Emergence, Evolution, and the Geometry of Logic:
Causal Leaps and the Myth of Historical Development
I. Emergence and the Problem of Emergent Properties
At what stage in its development does a foetus become a living human being? When is it proper to refer to a network of pulsating neurons as a “thought”? At what point does an accumulation of insightful thoughts deserve to be called a “new idea”? To what depth and breadth must a particular person’s ideas and other creative works extend before he or she comes to be recognized as “great”? Such questions, despite their apparent diversity, are all instances of the same underlying question: How is it possible to discern when (i.e., at what point in its historical development) an “emerging” property becomes what it can be observed to be, once it has fully emerged? This question has wide-ranging implications not only for science and the philosophy of science, but also for disciplines as diverse as logic, history, and even theology. Answering such an ambitious question in the limited space of a single essay will be impossible without strictly narrowing the scope of our discussion through several limiting assumptions.
Before discussing these interpretive assumptions, a brief overview of how the term “emergence” came to be used as a philosophical concept will provide an essential focus for our subsequent analysis.[1] Although various theories of emergence can be identified throughout the history of philosophy, the word “emergence” was first introduced as a technical philosophical concept in George Henry Lewes’ 1875 book, Problems of Life and Mind, where it referred to the evolutionary processes whereby non-living matter came to take on life and non-mental beings came to have mental properties. Early twentieth century philosophers such as and C.L. Morgan,[2] Samuel Alexander,[3] and C.D. Broad[4] were influenced by Lewes as they brought the concept of emergence into the mainstream of philosophical debate. Since then, especially during the last quarter of the twentieth century, the literature on emergence and emergent properties has been immense. Essentially, something (e.g., an object, property, or idea) can be said to “emerge” out of another thing (or level of reality) when the former somehow originates or is grounded in the latter, but displays such unique and unexpected characteristics that it takes on a “life” (i.e., a mutually interacting set of new properties) of its own. The issue of whether emergent properties (e.g., conscious thoughts) can be reduced to their underlying physical ground (e.g., certain brain states) remains one of most hotly-debated topics related to emergence.[5] Probably the most widely accepted contemporary position on emergence is that known as “non-reductive materialism” (see note 3), the view that emergent properties originate wholly within the physical domain, yet the qualities that manifest themselves cannot be explained merely in terms of their underlying physical interactions.[6] That is, once a higher-level property has emerged, we must treat the object (or at least its emergent property) as if it were more than just physical.[7] In this paper, I shall argue that a careful analysis of how emergence functions in formal logic can shed important light on how this “more than” actually arises.
Four assumptions will serve to narrow down the scope of our analysis in such a way as to avoid the need to deal with most of the philosophical issues that typically arise in discussions of emergent properties. First, I assume that properties do exist. While this assumption is controversial, the onus of proof in this case is on those who take the counter-intuitive position that they do not exist; thus I shall not deal with it any further here.[8] My second assumption is that some properties must emerge from their underlying objects or propositions in a way that contrasts with other properties that do not emerge but are somehow there from the start, so to speak. If this were not the case, if all properties were emergent (or if all were non-emergent), then our question would never arise, for there would be no background enabling us to detect an emergent property. I shall clarify this distinction shortly, though without attempting to present a full justification. Third, I assume that the difference between emergent and non-emergent properties is knowable—i.e., that properties exhibit identifying marks that conform to some logical pattern. Once again, this assumption is necessary, for without it our question would be unanswerable, if not meaningless. One purpose of this essay will be to provide a limited defense of this assumption by presenting a systematic, logical way of distinguishing between different types of properties. In the end, however, this point will retain the status of an assumption, so the most we will be able to conclude is that, if an emergent property is knowable, then its emergence should follow the type of logical pattern to be introduced here.
