Many of the computing systems programmed using Machine Learning are opaque: it is difficult to know why they do what they do or how they work. Explainable Artificial Intelligence aims to develop analytic techniques that render opaque computing systems transparent, but lacks a normative framework with which to evaluate these techniques’ explanatory successes. The aim of the present discussion is to develop such a framework, paying particular attention to different stakeholders’ distinct explanatory requirements. Building on an analysis of “opacity” from (...) philosophy of science, this framework is modeled after accounts of explanation in cognitive science. The framework distinguishes between the explanation-seeking questions that are likely to be asked by different stakeholders, and specifies the general ways in which these questions should be answered so as to allow these stakeholders to perform their roles in the Machine Learning ecosystem. By applying the normative framework to recently developed techniques such as input heatmapping, feature-detector visualization, and diagnostic classification, it is possible to determine whether and to what extent techniques from Explainable Artificial Intelligence can be used to render opaque computing systems transparent and, thus, whether they can be used to solve the Black Box Problem. (shrink)

The received view of dynamical explanation is that dynamical cognitive science seeks to provide covering law explanations of cognitive phenomena. By analyzing three prominent examples of dynamicist research, I show that the received view is misleading: some dynamical explanations are mechanistic explanations, and in this way resemble computational and connectionist explanations. Interestingly, these dynamical explanations invoke the mathematical framework of dynamical systems theory to describe mechanisms far more complex and distributed than the ones typically considered by philosophers. Therefore, contemporary dynamicist (...) research reveals the need for a more sophisticated account of mechanistic explanation. (shrink)

Models developed using machine learning are increasingly prevalent in scientific research. At the same time, these models are notoriously opaque. Explainable AI aims to mitigate the impact of opacity by rendering opaque models transparent. More than being just the solution to a problem, however, Explainable AI can also play an invaluable role in scientific exploration. This paper describes how post-hoc analytic techniques from Explainable AI can be used to refine target phenomena in medical science, to identify starting points for future (...) investigations of causal relationships, and to generate possible explanations of target phenomena in cognitive science. In this way, this paper describes how Explainable AI—over and above machine learning itself—contributes to the efficiency and scope of data-driven scientific research. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic in character and (...) are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

The philosophical conception of mechanistic explanation is grounded on a limited number of canonical examples. These examples provide an overly narrow view of contemporary scientific practice, because they do not reflect the extent to which the heuristic strategies and descriptive practices that contribute to mechanistic explanation have evolved beyond the well-known methods of decomposition, localization, and pictorial representation. Recent examples from evolutionary robotics and network approaches to biology and neuroscience demonstrate the increasingly important role played by computer simulations and mathematical (...) representations in the epistemic practices of mechanism discovery and mechanism description. These examples also indicate that the scope of mechanistic explanation must be re-examined: With new and increasingly powerful methods of discovery and description comes the possibility of describing mechanisms far more complex than traditionally assumed. (shrink)

This chapter subsumes David Marr’s levels of analysis account of explanation in cognitive science under the framework of mechanistic explanation: Answering the questions that define each one of Marr’s three levels is tantamount to describing the component parts and operations of mechanisms, as well as their organization, behavior, and environmental context. By explicating these questions and showing how they are answered in several different cognitive science research programs, this chapter resolves some of the ambiguities that remain in Marr’s account, and (...) shows that many different areas and traditions of cognitive scientific research can be unified under the mechanistic framework. (shrink)

Whereas most branches of neuroscience are thought to provide mechanistic explanations, systems neuroscience is not. Two reasons are traditionally cited in support of this conclusion. First, systems neuroscientists rarely, if ever, rely on the dual strategies of decomposition and localization. Second, they typically emphasize organizational properties over the properties of individual components. In this paper, I argue that neither reason is conclusive: researchers might rely on alternative strategies for mechanism discovery, and focusing on organization is often appropriate and consistent with (...) the norms of mechanistic explanation. Thus, many explanations in systems neuroscience can also be viewed as mechanistic explanations. (shrink)

This paper considers the way mathematical and computational models are used in network neuroscience to deliver mechanistic explanations. Two case studies are considered: Recent work on klinotaxis by Caenorhabditis elegans, and a longstanding research effort on the network basis of schizophrenia in humans. These case studies illustrate the various ways in which network, simulation and dynamical models contribute to the aim of representing and understanding network mechanisms in the brain, and thus, of delivering mechanistic explanations. After outlining this mechanistic construal (...) of network neuroscience, two concerns are addressed. In response to the concern that functional network models are non-explanatory, it is argued that functional network models are in fact explanatory mechanism sketches. In response to the concern that models which emphasize a network’s organization over its composition do not explain mechanistically, it is argued that this emphasis is both appropriate and consistent with the principles of mechanistic explanation. What emerges is an improved understanding of the ways in which mathematical and computational models are deployed in network neuroscience, as well as an improved conception of mechanistic explanation in general. (shrink)

