What role does non-genetic inheritance play in evolution? In recent work we have independently and collectively argued that the existence and scope of non-genetic inheritance systems, including epigenetic inheritance, niche construction/ecological inheritance, and cultural inheritance—alongside certain other theory revisions—necessitates an extension to the neo-Darwinian Modern Synthesis (MS) in the form of an Extended Evolutionary Synthesis (EES). However, this argument has been challenged on the grounds that non-genetic inheritance systems are exclusively proximate mechanisms that serve the ultimate function of calibrating organisms (...) to stochastic environments. In this paper we defend our claims, pointing out that critics of the EES (1) conflate non-genetic inheritance with early 20th-century notions of soft inheritance; (2) misunderstand the nature of the EES in relation to the MS; (3) confuse individual phenotypic plasticity with trans-generational non-genetic inheritance; (4) fail to address the extensive theoretical and empirical literature which shows that non-genetic inheritance can generate novel targets for selection, create new genetic equilibria that would not exist in the absence of non-genetic inheritance, and generate phenotypic variation that is independent of genetic variation; (5) artificially limit ultimate explanations for traits to gene-based selection, which is unsatisfactory for phenotypic traits that originate and spread via non-genetic inheritance systems; and (6) fail to provide an explanation for biological organization. We conclude by noting ways in which we feel that an overly gene-centric theory of evolution is hindering progress in biology and other sciences. (shrink)

The theory of niche construction adds a second general inheritance system, ecological inheritance, to evolution . Ecological inheritance is the inheritance, via an external environment, of one or more natural selection pressures previously modified by niche-constructing organisms. This addition means descendant organisms inherit genes, and biotically transformed selection pressures in their environments, from their ancestors. The combined inheritance is called niche inheritance. Niche inheritance is used as a basis for classifying the multiple genetic and non-genetic, inheritance systems currently being proposed (...) as possibly significant in evolution . Implications of niche inheritance for the relationship between evolution and development are discussed. (shrink)

Niche construction theory (NCT) is distinctive for being explicit in recognizing environmental modification by organisms—niche construction—and its legacy—ecological inheritance—to be evolutionary processes in their own right. Humans are widely regarded as champion niche constructors, largely as a direct result of our capacity for the cultural transmission of knowledge and its expression in human behavior, engineering, and technology. This raises the question of how human ecological inheritance relates to human cultural inheritance. If NCT is to provide a conceptual framework for the (...) human sciences, then it is important that the relationship between these two legacies is clear. We suggest that cultural processes and cultural inheritance can be viewed as the primary means by which humans engage in the universal process of niche construction. (shrink)

We propose a conceptual model that maps the causal pathways relating biological evolution to cultural change. It builds on conventional evolutionary theory by placing emphasis on the capacity of organisms to modify sources of natural selection in their environment (niche construction) and by broadening the evolutionary dynamic to incorporate ontogenetic and cultural processes. In this model, phenotypes have a much more active role in evolution than generally conceived. This sheds light on hominid evolution, on the evolution of culture, and on (...) altruism and cooperation. Culture amplifies the capacity of human beings to modify sources of natural selection in their environments to the point where that capacity raises some new questions about the processes of human adaptation. Key Words: adaptation; altruism; cooperation; evolutionary psychology; gene-culture coevolution; human evolution; human genetics; niche construction; sociobiology. (shrink)

In modern evolutionary theory, selection acts on particular genes and assemblages of genes that operate through phenotypes expressed in environments. This view, however, overlooks the fact that organisms often alter their environments in pursuit of fitness needs and thus modify some environmental selection pressures. Niche construction theory introduces a reciprocal causal process that modifies natural selection relative to three general kinds of environmental components: abiota, biota (other organisms), and artifacts. The ways in which niche-constructing organisms can construct or modify the (...) components differ. Modification of abiota, for example, may have different consequences from the construction of artifacts. Some changes in abiota may simply be caused by the by-products of metabolisms and activities of organisms. Alternatively, artifacts may be “extended phenotypes” that demonstrate obvious prior “design” and “construction” by organisms in the service of fitness needs. Nevertheless, adaptation should always account for the reciprocity between constructed niches and the living agents that construct them. Looking to well-adapted nature for inspiration for human-built artifacts must account for this reciprocity between phenotype and constructed environment as well as the novel features of human architecture, including frank intentionality of design and novel culturally acquired knowledge. (shrink)