My fourth assumption—perhaps the most controversial of all—is that relational patterns in formal logic often (if not always) can be correlated directly to the spatial relations exhibited by certain simple geometrical figures. I call the systematic analysis of such analogical relations “The Geometry of Logic”. This fourth assumption is unlike the other three in two respects. First, it is not a necessary assumption. Questions about the nature and function of emergent properties may be answered quite apart from such a correlation. Nevertheless, I believe the Geometry of Logic can be treated as a heuristic device that greatly enhances our ability to construct a clear and meaningful response to such questions. As we shall see, the usefulness of this device is that it exhibits a clear hierarchy of “levels” that can be directly compared with the levels of scientific explanation that are a core feature of any emergentist theory.[9] The second difference is that in this case I have already defended the assumption at great length elsewhere and have found it to be very useful in stimulating deeper insight into numerous philosophical issues.[10] In §II of this essay I shall therefore present an overview of the essential features of the Geometry of Logic, before going on to apply those features to a few central issues relating to emergence and evolution.
The remainder of this first section will be devoted to the task of clarifying what an emergent property is. Perhaps the best way to understand this term is to contrast it with its opposite. For the sake of simplicity of expression, I shall coin the word “mergent” to refer to any properties that are not emergent. What, then, is the difference between ordinary (mergent) properties and the special emergent properties that will occupy the main focus of our attention here? A property that is taken by the observer of an object or by the interpreter of a proposition to be a standard component of the object/proposition in a given context (usually one that is being viewed at a relatively low level of complexity) can be described as “mergent”: the property merges with the object and/or with the meaning of the proposition in the eyes of the observer/interpreter.[11] For example, the fact that there are words printed on the pages of this essay is a mergent property of the essay insofar as we describe the essay in terms of its physical properties. Without the appearance of such printed words, we could not identify these pages as constituting a published essay; the fact that words do appear on these pages is therefore entirely predictable, given the known context.
Emergent properties, by contrast, are properties that appear unexpectedly and are not (at least initially) regarded as necessarily connected to the object/proposition when we consider it at the lower level of complexity. To “emerge” is to “rise out of” or “leap away from” something in such a way that a latent possibility is manifested and becomes known. Thus, the fact that the words printed on these pages can be read together in such a way that they convey a meaning is, from the point of view of the physical paper and the ink printed on it, an emergent property. Whether or not the ink printed on these pages really does convey a meaning depends, of course, on a number of contingent facts about the linguistic skills of the writer and reader. If a meaning is conveyed, then it would not be merely a mergent property because the meaning is something that cannot be explained merely in terms of the paper and ink used to convey it. The meaning could never be discovered merely by analyzing the characteristics of the paper and ink, but only by viewing these objects from a higher level of complexity, as composing words, sentences, and paragraphs. As such, the perception of meaning that justifies a reader in calling this collection of papers and ink “an essay” exemplifies one kind of emergent property.
Can an emergent property ever lose its emergent character and somehow become a mergent property? Likewise, can a mergent property lose its status and somehow become emergent? To answer such questions, a secondary distinction must be made: both mergent and emergent properties can be either intrinsic or extrinsic.[12] Extrinsic properties are properties whose association with their object (whether necessary or contingent) has a nonlinguistic source. They may only seem to be what we expect them to be, due to cultural conditioning; or they may be what they are as a matter of physical necessity. Intrinsic properties, by contrast, are properties whose necessary or contingent status depends entirely on the assumed meaning of the words (i.e., on purely linguistic conventions).[13] Thus, the fact that a published essay has the property of having words on a printed page is an intrinsic property: only if we use the word “essay” in a way that radically departs from the standard definition would we be able to conceive of an essay that did not exhibit the property of having readable words. But the blackness of the ink conventionally used to print a scholarly essay is an extrinsic property. It is mergent in the sense that we have become so accustomed to seeing black words on the printed page that anything else would seem “inappropriate” to a scholarly essay, though only contingently. If it were printed in red ink, for example, this property might make some readers (e.g., scholars) question whether it really deserves to be called an “essay” at all.
