I have been thinking about resuming work on my new logic system. Since yahoo deleted my web pages I am forced to store this here for now.
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On Modeling Reality
By Ken Wonderski
Introduction
This document is simply a call for a new type of logic (which could be summarized as a many-valued, functional connector, temporal logic). After many years of working on a system to model reality, I have become convinced using existing tools (like predicate calculus) is a dead end. There are just too many issues which make the task nearly impossible. What these issues are and how they could possibly be addressed in a new type of logic system are the topics this document discusses. The resulting system, known as 'Conceptual Logic', is discussed in a separate paper.
Chapter 1 What We Know
As evidenced by the current crisis in reality research, there is a need to develop a more robust manner of modeling our world than currently exists. From a high level, this new logic system should be able to manipulate concepts rather than objects. It should deal with issues like infinity and time in a direct intrinsic manner, and from a neorealist perspective it should require the interaction of two or more belief systems in order to produce any statement of (perceived) reality.
When developing a new logic system, if it is to be used to model reality, it would be good to understand what you know and what you don't know. One way for a system to deal with this issue (what you know versus what you don't) is to impose system level boundaries. A system level boundary can be knowable (some absolute value) or unknown (infinity). So infinity is not necessarily a universal constant but rather a system level limit. In other words, one system's infinity could be smaller than another system's infinity. The new logic system must inherently support all types of infinity and easily allow for manipulation as just another concept if it is to be of any use in modeling reality as we think we know it.
Reality as we think we know it could simply be represented as another system. Our system has certain requirements and our abilities to perceive seem to also have limits which, as any quantum physicist can tell you, appear to be a subset of what we think we know. This peculiar phrase means that while we believe there is such a thing as an atom, for example, we really have never seen one, and even considering future attempts at magnification, we may indeed never be able to see one, directly or indirectly (it may be unknowable in this system at our level), but this does not deter us (nor should it) from assuming their presence and attempting to model them. What we have here is a system level constraint which we can address head on even though we believe there is more to the object then, pardon the pun, meets the eye, for we can establish a system level boundary at a quantum level (say, here is a set of rules which we believe describe the atom's behaviour at our level) which enables us to work with the atom as a concept while conceding that we not be able to understand it as an object.
One way of thinking about interrelated logical systems is to think of them as concentric spheres engulfing each other. The smallest sphere is surrounded by the next larger sphere, which in turn is surrounded by the next larger sphere. Each sphere is just a logical system of rules with boundaries and interfaces to adjacent systems. The rules in one sphere may not only be different at each level but transitive across levels up or down, or they may just be completely different in each sphere, it really doesn't matter for the purposes of calculations, except when there is an interaction between levels. Otherwise, each sphere has its own set of rules, quantized for its needs and adhering to its system level boundaries, rules and constraints.
So in this new logic system, rather than attempting to directly model an atom, we instead say we can manipulate the concept of an atom which behaves according to a certain set of rules, constraints, etc, within our system (just like in quantum physics) and we can even allow for the probability of it behaving differently in other systems. This allows us to do things like say there is no subliminal communication in system A but there is in system B. While this may not seem significant, it can be quite significant if these two systems share a region (in other words they interface in some way). Systems are all that are required if it is the case that they may be constructed of other systems. An atom (a system) may interact with another system (a different atom) and their interaction may be felt in the system which encompasses them. It would seem this is common sense. What may not be so sensical is the way the systems interface.
Chapter 2 Our Relationship to Our Environment
Recursive is the word that comes to mind when I think about how we interact with the immediate system we refer to as our environment. Whether we realize it or not each of us impact our environment far more than we give ourselves credit for. Every instant, every action (or inaction) we take subtly influences the system we reside in. It may even alter the behaviour of connected systems. Since our environment affects us and we affect our environment we are left with the disturbing consequences of the Heisenberg uncertainty principle, which is namely that we can not assume our acts of measuring do not affect the things we are trying to measure. We are interconnected and according to John Bell (a CERN physicist), in a subliminal manner. Even though we think we are manipulating two separate objects we are in reality effecting both concepts simultaneously, even though they may be interconnected in a extremely indirect manner.
The new logic system must deal with this interconnected recursiveness such that reality may be modeled. When everything is interconnected a perturbation anywhere must be accounted for everywhere. This includes all connected systems.
Chapter 3 Dealing With Uncertainty
There is an old saying that goes 'nothing is absolute'. While I will not discuss the philosophical ramifications of this statement (lest the Calvinists reading this may take exception), I will simply say that it is a good belief for a logical system to base itself on. Probabilities are safer when attempting to predict the future behavior of some concept. When one does not know everything, it is much safer to say something will probably happen (%99.99999) rather than it will absolutely happen (%100). It just seems like common sense when you don't know everything that you shouldn't predict in absolute terms. What this equates to in the new logic system is a supposition of something being infinitely True or infinitely False within the system of evaluation; nothing more, nothing less.
The new logic system must deal in conceptual probabilities at a quantum level such that traditional boolean relationships are not the only way to join concepts and systems. What this implies is a multi-valued logic with True and False becoming relative boundaries of a logic connective which may incorporate clipping or rounding. Think an 'OR' function which must not only accept True and False, but also a myriad of potential values between, which could be interpreted depending on how you choose to look at it, as 'Unknown' or 'Maybe' values. Rather than truth tables working with values which can be either True or False, the truth tables become truth functions operating on many valued variables. When systems interface they may share attributes but their boundaries on these attributes may vary. This could have an affect on certain calculations.
The new logic system must deal with the problem of interfacing logic systems and shared attributes with potentially conflicting values.
Chapter 4 The Consideration of Time
Time (whatever it is) has an interesting effect on everything and is therefore considered a meta level concept in the new system. Infinity becomes more constrained when one considers the effect of time on an equation. Obviously, when constrained by a time limit (either relative or absolute) many concepts turn out to be bound within a system rather than truly infinite.
Much like many-valued functional logic, the concept of time is central to the new system. Its inherent support is a core objective. The concept of an absolute universal heartbeat is not considered. Time may be absolute only within a given system. This means system A and system B may have a different heartbeat or the same heartbeat. If a heartbeat is defined as being infinitely small, as we have seen in previous sections, this is only relative to the system it occupies, so system A's infinitely small heartbeat may be larger (or smaller or the same) than system B's.
The new logic system must support both concepts of time (relative and absolute) and it must deal with all of the uncertainty surrounding these types of difficult philosophical concepts.
Chapter 5 The Derivation of Reality
When two systems interact, all the aforementioned issues must be addressed. While most amount to nothing more than scaling of values, what we end up with is the alteration of two (or more) different systems. The point here being that each system is altered in a completely local way. for example, if the way each of the two systems is altered is identical (highly unlikely) that's great, we have a pretty good grasp of reality, however, in most cases this will not be the case and so we are left with the problem that the derivation of reality, in other words what really happened, is very much a personal, or relative thing, specific to the system we are talking about. While this may sound odd it is quite normal to what we experience in our everyday lives. For example, yesterday I took my wife to the movies. She liked it, I wanted my money back. Two different results given the same experience. In other words, just because two systems interface (something we can call an event) does not mean they get the same out of it. Each shared event alters each affected system differently. It seems experience is a very personal (or local) thing. The reality we derive from an event affecting a set of systems must therefore be a connection of the differences of all affected systems.
And so finally we are left with this; the new logic system defines reality (from potentially conflicting inputs) as the set of changes resulting from the interaction of two or more systems.
