Everything interacts with its environment - from the smallest sub-atomic particle to the largest galaxy. We are no different.
Interaction insinuates dynamic inter-relationship. Knowledge can be defined as "post-active" comprehension. The dynamic inter-relationship involved in the comprehension necessary to achieve knowledge is the tension between opposites, or what may be called reciprocal reciprocation (RR).
A RR consists of two diametrically opposing concepts which cannot exist without each other. They are mutually exclusive in concept and definition, yet mutually inclusive in the operation of comprehension.
The opposition of the positive and the negative is the most readily recognized RR (ie. Yes and no). The simplest example is left and right. If something is left (yes) then it is not right (no) - and vice versa. A technological analogy of this would be the digital computer, where a circuit is either on (yes) or off (no).
Two important facets of RR need to be under stood. First, one must remember that RR allows comprehension so that definition may be determined - at which time we acquire what is called knowledge. Thus even the slightest differentiation of objects or ideas is done through the use of RR: something just left of center will still be realized to be to the right of something - or, something we comprehend to be blue-green will be neither blue nor green, but something else.
The second, and more subtle facet, is that of prioritization of comprehension. The standard concept of space, for instance, is meaningless unless one first comprehends the concepts of left and right, up and down, and width and depth. The concept of space, therefore, is a result of a cascading of basic RR concepts into a more abstract concept of a higher intellectual level (space). The higher level concepts then be defined and internalized (using RR) for use in the resolution of other ambiguities required for humans to expand knowledge.
Knowledge has been referred to as the comprehension of the realities of the universe. Defining reality has been argued throughout history, but there appears to be two legitimate states of existence.
First there is the objective existence proposed by the ancient Greeks. They proposed that something either exists or it does not exist. [Notice the reciprocal nature of the argument.] Since it would be incomprehensible to think that nothing exists, then something must exist. This is objective existence.
Secondly, there is the subjective existence so eloquently stated by Descartes in the phrase: "I think, therefore I am". This phrase resulted from a realization that no matter how much one can deny the reality of anything, one cannot deny that one is denying because one would still be denying. [Notice again the requirement of RR in the argument of denial]. Our cognitive process, then would be an integral part of this subjective existence.
These two states of existence (or reality) are a RR: one cannot be put into operation without the other. Our subjective existence allows comprehension of our objective existence, which allows our subjective existence comprehension of our objective existence, which allows.......
The resulting scenario may be called the "reality situation". This dynamic inter-relationship between objective and subjective existence is not a classical attempt at an explanation of reality, but rather, an undeniable situation in which the rational mind finds itself. It is impossible to separate our subjective observations from the objective universe because one is meaningless without the other. Consequently, as we cannot employ one without the other, all of our comprehensions required for knowledge come to us via this primary reciprocal reciprocation of subjective and objective existence.
The ramifications of this are profound:
1. RR does not allow for the comprehension of infinities. It only allows for comprehension of those things found within the finite parameters of various concepts because RR is an inherently finite inter-relationship. Therefore, the total amount of knowledge available to us is finite.
2. Since the rational mind operates within the "reality situation", there is something more to the universe than just knowledge. More than the obviousness of feelings and emotions, this involves the possibility of transcending outside our reality situation into a truly bizarre realm where RR no longer holds legitimacy. As a matter of definition, faith (that which one believes but cannot be proved) falls outside of our reality situation. Since we all have faith in logic, this demonstrates that in some manner we all operate outside our reality situation.
3. A misconception of a very basic RR may lead to major misconceptions of a more abstract concept (e.g. Ptolemy’s universe was predicated on the relevance of astral motion to our position on Earth). Could a misconception of basic concepts such as space or time be leading us down an analogous anomaly?
Realization of subjective and objective existence as the primary RR from which we derive knowledge can open new avenues for exploration as well as help clarify research. After all, how can you claim to know something if you don’t understand the process of knowledge itself?
By: Tom Roll, R.Ph.
Commentary by: Jim Myres, R.Ph.
Knowledge - the result or condition of knowing: clear perception: learning: information: skill: acquaintance. (Webster’s Dictionary 1989)
Sixty years ago Claude Shannon’s mathematical models created the science of Information Theory. Probability and entropy are the basis of information theory. Probability is linked to the amount and type of knowledge we get from an event or group of events who’s outcome is uncertain. In information theory, probability measures both knowledge and ignorance just as entropy does.
"Serious difficulties arise when scientists try to separate the idea of probability from the idea of information, because the first cannot be defined without the help of the second." (Campbell p63) A RR consists of two... opposing concepts... which cannot exist without each other. They are,,, mutually inclusive in the operation of comprehension.
The theory of probability is relevant to the discussion of knowledge - we look back five hundred years to the Renaissance and see new approaches to the understanding of knowledge and probability. Over time attempts were made to define probability as exclusively objective "out there in the world, exterior to the mind" or exclusively subjective, "in here in the mind." "Much of the subsequent history of probability... reflects the dilemma that theorists confronted when trying to make sense of probability’s duality." (Campbell p60)
The objectivist view of probability (out there) emphasized the recording of chance events. Objective existence proposed... that something either exists or it does not exist. The weakness of this view is that, observing an infinite series of events, is at best, impossible.
To the subjectivist probability is as Lord Keynes is quoted as saying "every proposition has a certain probability, and that this probability is represented by the degree of belief that a rational person, using all the evidence available, attaches to the proposition." (Campbell p82) I think, therefore I am. These views are also unsatisfactory because "rational belief" is a quantity beyond our ability to measure.
It is an accident of history that the concept of entropy was connected with physical particles obeying the laws of mechanics and thermodynamics. In information theory "the entropy principle is seen as a special case of a more general method of reasoning which does not depend on the laws of physics or mechanics at all." (Campbell p65)
In conclusion, Tom may have a valid theory of knowledge. I have been exposed to his ideas for too many years to make an objective judgement, which bring to mind a quote from a book I reads decades ago, "Squids can deceive other animals by squirting a cloud of inky material into the water, therby distracting attention from the actual squids themselves; but only man can organize inky material into symbolic patterns in a way that can distract attention from reality itself." (Bigelow p248). This is not an indictment of Tom’s work just a warning to be cautious about anything you read.
When I finally read Tom’s paper, a few weeks ago, I was struck by #1 of his "Ramifications," RR does not allow for the comprehension of infinities. As a recreational number theorist, I have been seduced by set theory as proposed by Georg Cantor. I have lived and dreamed of transfinite numbers and magnitudes of infinity – something I only pretend to understand. If Tom is right and RR does not allow for the comprehension of infinities then I may have been wasting my time. This may also be a clue to the conspicuous periodic insanity of Cantor and Kurt Godel, founders and fathers of set theory. For me, this reality has never been my preference - I choose to see dragons.
If you want to know more about Tom Roll you can listen to some of his original music, Google "Son of Hog."
Bigelow, Robert, The Dawn Warriors, Little, Brown & Company Limited, Toronto, 1969.
Campbell, Jeremy, Grammatical Man, Simon And Schuster, New York, 1982.