Complex Systems

Journal of Social Philosophy, EarlyView.

Journal of Social Philosophy, EarlyView.

What do a short car trip, a pandemic, the wood-wide fungal web, a challenging learning experience, a storm, transport logistics, and the language(s) we speak have in common? All of them are systems, or multiple sets of systems within systems. What happens in any set of circumstances will depend on a mix of initial conditions, complexity dynamics, and the odd wild card (e.g., a chance event). While it is possible to model and predict what might or perhaps should happen, it (...) is impossible to be certain. "It depends" thinking needs to be applied. Future-focused literature identifies complex systems thinking as an essential capability for citizenship, and this book sets out to show teachers how they might foster it-for themselves as well as for their students. There are implications for pedagogy, curriculum, and assessment. Multiple examples show what changes might look like, for students of different ages, and in different subject contexts. This is a book of several layers: It is both practical and philosophical. There is explicit discussion of parallels between complexity science and indigenous knowledge systems (specifically mātauranga Māori in the New Zealand context). The many examples are designed to appeal to general readers with an interest in the complex challenges facing contemporary societies, as well as to teachers at all levels of the education system. (shrink)

The book’s core argument is that an artificial intelligence that could equal or exceed human intelligence—sometimes called artificial general intelligence (AGI)—is for mathematical reasons impossible. It offers two specific reasons for this claim: Human intelligence is a capability of a complex dynamic system—the human brain and central nervous system. Systems of this sort cannot be modelled mathematically in a way that allows them to operate inside a computer. In supporting their claim, the authors, Jobst Landgrebe and Barry Smith, marshal evidence (...) from mathematics, physics, computer science, philosophy, linguistics, and biology, setting up their book around three central questions: What are the essential marks of human intelligence? What is it that researchers try to do when they attempt to achieve "artificial intelligence" (AI)? And why, after more than 50 years, are our most common interactions with AI, for example with our bank’s computers, still so unsatisfactory? Landgrebe and Smith show how a widespread fear about AI’s potential to bring about radical changes in the nature of human beings and in the human social order is founded on an error. There is still, as they demonstrate in a final chapter, a great deal that AI can achieve which will benefit humanity. But these benefits will be achieved without the aid of systems that are more powerful than humans, which are as impossible as AI systems that are intrinsically "evil" or able to "will" a takeover of human society. (shrink)

When we deal with complex things, like human subjects or organizations, we deal with identity – that which makes a person or an organization what it is and distinguishes him/her/it from other persons or organizations, a kind of “self”. Our identity determines how we think about and interact with others. It will be argued in this chapter that the self is constituted relationally. Moreover, when we are in the realm of the self, we are always already in the realm of (...) engaging with and mediating differences – the realm of ethics. The position which will be developed argues that approaching identity as a complex system allows us to resist thinking of identity as an easily identifiable and static entity. Identity is always being constituted within a complex and contingent world, where we have to make choices based on contingent values rather than on universal knowledge or the outcome of rational calculations. As a result, we have to keep in mind that our daily practices always already have an ethical component, and our decisions need to be continually evaluated and re-evaluated in the light of our (and others’) varying identities. (shrink)

Explores complexity theory and systems thinking to better understand how complex systems drift into failure. This book develops a vocabulary that allows us to harness complexity and find different ways of managing drift.

Is human free will compatible with the natural laws of the universe? To “compatibilists” who see free actions as emanating from the wants and reasons of human agents, free will looks perfectly plausible. However, “incompatibilists” claim to see the more ultimate sources of human action. The wants and reasons of agents are said to be caused by physical processes which are themselves mere natural results of the previous state of the world and the natural laws which govern it. This paper (...) argues that the incompatibilists make a mistake in appealing to such non-agent sources of human action. They fail to realize that free will may exist at one scale, but not at the scales where they look. When free will is considered from the correctly scaled perspective, it does seem compatible with determinism and natural laws. (shrink)