This secondary distinction suggests that extrinsic properties can change from being mergent to being emergent (or vice versa), when viewed from different contexts, whereas intrinsic properties cannot. For instance, although “printed with black ink on white paper” is a mergent property of “scholarly essay”, it is extrinsic insofar as our cultural conventions could change with time. If the editors and publishers of a few renegade academic journals decided to publish all scholarly essays in red ink, the practice might gradually catch on; as soon as all (or at least most) such journals began to follow this new convention—say, 100 years from now—red ink will have become a mergent property of published scholarly essays. People would just assume that if the essay is scholarly it will be printed in red ink. However, the same cannot be said for the more basic property of having words. An essay is still an essay whether it is printed in black or red ink; but if in 100 years we begin using the word “essay” to refer to blank sheets of paper, then the meaning of the word will itself have changed. Having words is thus an intrinsic mergent property of scholarly essays, as we currently understand them.
Emergent properties are related to this secondary distinction in a similar way. The most interesting type of property, as we shall see, is intrinsic emergence. This refers to a new property that arises unexpectedly when an old situation is viewed from a level of higher complexity (or when the situation somehow actually becomes more complex), yet the new property is necessary to the identity of the object under consideration. The four questions raised at the very beginning of this essay—concerning when life begins, when neural firings become a thought, when thoughts become a new idea, and when a person with ideas becomes great—are all examples of intrinsic emergence. A whole list of other examples, such as when two people who were formerly “just friends” come to be “in love”, would not be difficult to compile. As we shall see in §III, however, this fourth type of property is so different from the others that serious doubts can be raised as to whether it represents a real possibility at all. I shall therefore forego any further discussion of it until that point.
After briefly introducing the Geometry of Logic in the next section of this essay, I shall use it to illustrate some of the basic features of how emergence operates. I shall then apply it in §III to the task of clarifying the fourfold distinction made above, between different types of properties. The relationship between the logic of emergence and certain assumptions often made about the nature of evolution will be the main focus of our attention in that section. I shall conclude the essay in §IV by arguing that the proposed way of understanding the similarities and differences between the four types of mergent/emergent change calls into question a myth that has dominated academia—philosophers as much as scientists and other academics—for nearly two centuries. The myth, in a nutshell, is that the best (if not the only proper) way to examine the origins of an idea is to trace its historical development, uncovering the empirically discernable causes that led, step by step, to the point where a new idea, or “insight” (as I prefer to call it), was bound to emerge. Questioning this myth on the basis of the logic of emergence opens up a potential (though not a compelling need) for theological explanation to fill an explanatory gap that appears to remain in a state of inevitable mystery if we appeal to scientific explanation alone.
II. Patterns of Emergence in Geometrical Relations
Let us look now at how the Geometry of Logic can shed light on the nature and function of emergent patterns in general. After briefly introducing the four main logico-geometric figures used to depict systematic relations, I shall point out several interesting patterns of emergence that can be observed by viewing the diagrams as a series. This will demonstrate that geometric emergence, at least, is possible. It will also prepare us for attempting in §III to clarify the distinction made in §I between types of mergent and emergent properties and for examining the special problems associated with evolutionary emergence.
The Geometry of Logic is divided into two main parts, based on what I call “analytic logic” and “synthetic logic”. For our purposes, we can think of the former as relating to any logical distinction between two opposites (i.e., to any dyadic opposition) and the latter, to any logical distinction between three terms (i.e., to any triadic opposition), where two terms are analytic opposites and the third somehow combines or “synthesizes” the others.[14] The most obvious geometrical maps for the simplest (or “first-level”) forms of analytic and synthetic relations are the line segment (with its two opposite endpoints) and the triangle (with its three vertices), respectively. Figure 1 uses the “+” and “-” symbols to denote the simple conceptual opposition in a first-level analytic relation (1LAR), while Figure 2 adds a third term, “x”, to denote the simple synthesis of opposites in a first-level synthetic relation (1LSR).[15]
Figure 1: The Line Segment as a 1LAR Map
Figure 2: The Triangle as a ILSR Map
In both cases these simple forms of relation also give rise to more complex “levels”. The formula determining the structure of all analytic relations is:
2L = N
where “L” stands for the “level” of the distinction (i.e., how many pairs of opposites are being interrelated) and “N” stands for the “number” of different combinations. For instance, the most common type of analytic relation, the second-level analytic relation (or 2LAR), consists of two pairs of opposites that combine to produce four interrelated concepts (2 x 2 = 4). As such, it is best mapped onto the four endpoints of a cross (i.e., two line segments intersecting at their midpoints, with each segment representing the distinction between one pair of opposites), as shown in Figure 3.
