A Journal for Western Man




Entities and Spatial Continuity

G. Stolyarov II

Issue LIV- April 4, 2006





            My treatise, A Rational Cosmology, identifies three—and only three—fundamental, mutually exclusive types of existents: entities, qualities, and relationships.

            Entities are things which exist. A table, chair, bacterium, planet, human being, etc., are all entities.

            Qualities are attributes of entities, inseparable from entities themselves. Matter, volume, length, width, height, time, luminosity, etc., are all qualities. All qualities must belong to specific entities and cannot exist independently of some specific entities.

            Relationships are interactions among different entities that affect the qualities of those entities. Distance of separation, motion, acceleration, force, light, life, consciousness, volition, value, ideas, etc., are all relationships. No relationships can exist apart from entities that relate and qualities which are affected in the relationships’ course. Significant to note is that classifying an existent as a relationship does not imply that this existent’s truth is somehow “relative.” Relationships’ truth is as absolute as the truth of entities and qualities: motion, life, and value exist as certainly and as irrefutably as rocks, furniture, and people.

            This essay will focus on defining the first type of existent—the entity—in an attempt to avoid mistaken classifications of pseudo-concepts or reified concepts as entities.

Origins of the Task Before Us

            The trigger for this essay’s creation was an e-mail sent to me by a reader of A Rational Cosmology. He referred to Chapter II, where I endeavor to prove that the universe is not an entity:

The term “universe” does not denote an entity, however.  It is the sum of all entities that exist. It is not a “whole” in the sense that a planet, a star, or even a galaxy is a “whole.” As a matter of fact, it would be absurd to state that Chicago, Quasimodo, a telescope, and a hippopotamus compose some inextricably whole entity. It follows that it would be even more absurd to state that Chicago, Quasimodo, a telescope, a hippopotamus, and everything else compose some inextricably whole entity.

Arguing that my definition of “entity” is ambiguous, the reader proceeded to inquire whether I intended to argue that the universe is not a homogeneous entity or not a heterogeneous entity—a distinction I make later in Chapter II. A homogeneous entity is an entity inseparable into component parts: it exhibits uniform distribution of every quality possessed, its parts cannot be completely separated from one another, and it is unable to act to alter itself. I write that, though it is conceivable that such entities exist as the basic “building blocks” of more complex entities, no homogeneous entity has ever been definitively known to exist. From this, the reader inferred that the universe cannot be a homogeneous entity.

            The more difficult issue arose regarding whether the universe could be a heterogeneous entity. A heterogeneous entity is the sum of more basic constituent entities—related to one another in a certain manner. For example, a human being is the sum of numerous component entities; the human organism can be viewed as a combination of atomic entities, cellular entities, tissues, organs, or whole regions of the body. The reader did not see a distinction between calling the combination of body parts and organism and calling a combination of existent entities “the universe”—considered as an entity in its own right. He asked, “If the universe cannot be a whole insomuch as it is constituted by a Chicago, Quasimodo, a telescope, and a hippopotamus, how, then can we be entities as a bone, a brain, an arm, and a foot?“

            Yet one of these combinations—the body—is indeed an entity in its own right, while the other—the universe—is no entity at all. It is rather purely a human construct—a word used for verbal shorthand instead of listing all the entities that exist. When one wishes to make a generalization about qualities or relationships that all existing entities exhibit, it is much more convenient for one to speak about “universal qualities” than about “qualities of Chicago, Quasimodo, this telescope, that hippopotamus, etc.” Yet this is the whole function the concept “universe” serves; it is not an entity and not even an existent in its own right.

            By defining what an entity is—what qualities and relationships every existing entity must exhibit—I shall demonstrate why precisely “the universe” must be excluded from this category. Along the way, I shall make several important revisions to the proper definition of a heterogeneous entity—as the description of such entities given in A Rational Cosmology is too broad. Narrowing it is necessary to achieve logical consistency and adherence to reality.

Spatial Continuity as a Ubiquitous Quality of Entities

            Chapter III of A Rational Cosmology described some ubiquitous qualities of entities—qualities that all entities must possess by the very nature of their status as entities. These include matter, volume, length, width, and height. Chapter IV describes another such ubiquitous quality: time. I will not add to the discussion of these qualities here, except to say that the aforementioned writings provide proof that asserting an entity’s existence in these qualities’ absence is self-contradictory. Instead, I will supplement the list of ubiquitous qualities of entities with one more critical quality.

            Spatial Continuity: Every entity—homogeneous or heterogeneous—must have continuity among all of its parts. The test for spatial continuity is this: is it conceivable for one to trace a path from any point on the entity to any other point without any part of that path entering a region of “space-as-absence,” i.e., a region where the entity does not exist? If such a path is conceivable—no matter whether one’s current level of technological advancement actually permits one to trace it—the entity is continuous and is affirmed in this ubiquitous quality.

            In real life, it is quite easy to ascertain an entity’s continuity by actually observing the entity and seeing that every one of its parts is linked spatially. One does this by tracing the continuous path along the entity mentally and recognizing that—were he to actually, fysically trace such a path—it would fail to be anything but perfectly continuous.

            While many real objects are spatially discontinuous from one another, it is inconceivable that a single object with non-continuous parts could exist. A non-continuous entity is a contradiction in terms: it is disconnected spatially from itself.            