In this article, after a historical introduction, we give an epistemological point of view of the physics of complex systems. Complex systems are epistemologically interesting because of the fundamental interaction experiment/observer and physicists in their everyday life can experience the paradoxes given by this interaction. Here we describe some of these paradoxes, we make a parallel with quantum mechanics and give a possible philosophical solution, based on notorious physicists/philosopher from the past, transposing and reinterpreting their ideas to modern times. In (...) particular, we analyse the interaction with a complex system such as the living cell, and therefore we also analyse some biophysical implications of complexity. (shrink)

Community detection is a major issue in network analysis. This paper combines a socio-historical approach with an experimental reconstruction of programs to investigate the early automation of clique detection algorithms, which remains one of the unsolved NP-complete problems today. The research led by the archaeologist Jean-Claude Gardin from the 1950s on non-numerical information and graph analysis is retraced to demonstrate the early contributions of social sciences and humanities. The limited recognition and reception of Gardin's innovative computer application to the humanities (...) are addressed through two factors, in addition to the effects of historiography and bibliographies on the recording, discoverability, and reuse of scientific productions: (1) funding policies, evidenced by the transfer of research effort on graph applications from temporary interdisciplinary spaces to disciplinary organizations related to the then-emerging field of computer science; and (2) the erratic careers of algorithms, in which efficiency, flaws, corrections, and authors’ status, were determining factors. (shrink)

Typically, fair machine learning research focuses on a single decision maker and assumes that the underlying population is stationary. However, many of the critical domains motivating this work are characterized by competitive marketplaces with many decision makers. Realistically, we might expect only a subset of them to adopt any non-compulsory fairness-conscious policy, a situation that political philosophers call partial compliance. This possibility raises important questions: how does partial compliance and the consequent strategic behavior of decision subjects affect the allocation outcomes? (...) If k% of employers were to voluntarily adopt a fairness-promoting intervention, should we expect k% progress (in aggregate) towards the benefits of universal adoption, or will the dynamics of partial compliance wash out the hoped-for benefits? How might adopting a global (versus local) perspective impact the conclusions of an auditor? In this paper, we propose a simple model of an employment market, leveraging simulation as a tool to explore the impact of both interaction effects and incentive effects on outcomes and auditing metrics. Our key findings are that at equilibrium: (1) partial compliance by k% of employers can result in far less than proportional (k%) progress towards the full compliance outcomes; (2) the gap is more severe when fair employers match global (vs local) statistics; (3) choices of local vs global statistics can paint dramatically different pictures of the performance vis-a-vis fairness desiderata of compliant versus non-compliant employers; (4) partial compliance based on local parity measures can induce extreme segregation. Finally, we discuss implications for auditors and insights concerning the design of regulatory frameworks. (shrink)

The hard problem of consciousness has been a perennially vexing issue for the study of consciousness, particularly in giving a scientific and naturalized account of phenomenal experience. At the heart of the hard problem is an often-overlooked argument, which is at the core of the hard problem, and that is the structure and dynamics (S&D) argument. In this essay, I will argue that we have good reason to suspect that the S&D argument given by David Chalmers rests on a limited (...) conception of S&D properties, what in this essay I’m calling extrinsic structure and dynamics. I argue that if we take recent insights from the complexity sciences and from recent developments in Integrated Information Theory (IIT) of Consciousness, that we get a more nuanced picture of S&D, specifically, a class of properties I’m calling intrinsic structure and dynamics. This I think opens the door to a broader class of properties with which we might naturally and scientifically explain phenomenal experience, as well as the relationship between syntactic, semantic, and intrinsic notions of information. I argue that Chalmers’ characterization of structure and dynamics in his S&D argument paints them with too broad a brush and fails to account for important nuances, especially when considering accounting for a system’s intrinsic properties. Ultimately, my hope is to vindicate a certain species of explanation from the S&D argument, and by extension dissolve the hard problem of consciousness at its core, by showing that not all structure and dynamics are equal. (shrink)

The history of economic thought witnessed several prominent economists who took seriously models and concepts in physics for the elucidation and prediction of economic phenomena. Econophysics is an emerging discipline at the intersection of heterodox economics and the physics of complex systems, with practitioners typically engaged in two overlapping but distinct methodological programs. The first is to export mathematical methods used in physics for the purposes of studying economic phenomena. The second is to export mechanisms in physics into economics. A (...) conclusion is drawn that physics transfer is often justified at the level of mathematical transfer but unjustified at the level of mechanistic transfer. (shrink)