Figure 3: The Cross as a 2LAR Map
The formula determining the structure of all synthetic relations is similar to the one for analytic relations, the only difference being that the “2” is replaced by a “3”:
3L = N
Thus the second-level synthetic relation (2LSR) has nine combinations (3 x 3 = 9) and would need to be mapped onto a geometrical figure with nine distinct points.[16]
From the two basic applications of the Geometry of Logic (analysis and synthesis) emerges a third application, involving various combinations of analytic and synthetic relations. For our purposes the most significant of these “compound relations” (as I call them) is the twelvefold compound relation (12CR). This consists of a 2LAR with each of its four components divided into a 1LSR (4 x 3 = 12). Apparently accidental examples of this form of conceptual relation abound in daily life (e.g., the twelve hours on our clock dials, the twelve months on our zodiacal calendars, the twelve tribes of Israel, etc.), with more systematically predetermined examples sometimes playing an important role in philosophy (e.g., Kant’s twelve categories[17]), social sciences (e.g., Jung’s system of psychological types[18]), and even natural science (e.g., the system of twelve sub-atomic particles[19]). What is important to note here is that, in order to be a genuine 12CR, these relations must be regarded not merely as a haphazard collection of any twelve items, but as an integrated whole made up of four sets of three, where the four is a 2LAR and each set of three is a 1LSR. Of the various ways of mapping a 12CR, I prefer to use a circle divided by a cross into four quadrants, with each quadrant having two additional points equidistant between the two poles of the cross (like a clock dial), as shown in Figure 4.
Figure 4: The Crossed Circle as a 12CR Map
Rather than examining various other, more complex aspects of the Geometry of Logic, I shall now proceed to explain how certain features even of the simple diagrams introduced above can serve as instructive illustrations of how emergence operates. First, note that the two opposites in Figure 1 arise out of a prior unity that could be represented as a point.[20] Before carrying out the initial analytic division, nobody could have been sure that the point (as a representation of a given conceptual unity) would be divisible into opposites. But once the 1LAR emerges, it seems obvious. Likewise, the potential for these opposites to be reunited, as shown in Figure 2, is an emergent property that no amount of prior analysis could have enabled us to predict. It simply has to happen; then it seems obvious.[21]
With Figure 3 the emergence of intrinsic properties becomes more complex. Patterns arise that were somehow already implied in Figure 1, yet could never have become explicit until they emerged on the figure of a cross. For example, by tracing around the diagram from the 3 o’clock position, we now see for the first time a movement that passes from the most negative component (--), through the two mixed components (+- and -+), to the most positive component (++)—a movement that becomes even more complex in Figure 4. The most obvious example of this added complexity is that we now have three distinct types of opposition represented: primary polarity (-- vs. -+ and ++ vs. +-), secondary polarity (-- vs. +- and ++ vs. -+), and contradiction (++ vs. -- and +- vs. -+). As we shall see in §III, the two types of polarity correspond to the intrinsic-extrinsic and emergent-mergent distinctions, respectively (cf. Figure 5, below), but the contradictory opposites represent a third set of relationships, not previously noted in the foregoing discussion. The Geometry of Logic will therefore provide an ideal (i.e., a priori) method of clarifying the logic of emergent properties.[22]
Each higher level of logico-geometrical relation produces more and more complex patterns of emergence. In Figure 4, for example, we see not only a more detailed version of the movement from the component with the most negative value (---), through a series of gradual permutations, to the component with the most positive value (+++), but also a complex array of interrelationships between the twelve components. This includes not only a new form of polarity, defined by the relations between the third term in each component, but also various forms of “bipolarity”, where two terms are the same and only one differs. Moreover, numerous patterns of triads and quaternities emerge once we begin to analyze the relationships between the various components.
