Abstract
The present chapter deals with some general issues of an epistemological nature concerning the notion of complexity. Such issues are examined here only informally. Moreover, there will be no impassioned stance (a few personal remarks will be confined to footnotes), but only conceptual analysis. Its motivation hinges on the increasing use of the notion of complexity in social sciences, as if it had one definite meaning, whereas such a meaning is hard to find. Consequently, the expected benefits of its application within the social sciencesbring a growing risk of ambiguity, which hinders the establishment of solid grounds on which to test the use of the notion and evaluate its contribution to the advance of knowledge.
To reduce this risk, the manifold faces of complexity will be considered, not so much in a mathematical setting but by going back to a list of seminal works to which its current uses are in debt. Some of these works offered an exact formulation, some did not; together they gave rise to lines of research which are still far from convergence on a common theory. The present analysis provides warnings against excessive expectations and abuses of the notion resting on an appeal to rhetoric and aims to provide a step towards clarifying the scientific meaning of complexity.
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Notes
- 1.
Of course, an adequate account of the scientific method calls for many more details, including the recognition that its features combine in different ways for different subjects; therefore, it is hard to prescribe one and only one way of “doing science”. Yet these preliminary remarks already furnish a couple of suggestions for research on “QOL-exity” (i.e., Quality-Of-Life-complexity), namely, (1) there is no direct inference from any plurality of data to “Synthetic Indicators”, (2) the hypotheses used in collecting and organising the data should be explicit and crisply stated. If the study of complexity is part of science, it does not justify any shift to a new-style, computer-aided, inductivism (the rumour surrounding Big Data is a case in point), exactly just the appeal to “complexity” does not, by itself, imply a new framework for research in the social sciences, still less one ensuring unprecedented advances. It rather points to a theory of Synthetic Indicators as leading parameters of a dynamical system to be precisely defined.
- 2.
Systemic thinking does not need any particular “philosophy”. The ability to take into account the consequences of a decision, together with their unintended feedbacks, was always recognised as an ingredient of rationality, of direct relevance to any strategy in politics, business and conflict.
- 3.
It is precisely from a consideration of OR that one of the best books on complexity and its models starts: Bertuglia and Vaio (2011). This is recommended reading, especially for those social scientists who intend not just to build models by exploiting the machinery of complex systems, but also want a synoptic view of different methodological options.
- 4.
This is just an anticipation of conceptual difficulties to be analysed in the following. For the time being, let me add that, were complexity only an “approach” or a “style of thought”, there would be no reason to worry about such difficulties. There is a reason, i.e., they are obstacles to overcome, if we care for a definition of complexity that is cross-disciplinary, not so much to grasp a Platonic essence as to sustain the search for a set of axiomatic principles. That such a set is yet to be found is a challenge not to give up, and the appeal to a new “style of thought” does not relieve us of the task.
- 5.
The Physica series of journals had already been enriched in 1980 by D. Nonlinear Phenomena.
- 6.
Let me emphasise again that for the most part the books listed were collections of previously published papers, but the joining-up of ideas thus presented boosted their impact. (The entries in the list will be included, in standard reference format, within the bibliography at the end of this paper.)
- 7.
Similar suggestions, pointing to a cross-domain analysis of hierarchical organisation, came from Herbert Simon in the 1960s.
- 8.
Some years ago, on the occasion I met Nora Bateson, I referred to her father as the “Twentieth Century’s Socrates”. The original Socrates was not expected to provide his unlucky interlocutors with any theory and those who sold his brainstorming as a theory were simply cheating. Yet his questions made Plato’s theory possible. Indeed, Bateson was criticised for his lack of step-by-step arguments and his dealing with epistemological problems in a non-professional way, but many popular books on complexity have appeared in the 50 years or so since he wrote and none have matched his mastery of style.
- 9.
This space has its own dimensions and complexity enters the scene with the interactions among processes. Some updated formulations of such an approach can be found in Petitot et al. (1999).
- 10.
Lorenz published no book, even one of collected papers. His name (and research) became known to a large audience through the brilliant science writer James Gleick. His book about chaos, Gleick (1987), presented a fascinating collection of case studies intended to point at a theory left to the reader’s imagination.
- 11.
A chronological map of the history of research on complex systems is in Baianu (2011), p. 23, which also provides information about authors and lines of research not mentioned here. Let me remind the reader that the few and cursory historical references in this paper are supposed to provide an introduction to epistemological questions about complexity.
- 12.
Each provided a condition on a system and, jointly taken, the set of conditions could orient to characterise complex systems, though none of them could be taken as sufficient. Some of them might also be non-necessary. For instance, a system governed by a set of linear equations can salso how a kind of complex behaviour.
- 13.