This paper discusses the epistemic status of biology from the standpoint of the systemic approach to living systems based on the notion of biological autonomy. This approach aims to provide an understanding of the distinctive character of biological systems and this paper analyses its theoretical and epistemological dimensions. The paper argues that, considered from this perspective, biological systems are examples of emergent phenomena, that the biological domain exhibits special features with respect to other domains, and that biology as a discipline (...) employs some core concepts, such as teleology, function, regulation among others, that are irreducible to those employed in physics and chemistry. It addresses the claim made by Jacques Monod that biology as a science is marginal. It argues that biology is general insofar as it constitutes a paradigmatic example of complexity science, both in terms of how it defines the theoretical object of study and of the epistemology and heuristics employed. As such, biology may provide lessons that can be applied more widely to develop an epistemology of complex systems. (shrink)

This study shows firstly that it is necessary to characterize a computer simulation at a finer level than that of formal models: that of symbols and their various modes of reference. This is particularly true for those that integrate models and formalisms of a heterogeneous nature. This study then examines the ontological causes that, consequently, could explain their epistemic success. It is argued that they can be conveniently explained if one adopts a conception of nature that is both discontinuous and (...) finite. The latter thesis supports a naturalistic metaphysical position by invalidating, at its root, the argument made by speculative materialism against a scientific approach to the physical world that proceeds, like simulations, by finite representations and operations. (shrink)

This article aims to describe the last 10 years of the collaborative scientific endeavors on polarization in particular and collective problem-solving in general by our multidisciplinary research team. We describe the team’s disciplinary composition—social psychology, political science, social philosophy/epistemology, and complex systems science— highlighting the shared and unique skill sets of our group members and how each discipline contributes to studying polarization and collective problem-solving. With an eye to the literature on team dynamics, we describe team logistics and processes that (...) we believe make our multidisciplinary team persistent and productive. We emphasize challenges and difficulties caused by disciplinary differences in terms of terminology, units/levels of analysis, methodology, and theoretical assumptions. We then explain how work disambiguating the concepts of polarization and developing an integrative theoretical and methodological framework with complex systems perspectives has helped us overcome these challenges. We summarize the major findings that our research has produced over the past decade, and describe our current research and future directions. Last, we discuss lessons we have learned, including difficulties in a “three models” project and how we addressed them, with suggestions for effective multidisciplinary team research. (shrink)

Eshel Ben-Jacob’s manuscript entitled ‘Bacterial wisdom, Gödel’s theorem and creative genomic webs’ summarizes decades of work demonstrating adaptive mutagenesis in bacterial genomes. Bacterial genomes, each an essential part of a Kantian whole that is a single bacterium, are thus not independent of the environment as sensed; and a single bacterium is therefore a semiotic entity. Ben-Jacob suggests this but errs in 1) assigning autonomy to the genome, and 2) analogizing through computation without making clear whether he is doing so for (...) illustrative purposes or making committed ontological propositions. We reinterpret adaptive mutagenesis and related phenomena in ways both metaphysically rigorous and revealing. We conclude that bacteria are much farther removed from the ‘self-organizing’ world of inanimate process than from the Peircian world of signs; and a critical reappraisal of existing knowledge can enhance our understanding of selfhood, semiosis, and the roots of subjective experience. (shrink)

We live in a world full of mysteries. How do our brains create consciousness? Which animals are conscious, and which are not? How can we have free-will in a deterministic universe? What are the fundamental Laws of Nature? What caused the Big Bang? How can we make sense of Quantum Mechanics? Why is the universe so finely-tuned for Life? And how did Life begin? Despite investigating such mysteries for decades or more, scientists and philosophers are no closer to finding clear (...) and convincing answers that everyone can agree upon. The big question is: why do such mysteries exist, and can they ever be solved? -/- In Life, the Universe and Consciousness, A. T. Bollands introduces us to twelve so-called intractable problems, demonstrating how each one arises from a conflict between beliefs. And yet, beliefs that are in conflict cannot all be true, which means that one or more of them must be false. To solve each problem, therefore, all we need to do is work out which of our beliefs are false and correct them. This may sound easy, but these beliefs include the most fundamental assumptions of modern science. If that wasn’t enough, it turns out that these twelve intractable problems are related, such that we cannot solve any one of them satisfactorily until we have solved all twelve within the same coherent worldview. -/- Examining each of these problems in turn, we finally arrive at our twelfth intractable problem: What is Life? A. T. Bollands proposes a new definition for Life, and with it a new way of understanding the physical world – a scientific worldview he calls Universal Life. Armed with this new worldview, he proceeds to solve all twelve intractable problems one by one, thereby developing the Theory of Universal Life and the solution to the “Big Problem of 20th Century Science”. By successfully solving each problem, he shows that Universal Life offers us a simpler, more natural, more coherent and hence more credible explanation for ourselves and the world we live in than our current scientific worldview ever can. (shrink)