At its most extreme levels of complexity, where forms of relation can no longer be depicted by simple geometrical figures, the Geometry of Logic would have to make use of something like Mandelbrot’s Fractal Geometry instead. Fractal Geometry could provide an antisystematic (indeed, chaotic) alternative to standard (Euclidean) geometry; yet in the end it would lead to the same conclusion we have reached here, that geometric forms can provide us with deep insights into the astonishing ways emergent properties operate.[23] My purpose here, however, is not to draw any conclusions about the merits or demerits of the Geometry of Logic (this being one of the assumptions of this paper put forward in §I), but only to illustrate how emergent properties can lie dormant within lower levels and leap out at us when we examine the higher levels. The question this presents to us is whether what is true in this logical realm is also true in the ontological realm of our experience of objects in everyday life. To this question we shall now turn our attention.
III. Evolutionary Emergence in Natural Processes
Keeping in mind the essential features of the Geometry of Logic introduced in §II, we shall now turn our attention back to the basic distinctions made in §I. The first and most obvious point to note is that the two dyadic distinctions discussed there form a perfect[24] 2LAR. By mapping the intrinsic-extrinsic distinction onto the vertical and horizontal axes of a cross (i.e., associating it with the first term of each dyadic component), with the emergent-mergent distinction defining the polar opposition on each axis (i.e., the second term of each component),[25] we can construct a map relating these distinctions to four basic aspects of change, as shown in Figure 5.
Figure 5: Four Aspects of Change
As we saw in §I, extrinsic mergent properties, such as the blackness of the words on this page, could change but are generally assumed to remain the same. I have chosen the term “stagnation” to describe this kind of potential change, because a property that changes in this way is analogous to a pool of water that is stagnant but could become fresh if it ever began to move. Being the absence of change, stagnation is appropriately mapped onto the “--” position of the cross (cf. Figure 3). The polar opposite of stagnation is “flux”: a continuous flow of changes that never seems to settle on one form or content. Extrinsic emergence, as in the rather odd example of this essay being printed with red ink, typically has this characteristic. But this is only an appropriate example to the extent that such a change comes as a surprise. An extrinsic emergent property must continuously change if it is to maintain the element of surprise and resist becoming mergent. A better example, therefore, is speech itself; for every language is constantly changing. Indeed, the very possibility of communication arises out of the tension between stagnation and flux, the interaction between mergent and emergent types of extrinsic properties.
This tension would never be able to maintain its balance if it were not for the fact that some properties simply do not change, but remain constant. Intrinsic mergent properties have a permanence that grounds our ability to communicate and enables us to detect something genuinely new when it arises. If we could not count on an essay containing words, then the question of whether the words are printed in black or red ink would never arise. Yet like stagnation, permanence is itself balanced by a polar opposition to properties that are both like it (intrinsic) and unlike it (emergent). The type of change that characterizes such intrinsic emergent properties is best called “evolution”, for evolutionary changes help us identify a particular concept or object (e.g., an organism) and distinguish it from others like it. Such changes, like those relating to geometric emergence (see §II), arise out of a potential that was permanently present in the prior state, but did not manifest itself until a particular moment in time.
Just as stagnation and permanence are somewhat similar (both lacking signs of change) yet also different (only the former has the potential to change without destroying the identity of the property itself), so also flux and evolution represent fundamentally different types of change. “Flux” refers to a continuous development that advances according to clearly determined increments, though it may well have proceeded differently. The process that caused the red ink to replace the black ink would presumably be easy to determine; but the new color might just as well have been green. “Evolution”, by contrast, refers to a sudden change that could not have been foreseen, and whose causes (if any) may remain hidden, even though it seems necessary when viewed in retrospect. Biologists believe life evolved from non-living material; yet how this could have happened remains a matter of speculation that cannot be confirmed in a laboratory. Likewise, every human being was once a tiny foetus, totally dependent on another organism (i.e., its mother); yet at some point it evolves a distinct life of its own. Although empirical observation may enable us to make educated guesses, we cannot know for certain when or in what manner such emergent properties will arise until they actually emerge.