This chapter provides an overview of the basic research strategies and analytic techniques deployed in computational cognitive neuroscience. On the one hand, “top-down” strategies are used to infer, from formal characterizations of behavior and cognition, the computational properties of underlying neural mechanisms. On the other hand, “bottom-up” research strategies are used to identify neural mechanisms and to reconstruct their computational capacities. Both of these strategies rely on experimental techniques familiar from other branches of neuroscience, including functional magnetic resonance imaging, single-cell (...) recording, and electroencephalography. What sets computational cognitive neuroscience apart, however, is the explanatory role of analytic techniques from disciplines as varied as computer science, statistics, machine learning, and mathematical physics. These techniques serve to describe neural mechanisms computationally, but also to drive the process of scientific discovery by influencing which kinds of mechanisms are most likely to be identified. For this reason, understanding the nature and unique appeal of computational cognitive neuroscience requires not just an understanding of the basic research strategies that are involved, but also of the formal methods and tools that are being deployed, including those of probability theory, dynamical systems theory, and graph theory. (shrink)

People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning—as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. We present an alternative view, portraying symbolic reasoning as a special kind of embodied reasoning in which arithmetic and logical formulae, externally represented as notations, serve as targets for powerful perceptual and sensorimotor systems. Although symbolic reasoning often (...) conforms to abstract mathematical principles, it is typically implemented by perceptual and sensorimotor engagement with concrete environmental structures. (shrink)

According to Marr, explanations of perceptual behavior should address multiple levels of analysis. Rahnev & Denison (R&D) are perhaps overly dismissive of optimality considerations at the computational level. Also, an exclusive reliance on standard observer models may cause neglect of many other plausible hypotheses at the algorithmic level. Therefore, as far as explanation goes, standard observer modeling is no panacea.

At least two distinct modeling frameworks contribute to the view that mind and brain are Bayesian: Bayesian Rational Analysis (BRA) and Hierarchical Predictive Coding (HPC). What is the relative contribution of each, and how exactly do they relate? In order to answer this question, we compare the way in which these two modeling frameworks address different levels of analysis within Marr’s tripartite conception of explanation in cognitive science. Whereas BRA answers questions at the computational level only, many HPC-theorists answer questions (...) at the computational, algorithmic, and implementational levels simultaneously. Given that all three levels of analysis need to be addressed in order to explain a behavioral or cognitive phenomenon, HPC seems to deliver more complete explanations. Nevertheless, BRA is well-suited for providing a solution to the dark room problem, a major theoretical obstacle for HPC. A combination of the two approaches also combines the benefits of an embodied-externalistic approach to resolving the dark room problem with the idea of a persisting evidentiary border beyond which matters are out of cognitive reach. For this reason, the development of explanations spanning all three Marrian levels within the general Bayesian approach may require combining the BRA and HPC modeling frameworks. (shrink)

In this article, Carlos Pereda introduces the concept of “colonial reason” and explores how philosophical practices and modes of thought are entwined with colonial political structures of exploitation, exclusion, and oppression. Pereda argues that philosophy in Latin America risks perpetuating and reinforcing the colonial gesture, either by turning to the European centers of thought (thus pursuing debates that always take place elsewhere) or by isolating itself and idealising the “own.” According to Pereda, both approaches fail to dismantle colonial violence (...) within philosophy. In his alternative approach, Pereda outlines principles and methodological criteria for the decolonisation of reason and philosophy. He emphasises the importance of methodological prudence that discerns between innocent, paralysing, and strategic uses of identity expressions and advocates for modes of reading and argumentation that conceive philosophy as an inclusive and ongoing dialogue. In Pereda’s terminology, this entails fostering “permeable reason” that manifests itself through “nomadic thinking,” a form of thinking that is capable of questioning itself and being questioned. (shrink)

Minding Time: A Philosophical and Theoretical Approach to the Psychology of Time offers an innovative philosophical account of the most fundamental kinds of time representation.