We have recently started to understand that fundamental aspects of complex systems such as emergence, the measurement problem, inherent uncertainty, complex causality in connection with unpredictable determinism, time­irreversibility and non­locality all highlight the observer's participatory role in determining their workings. In addition, the principle of 'limited universality' in complex systems, which prompts us to search for the appropriate 'level of description in which unification and universality can be expected', looks like a version of Bohr's 'complementarity principle'. It is more or (...) less certain that the different levels of description possible of a complex whole ­­ actually partial objectifications ­­ are projected on to and even redefine its constituent parts. Thus it is interesting that these fundamental complexity issues don't just bear a formal resemblance to, but reveal a profound connection with, quantum mechanics. Indeed, they point to a common origin on a deeper level of description. (shrink)

In a previous paper we outlined a series of historical touchpoints between classical aether theories and modern theoretical physics which showed a shared conceptual lineage for the modern tools and methods of the most common interpretations and fluid based “Hydrodynamic” treatments of an electromagnetic medium. It was proposed that, though the weight of modern experimentation leaves an extremely narrow and convoluted window for even a reconceptualization of a medium, all of modern physics recognizes a plethora of behaviors and attributes for (...) free space and these physics are interchangeable with modern methods for treating superfluid-like continuums. Thus the mathematical equivalence of the methods do not comprise alternative physics but an alternative interpretation of the same physics. Though many individual components describing a “neo-aether” or “quintessence” are available, an overarching structural outline of how these tools can work together to provide an alternative working overview of modern physics has remained undefined. This paper will propose a set of introductory concepts in the first outline of a toy model which will later connect the alternative tools and conceptualizations with their modern counterparts. This introductory paper provides the simpler “100-miles out” overview of the whole of physics from this perspective, in an easily comprehensible, familiar and intuitive, informal dialog fashion. While this paper grants the largest and loosest introductory overview, subsequent papers in this series will address the finite connections between modern physics and this hydrodynamic view. (shrink)

In this paper, I defend an epistemological pluralism that moves away from universal and absolute rationality, as well as from a radical and arbitrary relativism, where any criterion is valid for decision making. Such epistemological pluralism maintains that subjects know the world in which they live according to different conceptual schemes. We posit a notion of truth linked to the justification process and practical effectiveness. Then we present the importance of traditional knowledge in the socio-ecological field and relative to complex (...) systems. Finally, we explain the relevance of epistemic equity between traditional and scientific knowledges in order to anticipate consequences and to make decisions less uncertain. (shrink)

The continued failure of our civilisation to mobilise an adequate response to the crisis of climate change is traced to a pathological condition of culture analogous to addiction in the case of an individual. The exponential increase in the use of fossil fuel energy has both fuelled, and been driven by, an increasingly mechanistic and materialistic world-outlook that is inimical to acceptance of the measures needed to prevent catastrophic anthropogenic climate change. A holistic view of nature, drawn from such disciplines (...) as chaos theory, complexity theory and Gaia theory, and allied to a spiritual outlook grounded in the Buddhist view of interdependence and kindred paradigms, is emerging as a response to the crisis that could form the basis of a rapid 'state-shift' of the human social / economic / cultural system, comparable to cases of spontaneous remission from cancer that is unresponsive to conventional treatment regimes. (shrink)