In 1961, Ernst Mayr published a highly influential article on the nature of causation in biology, in which he distinguished between proximate and ultimate causes. Mayr argued that proximate causes (e.g. physiological factors) and ultimate causes (e.g. natural selection) addressed distinct ‘how’ and ‘why’ questions and were not competing alternatives. That distinction retains explanatory value today. However, the adoption of Mayr’s heuristic led to the widespread belief that ontogenetic processes are irrelevant to evolutionary questions, a belief that has (1) hindered (...) progress within evolutionary biology, (2) forged divisions between evolutionary biology and adjacent disciplines and (3) obstructed several contemporary debates in biology. Here we expand on our earlier (Laland et al. in Science 334:1512–1516, 2011) argument that Mayr’s dichotomous formulation has now run its useful course, and that evolutionary biology would be better served by a concept of reciprocal causation, in which causation is perceived to cycle through biological systems recursively. We further suggest that a newer evolutionary synthesis is unlikely to emerge without this change in thinking about causation. (shrink)

We are grateful to the commentators for taking the time to respond to our article. Too many interesting and important points have been raised for us to tackle them all in this response, and so in the below we have sought to draw out the major themes. These include problems with both the term ‘ultimate causation’ and the proximate-ultimate causation dichotomy more generally, clarification of the meaning of reciprocal causation, discussion of issues related to the nature of development and phenotypic (...) plasticity and their roles in evolution, and consideration of the need for an extended evolutionary synthesis. (shrink)

In spite of its success, Neo-Darwinism is faced with major conceptual barriers to further progress, deriving directly from its metaphysical foundations. Most importantly, neo-Darwinism fails to recognize a fundamental cause of evolutionary change, “niche construction”. This failure restricts the generality of evolutionary theory, and introduces inaccuracies. It also hinders the integration of evolutionary biology with neighbouring disciplines, including ecosystem ecology, developmental biology, and the human sciences. Ecology is forced to become a divided discipline, developmental biology is stubbornly difficult to reconcile (...) with evolutionary theory, and the majority of biologists and social scientists are still unhappy with evolutionary accounts of human behaviour. The incorporation of niche construction as both a cause and a product of evolution removes these disciplinary boundaries while greatly generalizing the explanatory power of evolutionary theory. (shrink)

The fundamental tenet of contemporary sociobiology, namely the assumption of a single process of evolution involving the selection of genes, is critically examined. An alternative multiple-level, multiple-process model of evolution is presented which posits that the primary process that operates via selection upon the genes cannot account for certain kinds of biological phenomena, especially complex, learned, social behaviours. The primary process has evolved subsidiary evolutionary levels and processes that act to bridge the gap between genes and these complex behaviours. The (...) subsidiary levels are development, individual animal learning, and socioculture itself. It is argued that individual learning is pivotal to the derivation and biological analysis of culture. The differences between cultural and noncultural societies are stressed. It is concluded that such a multiple-level model of evolution can form the basis for reconciling opposing sides in the sociobiology debate. (shrink)

Our response contains a definition of niche construction, illustrations of how it changes the evolutionary process, and clarifications of our conceptual model. We argue that the introduction of niche construction into evolutionary thinking earns its keep; we illustrate this argument in our discussion of rates of genetic and cultural evolution, memes and phenogenotypes, creativity, the EEA (environment of evolutionary adaptedness), and group selection.

Group selection, as advocated by Sober and Wilson, is theoretically plausible, although it remains an open question as to what extent it occurs in nature. If group selection has operated in hominids, it is likely to have selected cultural not genetic variation. A focus on niche construction helps delineate the conditions under which cooperation is favoured. Group selection may favour between-group conflict as well as within-group cooperation.

One implication of Laland, Odling-Smee & Feldman's niche construction model concerns the significance of the role of behavioural or cultural traits in comparative analysis. In this commentary it is suggested that cladistic methods already recognise this importance, and that behavioural characters may play a key role in hominid speciation and the definition of species.

A comprehensive treatment of the concept of causation in evolutionary biology that makes clear its central role in both historical and contemporary debates. Most scientific explanations are causal. This is certainly the case in evolutionary biology, which seeks to explain the diversity of life and the adaptive fit between organisms and their surroundings. The nature of causation in evolutionary biology, however, is contentious. How causation is understood shapes the structure of evolutionary theory, and historical and contemporary debates in evolutionary biology (...) have revolved around the nature of causation. Despite its centrality, and differing views on the subject, the major conceptual issues regarding the nature of causation in evolutionary biology are rarely addressed. This volume fills the gap, bringing together biologists and philosophers to offer a comprehensive, interdisciplinary treatment of evolutionary causation. Contributors first address biological motivations for rethinking evolutionary causation, considering the ways in which development, extra-genetic inheritance, and niche construction challenge notions of cause and process in evolution, and describing how alternative representations of evolutionary causation can shed light on a range of evolutionary problems. Contributors then analyze evolutionary causation from a philosophical perspective, considering such topics as causal entanglement, the commingling of organism and environment, and the relationship between causation and information. Contributors John A. Baker, Lynn Chiu, David I. Dayan, Renée A. Duckworth, Marcus W Feldman, Susan A. Foster, Melissa A. Graham, Heikki Helanterä, Kevin N. Laland, Armin P. Moczek, John Odling-Smee, Jun Otsuka, Massimo Pigliucci, Arnaud Pocheville, Arlin Stoltzfus, Karola Stotz, Sonia E. Sultan, Christoph Thies, Tobias Uller, Denis M. Walsh, Richard A. Watson. (shrink)