            Consider what it means for an entity to have spatial boundaries. A boundary is a set of points on an entity which describe the outermost extent of the entity. The fact that a given entity has a boundary implies that no part of that entity exists outside that boundary. Since every individual entity must have finite measurements of every spatial quality, every individual entity must be enclosed by a boundary; otherwise, the entity would be infinite—a logical impossibility, as I show in Chapter IX. If the entity is spatially continuous, then it is possible to trace a path from any point on the entity’s boundary to any other point. Thus, the entity’s boundary is unitary; there is only one boundary, and it marks the entity’s outermost extent. No part of that entity can exist beyond the unitary boundary that surrounds the entire entity.

            Let us now presume some entity which is not spatially continuous. This means that it is impossible to trace a path from any one point on the entity’s boundary to any other point. Thus, the entity’s boundary is non-unitary. This hypothetical entity would need to have multiple boundaries that are not spatially connected! However, since a boundary is a set of points beyond which no part of the entity exists, the scenario of a non-continuous entity is a contradiction in terms. If there are parts of an entity entirely spatially detached from other parts, they are hence beyond the boundaries of the other parts, since those boundaries do not surround them. These parts—being beyond the entity’s boundaries—are thus beyond the entity’s outermost extent. They are beyond that, which no parts of the entity can be beyond! Clearly, this is an assertion that A≠A. We have proved that the very idea of a spatially non-continuous entity fatally undermines itself.  The only way to resolve this dilemma is to concede that the parts beyond the entity’s boundaries are discrete entities in themselves and not part of the fictitious disjointed entity presumed at the beginning.

            The requirement of spatial continuity as a ubiquitous quality of entities implies that certain revisions must be made to my statements in Chapter II of A Rational Cosmology. For example, a galaxy can no longer be considered an entity, since the stars and planets composing it are not spatially continuous with one another; much “space-as-absence” separates them in all directions. The galaxy is rather a proximate cluster of discrete entities—stars and planets—that relate to one another in systematic, interesting, and noteworthy ways. Cities, however, can still be viewed as entities—provided that one includes all the buildings and the ground they stand on in the designation and provided that the spatial continuity requirement is met. Chicago can still be viewed as an entity—minus the people living there—if one can trace a path between any two points on any two buildings and not once leave the city’s boundary.

            Furthermore, I no longer maintain my prior assertion that it is possible for a heterogeneous entity to have disjointed parts—since this would preclude its entity status. The moment one of an entity’s parts is severed from it and rendered discontinuous to it, the entity splits in two. Even an atom falling off a human being implies that one heterogeneous entity has become two discrete heterogeneous entities: the remaining human and the atom.

            An even more radical implication of the discovery that spatial continuity is necessary for entities is a rejection of modern scientists’ bromide that atoms are “mostly empty space.” It simply cannot be that spatially continuous macro-entities are made of spatially discontinuous micro-entities. Rather, it must follow that every atom is spatially continuous with itself, and that every atom in every larger heterogeneous entity is spatially continuous with every other atom in that entity. This realization is categorically not at odds with empirical knowledge; atoms have never been observed directly, and thus the assumption that they are “mostly empty space” is just a contingent “operational hypothesis” that could be rendered mathematically consistent with some other data. Yet some better understanding is needed to reconcile atomic theory with the logical truth that every entity must be spatially continuous with itself. It is clear that primitive models of sferes orbiting around other sferes do not accurately describe atomic structure. Perhaps if scientists abandoned warrantlessly conceiving of protons, neutrons, and electrons as tiny, round balls, they would be able to explain both atoms’ internal continuity and their ability to be continuous with one another in large combinations.

The universe is not spatially continuous. Thus, the universe is not an entity.

            If the universe were a heterogeneous entity, it would fail the test of spatial continuity. Such an entity would be comprised of multiple parts entirely spatially disconnected from one another. Even two planets are separated from one another by millions of kilometers where no entities exist. It would thus be impossible to trace a path from one planet or star to another planet or star. Hence, it is inappropriate and logically contradictory to classify the listing or summation of these planets and stars as a single entity-in-itself. “The universe” is only a compendium, created by the human mind, of the various discrete entities that exist. The term itself is mere summary notation, not some over-arching super-entity.

            Hence, we can see how a spatially continuous combination of multiple distinct entities—such as a human body or even a city (minus the inhabitants)—can be called a single heterogeneous entity-in-itself, whereas a spatially discontinuous total of all discrete entities that exist—the universe—cannot be anything more than just a convenient collective designation of no independent ontological existence. My reader’s dilemma has been resolved and rational cosmology improved by the explicit analysis of spatial continuity’s necessity as a ubiquitous quality of every necessity.

G. Stolyarov II is a science fiction novelist, independent filosofical essayist, poet, amateur mathematician, composer, contributor to Enter Stage Right, The Autonomist, Le Quebecois Libre, and the Ludwig von Mises Institute, Senior Writer for The Liberal Institute, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress. His newest science fiction novel is Eden against the Colossus. His latest non-fiction treatise is A Rational Cosmology. Mr. Stolyarov can be contacted at gennadystolyarovii@yahoo.com.

This TRA feature has been edited in accordance with TRA’s Statement of Policy.

Read Mr. Stolyarov's new comprehensive treatise, A Rational Cosmology, explicating such terms as the universe, matter, space, time, sound, light, life, consciousness, and volition, at http://www.geocities.com/rational_argumentator/rc.html.