Chapter 7

Ultralogics

7.1 A Brief Rest

From this point on, the material presented is so significant that I've taken a month off from writing this book to complete an important associated project. I previously mentioned that, while this book has been in progress, I've also been rewriting the entire mathematical theory upon which it's based.[16] I want to assure that what you read within the following pages is as correct as the human mind can produce. I was determined to rejustify all those aspects of the mathematical theory that directly influence the forthcoming disclosures. This I've accomplished.

I've given you a lot to think about in the previous pages. In reality, many new and deep concepts have been presented. You could spend considerable effort just investigating how theoretical science is being used to control your thinking, how you are often prevented from knowing about other theories that correlate to your personal belief-system, and probably write a book restricted to thousands of examples. Perhaps, I'm expecting too much from you.

I can hear the cry "I don't understand what your writing about. All these technical terms and ideas are to much for my meager brain." For almost thirty years, I've heard the same complaints from many of my students. Often, I don't understand what it is that they don't understand. Indeed, what does it mean to understand a concept? I won't discuss it much, but I've actually created a mathematical model for the processes of understanding.

Well, as I've written before, to understand a concept that is being partially described by words, you must have a language. There's nothing I can do to alter the methods humans use to communicate. If the concept is new, you need a new language. New technical terms are often associated with old technical terms or other technical terms previously introduced. All of these terms are expressed with appropriate connecting structures in collections of sentences. These sentences give word-pictures that depict relationships between all such technical terms. Sometimes these relationships are illustrated by diagrams in the hopes of aiding comprehension. Indeed, the more distinct ways a concept is illustrated in word-pictures, diagrams, or whatever, the better opportunity one has in gaining a more in-depth understanding. Defining technical terms and using all of these educational techniques doesn't, however, end the effort an individual must put forth.

Some students don't want to expend any effort in learning a new concept. Some believe that their mind must instantaneously grasp the new idea. If it doesn't, then they'll give up. They don't search for that allusive moment when the mind says "Ah! yes, I see what you mean." And it can be a prolonged search. A concept often has great content, content that can't be completely described. It takes time and effort to understand. It takes hours, days and even years of deep thought and reflection. You may need to go to other authors and use many distinct and often clever means before that moment of "Aha!" arrives. It's a very slow and exhausting process.

On second thought, I don't really believe I'm expecting too much. I honestly believe that you're capable of firmly grasping all that has been and will be discussed by me, if you wish. For too long, the scientific community has placed itself out of reach of the general public by claiming that "the material is simply much to complex for you to understand." Stick with it and go slowly. I have confidence in you. Indeed, you'll slowly acquire much of the same intuitive feelings I have about the workings of the NSP-world.

7.2 What Is Formal Deduction?

We now come to the final concept, the final "thing" needed to produce a universe. In what follows, I'll give you some idea of the concrete everyday experience that has been abstracted in order to obtain the behavior of this "thing." You perceive a written set of statements, mentally process these statements and then your mind (brain? whatever) directs you to write down some deduced conclusions. As I've mentioned, I have no idea how the brain actually performs this task and for our purposes such knowledge is unnecessary. Logicians have discovered a set of written rules that duplicate this mental process in the following sense. From a given set of statements - the hypotheses - the rules direct us to write down in a very simple step-by-step fashion a finite set of statements. Each statement written down corresponds to a deductive conclusion that agrees with one obtained by the above physically real mental process.

The rules are so specific that computer programs have been created that allow a machine to check and determine if our written collection of statements is deduced in accordance with the rules. The formal application of these rules of logic yields a formal collection of written statements called a formal deduction, a deduction that can be easily checked.

The rules for logical deduction may also be abstracted and embedded into the same mathematical structure - the G-structure - that's used to obtain the event sequences, the IUN-selection process and ultrawords. Indeed, the logical rules I've abstracted are considered to be extremely simple in character and are compatible with all know forms of human deduction.

The idea that certain physical behavior is absolutely random assumes, without any possible verification, that there is no logical way to "predict" even a general event sequence for such behavior. Indeed, the behavior is lawless, there is no logical relation between the behavior of a particular entity at one instance of time and its behavior at another instant of time. Recall that this notion is one of the methods used by many so-called intellectuals in their attempts to control your thinking about Natural phenomena.

