Emergence and complexity in austrian economics

EMERGENCE AND COMPLEXITY IN AUSTRIAN ECONOMICS
J. Barkley Rosser, Jr.

James Madison University

[e-mail]
March, 2011

Acknowledgements: The author wishes to acknowledge useful comments from Paul Lewis and participants in an SDAE session at the 2010 Southern Economic Association meetings where an earlier version of this paper was presented.

“The totality is not, as it were, a mere heap, but the whole is something besides the parts.”

• 
  Aristotle, Metaphysics, Book H 1045a, 8-10.
  

Introduction
A deep theme of Austrian economics has been that of spontaneous order or self-organization of the economy. The origin of this theme dates to the putative founder of the Austrian School, Carl Menger, with his theory of the spontaneous emergence of money for transactions purposes in primitive economies being archetypal example (Menger, 1892). Menger drew this approach from the Scottish Enlightenment figures David Hume, Adam Ferguson, and Adam Smith, with the latter’s Wealth of Nations (1776) particularly important. The most important developer of this idea within the tradition after Menger was F.A. Hayek (1948), who would identify this self-organization phenomenon with emergence, later expanding upon this into the broader concept of complexity (Hayek, 1952, 1967). Caldwell (2004) argues that this became an increasingly important focus of Hayek’s thought in the later years of his life. Among those examining this development in more detail besides Caldwell have been Koppl (2006, 2009), Rosser (2010a),¹ and Lewis (2010).

This essay will consider more thoroughly the relationship between the concepts of emergence and complexity and the roles that they have played in Austrian economics as well as more broadly in philosophy and science. An important point is that both of these concepts do not possess precise meanings; they are “terms of art” within philosophy. However, while closely linked through the general idea of a whole being “greater than the sum of its parts” (or at least not equal to that sum), they are not identical, with complexity being the broader concept. It must also be recognized that focusing on such concepts has not been central to, or even particularly a part of, certain branches of Austrian economics or of much concern to some of its adherents.

Aspects of the Emergence Concept

The concept of emergence is a subject of considerable controversy within philosophy from where it initially emerged into many other disciplines, ranging from chemistry to psychology through biology into economics and others, although often with these applications merging together across disciplines. A sign of this is that most discussions of emergence identify the modern founder of the idea to be the economist-philosopher, John Stuart Mill (1843) in one of his works of philosophy rather than economics, although he identified what was later identified as emergence with what he called heteropathic laws (to be distinguished from homeopathic and did not use the term “emergence.” Rather in the spirit of the quotation above from Aristotle, Mill saw heteropathic laws operating in a process when the resultant of the process could not be viewed simply as the sum of its parts as in vector addition. While it may have clearly identifiable parts that combine, this combination generates something substantially different from the parts.² His original example was from chemistry, involving the following equation:

CH₄ + 2O₂ => CO₂ + 2H₂O, (1)

that is, methane combined with oxygen yields carbon dioxide and water, a distinct transformation of one pair of entities into two quite different ones.

Inspired by Mill’s discussion, the psychologist, George Henry Lewes (1875, p. 412) coined the term “emergent,” from which the modern scientific “emergence” would emerge, as being something arising from “cooperation of unlike kinds” with the resulting emergent being such that “it cannot be reduced to their sum or difference.” This irreducibility aspect of emergence has since come to be identified with what is called strong emergence (Bedau, 1997), with weak emergence more readily reducible to its basal components (or more easily deduced from them). Lewes’s strong emergence would go on to become the foundation of the later British emergentist movement, whereas the more recent concept of weak emergence has been used in modern computational complexity theory and is identified with patterns that arise from computer simulation systems such as the Game of Life of Conway (Gardner, 1970).³