The goal of creating Artificial General Intelligence (AGI) – or in other words of creating Turing machines (modern computers) that can behave in a way that mimics human intelligence – has occupied AI researchers ever since the idea of AI was first proposed. One common theme in these discussions is the thesis that the ability of a machine to conduct convincing dialogues with human beings can serve as at least a sufficient criterion of AGI. We argue that this very ability (...) should be accepted also as a necessary condition of AGI, and we provide a description of the nature of human dialogue in particular and of human language in general against this background. We then argue that it is for mathematical reasons impossible to program a machine in such a way that it could master human dialogue behaviour in its full generality. This is (1) because there are no traditional explicitly designed mathematical models that could be used as a starting point for creating such programs; and (2) because even the sorts of automated models generated by using machine learning, which have been used successfully in areas such as machine translation, cannot be extended to cope with human dialogue. If this is so, then we can conclude that a Turing machine also cannot possess AGI, because it fails to fulfil a necessary condition thereof. At the same time, however, we acknowledge the potential of Turing machines to master dialogue behaviour in highly restricted contexts, where what is called “narrow” AI can still be of considerable utility. (shrink)

Among the very architects of the recent re-emergence of emergentism in the physical sciences, Robert B. Laughlin certainly occupies a prominent place. Through a series of works beginning as early as his Nobel lecture in 1998, a lecture given after having been awarded, together with Störmer and Tsui, the Nobel prize in physics for its contribution in the elucidation of the fractional quantum Hall effect, Laughlin openly and relentlessly advocated a strongly anti-reductionistic view of physics – and, more particularly, of (...) the interface between condensed matter and particles physics – which culminated in what can be considered his emergentist manifesto: A Different Universe. Reinventing Physics from the Bottom Down (2005). In spite of this prominent role in the vindication of emergentism, rare are the philosophers, among whom even those sympathetic to the idea of emergence, who have paid serious attention to Laughlin’s insights. The subtleties of his view – it is true, often concealed in many technicalities – have accordingly, and somewhat unfortunately, mainly passed unnoticed. (shrink)

We critically analyse the point of view for which laws of nature are just a mean to compress data. Discussing some basic notions of dynamical systems and information theory, we show that the idea that the analysis of large amount of data by means of an algorithm of compression is equivalent to the knowledge one can have from scientific laws, is rather naive. In particular we discuss the subtle conceptual topic of the initial conditions of phenomena which are generally incompressible. (...) Starting from this point, we argue that laws of nature represent more than a pure compression of data, and that the availability of large amount of data, in general, is not particularly useful to understand the behaviour of complex phenomena. (shrink)

This essay furthers debate about the burgeoning science of Probabilistic Event Attribution (PEA) and its relevance to imminent climate policy decisions. It critically examines Allen Thompson and Friederike Otto’s recent arguments concerning the implications of PEA studies for how the United Nations Framework Convention on Climate Change (UNFCCC) policy framework should be revised during the 2016 ‘review and decision.’ I show that their contention that PEA studies cannot usefully inform decision-making about adaptation policies and strategies is misguided and argue that (...) the current UNFCCC treaty, the “Paris Agreement,” supersedes their proposed revision. (shrink)

Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called ‘ergodic hierarchy’, which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, that notion (...) of randomness requires clarification. The mathematical definition of EH does not make explicit appeal to randomness; nor does the usual way of presenting EH involve a specification of the notion of randomness that is supposed to underlie the hierarchy. In this paper we argue that EH is best understood as a hierarchy of random behaviour if randomness is explicated in terms of unpredictability. We then show that, contrary to common wisdom, EH is useful in characterising the behaviour of Hamiltonian dynamical systems. (shrink)

We consider an integrable, nonlocal and nonlinear, Schrödinger equation as a model for building space–time patchings in inhomogeneous loop quantum cosmology. We briefly review exact solutions of the NNSE, specially those obtained through “geometric equivalence” methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.