What if a IUN-process could be applied to an ultraword and a Natural system produced, a system whose behavior is "predicted" independent of whether or not it is conceived of as random in character? Is this a fantastic possibility? I think not if the process comes from an interpretation of an entity in a mathematical theory. The philosophical concept of absolute randomness does not come from such a association. It, probably, can't be mathematically modeled. Ultrawords can be used to predict behavior that is perceived to be scientifically random in character. The notion of using ultrawords to produce such random behavior is not chosen for abstruse political or philosophical reasons. Ultrawords mathematically exist and I'm giving them a possible meaning. But is there a "logic" that guides all ultraword predictions; indeed, is there even a "logic" that "predicts" what some believe is random behavior?

As I've stated, ultrawords are only necessary as an intermediate step. They can aid in human comprehension of those processes that might produce a general event sequence - processes that are only partially comprehensible. As such an intermediate step, ultrawords may be conceived of as a catalyst; they are a necessary platform from which to launch a universe. Of course, we have also given them a physical meaning. Shortly I'll discuss what could happen to an ultraword when the conditions are just right.

Remember that scientists use logical deduction. At the least, deductive methods are applied to the rules of the scientific method, rules for experimental inquiry and rules for constructing the machines used to gather data. For logicians to explain by rules how nontrivial logical deduction occurs, a set of hypotheses is necessary. A logical process can then be thought of as something that "operators" upon this set and out pops the deductions. The logical rules determine specific relationships and properties between string of symbols and it's these properties that are mathematically modeled. What results from this modeling is quite remarkable when given a physical interpretation. What results is a force-like process that has many describable properties and a portion of these properties mirror the behavior we associated with a very simple form of human deduction. Indeed, this force-like process exists only because we can describe and mathematically model human logical processes. But this force-like process has numerous properties that do not mirror any form of human reasoning. This force-like process is called an ultralogic and is our major IUN-process.

In this book, I'm going to discuss, somewhat, how an ultralogic compares with human logical processes c such a comparison is significant for certain philosophical concepts. Therefore, what comes next is a linguistic interpretation for an ultralogic.,

7.3 Linguistic Ultralogics

I'll do my best to explain some of the amazing results automatically produced by an "ultralogic" mathematical model. I can't describe them all, however. Once again, this is an example of where human description is very inadequate. I seem to know intuitively certain behavior patterns, but I can't think of any completely satisfactory description that corresponds to my mental impressions. Here's a name for one technical object that will help me develop, at least, a partial description. Certain logic-like processes that take ultrawords and produce, in a step-by-step time ordered sequence, each member of a general developmental paradigm are called ultralogics. [In older writings in this subject, ultralogics are sometimes called supermind processes.]

What makes human logical processes different from one another? One of the differences is that our mind seems to process different expressions in slightly different ways. Thus a change in the way a hypothesis is stated may lead to additional or more detailed deductions. In order to account for changes in the expressiveness of a language, logicians increase or alter the formal rules they use. Since ultrawords are not expressible, in their entirety, in any human language, it should be expected that the rules that correspond to an ultralogic are different from those of human thought. Indeed, these rules are very different but still have certain common features. Some understanding of how an ultralogic behaves is obtained by comparing ultralogic results and rules with ordinary human thought processes.

(i) If an ultralogic is applied to any set of symbols from any human language, such as a standard hypothesis, then the human language that results (the deductive conclusions) will be exactly the same as that produced by the most basic of human logical processes.
Previously, I mentioned that there could be some sort of Natural process that seems to parallel the patterns of human thought. Relative to this idea, statement (i), especially as it applies to a possible physical process, is extremely significant. Statement (i) means that there is NO difference between the outcomes of ultralogic processes and ordinary human deduction when you use hypotheses written in a human language and consider deductions that are written only in such a language as well. The logical patterns are obvious and not hidden from view. Processes that preserve the original language objects are called extensions of the original process.

On the other hand, for behavior that doesn't appear to have a set of hypotheses or doesn't seem to follow some logical pattern can there be a hidden "logical" process and, perhaps, a hidden hypothesis that produces descriptions for such chaotic behavior? [In what follows, that * my be translated by the word "hyper."]

