ABSTRACT: In contemporary analyses, teleological narratives are often mistakenly opposed to "nonlinear" narratives. Many secular teleologists throughout history described telos as a product of feedback, not as a direct cause separate from the process it is said to guide. Moreover, in many teleological accounts of causation, a telic state is seen as the inevitable result of random interactions. The importance of chance to the concept of telos has been ignored by arguments that have confused nonlinear telic causality with reductive material causality. Today nonlinear dynamics theorists and structural evolutionary theorists use the terms "structural attractors," "emergent complexity," and "self-organization" to describe the same kinds of phenomena that interested Aristotle, Kant, Bergson, and many other teleologists and vitalists.
According to Immanuel Kant, whose writings greatly influenced 19th century teleology, the probability that a creation as complex as this world could have formed by unconstrained chance and mechanistic necessity alone was unlikely. While he accepted the fact that each separate causal chain may be mechanistically determined, he assumed that various causal chains interrelate fortuitously. And he assumed that there must be some sort of principle that constrained these interactions and resulted in the directedness, the purposefulness that we often sense in natural events. According to Kant in nature we find "perfect coordination," a "harmony," and things "with different natures" working in "cooperation." Kant and those who followed him believed that the whole is more than the sum of its parts.They did not think that output was directly proportional to input. And they thought the laws of any overall design could only be understood by studying systems holistically.
Another point I would like to stress is that teleologists, in general, never believed that telos is imposed upon creation by a god that exists beyond time, external to the human world. Rather, a nonphysical cosmic intention was believed to be immanent in physical events themselves. To summarize, according to teleology, then, there are universal laws that govern random interactions and consequently nature is more constrained--or you might say--more directed than reductive analysis would imply.
If teleology is understood as the study of systems that cannot be described reductively, that is, nonlinear systems, it becomes more interesting to us in the humanities because, well, "nonlinear" is in these days and "linear" is out. I'm not sure what we mean, however, when we use these terms to describe literary styles or types of plots. Most people use "nonlinear" in a perfectly vague sort of way meaning some synonym of "good" without thinking of the technical meaning of the term in, say, mathematics or physics. When "linear" is applied to teleology, however, it brings with it a mistaken association with reductionism, mechanism, and lifelessness. Teleology should evoke notions of vitalism, intentionality, autonomous and free behavior.
I'm not saying that teleologists had the right answer, but I do think they understood the problem the right way in terms of anti-reductionism. Recently nonlinear dynamics theorists have returned to the study of telic phenomena, which they refer to as "self-organization." They claim that the emergent complexity that characterizes self-organization is truly more than the sum of its parts. Furthermore, they say the formation of spontaneously self-organizing systems are indeed governed by universal laws.
But even if teleology is vindicated somewhat by these findings, we still have the problem that its method of reasoning is analogical, comparing the way nature creates plants and animals to the way humans use and create tools and works of art. Nature cannot think, after all. Nature cannot plan ahead. Even if the ecosystem as a whole does seem organized, it still cannot be compared to a person who has a localized center (a brain) that can direct and control actions.
However, recent research has taught us that it is wrong to think that humans have localized centers that direct and control actions. The "brain" functions more like a distributed system. It turns out that intentional human behavior is not very different from self-organized behavior that occurs in nature. Perhaps the analogy is better the other way around. Cosmic telos teaches us more about human intentionality than human intentionality teaches us about cosmic telos.
The idea that teleological or goal-directed activity is linear comes, I think, mostly from 20th century analytic philosophers who, impressed by scientific reductionism, looked at human intentionality this way:
Action 1 ® Action 2 ¦¬ Purpose or Idea
A person performs one action in order to be able to perform the second action in order to accomplish a final goal or achieve some purpose. Then they argue whether or not Purpose can be said to cause Action 1 and Action 2, as if the end could cause the beginning. In my opinion, no one has ever made a good argument for the necessity of teleological explanations using this line of reasoning.
A teleological explanation is only necessary if, a purpose is fulfilled in a way that could not have been predicted by analyzing the initial conditions, or the starting point that led to the goal. In retrospect, however, it appears as if each stage in the process was a precondition for the advantageous or more complex property, quality, or event that eventually emerged. This is the very situation that nonlinear dynamics theorists now explain: they claim self-organizing systems are irreducible and hence unpredictable because effective factors (e.g., function or context) unaccounted for in the system's initial measure of energy are later generated by the dynamics. Thus one may say that these complex systems are capable of spontaneous increase in complexity or progressive behavior. At the same time, however, the degree of unpredictability is constrained by the dynamics that govern the system as a whole. Behavior, then, is directed as well as original. Only a nonlinear feedback situation could end in an act that could be considered intentional, that is, determined and yet free.
