Proposed Definitions
The purpose of this paper is to propose and discuss some definitions for the words and phrases "existence", "exists", "what is", and "location". They are all centered around the concept of a whole, or an entirety. What exactly is a whole or entirety? Well, various definitions of these words, along with the words complete and totality, from Webster's Dictionary (1) include: "complete implies inclusion of all that is needed...", "not lacking any of the parts...", "whole and entire imply unbroken unity, stressing that not a single part, individual, instance, etc. has been omitted...". This combination of definitions will be used here to define whole. Based on this meaning of whole, the other proposed definitions follow. o "Existence" and "Exists": The definitions of "existence" and "exists" are based on the concept of a whole or entirety. A whole, by virtue of its wholeness or completeness, has an edge or boundary (wholes without edges or boundaries, indicating their completeness and that all has been included, wouldn't be wholes). This edge is not a specific structure but is, rather, just the wholeness, entiretyness or completeness of the whole itself. Because it has an edge or boundary, a whole becomes something that has substance; that is, it is a "thing"; it "exists"; it "is". The edge is the key to making any whole real and capable of being called "existent" or "is". The "existence" of a whole can only be seen from a reference frame (ie, observation point) that can see the edge of the whole. That an edge or boundary is needed to give something "existence" also makes common sense. If the definition of what is included in a thing is not complete (ie, there is no edge or boundary defining what is included), not only is that thing not whole, it just seems like it cannot exist. For instance, try to picture a ball in your mind where that ball has no edge. It's pretty hard to do. Even if you picture a partial ball, that part of the ball that is there must have an edge defining what part is there. One cannot even think of abstract concepts, like love and truth, as existing if what is meant by love and truth are undefined (ie, not whole in their definitions). All of the above reasoning leads to the definition of "existence" as a whole, with its associated edge, and of "exists" as the property of being whole. An edge also allows a whole to be observed and, thus, described as occupying spatial volume. Thus, a whole (ie, something that "exists") will also be defined as, and, henceforth, taken to mean, volume. Some properties of the edge of a whole and, therefore, of something that "exists" are: - The edge of a whole is not a specific, separate structure nor is it the size or contents of the whole; instead, it is just the wholeness, entiretyness, or completeness itself. This edge is viewable by an external observer of the "existent" whole. This is identical to how we observe things that "exist" and that we see in our daily lives. The edge of something we see is not a separate structure; instead, it is just the "end" (or marker of wholeness or completeness) of that thing. - The edge of a whole forms an "outside" external to that whole. The very nature of an edge means there are two sides to it, an inside and an outside. - A whole can be thought of as a set, state or reference frame. A whole has an edge, which limits, defines and gives "existence" to that whole. Likewise, a set is a whole or complete grouping of some elements. The wholeness and completeness of this grouping is what gives rise to our ability to define it as a set and to put the curly braces around and give "existence" to the set. The "existence" of a set is independent of the contents of the set as shown by the "existence" of sets of all different types of contents. In parallel the "existence" of a whole is independent of the contents of the whole. Overall, both sets and wholes "exist" because they are whole, complete amounts and, therefore, have edges (or curly braces in the case of a set). State and reference frame will also be used to mean set. The relationship of the above definitions to the world of ideas and "real world" objects is considered next. Based on the above, anything that "exists" "exists" because it is a whole. A whole has an edge which gives that whole "existence". Now, also assume that both ideas and "real world" objects "exist" (it doesn't matter where they "exist" as long as they "exist" somewhere). Based on the definitions given here, they "exist" for the same reason as anything else: their contents or descriptions are whole and they, therefore, have an edge. Thus, at a fundamental level, ideas and "real world" objects "exist" for the same reason and could be considered to have the same definition: they are whole or complete descriptions of something. Whether or not one calls this whole description an idea or a "real world" object is secondary to the fact that it is a whole description. This jives with the reasoning in the preceding paper (2), which concluded that ideas and objects have the same definition. This conclusion is in contrast to the Platonist idea that ideas exist independently of the material world. The reasoning in this paper