This article argues for a new interpretation of the realist claim that politics is autonomous from morality and involves specific political values. First, this article defends an original normative source: functional normativity. Second, it advocates a substantive functional standard: political institutions ought to be assessed by their capacity to select and implement collective decisions. Drawing from the ‘etiological account’ in philosophy of biology, I will argue that functions yield normative standards, which are independent from morality. For example, a ‘good heart’ (...) is one that pumps blood well, and a good army is one that it is effective at exerting military force. I then interpret realism’s naturalistic conception of politics as an etiological function of social groups: namely making binding collective decisions under persistent disagreement. I conclude that political institutions should be evaluated realistically by how well they perform this task. Finally, I assess trade-offs between this functional political normativity and other moral values. I conclude that justice, fairness, freedom and equality remain obviously important concerns, but only once the basic political function is secured. (shrink)

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

A study in the logic of theory change, examining the properties of maxichoice contraction and revision operations.

This article argues for a new interpretation of the realist claim that politics is autonomous from morality and involves specific political values. First, this article defends an original normative...

Many moral philosophers have criticized intensive animal farming because it can be harmful to the environment, it causes pain and misery to a large number of animals, and furthermore eating meat and animal-based products can be unhealthful. The issue of industrially farmed animals has become one of the most pressing ethical questions of our time. On the one hand, utilitarians have argued that we should become vegetarians or vegans because the practices of raising animals for food are immoral since they (...) minimize the overall happiness. Deontologists, on the other hand, have argued that the practices of raising animals for food are immoral because animals have certain rights and we have duties toward them. Some virtue ethicists remain unconvinced of deontic and consequentialist arguments against the exploitation of animals and suggest that a virtue-based approach is better equipped to show what is immoral about raising and using animals for food, and what is virtuous about ethical veganism. (shrink)

One of the world's most renowned theoretical physicists, Carlo Rovelli has entranced millions of readers with his singular perspective on the cosmos. In Helgoland, Rovelli examines the enduring enigma of quantum theory. The quantum world Rovelli describes is as beautiful as it is unnerving. Helgoland is a treeless island in the North Sea where the 21-year-old Werner Heisenberg first developed quantum theory, setting off a century of scientific revolution. Full of alarming ideas (ghost waves, distant objects that seem to be (...) magically connected, cats that appear both dead and alive), quantum physics has led to countless discoveries and technological advancements. Today our understanding of the world is based on this theory, yet it is still profoundly mysterious. As scientists and philosophers continue to fiercly debate the theory's meaning, Rovelli argues that its most unsettling contradictions can be explained by seeing the world as fundamentally made of relationships, not substances. We and everything around us exist only in our interactions with one another. This bold idea suggests new directions for understanding the structure of reality and even the nature of consciousness. Rovelli makes learning about quantum mechanics an almost psychedelic experience. Shifting our perspective once again, he takes us on a riveting journey through the universe so we can better understand our place in it. (shrink)

The project of growing meat artificially represents for some the next best thing to humanity. If successful, it could be the solution to several problems, such as feed- ing a growing global population while reducing the environmental impact of raising animals for food and, of course, reducing the amount and degree of animal cruelty and suffering that is involved in animal farming. In this paper, I argue that the issue of the morality of such a project has been framed only (...) in terms of the best conse- quences for the environment, animals, and humans, or in terms of deontic princi- ples. I argue that to appreciate how deep and difficult this issue is, it is necessary to consider it in terms of a virtue-oriented approach. Such an approach will reveal aspects that are not apparent, not contemplated by typical approaches, but are essen- tial to our understanding of the morality of lab-grown meat. As I argue, evaluating the issue from a virtue-oriented perspective suggests that the project of in vitro meat should not be supported because it stems from unvirtuous motivations. (shrink)

In this paper I unpack a realistic conception of politics by tightly defining its constitutive features: conflict and order. A conflict emerges when an actor is disposed to impose his/her views against the resistance of others. Conflicts are more problematic than moralists realize because they emerge unilaterally, are potentially violent, impermeable to content-based reason, and unavoidable. Order is then defined as an institutional framework that provides binding collective decisions. Order is deemed necessary because individuals need to cooperate to survive, but (...) groups cannot spontaneously secure collective decisions and are prone to conflicts. Particularly, the fact that potentially violent conflicts emerge unilaterally means that order requires coercion. I conclude that mischaracterizing conflict and order leads to undesirable normative principles, and that this criticism can be leveraged not only against Rawlsian liberals who moralize conflicts away, but also against some agonists who underestimate the need for order and some communitarians who underplay both circumstances. (shrink)