(Intentional behavior can't be completely determined. Intentional behavior can't be completely indeterminate. I wish I could take more time to unpack this for you. If this is not clear, I hope you will ask me questions.)
This formula here does not represent telic activity, at all, because it can be restated so that Actions 1 and 2 are reduced to a "linear" description.
Idea ® Action 1 ® Revised Idea ® Action 2 ® Result
An idea or desire based on prior experience drives the actor forward in time. There is no need to bring in final cause. According to this model, with sufficient information of the initial conditions, one could predict the result. Analytic philosophers make the mistake of trying to fit teleology into a reductionist paradigm.
So who has referred to teleological narratives as linear? The first critic that comes to mind, whom most of you probably know, is J. Hillis Miller. In Ariadne's Thread: Story Lines, he claims a linear narrative "tends to organize itself or to be organized in a causal chain" and follows "inevitable sequence," according to a "telos, arche, or ground." According to Miller, a linear narrative has a more or less arbitrary order imposed upon it from the outside. The author wrenches the narrative into a shape that conforms to some moral, social, or religious code. As Angus Fletcher has noted, this kind of narrative "should be called 'linear' only with the express understanding that ... the line is not a very straight line. "
Miller, of course, is thinking of Derrida, who critiques the notion of a "center" which he equates with both arche and telos. Now the arche usually refers to an originary cause (for many thinkers it's primal matter), while telos should refer to an end cause, final cause. Derrida intentionally conflates them, and bases much of his critique of structuralism on this conflation. I argue that there are very good reasons to keep separate the concept of the arche (which is a material cause) and final cause (which is an abstract principle as cause).
Teleologists throughout history argued that telos is known as the universal laws that govern systems as wholes. Such laws emerge; that is, they have no a priori existence, except perhaps in so much as mathematical laws might exist as concepts prior to their expression in dynamical systems. Furthermore, teleologists thought these laws were given in feedback processes. Thus, the concept of structure, as far as teleologists were concerned, did not depend, as Derrida has argued, on the existence of "a linked chain of determinations from the center." Contemporary physics has demonstrated that telic structures, that is, dynamically stable structures, emerge from nonlinear processes. These structures are governed by principles that are given in the dynamics of each system itself and do not exist outside of it. Telos is not material; it governs structurality without having material structure itself.
Now that reductionism is pretty much dead in the sciences and now especially with the hindsight of nonlinear dynamics, it becomes clearer what those teleologists were trying to say. Derrida was wrong to conflate final cause with originary cause.
But let me stop here to say that Derrida is a pretty bright critic after all, and so it's worthwhile to try to understand the fault that he did find with teleology.
There are actually two very different groups that are referred to as "teleologists." First, there are real teleologists that I've already described. Aristotle, Kant, the teleomechanists and some vitalists. They argued that inherent design (that is, pattern/orderliness) in biological systems is created by internal automatic principles. Nevermind who may have thought up those principals. They did not go there. Not in their teleology. In their religion maybe yes, but not in their teleology.
And then there are the others, which I consider pseudo-teleologists, who used teleology in the service of religion, for example Charles Bell and William Paley. They are associated with what's known as the "argument from design. " They argued, in contrast to Kant, that apparent design in nature proved the existence of a supernatural designer, (a centralized control) external to the universe, who could look ahead, plan, actively limit, guide, and control things according to His (sometimes arbitrary) idea of fitness. This second group of teleologists is associated with Christianity and the idea of Divine Providence. And it is probably this second group that Miller and Derrida have in mind. This group is also guilty of conflating originary cause and final cause, conflating the one outside the system who separately conceives the idea of fitness and the fitness that is eventually found.
An analogy may help further clarify the difference between these two different kinds of teleologists. If the first group (in which I include Aristotle, Kantian teleomechanists and contemporary evolutionary biologists know as structuralists) can be associated with the following sequence of numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23
the Second group (in which I include Christians, authors of contrived fiction) can be associated with this sequence:
14, 23, 28, 33, 42, 51, 59, 68.
The first sequence is governed by a rule that can be discovered by examining the sequence itself. What is the rule? Each number is a prime number. This sequence may be compared to the laws that govern systems that spontaneously self-organize; you can discover the laws by examining the process of pattern formation itself. (Warning, this is just an analogy; nonlinear dynamics is a little more complicated.)