suggests that ideas are not independent of the material world; instead, they are one-and-the-same as the material world at the most fundamental level. That is, both ideas and objects are wholes, whose edges give them substance and "existence". An idea is just an "existent" whole that hapens to be in someone's head, and an object is just an "existent" whole that happens to be outside someone's head. In sum, "existence" is defined as a whole, with its associated edge, and "exists" is the property of being whole. An edge allows a whole to be observed and, thus, described as occupying spatial volume. Thus, things that "exist" occupy volume, at least in the reference frame they "exist" in. o "What Is": It is assumed here that any whole that "exists" independent of all other wholes is called "what is". Another way of saying this is that "what is" just "is" without outside explanation. An example of "what is" is the seemingly unending space of our existence (ie, the universe or multiverse), which seems like it just can't be explained; it just "is". Traditionally, in order for one to explain something, one must step outside that thing and provide a cause for it. Therefore, in order to say that a whole just "is" without outside explanation (ie, that it is "what is"), there can be no larger whole, or volume, from which that first whole can be explained. This, then, leads to the definition of "what is" as the largest whole, or, taking whole to mean volume, the largest amount of all volume. As the largest whole, "what is" has, like all wholes, an edge, which makes it "exist". Therefore, "what is" "exists", like all things that "exist", due to its being a whole. As an example of the differences between "exists" and "what is", assume that our universe is just one component of a bigger multiverse and that the whole of this multiverse is the largest of all wholes or volumes. In this case, one would say that our universe "exists" or "is" but not that it is "what is". Only the multiverse as the largest whole/volume would "exist" independently of any other whole and be "what is". Some properties of "what is" that derive from the above definition are listed below. - As with any whole, "what is"'s edge is not a specific, separate "structure"; it is just the wholeness, entiretyness or completeness of the whole of "what is". One implication of this is that the "existence" of "what is" (as well as of every whole), is dependent on every part of that "what is" because if even a single part of "what is" is missing or not included, the whole of "what is" would no longer be the largest whole or amount of all volume and would no longer be "what is". This dependence of the whole on the presence of every part is reminiscent of Zen philosophy. For example, in `!This Very Moment : A Brief Introduction to Buddism and Zen for Unitarian Universalists`! (3), Ford states: "It can be said the universe depends on each person, plant, and speck of dust for its existence."\(u)1\(d) - If the volume of "what is" is infinite, then the edge of this infinite "what is" is not observable from the viewpoint of an internal observer within "what is". This edge must still "exist" in order for "what is" to "exist"; it just wouldn't be observable to an internal observer. However, the edge would be observable from the viewpoint of a hypothetical, infinite-sized external observer of "what is". If the volume of "what is" is finite, its edge would be viewable by both an internal and external observer of "what is". The statement that the edge of an infinite "what is" is unobservable to an internal observer appears to be contradictory to the definition of something that "exists", like "what is", as having an edge. However, it is not. As discussed in an accompanying paper (4), an infinite set can seem to both have no edge and have an edge from the viewpoints of an internal finite and an external infinite observer, respectively. In an infinite volume of "what is", human minds are internal observers. Therefore, one's mind can never get to the actually infinite edge of "what is" and, thus, cannot see or visualize this edge. We and our minds are trapped inside. This is so even though our minds are part of the wholeness or entiretyness of "what is". Even though we can't see it, "what is", by virtue of its wholeness, must have an edge for it to "exist", but this edge will only be observable to a hypothetical outside observer. Such an external observer would not be required in order to form the edge but would be the only one able to view it. Unfortunately, because "what is" is the largest amount of all volume, there is no external observer, and, thus, no one to observe the edge. If "what is" is finite, it, of course, has both an internally and externally viewable edge. - As with any whole, the edge of the whole of "what is" forms an "outside" external to it. What is at the outside of the edge of the largest whole or volume of "what is"? Because all volume is contained within "what is", it must be that no volume (that is the lack of volume) is outside its edge. - As with any whole, "what is" can be thought of as a set, state or reference frame. - "What is" is a concept. As mentioned above, ideas "exist" because, like all things that "exist", they are wholes, with edges. This goes along with the definition of an idea, given in an accompanying paper (2) as a complete (ie, whole) description of something. Ideas are usually thought of as occuring in a larger set of ideas such as the mind, but if, as mentioned in this accompanying paper, an idea is just a complete or whole description of something, then any whole/volume, in the mind or outside it, can be considered to be an idea because every whole/volume is a complete description of itself. Also, in the accompanying paper (2), a concept was defined as a type of idea which has no specific location or time stamp relative to other ideas within a larger set of ideas. For example, a picture, in one's mind, of a generic chair with no particular location and time stamp is defined as a concept, but a picture of a specific chair in Denver at 2:00 P.M on 10/1/02 is defined as a simple idea. This means that any whole/volume, inside or outside the mind, that has no specific location or time stamp relative to other wholes/volumes can be considered to be a concept. Two ways to remove the relative time and location stamps of an idea are, one, to have some mechanism, such as cognition within the mind frame, remove it or, two, to have the idea not be a member of some larger set and therefore not have a relative time and location stamp given by its relationship with other ideas in the set. With a whole/volume, this second mechanism occurs only when that whole/volume is the largest whole or largest amount of all volume (ie, "what is"), because only in this case, is their no larger set containing the whole/volume and, therefore, no relative time and location stamps given to the whole/volume. Thus, the largest whole or amount of all volume, "what is", is a whole that completely describes itself and has no relative time and location stamp and can thus be considered to be a concept. This concept "exists" or "is" independent of the mind since all minds are within "what is". - "What is"'s edge springs from the wholeness of "what is" itself and not from the human mind. One might argue that it is just the human mind which is, after-the-fact, putting the edge on to an edgeless and unending space of "what is", just because the mind is constrained to thinking about "things" in terms of having edges. Because one is trapped within one's mind frame, this can never be disproven; however, two arguments against this idea are as follows. First, if the mind is what is putting the edge on and, therefore, giving "existence" to the whole of "what is", this implies that "what is" is really just a subset of the bigger whole of the mind. That is, the true largest whole/volume, or "what is", is really just the mind. But, then what puts the edge on and gives "existence" to the wholeness of the mind? The wholeness of the mind itself or a bigger mind? This reasoning could lead to an infinite progression of bigger and bigger minds putting on edges and giving "existence" to wholes, but, eventually, some whole must have an edge and "exist" independent of any other minds or else nothing will ever "exist". Even if one considers this "whole-that-must-exist" to be a mind itself, its "existence" cannot be due to a bigger mind/whole making it "exist". Its "existence" must be due to something else intrinsic to itself. As discussed above, this something else is its wholeness and subsequent edge. In conclusion, eventually some whole must "exist" due to its own wholeness, or edge, and not due to a larger mind making it "exist". This whole, even if it is a mind, is "what is". In other words, the "existence" of "what is" is independent of any other mind. Second, while it is possible that it is just the human mind that is putting the edge on an edgeless "what is" after-the-fact, it is also equally possible that the mind is realizing up front that "what is" is the largest whole/volume, understanding that wholes have edges, and then accurately recreating this pre-existing edge in the mind's eye. In other words, it is possible that the mind is smarter than we think and is not applying the edge to an edgeless "what is" but is just visualizing the preexisting edge of "what is". This makes sense if one thinks of the mind's eye as a recreation of the external frame of "what is". o "Location": "Location" is the place where something "is" or "exists", relative to other things that "exist". That is, "location" is a relative concept. This indicates that "location" is a whole, or volume, with its associated edge (ie, where something "exists"), that is accompanied by at least one other whole/volume (ie, one other thing that "exists"). Two or more wholes/volumes are needed in order to establish the position of one whole/volume (ie, its "location") relative to the other whole/volume. While the largest whole/volume, "what is" "exists" it cannot be said that it has a "location" because there are no other wholes/volumes whose position it can be relative to.Conclusions