The foregoing distinction between “flux” and “evolution” can be clarified by relating it to a corresponding distinction made by Kant. In his Opus Postumum, he contrasts two types of “transition”: a “step” is a change from one position to an immediately adjacent position, whereas a “leap” is a change that skips over one or more intermediate position(s).[26] The former describes the type of transition characteristic of flux, while the latter corresponds to that of evolution. Take an object, A, that has a mergent property, X, at time t1, and imagine it comes to have an emergent property, Z, at time t3. Property Z is intrinsic if there is no third property that mediates between properties X and Z. It is extrinsic if the path from X at t1 to Z at t3 passes through another property, Y, at t2. In the former case A evolves, whereas in the latter it undergoes the constant change characteristic of flux.
Kant’s distinction foreshadows Kierkegaard’s later treatment of faith as an irrational “leap” across the abyss of one’s own existence. That Kierkegaard’s “stages of life” (the aesthetic, the ethical, and the religious) are to be regarded as evolving out of each other, rather than as causally determined by what goes before, is evident from the stress he puts on their paradoxical character. Without going into the details of Kierkegaard’s theory, we can take note of the challenging question this raises: if evolution (the emergence of a new intrinsic property) requires something like a “leap of faith”, then is it even possible? Answering this question will be our main concern for the remainder of this section.
Intrinsic emergence may be logically possible in the highly abstract realm of mathematics (see §II), but is it a real possibility in the natural world? I believe a detailed analysis of the phenomenon of natural evolution would show that it is, though its epistemological status is highly paradoxical (see note 28, below). Classical (Darwinian) evolutionary theory claims that organisms tend to pass on from generation to generation those properties that are more likely to help them adapt to their environment, that the organisms carrying out this selection process most efficiently will survive the longest, and that organisms will tend to find gaps in the natural world in order to evolve in ways that are not already exhausted by existing organisms. In terms of the framework given in Figure 5, this means natural organisms tend to inherit the most advantageous extrinsic mergent properties and somehow the species has the ability to supplement these, over a long period of time, with intrinsic emergent properties. Once the latter evolve, they (being intrinsic) become integrally related to the very identity of the species in question, so that they too are passed on genetically.
But how is this possible? All too often evolutionary theorists, failing to distinguish between the four types of change introduced above, attempt to explain evolutionary transformations in entirely causal terms. That is, they hypothesize complicated accounts of how a given species might have developed, step-by-step, from having property X, through the intermediate stage of having property Y, to the current stage of having property Z. Such a theory of smoothly flowing development admittedly describes how many simple causal phenomena undergo observable changes; yet when applied to long-term evolutionary changes, it quickly becomes absurd. For as long as there is no new input into a system, mere flux cannot produce anything fundamentally new. Evolution proper cannot take place merely as a series of minute increments that eventually manages to span the gap from one side of an abyss to the other. It will normally involve such causal fluctuations in some way; but what makes it evolution, as opposed to mere environmental adaptation, is the ability to disclose an unrealized potential that already existed in the original (pre-evolutionary) state.
How merely sentient life-forms (i.e., life-forms with pre-conscious awareness capable of perception) emerged from the lifeless cosmic “soup”, how animal consciousness emerged from these simpler sentient life-forms, and how human self-consciousness emerged from the lower-level consciousness of our animal cousins are all questions that cannot possibly be answered by theories of incremental change alone.[27] Consciousness may be rooted in a pre-conscious level of awareness, but it is also something fundamentally new. Self-consciousness and rationality are likewise dependent on an evolutionary progression from the kind of conscious life we observe in the animal kingdom; but to reduce the former to the latter would be to ignore the mysterious origin of language itself. This view of evolutionary biology has been developed in considerable detail in Teilhard de Chardin’s many books,[28] so I shall not attempt to defend it any further at this point. Of the many other, more recent theories that have been developed along lines that are compatible with the position advanced here, two that are particularly worthy of mention are Catastrophe Theory, expounded by René Thom and Christopher Zeeman,[29] and Paul MacLean’s theory of the Triune Brain.[30]
The myth assumed by so many (though increasingly few) evolutionists is that, if we could only observe the evolutionary process as it happened, then we could locate the proverbial “missing link” that would enable us to give a complete, step-by-step explanation of the transition from one level to the next. Our study of emergent properties, however, has shown this to be a category mistake. Such an assumption fails to distinguish between evolutionary change and the causal processes that guide the extrinsic flux studied by ordinary science. Genuine evolution refers to intrinsic emergence, which proceeds (whether in branches of mathematics such as geometry or in branches of natural science such as biology) by sudden leaps—“emergencies”, as it were—rather than by a step-by-step progression.