The key assumption behind evolutionary epistemology is that animals are active learners or ‘knowers’. In the present study, I updated the concept of natural learning, developed by Henry Plotkin and John Odling-Smee, by expanding it from the animal-only territory to the biosphere-as-a-whole territory. In the new interpretation of natural learning the concept of biological information, guided by Peter Corning’s concept of “control information”, becomes the ‘glue’ holding the organism–environment interactions together. The control information guides biological systems, from bacteria (...) to ecosystems, in the process of natural learning executed by the universal algorithm. This algorithm, summarized by the acronym IGPT (information-gain-process-translate) incorporates natural cognitive methods including sensing/perception, memory, communication, and decision-making. Finally, the biosphere becomes the distributed network of communicative interactions between biological systems termed the interactome. The concept of interactome is based on Gregory Bateson’s natural epistemology known as the “ecology of mind”. Mimicking Bateson’s approach, the interactome may also be designated “physiology of mind”—the principle behind regulating the biosphere homeostasis. (shrink)

Niche construction is a concept that captures a wide array of biological phenomena, from the environmental effects of metabolism to the creation of complex structures such as termite mounds and beaver dams. A central point in niche construction theory is that organisms do not just passively undergo developmental, ecological, or evolutionary processes, but are also active participants in them Evolution: From molecules to men, Cambridge University Press, Cambridge, 1983; Laland KN, Odling-Smee J, Feldman MW, In: KN Laland and (...) T Uller Evolutionary causation: Biological and philosophical reflections, MIT Press, Cambridge, MA, 2019). In this paper, we distinguish between two fundamentally different ways in which organisms are active participants: as agents and as contributors. Roughly, organisms act as agents when niche constructing effects are a result of a goal-directed behavior over which the organisms have some degree of control. Organisms act as contributors when the niche constructing effects do not arise from a goal to perform the constructive activity. As illustrative examples we discuss plants altering leaf-morphology to optimize light exposure as reported by Sultan and bacteria creating novel niches through excreting energy-rich metabolites. The difference between agential and contributional niche construction is important for understanding the different ways organisms can actively participate in development, ecology, and evolution. Additionally, this distinction can increase our understanding of how the capacity of agency is distributed across the tree of life and how agency influences developmental and evolutionary processes. (shrink)

This volume is the best available tool to compare and appraise the different approaches of today’s biology and their conceptual frameworks, serving as a springboard for new research on a clarified conceptual basis. It is expected to constitute a key reference work for biologists and philosophers of biology, as well as for all scientists interested in understanding what is at stake in the present transformations of biological models and theories. The volume is distinguished by including, for the first time, self-reflections (...) and exchanges of views on practice and theoretical attitudes by important participants in recent biological debates. The questions of how biological models and theories are constructed, how concepts are chosen and how different models can be articulated, are asked. Then the book explores some of these convergences between different models or theoretical frameworks. Confronting views on adaptive complexity are investigated, as well as the role of self-organization in evolution; niche construction meets developmental biology; the promises of the emergent field of ecological-evolutionary-development are examined. In sum, this book is a marvellous account of the dynamism of today’s theoretical biology. Foreword: Carving Nature at its Joints? Richard Lewontin Chapter 1: Introduction Anouk Barberousse, Michel Morange, Thomas Pradeu Chapter 2: Articulating Different Modes of Explanation: The Present Boundary in Biological Research Michel Morange Chapter 3: Compromising Positions: The Minding of Matter Susan Oyama Chapter 4:ions, Idealizations, and Evolutionary Biology Peter Godfrey-Smith Chapter 5: The Adequacy of Model Systems for Evo-Devo: Modeling the Formation Of Organisms / Modeling the Formation Of Society Scott F. Gilbert Chapter 6: Niche Construction in Evolution, Ecosystems and Developmental Biology John Odling-Smee Chapter 7: Novelty, Plasticity and Niche Construction: The Influence of Phenotypic Variation on Evolution Kim Sterelny Chapter 8: The Evolution of Complexity Mark A. Bedau Chapter 9: Self-Organization, Self-Assembly, and the Origin of Life Evelyn Fox Keller Chapter 10: Self-Organization and Complexity in Evolutionary Theory, or, In this Life the Bread Always Falls Jammy Side Down Michael Ruse. (shrink)

I distinguish different versions of the “niche construction” idea. Some are primarily scientific, while others are more philosophical. Laland, Odling-Smee & Feldman's is mostly scientific, but given that fact, there are some changes they could make to their account. I also compare the target article to Lewontin's classic 1983 paper.