Inverted commas are due to the manifold ways of approaching complexity which thus far have not reached unification. In what follows I prefer to use “complexity framework”.
- 14.
A personal remark may be telling at this point. In the early 1970s, as a student, my interest in complex systems was sparked by one of the most open-minded Italian physicists of that period, Giuliano Toraldo di Francia, whose courses in Florence treating foundational problems of physics I had the good fortune to follow. He gave me the opportunity to meet Prigogine and Thom. My research centred on topics, such as models of semantic cognition, which then appeared distant from applications of the complexity framework. But I was already searching for a general setting for the “cross-boundary” universality mentioned above. I found it in category theory. However the link between category theory and dynamical systems theory was at that time unclear to me, I later became aware that Bill Lawvere had already developed a categorical approach to dynamical systems Lawvere and Schanuel (1986), and that Rosen had explored applications of category theory to biological systems. Recent papers on category-theoretic treatments of dynamical systems have investigated issues of complexity from a perspective which draws on Rosen’s work. Further advances are in prospect. But so far proposals to bridge the two theoretical frameworks remain too generic to provide an insight into specific open problems, or too tied to the study of particular systems which appear of little relevance for social sciences. This picture may change. If so, it will provide further evidence that my theses in Peruzzi (2006) apply to the emergence of cognitive patterns. See section Emergence below. One of the first papers in this direction was Ehresman and Vanbreemersch (1987).
- 15.
In Popper’s view it was the persistence of this idea in the social sciences which was mainly responsible for their backwardness in contrast to the natural sciences. Note here, however, that if “complexity” denotes an essential quality of a system, Popper’s distinction becomes blurred.
- 16.
On the conviction that (a) the achievements of science left about nothing substantial to be explained, Horgan claimed that (b) science is by now becoming postmodern, with complexity as part of this mutation. This claim was subsequently shared by some of those who advocated for (c) complexity as the new paradigm. Eminent proponents of (c) shared his idea that (d) mathematics is no longer the land of proof in announcing that (e) the deductive method has to be replaced by wide-ranging experimentalism through engineering of mathematical models. So far, none of (a)–(d) has been convincingly argued; rather there is evidence against each of them. In addition, there are doubts about the consistency of the conjunction of the four claims.
- 17.
- 18.
For other remarks on Kuhn-style epistemology in connection with complexity, see Bertuglia and Vaio (2011) chap. 4.
- 19.
It seems Einstein didn’t think the same when he felt the need to go to the root of the concepts of space and time in terms of an operationally sound definition of simultaneity – and his lack of opportunism was well repaid.
- 20.
In mathematics, any category of tangent spaces fibered over a connected base space is an example of a whole with inseparable parts. In physics, the notion of field is not reducible to the behaviour of test particles and, turning to Quantum Mechanics, David Bohm’s notion of an “implicate order” is an attempt to answer questions similar to those posed by the long-range coherence social scientists study.
- 21.
Additional care is recommended in using “mechanical” as if it had the same meaning in mathematics and physics. In mathematics it refers to a computable procedure and it is just in this sense we talk of a Turing “machine”. Though the two meanings have interesting connections, see Moore (1990), they are not equivalent. Note also that there are indeterministicTuring machines and that the Church-Turing Thesis about recursive functions as exhausting the domain of what is informally said to be “computable” is a hypothesis, rather than a theorem. Moreover, there are many degrees of computability which do not match with the different kinds of mechanics in physics. Hence, the recognition of such a double spectrum of notions calls for more, not less, rigour in talking of the complexity of a system.
- 22.
For a detailed analysis of the range of meanings compositionality can have and their different implications, see Peruzzi (2005). Thus, even if complex is contrary to independent rather than to simple, the gain is low.
- 23.
Note that if the “size” of modules is smaller and the coherence of conceptual patterns (as emergent properties) constrains holistic aspects to local structure, there is space for dynamical models instantiating a kind of intermediate complexity. A dynamicist view of the mind should also be mentioned as a source of further models, as those worked out under the heading “mind as motion”, as proposed in van Gelder and Port (1995) and in some of the essays collected in Peruzzi (2004).
- 24.
It is pertinent to point out that emergence can also be massively order-destructive, rather than the sort of (pacified) Hegelian Aufhebung many take it to be.
- 25.
For a comparison between different measures of complexity, see Mitchell (2009) chap. 7.
- 26.
This problem brings back to mind the so called “paradox of analysis”. Given a pair of expressions such that the second offers an analysis of the meaning of the first, the effectiveness of this analysis lies in the way it compresses or expands information; but if it is really effective, it cannot be fully faithful, and if it is fully faithful the two expressions are notational variations – within one and the same language. An axiomatic approach proves useful to bypass this “paradox”, but for what concerns a first-order language, one should not forget that one and the same set T of axioms admits non-equivalent models and that an empirical model of two non-equivalent sets of axioms, T and T’, can be such that it satisfies T if and only if it satisfies T’. In case T is a theory of “complexity”…
- 27.