In a context of pervasive digitalization of the social world, both before and during the COVID-19 pandemic, the field of education has undergone major changes with the development of digital practices and settings. However, the physical presence of the subjects and the body remain something primordial and irreplaceable in traditional educational processes. Thus, it is often assumed that virtuality is opposed to the corporeal reality of the subjects involved in teaching, learning and studying. In this paper we aim to critically (...) challenge this assumption by addressing the phenomenon of virtuality in a more original sense: as a fundamental dimension of corporeality itself. Drawing on Merleau-Ponty’s phenomenological insights, we argue that the experience of the virtual is inherently embodied and fully real. We understand corporeality and virtuality as entangled and multidimensional phenomena. At the same time, this leads us to rethink the digital as only one possible medium in which virtuality can appear as inherent to embodied experience. We develop our phenomenological approach in three instances. First, we question and bracket two common assumptions about corporeality. From our critical perspective, assumptions about a disembodied digitality and a devirtualized corporeality represent extremes within which educational discourses currently move. Second, we address the inherent virtuality of embodied experience. We outline the heuristic concept of the virtual body to describe corporeality and virtuality as entangled and multidimensional phenomena that encompass extension, intercorporeality and intermediality. Finally, we make some remarks on the relationships of corporeality and virtuality considering the challenges of digital education. (shrink)

Marcus William Hunt argues that when co-parents disagree over whether to raise their child (or children) as a vegan, they should reach a compromise as a gift given by one parent to the other out of respect for his or her authority. Josh Millburn contends that Hunt’s proposal of parental compromise over veganism is unacceptable on the ground that it overlooks respect for animal rights, which bars compromising. However, he contemplates the possibility of parental compromise over ‘unusual eating,’ of animal-based (...) foods obtained without the violation of animal rights. I argue for zero parental compromise, rejecting a rights-oriented approach, and propose a policy that an ethical vegan parent and a non-vegan co-parent should follow to determine how to raise their children. (shrink)

In this paper I unpack a realistic conception of politics by tightly defining its constitutive features: conflict and order. A conflict emerges when an actor is disposed to impose his/her views against the resistance of others. Conflicts are more problematic than moralists realize because they emerge unilaterally, are potentially violent, impermeable to content-based reason, and unavoidable. Order is then defined as an institutional framework that provides binding collective decisions. Order is deemed necessary because individuals need to cooperate to survive, but (...) groups cannot spontaneously secure collective decisions and are prone to conflicts. Particularly, the fact that potentially violent conflicts emerge unilaterally means that order requires coercion. I conclude that mischaracterizing conflict and order leads to undesirable normative principles, and that this criticism can be leveraged not only against Rawlsian liberals who moralize conflicts away, but also against some agonists who underestimate the need for order and some communitarians who underplay both circumstances. (shrink)

The project of growing meat artificially represents for some the next best thing to humanity. If successful, it could be the solution to several problems, such as feeding a growing global population while reducing the environmental impact of raising animals for food and, of course, reducing the amount and degree of animal cruelty and suffering that is involved in animal farming. In this paper, I argue that the issue of the morality of such a project has been framed only in (...) terms of the best consequences for the environment, animals, and humans, or in terms of deontic principles. I argue that to appreciate how deep and difficult this issue is, it is necessary to consider it in terms of a virtue-oriented approach. Such an approach will reveal aspects that are not apparent, not contemplated by typical approaches, but are essential to our understanding of the morality of lab-grown meat. As I argue, evaluating the issue from a virtue-oriented perspective suggests that the project of in vitro meat should not be supported because it stems from unvirtuous motivations. (shrink)

In twentieth-century continental philosophy, German philosophical anthropology can be seen as a sort of conceptual laboratory devoted to human/animal research, and, in particular, to the discontinuity between human and non-human animals. Its main notion—the idea of the special position of humans in nature—is one of the first philosophical attempts to think of the specificity of humans as a natural and qualitative difference from non-human animals. This school of thought correctly rejects both the metaphysical and/or religious characterisations of humans, and the (...) positivistic gradualism, that sees the human being as an animal endowed with a greater degree of certain faculties. At the same time, German philosophical anthropology still takes it for granted that such natural-qualitative novelty is unique in the realm of the living, that in correspondence with humans there is the hiatus, the discontinuity par excellence. The semiotic side of this view is the distinction between signs and symbols developed by Ernst Cassirer and Susanne Langer: animal signs would be mere proxies for perceptive elements or stimuli, whereas only human symbols could convey complex representation of objects and situations. The goal of this contribution is to criticise the alleged uniqueness of the hiatus and its semiotic implications through the opposite approach of the diffuse discontinuities. This approach that focuses on the semiotic traits of different species-specific environments can be traced back to Jakob von Uexküll’s biosemiotical phenomenology, which thinks of discontinuities as a normal phenomenon of animal life. (shrink)

This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of safe contraction of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its properties both in general and (...) under various natural constraints. (shrink)