IV. Evolutionary Emergence, Insight, and the Myth of Historical Development
In the foregoing discussion of natural evolution we noted a common tendency to interpret evolutionary change as a continuous flux, rather than in terms of the discontinuity characterized by intrinsic emergent properties. The best way to counteract this common assumption is to observe the interesting parallels that exist between evolution on the grandest scale and other, smaller-scale forms of evolution. Recall the opening question of this essay. Just as we cannot observe any “magic moment” in the development of a foetus when it suddenly ceases to be a piece of “dependent tissue” and becomes an independent human being, so also genuinely evolutionary changes in general cannot be localized as happening at any given point in time. The reason bio-ethicists have such difficulty determining when life “begins” is essentially the same as the reason archaeologists cannot find the “missing link”. Step-by-step growth is nowhere more apparent, and our knowledge of the stages nowhere more carefully studied, than in the transformation of a tiny sperm-approaching-an-egg into a newborn baby; video cameras have captured virtually the entire process on film, yet none have ever been able to detect the moment when human life as such begins. We simply do not know if it is present until after it has already clearly emerged. The onset of life, like all evolutionary change, is recognizable only a posteriori—i.e., only after the change has taken place.[31]
With this in mind, let us return now to the common assumption mentioned briefly near the end of §I, that new ideas emerge through a step-by-step process of cause and effect, not unlike the kind of process that is often assumed to take place in natural evolution. Understanding a philosopher’s “development”—how he or she arrived at a new idea—is often regarded as a prerequisite for (and sometimes even as more important than) understanding the ideas themselves. The effects of this typically unquestioned assumption on scholarship can range from a very legitimate conviction that such historical knowledge will assist one in forming a good interpretation, to an illegitimate belief that the latter is impossible without (and can perhaps even be replaced altogether by) the former. Obviously, gaining insight into the historical factors that gave rise to a given idea can help us understand the idea. But if a new idea arises (as I believe great ideas typically do) as an intrinsic emergent property in relation to its historical roots (i.e., as a “leap” rather than as a “step”), then a detailed knowledge of its historical background (though unquestionably helpful) is not as essential as it is often assumed to be.[32]
Our study of the logic of emergence reveals that this “myth” (i.e., unquestioned assumption) can be applied properly only to properties (in this case, ideas) that arise through an extrinsic emergent process. The far more interesting, intrinsic emergent properties (such as insights, in the case of human thought processes) always manage to elude the grasp of those who seek to tie them down in this way. Once this distinction is clearly recognized, scholars in all disciplines will be empowered to make more accurate assessments of the way old ideas pass away and new ideas emerge. An example from the history of philosophy may help to clarify how important this can be for anyone involved in the task of interpreting another person’s ideas.
The old “patchwork” interpretation of Kant’s Critique of Pure Reason, advanced during the first half of this century by Erich Adickes in Germany and Norman Kemp Smith in the U.K., is a case in point. These scholars and those who followed their lead assumed that by carefully estimating the date when Kant wrote each of his various arguments they could reconstruct a step-by-step account of how Kant developed his ideas; they then attempted to explain apparent inconsistencies as due merely to Kant’s tendency to forget what he had previously written as his ideas evolved. One paragraph may be judged to be a late addition, while the next may be regarded as a leftover from an earlier way of thinking. In some cases, such an analysis may succeed in recovering the actual flow of Kant’s (or any other scholar’s) thinking, in its chronological development; but it will never reveal the evolutionary source of his new insights. By completely ignoring Kant’s own emphasis on the systematic coherence of his philosophy, this historical approach provides an easy excuse for the interpreter to avoid the difficult task of finding a higher perspective that enables us to fit all Kant’s ideas together into a coherent whole. Moreover, it neglects the fact that insights (especially those of a truly great thinker, such as Kant) are more likely to emerge as leaps than as steps.