(ii) There is an ultralogic, denoted by *S, that when applied to an ultraword produces every description within a general developmental paradigm. The logic also yields numerously many other objects that behave like descriptions but can't be expressed in their entirety in any human language. In this sense, an ultralogic is stronger or more powerful than human logic.
Yes, *S could be associated with a hidden process that satisfies the philosophical requirement that all general developmental paradigms are composed of "logically" produced descriptions. This includes descriptions for behavior that appears to be chaotic or random in character.

The logic *S is a nontrivial extension of human logical processes, and it can be differentiated from human thought processes by the fact that it produces objects distinct from any human language. This ultralogic is more powerful than human logic since it can perform human logic and a lot more. I note that, in general, one logic is stronger than another logic if it's capable of producing all the results of the other logic and more. That's why ultralogics are also said to be stronger than human logic.

I might point out another remarkable fact. In a few cases, one can actually have a partial understanding of what the ultralogic produced extra descriptions are trying to say since only a few standard (i.e. human) language symbols are missing. An ultralogic is starting to behave like a super-brain or super-mind or even like a super-supercomputer, or something of that nature. But it's still very, very different from these.

In most cases, there is no standard logical process that can be applied to an ultraword. Only such things as ultralogics have any meaning for ultrawords. I can hardly wait to give ultralogics - these super-mental like processes - some physical interpretation. But it's useful to describe two more meaningful ultralogic properties.

(iii) The ultralogic *S produces all of its deductive conclusions in a manner that cannot be duplicated by human thought. I term this as a linguistic ultrauniform process.
I now have a slight problem. Ultrauniform is mathematically defined using expressions from a discipline called general topology. If you know some technical mathematical definitions, then ultrauniform mirrors many of the properties of a concept called uniform continuity. Can I give a partial nontechnical description for this property? I'll try.

When a step-by-step formal deduction is written, each string of symbols written down is give a number. Usually, you'd write the step numbers for a five line proof as (1), (2), (3), (4), (5). There is nothing to prevent you from writing these numbers in the form (1.000001), (1.000003), (1.000004), (1.000009), (1.00001) for all one needs is an indication of the order. What I mean by this is how one step follows from a previous one in a mental construction, a mental construction that has as its last step the statement being deduced. Notice that the difference between the numbers in the second example is very small. One might say for this second numbering that there is a very small step between successive parts of such a mental construction.

For an ultralogic, you could say that the steps are infinitely close together. This means that the difference between step numbers is smaller than any human or machine could ever measure. Another possible way to describe an ultralogic's step-by-step sequence of deduction is that it's more refined than any of the logical steps in any logical sequence produced by any thinking biological object or machine.

Thus far, these results certainly imply that ultralogics are very different from human thought processes although they are extensions of such human processes. By-the-way, please note that in this book I'm not giving any other philosophical interpretation to the concept of an ultralogic except for the forthcoming MA-model interpretations.

Suppose that you consider our solar system as a Natural system. The Earth and the Sun are Natural systems, and can be considered as subnatural systems. When a general developmental paradigm for the development of the solar system is studied, it can contain other sub-general developmental paradigms for the development of human life, the Earth, the Sun and much more. Each of these millions of sub-general developmental paradigms are generated by an ultralogic applied to an ultraword.

I've mentioned that there's an ultimate ultraword that determines all of the ultrawords for all of the possible general developmental paradigms. Does there exist a specific ultralogic that can be applied to an ultimate ultraword in such a way that all of the necessary ultrawords and there associated general developmental paradigms are produced in the proper order?

(iv) Given any set of general developmental paradigms (including sub-general developmental paradigms) and the set of associated ultrawords. Then there exists an ultimate ultraword such that if the single ultralogic *S is applied to it, then all of the ultrawords and all of the of the general developmental paradigms are produced.
Why might (iv), which is closely related to statement (v) of Chapter 6, be significant to theoretical scientists?