The principal findings of this paper are proposed definitions of the terms "existence", "exists", "what is", and "location". They are all centered around the idea that a whole has, by virtue of its wholeness and entiretyness, an edge. This edge is what defines, limits and gives "substance" and "existence" to a whole. Some advantages of the proposed definitions are that they are specific, easy to apply, clarify some confusion as to the definitions of these words and have some application to the concept of integers and to recent advances in physics, as described below. The concept that a whole has an edge and "exists" provides a natural explanation for different aspects of nature. For one, the "existence" of integers. After all, what is an integer? It is a whole amount instead of a fractional amount, it "exists", and it always seems to have an edge when one visualizes it. That is, when one visualizes an integer, one visualizes some whole "thing" (a ball or circle, for instance) defined by an edge. Therefore, if any wholes/volumes "exist", then integers, as whole amounts, also must "exist". In addition to the "existence" of integers, the idea that things that "exist" are whole amounts (with their associated edges) provides a natural explanation for why there are three spatial dimensions. Three dimensions is the smallest number of dimensions needed to fully enclose a whole/volume with an edge and, thus, make it "exist". The reasoning that things, including sets, "exist" because they are wholes, with edges, also relates to the Russell Paradox (5). This paradox goes as follows. Consider a set R which is the set of all sets that are not members of themselves. If R is a set and not a member of itself, then R is a member of R, which indicates that if R is a set, then it's in itself only if it's not in itself. Therefore, R can't be a set. I believe that a resolution to this paradox can be found based on the reasoning given in this paper. That is, a set (or any whole) exists only because it is a whole grouping (ie, that it's membership list is completely defined). Only once it is a whole grouping does set R exist. So, while the complete membership list of potential future set R is still being defined, and contains, say, elements X and Y, at that time, R does not yet even "exist" (R only "exists" AFTER its complete membership list has been defined). Thus, R, which does not yet "exist", cannot be a member of itself. However, once its membership list is defined and R "exists", then R could be a member of a new set, R1, whose members are sets that are not members of themselves. This set could include X, Y and R. Overall, this reinforces the conclusion of set theorists that no set can be a member of itself. Furthermore, it indicates that all sets are defined and, therefore, "exist" with respect to the reference frame of the definer. That is, when R is originally being defined, the definer's reference frame contains only X and Y. But, once R is defined, the definer can see the wholeness, or edge, of R and can therefore see the outside of R. This allows the definer to see R from a different reference frame, one in which set R exists. I believe this is somewhat similar to Russell's theory of types (5), which he used to help explain his paradox. Next, a relationship between the definitions proposed here and some recent ideas in string theory physics is proposed. In a paraphrasing of string theory's holographic principle, Michael Green notes that: "a general feature of quantum gravity is that physical information inside any volume is encoded on the surface of that volume." (6). This is highly similar to the concept that the edge (that is, the surface) is what defines and gives "existence" to a whole. The wholeness of any whole/volume is represented entirely in its edge. Indeed, the strings of string theory seem to be nothing more than edges, which means that they are nothing more than wholes/volumes. Finally, in discussions of the seemingly unending space of our "existence" (ie, "what is"), it is often expressed that there is something just beyond our grasp that humans can't quite see that would do more in explaining why "what is" "exists". Based on the results presented here, there is. If "what is" is infinite, and because human minds are trapped within the wholeness of "what is", then the human mind can never see its whole or entire amount and can, therefore, never see the edge, or reason for "existence", of "what is". However, even though humans cannot observe this directly, it is argued here that the unending space of "what is", has an edge (due to its wholeness) and "is" independent of the human mind. References 1. Webster's New World Dictionary of American English, Third College Edition, Simon & Schuster, Inc. 1988. 2. Ideas and Concepts and Their Relationships to "Real World" Objects and Cosmology, http://www.geocities.com/roger846/theory.3.html, 2001. 3. James Ishmael Ford, `!This Very Moment : A Brief Introduction to Buddism and Zen for Unitarian Universalists`! (Boston: Skinner House Books, 1996), 25. 4. Infinite Sets: How Do Internal and External Observers View Infinite Sets?, http://www.geocities.com/roger846/theory.2.html, 2001. 5. Russell, Bertrand, Note: I haven't gotten this reference yet. Sorry. 6. Michael Green, "Strings Draw Theorists Together," `!Physics World`! 13, no. 3 (March, 2000): 22.
Email: [email protected]
Copyright, 2001