The second sequence is also governed by a rule. Can any one tell me what it is? Any New Yorkers? The rule governing this sequence cannot be discovered by examining the sequence itself. It represents the stops on the Lexington Avenue subway line in New York. The rule comes from outside the sequence and is imposed upon it.
This second kind of teleology is associated with the idea of the deus ex machina, with contrived fiction and what's known as accidental functionality. Real teleologists tried to distinguish between accidental functions, which are singular and merely coincidental (for example, a rock drops on my desk and functions as a paperweight) and functions that are repeatable and lead to law-like systems (for example, the functional relationship between the parts of an organism and the organism as a whole).
However, let me end by saying I have difficulty seeing the "linearity" in either situation. Any line that could link together either coincidental similarities or stochastic behavior in a functional relationship could not be a very straight or predictable. Whatever kind of teleology one is talking about "linear" does not seem to be an accurate description, if "linear" is supposed to mean simple and predictable. Telic phenomena emerge from functional and contextual relationships therefore they cannot be described reductively. If I can suggest better adjectives (nonlinear also has its drawbacks), it would be more accurate to use "dynamically stable" or "structurally complex" to describe teleological narratives.
 "Idea of a Universal History from a Cosmopolitan Point of View, " Theories of History, ed. Patrick Gardiner (Glencoe: Free Press, 1959), 29. See also Preface to Universal Natural History and Theory of Heaven: An Exploration of the Constitution and the Mechanical Origin of the Entire Structure of the Universe Based on Newtonian Principles, trans. Ian C. Johnston (Nanaimo, BC: Malaspina University-College, 1998), available at http://www.mala.bc.ca/~johnstoi/kant2e.htm#preface.
 Reductionism is associated with classical determinism, particularly that of Laplace, who late in the 18th century argued that if one were able to know the exact position and velocity of every particle of matter in the universe at any given time, then one would be able to predict the future (or retrodict the past) with perfect accuracy. In other words, reductionists believe that any whole is just the sum of its individual parts. Anti-reductionists argue that interactions and dynamics have real effect on outcomes (i.e., they add something more) and hence the future cannot be predicted even with perfect knowledge of the present.
 Linear functions are functions that have x as the input variable, and x is raised only to the first power. Functions such as these yield graphs that are straight lines, and, thus, the name linear. Linear functions have constant first differences. That is, every time x increases by 1, y increases by a constant amount. In a nonlinear (exponential) function each output is a constant multiple of the previous output.
As nonlinear systems pass from one state to the next, they also do so according to rule, but each new state can have attached a different rule. (Linear systems, in some sense, have the same rule attached to each state.) It is due to strong interactions between components that nonlinear stochastic systems can spontaneously self-organize.
Linear also refers to an output that is directly proportional to the input, and to sequential development.
 For a broad sample of this literature, see Frederick Adams, "A Goal-State Theory of Function Attributions, " Canadian Journal of Philosophy 9 (1979): 493-518; C. J. Ducasse. "Explanation, Mechanism and Teleology, " The Journal of Philosophy 22 (1925): 150-155; Douglas Ehring, "Goal-Directed Processes, " Southwest Philosophical Studies 9 (1983): 39-47; David Papineau, "Representation and Explanation, " Philosophy of Science 51 (1984): 550-572; Charles Taylor, The Explanation of Behavior (New York: Humanities Press, 1964); William Wimsatt, "Teleology and the Logical Structure of Functional Statements, " Studies in History and Philosophy of Science 3 (1972): 1-80; Andrew Woodfield, Teleology (Cambridge: Cambridge University Press, 1976); and Larry Wright, "Explanation and Teleology, " Philosophy of Science 39 (1972): 204-218.
 J. Hillis Miller, Ariadne's Thread: Stories Lines (New Haven: Yale University Press, 1992), 18.
 The Prophetic Moment: An Essay on Spenser (Chicago: University of Chicago Press, 1971), 41-42.
 From a lecture delivered in 1966, published as "Structure, Sign, and Play in the Discourse of the Human Sciences, " trans. Richard Macksey and Eugenio Donato in The Critical Tradition: Classic Texts and Contemporary Trends, ed. David H. Richter (Boston: Bedford Book, 1989), 959-971.
 Manindra Agarwal, Nitin Saxena and Neeraj Kayal have devised a polynomial time deterministic algorithm to test if a specified number is prime or not. It works on generating a whole set of equalities (smaller questions) instead of asking on block "is this number prime?"
 This analogy was adapted from Murray Gell-Mann's example in The Quark and the Jaguar: Adventures in the Simple and the Complex (New York: Freeman and Company, 1994).