A few pages back, I substituted the term "standard language" in place of human language. I'll now do the same thing for the rules that mirror human deduction. But in this case, there's much more involved. There are sets of rules that yield patterns that are similar to human logic but are NOT equivalent to the usual mental processes that you've encountered. Some scientists believe that these other rules are more appropriate for certain theories. I won't involve you in a detailed examination of these other logic-like rules and patters. It's enough that you know they exist. What this means is that there are now, and there might be in the future, many scientific theories that actually require these other rules for their deductive conclusions. The ordinary human logical processes and all of these additional logic-like processes I group under the one expression standard logics.

In general, standard logics are not compatible; you can't mix them up in the same deduction. Thus, a collection of general and sub-general developmental paradigms may require incompatible human logical processes if they are produced by deduction from sets of hypotheses. And, of course, you also have those general developmental paradigms that appear to follow no pattern and have no hypotheses. Statement (iv) shows that, in this model, there is an ultimate unifying logical process, *S and an ultimate hypothesis-like ultraword. This is a significant philosophical result. There may be "something" that logically ties together all of these seeming incompatible processes, "something" that possesses some exceptional mind-like properties.

There is one comparative statement that encapsulates in its content all of the relations between any form of human logical deduction and an ultralogic such as *S.

(LU) The ultralogic *S is infinitely more powerful than, faster than, refined than, uniform than any form of human deduction. Indeed, take any property P for human deduction that can be modeled mathematically. Then, whenever "better than" has its ordinary meaning, the ultralogic *S is infinitely better than property P.
There are infinitely many ultralogics that can be substituted into (LU) in the place of *S. But, *S is of a special type. In fact, *S, when restricted to a Natural language that you and I use to think, is a human deductive process S. But S would be considered as a very trivial, extremely weak, if not, a foolish process that's too weak to produce the "great" deductive results of modern science. What comes next is a physical interpretation for the ultralogic *S, an interpretation that justifies the belief that there logically exists a universe producing process that has properties that are similar to thought patterns. The ultralogic *S, when restricted to the Natural world is so very weak, so hardly observable. But the fact that, from the NSP-world viewpoint, it can produce a universe is absolutely remarkable.

7.4 Physical Ultralogics

In this section, I'll discuss the last and most significant interpretation needed before I can give you a detailed explanation of the properties of the MA-model. You should pay particular attention to the following results, results not generated by my imaginative mind, but results that are automatically obtained from a mathematical model. I repeat that I have little control over what the mathematical model is saying. I'm simply acting as a translator.

Recall what an event means. When you have a description of how a Natural or ultranatural system behaves or appears at a moment of time, then the event is the assumed or actual phenomenon, at the least, being partially described. Our model says that an event can be a Natural event or an N-event, and such an event takes place within our universe. An event may involve processes or it may involve objects, and these processes or objects may need named constituents like an electron, or an Earth, or Sun. Such objects are called Natural objects or N-objects. On the other hand, the force-like process also called an ultralogic, when applied to an ultraword, can produce "things" that can't be Natural processes or Natural objects. I physically interpret all such "things" as ultranatural events or UN- events. This mathematical model actual describes entities that behave like natural objects but, due to their properties, can't be natural objects. These things I call ultranatural objects or UN-objects. Also there are processes occurring that can't be Natural processes and these are called ultranatural processes or UN-processes for short.

In section 6.3, I described the idea of intrinsic Natural processes or IN-processes. One of these was a process that mirrors finite human choice, another imitates human logical processes. Then you have the significant intrinsic ultranatural processes or IUN-processes termed IUN-selection and another IUN-process termed an ultralogic. These IUN-processes take place in a portion of the NSP-world. Like the Everett-Wheeler-Graham theory many scientists accept, some of these NSP-world processes can't be detected within the Natural world by means of any laboratory experimentation. This, however, doesn't detract from their possible existence and, moreover, many other IUN-processes indirectly or directly affect the Natural universe.

In this section, I'll denote the basic physical ultralogic process by the same symbol *S as used in the linguistic interpretation. Now simply consider *S to be a force-like process that produces things. Such a force-like process can't be detected directly. Of course, neither can subatomic forces. However, many of the results of *S can be detected since they are but Natural events. This is why I call such a force-like process an intrinsic ultranatural process. [I mention that re-interpreting "logical" operators as physical "operators" is not totally new since a similar intuitive approach is used within the discipline called "Quantum Logic."] With this brief review of appropriate terms, I can now physically interpret the ultralogic process.