The British emergentist movement reached a peak of influence in the 1920s, albeit with the divisions between strong and weak emergence already visible at that time. The strong emergentist camp was lead by C.D. Broad (1925) who was more directly inspired by Mill. In the depiction of a multi-layered reality, the higher emergent levels would be ontologically distinct and relate to each other in a direct causal manner at the higher levels.⁴ In much of this literature the levels are eventually across disciplines, with physics being viewed as the foundation, out of which emerge chemical phenomena, out of which emerge biological ones, then the psychological, and then the social sciences, with some going beyond that to more metaphysical levels such as theology.⁵

In contrast, Samuel Alexander (1920) and C. Lloyd Morgan (1923) put less emphasis on the distinct operations at the higher level and more on the element of novelty of what emerged at the higher level. While Lewes and Broad were more concerned with the theory of mind, Morgan in particular was more focused on biology and evolution, a point we shall return to later, given the concern of Hayek in particular for evolutionary processes. Hayek (1967) specifically noted this line of influences from Mill to Lewes to Morgan in his own discussion of emergence within complex systems.

Within the more current philosophical literature there have been efforts to pin down more precisely the concept of emergence, with various debates arising from these efforts, with many of them involving invoking various terms to define it, with the result being that the debates then shift to arguing about the definitions of these terms. Thus, one of the more prominent such efforts was due to James van Cleve (1990, p. 221). He posed the following:

“If P is a property of w, then P is emergent if and only if P supervenes

with nomological necessity, but not with logical necessity, on the properties of the

parts of w.”⁶

Needless to say, this raises the question of what does one mean by such terms as nomological and supervenes? The former is clearer than the latter and refers to laws. Thus, whatever phenomenon emergence is it is fundamentally due to physical or scientific laws, not some logical relationship (Popper, 1934; Hempel and Oppenheim, 1948). It is a phenomenon of the material world, which distinguishes it from some of the more vitalistic and theological viewpoints lurking in the discussions by some of the British emergentists, notably Alexander. This does not mean that logic is ruled out of nomological necessity. Indeed, Hempel and Oppenheim (1948) in particular discuss “deductive-nomological” systems in which logical deduction plays a crucial role for much of the system building, although always deriving from some fundamental scientific law or laws. This approach is not inconsistent with Hayek’s approach to psychology in The Sensory Order (1952) in which the mind operates by sets of rules that are eventually based on the physical laws governing the behavior of the neurons in the brain, even as Hayek tends to favor a more inductive view than a deductive one.

This leads us to the arguably more problematic concept of supervenience, which has engendered considerable controversy that lies at the heart of the issues of the nature of emergence, including the division between strong and weak emergence. The term comes from the Latin supervenire, which in turn was used to translate the term epiginomenon from Aristotle in the Middle Ages (McLaughlin, 1997, Appendix). The term has been argued to imply that something “extra” or “unexpected” or, to use a term associated with Morgan and the weak emergence school, “novel” is involved in what is emergent (McLaughlin, 1997; Welshon, 2002).

However, more has been put on the plate of this concept than just these items. In particular, there has been much debate about its relation to downward causation from the higher emergent level to the lower basal one from which it emerged. Lewis (2011) argues that Hayek’s views imply downward causation, with emerged institutions and spontaneous orders in economies strongly influencing lower level entities in their decisionmaking and actions, even he did not support it strongly. But some philosophers of emergence argue that supervenience does not imply such downward causation, particularly Jaengwon Kim (1993, 1999), Humphreys (1997a,b) and O’Connor and Wong (2006). In essence they argue that anything going on at the higher level must be due to things going on at the lower levels, and so the idea that the higher level is independently influencing the lower level is an epiphenomenon.

For Kim this becomes the basis for a broader critique and doubt about the concept of emergence in philosophical or metaphysical terms, although Humphreys is more willing to accept that emergence occurs in the physical world through fusion at the lower levels. For Kim, emergence and supervenience imply physical non-reductionism, with Kim thus ultimately siding with the reductionist position seen as having overthrown British emergentism when quantum mechanics fully appeared in the 1930s. However, in economics it does not seem unreasonable to argue the Mengerian emergence of money does supervene upon substantially upon agents in the economy in a serious way such that they behave very differently when money exists compared with when it does not. Of course, the form of emergence that is accepted by the most skeptical who will accept emergence at all, such as van Cleve (1990) is the mind, with this fitting in perfectly with Hayek’s (1952) view from The Sensory Order, with of course emergence in economic systems ultimately arising further out of the mental operations of individuals.