Where, then, do insights come from? Such a question, as our overview of the Geometry of Logic in §II so clearly illustrates, can only be answered from the perspective of the next higher stage of an evolutionary process. In the case of human rationality, this suggests that the origin of our insights, of the new ideas that characterize the historical development of any creative thinker, is fundamentally inexplicable when viewed from our own evolutionary stage. This leaves us with one of two alternatives: we can either admit our ignorance and stop trying to answer the question, or we can postulate the existence of a higher level in the evolution of consciousness and try to imagine what it would be like to view human rationality from that perspective.[33]
The second option, for those who are willing to take it—something nobody content with the first option can be forced to do—suggests an interesting way of applying the logic of emergence to the question of God’s existence. The study of how intrinsic emergent properties have evolved in life-forms gives rise to the possibility of developing a theological proof “from evolution”. Such a proof could take two forms. First, it could argue on the basis of the evolution of consciousness that insights themselves (i.e., the experience of thinking a thought that has an intrinsic emergent character) must come from a higher-level consciousness that somehow transcends human consciousness. The problem here is that the way ideas emerge in the minds of rational beings can also be explained (though I believe only partially) in the fluctuating terms of extrinsic properties—properties that can and often do eventually become mergent, as explained in §I.
A second form of the theological proof from evolution could start not from insight (i.e., the peculiarly human ability to think new thoughts), but from the inexplicable fact that natural events other than life-forms also emerge. The principle of continuous development postulated by the theory of Natural Selection can explain only extrinsic mergence and emergence, not their intrinsic counterparts. For as suggested above, such properties can change and develop only by combining old properties of existing objects in new ways. “There is nothing new under the sun” is a basic principle of extrinsic properties. The surprise that characterizes our experience of extrinsic emergence is due not to the property being genuinely new, but merely to our cultural conditioning. If red ink is used to print this essay, this fact will not imply that red ink has in any way evolved; it has been here all along, waiting to surprise us—and perhaps eventually to become a mergent property of scholarly essays, should the process of flux begin to stagnate. But if, by contrast, genuinely new properties emerge instead—that is, if evolution (defined in terms of intrinsic emergence) happens—and if the origin of such changes cannot be attributed to human rationality (as in the case of new ideas), then a gaping hole is left in our explanatory scheme. That hole could be filled, at least potentially, by God.
In this essay I have not even begun to construct a formal argument for God’s existence based on the discovery of intrinsic emergent properties in evolutionary processes. At most, I have merely established the framework within which such an argument could be constructed. The argument could be two-pronged: beginning from the nature of geometrical evolution (as outlined in §II), it would demonstrate that intrinsic emergence requires a higher-level perspective in order for the source of a lower-level property to be fully identified; the argument would proceed to examine particular examples of natural evolution, arguing that the only way the emergence of such intrinsic properties could ever be adequately explained (if an explanation is desired) would be to trace them to a Being who is somehow at a higher-level of evolution than human consciousness on the one hand and at a higher level of evolution than the material world on the other. That is, just as the evolution of human rationality (with its capacity for insight) can be explained only by referring to the emergence of a higher-level mental reality, so also the evolution of physical properties in nature can be explained only by regarding them as rooted in the emergence of a higher-level physical reality. Although such teleological explanations are far from being generally accepted by philosophers and scientists these days, they do find significant prima facie support from our study of how emergence functions in the Geometry of Logic.
The foregoing answer to the question of how emergent properties are possible remains admittedly tentative at this point. However, I believe it is the only answer possible, given the limitations imposed upon us by the logic of emergence. The clear example of how emergence functions with logical necessity in the Geometry of Logic provides irrefutable evidence that intrinsic properties do emerge, at least in a purely mathematical context; and evolutionary biology supplements this with numerous examples of such emergent “leaps” in nature. Unfortunately, taken on its own terms, the possibility of such intrinsic emergence is unexplainable. It simply happens.[34] Those who are dissatisfied with such a conclusion do have recourse to a way out of the dilemma, but the way of escape remains as hypothetical as the proposed solution—until the day when human rationality itself evolves again and a higher level of understanding emerges.
FOOTNOTES