On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this justification for the case of Hamiltonian systems by proving that the KSE is equivalent to a generalized version of Shannon's (...) communication-theoretic entropy under certain plausible assumptions. I then discuss consequences of this equivalence for randomness in chaotic dynamical systems. Introduction Elements of dynamical systems theory Entropy in communication theory Entropy in dynamical systems theory Comparison with other accounts Product versus process randomness. (shrink)

It is shown that three common conditions for scientific explanations are violated by a widely used class of domain-independent explanations. These explanations can accommodate both complex and noncomplex systems and do not require the use of detailed models of system-specific processes for their effectiveness, although they are compatible with such model-based explanations. The approach also shows how a clean separation can be maintained between mathematical representations and empirical content.

The first of its kind, this book is an in-depth history of hydrodynamics from its eighteenth-century foundations to its first major successes in twentieth-century hydraulics and aeronautics. It documents the foundational role of fluid mechanics in developing a new mathematical physics. It gives full and clear accounts of the conceptual breakthroughs of physicists and engineers who tried to meet challenges in the practical worlds of hydraulics, navigation, blood circulation, meteorology, and aeronautics, and it shows how hydrodynamics at last began to (...) fulfill its early promise to unify the different worlds of flow. Richly illustrated, technically thorough, and sensitive to cross-cultural effects, this history should attract a broad range of historians, scientists, engineers, and philosophers and be a standard reference for anyone interested in fluid mechanics. (shrink)

The present paper focuses on a particular class of models intended to describe and explain the physical behaviour of systems that consist of a large number of interacting particles. Such many-body models are characterized by a specific Hamiltonian (energy operator) and are frequently employed in condensed matter physics in order to account for such phenomena as magnetism, superconductivity, and other phase transitions. Because of the dual role of many-body models as models of physical sys-tems (with specific physical phenomena as their (...) explananda) as well as mathematical structures, they form an important sub-class of scientific models, from which one can expect to draw general conclusions about the function and functioning of models in science, as well as to gain specific insight into the challenge of modelling complex systems of correlated particles in condensed matter physics. In particular, it is argued that many-body models contribute novel elements to the process of inquiry and open up new avenues of cross-model confirmation and model-based understanding. In contradistinction to phenomenological models, which have received comparatively more philosophical attention, many-body models typically gain their strength not from ‘empirical fit’ per se, but from their being the result of a constructive application of mature formalisms, which frees them from the grip of both ‘fundamental theory’ and an overly narrow conception of ‘empirical success’. (shrink)

The proposed transdisciplinary field of ‘complexics’ would bring together allcontemporary efforts in any specific disciplines or by any researchersspecifically devoted to constructing tools, procedures, models and conceptsintended for transversal application that are aimed at understanding andexplaining the most interwoven and dynamic phenomena of reality. Our aimneeds to be, as Morin says, not “to reduce complexity to simplicity, [but] totranslate complexity into theory”.New tools for the conception, apprehension and treatment of the data ofexperience will need to be devised to complement existing (...) ones and toenable us to make headway toward practices that better fit complexictheories. New mathematical and computational contributions have alreadycontinued to grow in number, thanks primarily to scholars in statisticalphysics and computer science, who are now taking an interest in social andeconomic phenomena.Certainly, these methodological innovations put into question and againmake us take note of the excessive separation between the training receivedby researchers in the ‘sciences’ and in the ‘arts’. Closer collaborationbetween these two subsets would, in all likelihood, be much moreenergising and creative than their current mutual distance. Humancomplexics must be seen as multi-methodological, insofar as necessarycombining quantitative-computation methodologies and more qualitativemethodologies aimed at understanding the mental and emotional world ofpeople.In the final analysis, however, models always have a narrative runningbehind them that reflects the attempts of a human being to understand theworld, and models are always interpreted on that basis. (shrink)

A class of quasilinear parabolic systems with quadratic nonlinearities in the gradient is considered. It is assumed that the elliptic operator of a system has variational structure. In the multidimensional case, the behavior of solutions of the Cauchy-Dirichlet problem smooth on a time interval $[0,T)$ is studied. Smooth extendibility of the solution up to $t=T$ is proved, provided that “normilized local energies” of the solution are uniformly bounded on $[0,T)$. For the case where $[0,T)$ determines the maximal interval of existence (...) of a smooth solution,the Hausdorff measure of a singular set at the moment $t=T$ is estimated. (shrink)

We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori. We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the “planets”. The proofs are based on averaging theory, KAM theory and variational methods.