The definitions of emergence that emphasize the appearance of something novel or unexpected at a different level from the initial also includes special cases in which the emergence involves the actual appearance or creation of the new level itself. This is implied in the evolutionary history of the universe from sub-atomic particles in physics that aggregated into atoms, then later into chemical molecules, then into more complicated organic molecules, into life, into multi-cellular organisms,⁷ and so on. This process of the emergence of entirely new levels has been labeled anagenesis by Boulding (1978) and Jantsch (1979), and has been analyzed by Rosser et al. (1994). Such processes exhibit not only emergence, but at the biological and social levels involve complex evolutionary processes, much as in the view of the British emergentists, a theme covered more fully below.

Emergence and Complexity

As noted above, emergence can be seen as a part of the broader complexity concept. Indeed, it is hard to conceive of an example of emergence that could not also be viewed as representing a complex dynamic. This may be a matter of “complexity” simply having even more definitions than “emergence,” but it is also because at a very general level, one of the things that is associated with the concept of complexity is the linking together of parts into wholes that are greater than the sum of the parts, which is also how emergence has been described almost from its beginning. However, complexity has been used in ways that do not so clearly reflect this characteristic, so while it is very hard to conceive of an emergence process that is not also a complex one, there are almost certainly complex systems or processes that do not necessarily involve emergence.

Over a decade ago, Seth Lloyd proposed a list of 45 definitions of complexity (Horgan, 1997, p. 303), and this list is not exhaustive by any means. Rosser (2009a) identifies this level of complexity as being meta-complexity. Below this are the various categories of complexity. Most important for our discussion at this stage are the broad categories of computational complexity and dynamic complexity.

The former has many definitions itself, with Velupillai (2009) providing useful of the many varieties. This involves considering a system from the standpoint of computability, with complexity being tied roughly to the length of algorithms needed to solve the programs that characterize the system.⁸ Some consider true computational complexity to hold only for systems that are not computable at all, that suffer from an inevitable halting problem (Blum et al., 1998; Koppl and Rosser, 2002). Others focus on degrees of computational complexity involving levels, such as the matter of the relation between N and NP in solvability, with the exact relation of these an ongoing matter of dispute (da Costa and Doria, 2010). The potentially precise measurability of computational complexity is something that is stressed by those advocating its use in economics as the supreme definition of complexity (Markose, 2005; Velupillai, 2009). Some defenders of this complexity concept (McCauley, 2004) denounce the concept of emergence as being poorly defined and thus inferior. He extends this criticism even to those who study computable systems exhibiting emergence that can be used to study evolutionary dynamics (Crutchfield, 1994). Instead McCauley particularly favors the work of Moore (1990) that emphasizes the role of novelty as crucial to complexity, one of the ideas stressed by many students of emergence as discussed above.

Dynamic complexity has been defined by Rosser (1999) following Day (1994) as occurring in dynamical systems that do not converge to a point, a limit cycle, or a smooth expansion or contraction endogenously.⁹ This is generally broken down into the “four C’s” of cybernetics, catastrophe theory, chaos theory, and agent-based complexity.¹⁰ This latter is often viewed by many as being the “real complexity,” at least in economics, with a strong influence on its development from the Santa Fe Institute. Such systems are generally nonlinear systems, or easily transformed into them,¹¹ although not all nonlinear dynamical systems exhibit dynamic complexity, and some that do exhibit it only do so for certain ranges of parameter values and starting values of the system.

While not all of these dynamically complex systems exhibit emergence, some do, most frequently those associated with the agent-based complexity in which agents interact locally with these interactions often leading to the emergence of order out of initially disordered states. The classic example was the model of the emergence of urban segregation out of an initially integrated urban area, due to Schelling (1971).