The relation between complexity and incompleteness would deserve further, more careful, examination.
- 28.
“Systems almost always have the peculiarity that the characteristics of the whole cannot (even in theory) be deduced from the most complete knowledge of the components, taken separately or in other partial combinations. This appearance of new characteristics in wholes has been designated as emergence”, Mayr (1982), p. 63.
- 29.
This recovery was stimulated by the growth of interest for Hartmann’s stratified ontology. The merit of this recovery mainly goes to Roberto Poli, see Poli (2012). Some analytic philosophers connected Hartmann’s stratification with the concept of “supervenience” in philosophy of mind, but such a connection is misleading.
- 30.
I don’t intend to deny that emergence, together with nonlinearity, is one of the essential motivations for the appeal to complexity in social sciences – in particular, emergence allows to avoid the dichotomy between dualism and reductionism. Though the impact of an emergentist perspective on foundations of social sciences is yet to be evaluated, it has to be consistent with the nested hierarchy of systems from cells to conscious minds, with top-down feedbacks. I introduced the term “entwined naturalism” to label such a view, which keeps track of both bottom-up and top-down causality, see Peruzzi (1994).
- 31.
There is large debate on this issue filled with any kind of subtleties. Hilary Putnam brilliantly questioned Kim’s argument, see Putnam (1999), but since Putnam’s objections do not support emergentism, their examination would lead us off topic.
- 32.
Early twentieth century’s emergentism had a metaphysical import which hindered efforts to establish the scientific credentials of a theory of emergence.
- 33.
My personal opinion is that the resulting two dimensional analysis (micro/macro, local/global) is a key to that “unity of science” proposed by logical empiricists, and it is more than a merely formal key because it is made of notions directly theoretical, rather than meta-theoretical as those which became the tool-chest of philosophy of science: in a nutshell, the language of dynamics comes first, logical analysis of language follows.
- 34.
Just as biophysics and theoretical biology need much more mathematics than biologists are usually requested to know, a complex systems approach to social sciences demands a similar familiarity with mathematical tools, which would mean drastic changes in the syllabus for the next generation of social scientists. I doubt this demand will be met, if not for what concerns already established trends in “modelling”, thus stopping before the foundational analysis proper.
- 35.
- 36.
Topology is also a source of a special notion of complexity, which deserves mention here, for it draws attention on an issue which I consider of great epistemological meaning: is it possible that one and only one dimension is associated with the very existence of a kind of structure observed in reality? The answer is positive: knots exist in 3D and only in 3D. Moreover, since braids and knots are strictly related (a knot is obtained from a braid when the extremal points of any single cord in the braid are glued together), the very idea of “knotted structure” frequently implicit in talking about complexity would reveal a commitment to macro-spatial experience. This is a basic example of complexity, essentially related to a space of low dimension, and there is a precise way to measure its “degree”. Algebraic topologists found a way (actually, more than one) to compute the degree of a knot.
- 37.
Since a few years I am collaborating to the QOL project in Tuscany, and thanks to the great work by such an expert statistician as Filomena Maggino, this research group provides the Regional Council with a feedback on political decisions. This experience led me to two considerations. First, the use of synthetic indicators is a source of, say, “suggestions” only in conjunction with ethical hypotheses and long-term projections of qualitative nature. Second, neither such hypotheses nor such projections warrant the existence of an attractor and, in case more than one could exist, we are unable so far to determine which attractor satisfies the optimal balance point between the multidimensional factors to be considered for QOL.
- 38.
This, as long as philosophy is intended as the land in which everyone, from ordinary people to top scientists, can say anything about anything. Since I belong to that small community of researchers who subscribe the project of a scientific philosophy (no to be confused with philosophy of science), I would say the above convergence is not welcome at all; since the audience by which it is welcome is large and its growth rate is still positive, the risk of losing the baby with the bathwater is higher. Of course, it is a rough estimate.
- 39.
As far as I know, this is an open problem.
- 40.
I am grateful to Filomena Maggino for stimulating remarks on some topics dealt with in this paper. I also thank John Bell and Mike Wright for suggestions in order to improve the English form.
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Peruzzi, A. (2017). Complexity: Between Rhetoric and Science. In: Maggino, F. (eds) Complexity in Society: From Indicators Construction to their Synthesis. Social Indicators Research Series, vol 70. Springer, Cham. https://doi.org/10.1007/978-3-319-60595-1_1
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