This article discusses the relation between empirical and normative approaches in bioethics. The issue of dwarf tossing, while admittedly unusual, is chosen as a point of departure because it challenges the reader to look with fresh eyes upon several central bioethical themes, including human dignity, autonomy, and the protection of vulnerable people. After an overview of current approaches to the integration of empirical and normative ethics, we consider five ways that the empirical and normative can be brought together to speak (...) to the problem of dwarf tossing: prescriptive applied ethics, theoretical ethics, critical applied ethics, particularist ethics and integrated empirical ethics. We defend a position of critical applied ethics that allows for a two-way relation between empirical and normative theories. Against efforts fully to integrate the normative and the empirical into one synthesis, we propose that the two should stand in tension and relation to one another. The approach we endorse acknowledges that a social practice can and should be judged both by the gathering of empirical data and by normative ethics. Critical applied ethics uses a five stage process that includes: (a) determination of the problem, (b) description of the problem, (c) empirical study of effects and alternatives, (d) normative weighing and (e) evaluation of the effects of a decision. In each stage, we explore the perspective from both the empirical (sociological) and the normative ethical point of view. We conclude by applying our five-stage critical applied ethics to the example of dwarf tossing. (shrink)

We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of many-sorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL toward providing a meaningful algebraic counterpart also to logics with a many-sorted language, and possibly including non-truth-functional connectives. The proposed behavioral approach covers logics which are not algebraizable according to the standard approach, while also bringing a new (...) algebraic perspective to logics which are algebraizable using the standard tools of AAL. Furthermore, we pave the way toward a robust behavioral theory of AAL, namely by providing a behavioral version of the Leibniz operator which allows us to generalize the traditional Leibniz hierarchy, as well as several well-known characterization results. A number of meaningful examples will be used to illustrate the novelties and advantages of the approach. (shrink)

The Heythrop Journal, Volume 63, Issue 5, Page 869-885, September 2022.

The article elaborates an exegetical study of the figure of “Hell” present in the work of the martinican psychiatrist Frantz Fanon. This trope is thought of as a core element of the narrative of Black Skin, White Masks that is linked to reflections on racist alienation, the epidermis, the gaze, and the zone of non-being. Exploring the different modulations of “Hell”, the article makes a displacement that seeks to argue how the infernal of Fanon’s story, more than a metaphor, accounts (...) for the “real-lived” of the colonial world. Consequently, the racialized body and its lived experience offer a reading about “Hell” in an anaphoric and existential key that strains the modern-hegemonic grammars about the identities. From this starting point, the work discusses the problem of temporality linked to the critical tenor that at various moments in Black Skin... assumes the infernal architecture of colonialism narrated by Fanon. (shrink)

The book is a comprehensive introduction to the work of the Estonian-German biologist Jakob von Uexküll. After a first introductory chapter by Morten Tønnessen and a second chapter on Uexküll's life and philosophical background, it contains four chapters devoted to the analysis of his main works; they are followed by a vast eighth chapter which deals with the influence Uexküll had on other philosophers and scientists, and by a conclusions focused on the possibility of updating Uexküll's work. The monograph combines (...) a careful reconstruction of the historical context in which the Uexküllian concepts emerged (the debate between mechanism and vitalism, contemporary scientific studies) and a thorough analysis of the philosophical contents of the Uexküllian views. As far as the key issue is concerned, Uexküll's notion of Umwelt refers to the perceptive and operative world which surrounds animal species; it is a subjective species-specific construction which provides living organisms with great security and behaviour stability. Moreover, the relationship that the animal carries out with its environment proves to be a complex system of semiotic interactions: its behaviour is not a set of mechanical reactions, but the result of a spontaneous attribution of meaning to the outside world, whose environmental elements are actively interpreted by the subject. The environment of animal species becomes a field of meaning, an exceedingly complex subjective elaboration; this can lessen the distance between animals and men, crediting both with the cognitive ability to grasp meanings and to use signs. (shrink)

The concept of dignity is notoriously vague. In this paper it is argued that the reason for this is that there are three versions of dignity that are often confused. First we will take a short look at the history of the concept of dignity in order to demonstrate how already from Roman Antiquity two versions of dignity can be distinguished. Subsequently, the third version will be introduced and it will be argued that although the three versions of dignity hang (...) together, they should also be clearly distinguished in order to avoid confusion. The reason for distinguishing the three versions is because all three of them are only partially effective. This will be demonstrated by taking the discussion about voluntary ‘dying with dignity’ as an example. Inspired by both Paul Ricoeur’s concept of ethics and the ethics of care a proposition will be done as to how the three versions of dignity may sustain each other and help achieve what neither one of the versions can do on its own. (shrink)