Rosser (2009b) presents a variety of approaches to modeling emergence computationally. Among these, Lee (2005) poses a formulation in which emergence occurs when a state becomes more computationally complex through a transformational function in a computable system, although it may not be computable to estimate this computational complexity. Lee draws on hierarchical models following Langton (1992), who compares the four-level hierarchy of Chomsky (1959) with that of Wolfram (1984). While Chomsky’s focuses more on levels of language, Wolfram’s is based on cellular automata. These models are put into computable evolutionary contexts by Kaufmann (1993) and by Mirowski (2007) in terms of the evolution of market forms into hierarchies.

While Hayek did not involve himself with computer simulations (or even the sort of playing on chess boards that Schelling initially did), others such as Vriend (2002) have seen Hayek’s views as compatible with this view of dynamic complexity. Probably the first Austrian economist to notice Hayek’s work on complexity and to draw attention to it as being such was Lavoie (1989)who emphasized the self-organization arguments of Hayek (1948), arguments echoed by Per Bak (1996) in a more overtly computational context.

As has already been pointed out, in Hayek’s view, emergence and complexity are essentially the same thing, given his linking of the concept of complexity to the emergentist tradition of Mill, Lewes, and Morgan. This emergentist view is consistent also with Hayek’s view of the emergence of mental properties from the interactions of the hierarchies of neuronal linkages in the brain. However, Hayek also has links to the computational complexity view given his references to diagonal proofs in the Gödel incompleteness theorems, using these to emphasize that the mind cannot fully know itself, with others emphasizing that this can be applied to the idea of a central planner also not being able to fully know an economy that contains the central plan within it, the problem of self-reference (Koppl and Rosser, 2002). Thus, in his deepest analysis of the mind and its relation to his deepest critiques of economic planning, Hayek combines both the emergentism of dynamic complexity with computational complexity, wherein the need to go to a higher meta-system to understand fully a particular system can itself be seen as another form or emergence.
Evolutionary Complex Emergence

It has been much discussed (Caldwell, 2004) that over time Hayek increasingly moved towards an evolutionary perspective on the economy. This provided the way through which Hayek more seriously integrated his views on emergence and complexity into the study of the economy, while leaving his considerations of computational complexity in the theory of the mind behind. Not only did markets spontaneously emerge through processes of self-organization out of the interactions of dispersed, heterogeneous agents, but higher level institutions of society did so as well such as systems of law and customs of social behavior. He saw these emerging through a complex evolutionary process in which natural selection operated at the higher level of the emergent form, as in the strong emergence view where higher level entities interact directly and in which downward causation operates. Thus, the nature of the emergent form influences the behavior of the agents, without this being simply an epiphenomenal manifestation of the agents indirectly influencing themselves, although ultimately the natural selection is operating at the individual level.

This is really an example of multi-level evolution as modeled by James F. Crow (1955) and George R. Price (1970). These approaches to natural selection seek to reconcile the holistic approaches of the rejected British emergentists with the reductionist approaches that say that all natural selection operates fundamentally at the level of the gene, and not even at the level of the individual, per se (Dawkins, 1976). This really becomes an effort to reconcile the strong and weak views of emergence, with the process ultimately operating at the most fundamental level at the base, the gene in biological evolution, and the individual in socio-economic evolution, but also mediated through the higher levels of groups in both cases. There is a balancing of both upward and downward causation in this approach, at least implicitly in the later work of Hayek.

Lewis (2011) points to the Epilogue of the third volume of Hayek’s Law, Legislation and Liberty (1979, p. 158) as a place where Hayek more specifically endorses a form of downward causation in terms of evolutionary laws acting on populations, supporting the views of Campbell (1974) in doing so. He clearly supports the formulation that lower level entities in the ontological hierarchy become constrained by emergent properties in the higher level. While he does not clearly do so, his view is consistent with the stronger position that that higher level emergence might actually reconstitute the entities at the lower levels rather than merely constraining them.