(i) For any changing Natural system, there exists an intrinsic ultranatural process *S that uniquely yields the Natural events that comprise the changing Natural system. This IUN-process is not directly detectable within a laboratory setting although all the N-events are indirect evidence for its existence.
The next result has numerous applications. The IUN-process *S can produce a lot more than Natural events.
(ii) The force-like process *S, when it yields these Natural events, also produces numerous ultranatural events. These UN-events are closely associated with the Natural events and aid in and are necessary to sustain the Natural system's evolution.
There's an additional aspect to statement (ii). Nothing that can be done in the Natural world can change the result that *S yields these UN-events. All that any scientifically acceptable intervention can do is to eliminate or alter the Natural events. You could fly a airplane through a cloud of water droplets and greatly disturb their positions. Such an adventure would not eliminate the UN-events under this interpretation. Further, note that the process *S is relative to a particular ultraword.
(iii) It's possible for *S to produce a sequence of only ultranatural events that can only occur in the pure NSP-world.
Statement (iii) is somewhat significant when used in the MA-model. You get ultranatural events whenever you get Natural events. On the other hand, you can obtain a sequence of ultranatural events without getting any Natural events.
(iv) The force-like process *S cannot be reproduced within the laboratory setting. The process *S takes place in a physically ultrauniform manner.
What do I mean by physically ultrauniform? As mentioned previously, there are many things that scientists consider to be "uniform," one of these is called uniform continuity. I'll try in the next chapter to explain the concept of continuity. For an ultralogic, ultrauniform is of a similar character. Basically what it means for an ultralogic is that the process is very, very refined in character. The *S process proceeds in extremely small steps, steps that are smaller than the steps for any process that can occur within our universe. Viewing this another way, one can say that over a very small finite Natural world time span, the process uses an enormous number of "steps" to reach its conclusion. Actually, ultrauniformity is so scientifically beautiful that it is not fully describable in a non-technical language.

The next statement is very interesting and helps to answer the basic Wheeler questions.

(v) The force-like process *S applied to ultrawords produces Natural event sequences and all that they comprise, and also produces, simultaneously, ultranatural event sequences and all that they comprise.
It's the ultralogic *S and the appropriate ultraword that answers completely the Wheeler questions.
(vi) The force-like process *S applied to an ultimate ultraword produces not only a general event sequence that yields a Natural system but, simultaneously, produces all the sub-event sequences that yield all of the sub-Natural systems. One might also say that the process *S is more powerful than any process that can occur within the universe.
Thus any Natural system and, indeed, an entire universe can be produced in an ultrauniform manner by application of the force-like process *S to just one ultimate ultraword. The force-like process *S produces and holds everything together, so to speak. Unfortunately, this process can't be duplicated within a Natural world environment.

Looking at specific time intervals yields the next important characterization.

(vii) The force-like process *S can, over certain time intervals, produce a system development that is comprised of ultranatural events or ultranatural objects only. Over other time intervals, the process can produce a combination of natural events and ultranatural events along with natural objects and ultranatural objects.
There are many other properties I could reveal about these intrinsic ultranatural processes, ultrawords and all the rest. I've written on this subject at great length but I've done enough to prepare you adequately for the MA-model and need not continue. However, there are infinitely many properties about ultrawords and ultralogics and the like of which we can have NO knowledge.

Yes, there's a mathematical model that appears to vindicate those scientists and philosophers who believe that our universe is controlled by force-like processes that imitate those associated with human thought. But, much to my surprise, these processes may be rationally assumed to be a simple restriction of a much more powerful process that can only be slightly understood by the human mind. This more powerful process may be assumed to be hidden from direct scientific observation. But, although I've answered Wheeler's basic questions and many others with these discoveries, I haven't answered them in a manner that's acceptable to the majority of the scientific community. Why not? Because these processes have additional properties, properties that contradict some of the basic assumptions used by those scientists who are perpetrating the great scientific deception. For these "ultra" processes coupled with various logically acceptable scenarios yields the MA-model and much more.


Chapter 8 or return to contents page.

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