional, and other brain reactions, to the words in their context and
the person's situation, as well as the propensity of the person to use valid or
invalid reasoning methods. It is only through time-binding that agreement
is achieved regarding any particular set of statements as to their relative
levels of abstraction.
With that in mind, we have some shared knowledge of certain definitions that
are fairly consistently evaluated regarding each other. These comprise the
following (not necessarily complete) general levels.:
- Observation statements.
- Description statements
- Theories to explain observations
- Inferences as to facts not explicitly observed (usually based on 1, 2, and
3)
(including making assumptions and "jumping to conclusions" - not
different in kind, just in validity of reasoning.)
- Speculations as to causes - (usually based on the above, but sometimes
without valid logic)
- Attribution of motive - (similar to cause, but where people are involved)
- Judgments of value - (good, bad, desirable, undesirable,
"worthless", etc.)
- Emotional reactions - (love, hate, like, anger, depression, etc.
- Etc., - recycling (4) through (8) above repetitively - with and without
more of (1) through (3)
To go from each of the above levels to the next involves the 11 levels
described earlier. To go from observation to description involves the
eleven steps previously described. To go from descriptions to theories
involves 10 more steps. (If you think the math is funny, you forgot to take into
consideration that the end of the first process is the start of the next.
The step 1 of the next abstraction begins with the step 11 of the previous
process.) That means that the full complexity of going from observation to
emotional reactions expressed in words involves 81 levels of abstracting,
and there are ten (10) more levels for each additional higher level of
abstracting.
Consciousness of abstracting traditionally involves keeping in mind, from
moment to moment, all the steps that involve abstracting or "leaving
out" information, when we are making assumptions, being aware of our
inferences, recognizing our judgments, and realizing when we are experiencing
emotional reactions. We are expected to do this so that we can insure the appropriateness
of all these steps, and to be aware that they are based on incomplete and
possibly incorrect information.
- We always miss possible information, because we cannot see or know
everything.
- Our verbal descriptions may be inadequate or possibly incorrect, because
we cannot say "all" about anything.
- Our theories may be inadequately tested, and they just might fail in this
instance. (Timen+1 is not timen.)
- Our inferences or assumptions could be wrong. (Assumptions are not
"bad"; we just have to be prepared.)
- Our guesses about cause could be wrong. (We might have used the wrong
theory.)
- Our guesses about other people's motives may be wrong. (We can't know the
"whole" story.)
- Our judgment about the worth of something may be out-of-step with our
culture. (One man's poison . . .)
- Our emotional reactions may be counter-productive.
- Our reactions to our reactions might take us "way out in left
field".
But let not all these possibilities paralyze us. Go forth and act, but be
prepared.
Annotated bibliography of general semantics papers
General Semantics and Related Topics