Since the death of Hayek, others have pushed these ideas of evolutionary emergent complexity. Hodgson and Knudsen (2006, 2010) have argued vigorously that evolution is the supreme complex process of them all, with emergence a fundamental manifestation of it. Kaufmann’s (1993) approach has stimulated great controversy as he has debated with such figures as Gould (2002) that complex emergence provides an additional layer of causation and development beyond the conventional neo-Darwinian synthesis view of evolution. Kaufmann’s approach has the added element of bringing in computational approaches and issues, which make many more traditional evolutionary biologists uncomfortable and in many cases outright skeptical.

Mirowski’s (2007) controversial approach has all of these elements that resemble the Hayekian view in many ways, even as Mirowski disagrees with Hayek on various points. He defines markets overtly as algorithms, throwing the discussion fully into the realm of the matter of computational complexity.¹² However, these algorithms themselves evolve, this implying an evolution of market institutions, with natural selection operating on the different kinds of market systems. Furthermore, hierarchical patterns develop as this evolutionary process leads to the emergence of higher level market institutions over time out of lower level ones, with the higher level ones very definitely operating in a downward causation manner to embed the lower level ones within themselves. Thus, futures markets arose out of spot markets, options markets arose out of futures markets, and derivatives markets arose out of options markets, with ever higher orders of derivatives continuing to emerge over time, although with the possibility of some of these levels disappearing evolutionary in the face of systemic collapse due to fragility and endogenous breakdowns as in the crisis of 2007-08.

In any case, we see an increasing trend of thinking that sees these processes linked closely, if not perfectly. Emergence is a special form of complexity, and it is often the most important and dramatic even that happens in the course of evolutionary processes. This holds true for both economic and biological evolution.
Conclusion

Austrian economics exhibits a variety of views regarding emergence and complexity. An important strand emphasizes it strongly, with Carl Menger and Friedrich Hayek, especially in his later years, being the leading examples of this thread in the tradition. At the other extreme are such essentially orthodox neoclassical figures as Eugen von Böhm-Bawerk and others of his period. In between these extremes stand numerous other figures in the Austrian tradition, notably Ludwig von Mises and his protégée, Israel Kirzner, whose emphasis on entrepreneurial activities driving the evolution of the economy in an uncertain environment partake of elements of this view, even as at times, von Mises in particular may seem more orthodox with his strict a priorism that seems to rule out such evolutionary emergence or complexity.

However, the idea of complex emergence involving the development at higher levels of entities that are somehow more than or at least different from the “sum of their parts” was strongly pursued by F.A. Hayek, especially later in his life. It drew on both his work in psychology to study the emergence of mind from neurological processes and structures and rules, with some of his work on this linking to ideas from computational complexity, while his studies of the emergence of market structures and broader social structures such as systems of law draws more specifically on evolutionary processes that operate interactively between the lower and higher levels in both upward and downward causation in a balancing of strong and weak emergence. In this effort, Hayek’s work foreshadows more recent work by such figures as Langton, Wolfram, Kaufmann, and Mirowski who all see complex emergence as profoundly linked to evolutionary processes.
References

Albin, P.S. 1982. The metalogic of economic predictions, calculations and propositions. Mathematical Social Sciences 3, 329-358.

Alexander, S. 1920. Space, Time, and Deity. Macmillan, London.
Aristotle. 4^th century BCE. Metaphysics.
Bak, P. 1996. How Nature Works: The Science of Self-Organized Criticality. Columbia University Press, New York.
Bedau, M. 1997. Weak emergence. Philosophical Perspectives 11, 375-399.
Blum, L.; Cucker, Shub, M.; Smale, S. 1998. Complexity and Real Computation. Springer-Verlag, New York.
Boulding, K.E. 1978. Ecodynamics: A New Theory of Societal Evolution. Sage, Beverly Hills. Schlipp, P.A. (ed.). The Philosophy of Karl R. Popper. Open Court, La Salle, pp. 412-463.
Chomsky, N. 1959. On certain formal properties of grammars. Information and Control 2, 11-54.
Conlisk, J. 2007. Comment on “Markets come to bits: Evolution, computation, and markomata in economic science.” Journal of Economic Behavior and Organization 63, 243-246.
Crow, J.F. 1955. General theory of population genetics: A synthesis. Cold Spring Harbord Quantitative Symposium on Biology 20, 54-59.
Crutchfield, J. 1994. The calculi of emergence: Computation, dynamics and induction. Physica D 75, 11-54.
da Costa, N.C.A.; Doria, F.A. 2010. Hypotheses that imply the independence of P = NP from strong axiomatic systems. In: Zambelli, S., (ed.). Computable, Constructive and Behavioural Economic Dynamics: Essays in Honour of Kumaraswamy (Vela) Velupilla. Routledge, London, pp. 79-108.
Dawkins, R. 1976. The Selfish Gene. Oxford University Press, Oxford.
Day, R.H. 1994. Complex Economic Dynamics, Volume I: An Introduction to Dynamical Systems and Market Mechanisms. MIT Press, Cambridge, MA.
Dhamaraj. N.; Velupillai, K.V. 2010. Nonlinear dynamics, complexity and randomness: Algorithmic foundations. Mimeo, Department of Economics and CIFREM, University of Trento.
Eigen, M.; Schuster, P. 1979. The Hypercycle: A Principle of Natural Self-Organization. Springer-Verlag, Berlin.
Gardner, M. 1970. Mathematical games: The fantastic combinations of John Conway’s new solitaire game “Life.” Scientific American 223(10), 120-123.
Goodwin, R.M. 1947. Dynamic coupling with especial reference to markets having production lags. Econometrica 15, 181-204.
Gould, S.J. 2002. The Structure of Evolutionary Theory. The Belknap Press of Harvard University Press, Cambridge, MA.
Harper, D.A.; Endres, A.M. 2010a. Capital as a layer cake: A systems approach to capital and its multi-level structure. Journal of Economic Behavior and Organization 74, 30-41..
Harper, D.A.; Endres, A.M. 2010b. The anatomy of emergence, with a focus upon capital formation. Mimeo, Department of Economics, New York University.
Hayek, F.A. 1948. Individualism and Economic Order. University of Chicago Press, Chicago.
Hayek, F.A. 1952. The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology. University of Chicago Press.
Hayek, F.A. 1967. The theory of complex phenomena. In: Studies in Philosophy, Politics, and Economics. University of Chicago Press, Chicago, 22-42,
Hayek, F.A. 1979. Law, Legislation and Liberty, Vol. 3. University of Chicago Press, Chicago.
Hegel, G.W.F. 1842. Enzyclopadie der Philosophischen Wissenschaften im Grundrisse Part 1, Logik, Vol. VI, Duncken und Humblot.
Hempel, C.; Oppenheim, P. 1948. Studies in the logic of explanation. Philosophy of Science 15, 135-175.
Hodgson, G.M.; Knudsen, T. 2006. Why we need a generalized Darwinism and why generalized Darwinism is not enough. Journal of Economic Behavior and Organization 61, 1-19.
Hodgson, G.M.; Knudsen, T. 2010. Generative replication and the evolution of complexity. Journal of Economic Behavior and Organization 75, 12-24.
Horgan, J. 1997. The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age. Broadway Books, New York.
Humphreys, P.W. 1997a. How properties emerge. Philosophy of Science 64, 1-17.
Humphreys, P.W. 1997b. Emergence, not supervenience. Philosophy of Science 64, S337-S345.
Jantsch, E. 1979. The Self-Organizing Universe: Scientific and Human Implications of the Emerging Paradigm of Evolution. Pergamon Press, Oxford.
Kaufmann, S.A. 1993. The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, Oxford.
Kim, J. 1993. Supervenience and Mind. Cambridge University Press, Cambridge, UK.
Kim, J. 1999. Making sense of emergence. Philosophical Studies 95, 3-36.
Koppl, R. 2006. Austrian economics at the cutting edge. Review of Austrian Economics 19, 231-241.
Koppl, R. 2009. Complexity and Austrian economics. In: Rosser, J.B., Jr., (ed). Handbook of Complexity Research. Edward Elgar, Cheltenham, pp. 393-408.
Koppl, R.; Rosser, J.B., Jr. 2002. All I have to say has already crossed your mind. Metroeconomica 53, 339-360.
Langton, C.G. 1992. Life at the edge of chaos. In: Langton, C.G.; Taylor, C.E.; Farmer, J.D.; Rasmussen, S. (eds.). Artificial Life II. Addison-Wesley, Redwood City, pp. 41-91.
Lavoie, D. 1989. Economic chaos or spontaneous order? Implications for political economy of the new view of science. Cato Journal 8, 613-635.
Lee, C. 2005. Emergence and universal computation. In: Velupillai, K.V. (ed.). Computability, Complexity and Constructivity in Economic Analysis. Blackwell, Oxford, pp. 198-217.
Lewes, G.H. 1875. Problems of Life and Mind. Kegan Paul Trench Turbner, London.
Lewis, P. 2011. Emergent properties in the work of Friedrich Hayek. Journal of Economic Behavior and Organization, this issue..
Markose, S.M. 2005. Computability and evolutionary complexity: Markets as complex adaptive systems. Economic Journal 115, F159-F192.
McCauley, J.L. 2004. Dynamics of Markets: Econophysics and Finance. Cambridge University Press, Cambridge, UK.
McLaughlin, B.P. 1997. Emergence and supervenience. Intellectica 2, 25-43
Menger, C. 1892. On the origin of money. Economic Journal 2, 239-255.
Mill, J.S. 1843. A System of Logic: Ratiocinative and Inductive. Longmans Green, London.
Mirowski, P. 2007. Markets come to bits: Evolution, computation, and markomata in economic science. Journal of Economic Behavior and Organization 63, 209-242.
Moore, C. 1990. Undecidability and predictability in dynamical systems. Physical Review Letters 64, 2345-2347.
Morgan, C.L. 1923. Emergent Evolution. Williams and Norgate, London.
O’Connor, T.; Wong, J.Y. 200. The metaphysics of emergence. Noûs 39, 658-678.
O’Driscoll, G.P., Jr.; Rizzo, M.J. 1985. The Economics of Time and Ignorance. Basil Blackwell, Oxford.
Popper, K. 1934. The logic of scientific discovery. Hutchinson, London.
Price, G.R. 1970. Selection and covariance. Nature 227, 520-521.
Rosser, J.B., Jr. 1991. From Catastrophe to Chaos: A General Theory of Economic Discontinuities. Kluwer, Boston.
Rosser, J.B., Jr. 1992. The dialogue between the ecologic and economic theories of evolution. Journal of Economic Behavior and Organization 17, 195-215.
Rosser, J.B., Jr. 1999. On the complexities of complex economic dynamics. Journal of Economic Perspectives 13, 169-192.
Rosser, J.B., Jr. 2009a. Introduction. In: Rosser, J.B., Jr. (ed.). Handbook of Complexity Research. Edward Elgar, Cheltenham, pp. 3-11.
Rosser, J.B., Jr. 2009b. Computational and dynamic complexity in economics. In: Rosser, J.B., Jr., (ed.). Handbook of Complexity Research. Edward Elgar, Cheltenham, pp. 22-35.
Rosser, J.B., Jr. 2010a. How complex are the Austrians? In: Koppl, R., Horwitz, S., Desrochers, P., (eds). What is so Austrian about Austrian Economics? Advances in Austrian Economics 14. Emerald Group, Bingley, pp. 165-179.
Rosser, J.B., Jr. 2010b. Constructivist logic and emergent evolution in economic complexity. In: Zambelli, S. (ed.). Computable, Constructive and Behavioural Economic Dynamics: Essays in Honour of Kumaraswamy (Vela) Velupilla. Routledge, London, pp. 184-197.
Rosser, J.B., Jr.; Folke, C.; Günther, F.; Isomäki, H.; Perrings, C.; Puu, T. 1994. Discontinuous change in multi-level hierarchical systems. Systems Research 11, 77-94.
Schelling, T.C. 1971. Dynamic models of segregation. Journal of Mathematical Sociology 1, 143-186.
Smith, A. 1776. The Wealth of Nations. Strahan and Cadell, London.
Turing, A.M. 1952. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B 237, 37-72.
van Cleve, J. 1990. Magic or mind dust: Panpsychism vs. emergence. Philosophical Perspectives 4, 215-226.
Velupillai, K.V. 2009. A computable economist’s perspective on computational complexity. In: Rosser, J.B., Jr. (ed.). Handbook of Complexity Research. Edward Elgar, Cheltenham, pp. 36-83.
Vriend, N.J. 2002. Was Hayek an Ace? Southern Economic Journal 68, 811-840.
Welshon, R. 2002. Emergence, supervenience, and realization. Philosophical Studies 108, 39-51.
Wolfram, S. 1984. Universality and complexity in cellular automata. Physica D 10, 1-35.
Zambelli, S. 2007. Comments on Philip Mirowski’s article: “Markets come to bits: Evolution, computation and markomata in economic science.” Journal of Economic Behavior and Organization 63, 354-358.

1 Rosser (2010a) in particular identifies Böhm-Bawerk as the leading example of an Austrian economist whose models involve essentially no complexity at all. A number of other Austrian figures exhibit elements of complexity at times, although less so than Menger or Hayek, with von Mises and Kirzner being examples.

2 This somewhat resembles Hegel’s (1842) distinction between quantitative change and qualitative change, formulated just prior to Mill’s work and independently of it. Hegel’s classic example of a quantitative change to a qualitative one is how water undergoes major changes of state at certain critical temperatures, an example Lewis (2011) presents as an archetypal example of emergence, although he notes that the appearance of any of water’s emergent states involves a substantive difference from the state of an isolated H₂O molecule from a sufficient aggregation of them to produce one of the standard forms of water..

3 Inspired by work of John von Neumann, Conway’s “Life” introduced cellular automata, the basis for many later simulation models and systems.

4 Broad was particularly focused on the mechanist versus vitalist debate, taking the side of vitalism, which was viewed as being defeated by the emergence of reductionist quantum mechanics in the 1930s, often viewed as being the death knell of the broader British emergentist movement. Given this link to vitalism, it is not surprising that the “Father of Medicine,” Galen, is sometimes viewed as a precursor of emergentism along with Aristotle.

5 Harper and Endres (2010a) emphasize use the levels approach to consider layers within the structure of the capital stock. Extending this to emergence, they (Harper and Endres, 2010b) focus on the ideas of novelty, uncertainty, and irreducibility. They note the focus of O’Driscoll and Rizzo (1985) on uncertainty.

6 Van Cleve felt that this definition is so strong that it rules out almost any form of emergentism except possibly for mental conscious properties.

7 Eigen and Schuster (1979) describe this particular emergence as the hypercycle. Rosser (1991, 1992) extended this idea to broader systemic processes with the concept of hypercyclic morphogenesis.

8 The first to study computational complexity in economics was Albin (1982).

9 Dhamaraj and Velupillai (2010) refer this as “Day-Rosser complexity.”

10 Rosser (1999) originally referred to agent-based complexity as “small-tent complexity” in contrast with the “big tent complexity” of the broader dynamic type.

11 Examples of linear dynamical systems exhibiting this are the coupled linear dynamical systems whose one equation representations are nonlinear due to Goodwin (1947) and Turing (1952).

12 This has led to criticism from both those who say that markets are human exchange systems rather than algorithms (Conlisk, 2007) and those who argue that his invocation of the Chomsky hierarchy system insufficiently maps into proper measures of computational complexity (Zambelli, 2007).