The standard picture of evolution, is externalist: a causal arrow runs from environment to organism, and that arrow explains why organisms are as they are (Godfrey-Smith 1996). Natural selection allows a lineage to accommodate itself to the specifics of its environment. As the interior of Australia became hotter and drier, phenotypes changed in many lineages of plants and animals, so that those organisms came to suit the new conditions under which they lived. Odling-Smee, Laland and Feldman, building on (...) the work of Richard Lewontin, have shown that while sometimes appropriate, this is an inadequate conception of the relationship between organisms and the environments in which they live. Over time organisms alter their environment as well as being altered by their environments (Lewontin 1982; Lewontin 1983; Lewontin 1985). For example, animals modulate the effects of their physical and biological environment by building shelters: the beaver’s dam and lodge system, and termite mounds are two famous cases of animal structures, but they are few of many. There are many thousands of animals which make nests, burrows and other shelters. Likewise, animals make tools that give them access to resources from which they would otherwise be excluded: thus the Galapagos woodpecker finch uses a cactus needle to extract insects from crevasses in bark — insects that they would otherwise be unable to catch (Tebbich, Taborsky et al. 2001). Tool making is not as common as shelter-making, but it is common. For example many animals make traps: there are many species of pit-making antlions. Thus in part organisms make the world in which they live. They partially construct their own niches. Odling-Smee, Laland and Feldman argue that this has five major and under-appreciated consequences for biological theory. (shrink)

Industrial melanism, according to the traditional explanation, amounts to niche construction since it involves changes in predation pressure. Indeed, it would be difficult to imagine selection without niche construction. This cannot be what Laland, Odling-Smee & Feldman mean. They offer convincing examples, but they should provide a better definition of “niche construction” to indicate how their view supplements traditional evolutionary biology.

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The “impossibility results” in algorithmic fairness suggest that a predictive model cannot fully meet two common fairness criteria – sufficiency and separation – except under extraordinary circumstances. These findings have sparked a discussion on fairness in algorithms, prompting debates over whether predictive models can avoid unfair discrimination based on protected attributes, such as ethnicity or gender. As shown by Otto Sahlgren, however, the discussion of the impossibility results would gain from importing some of the tools developed in the philosophical literature (...) on feasibility. Utilizing these tools, Sahlgren sketches a cautiously optimistic view of how algorithmic fairness can be made feasible in restricted local decision-making. While we think it is a welcome move to inject the literature on feasibility into the debate on algorithmic fairness, Sahlgren says very little about what are the general gains of bringing in feasibility considerations in theorizing algorithmic fairness. How, more precisely, does it help us make assessments about fairness in algorithmic decision-making? This is what is addressed in this Reply. More specifically, our two-fold argument is that feasibility plays an important but limited role for algorithmic fairness. We end by offering a sketch of a framework, which may be useful for theorizing feasibility in algorithmic fairness. (shrink)

Conscientious objection has spurred impassioned debate in many Western countries. Some Norwegian general practitioners (GPs) refuse to refer for abortion. Little is know about how the GPs carry out their refusals in practice, how they perceive their refusal to fit with their role as professionals, and how refusals impact patients. Empirical data can inform subsequent normative analysis.

In the modern age, the political secret has acquired a bad reputation. With modern democracy’s ideal of transparency, political secrecy is identified with political crime or corruption. The article argues that this repression of secrecy in modern democracies falls short of a substantial understanding of the structure and workings of political secrecy. By outlining a genealogy of political secrecy, it elucidates the logic as well as the blind spots of a current culture of secrecy. It focuses on two fundamental logics (...) of secrecy, deduced from the Latin terms ‘ arcanum’ and ‘ secretum’. Whereas the logic of arcanum regards secrecy as a legitimate dimension of government, a modern logic of secretum is marked by an inextricable dialectics between the withdrawal and communication of knowledge, between secrecy and publicity. Here, the secret is not so much a piece of withheld knowledge as a ‘secrecy effect’ that binds the realm of secrecy to the public sphere by a dialectics of permanent suspicion and scandal. Instead of falling into the trap of this ‘secrecy effect’ it is worth taking a closer look at the tradition of thought on the arcana imperii, from Tacitus to early modern doctrines of raison d’état to Carl Schmitt. What this tradition deals with is the functionality of secrecy and its complicated relation to the law. The arcana tradition elaborates the crucial point of secrecy: its potential, but also its profound ambivalence. Secrecy opens up a discretionary space of action exempt from the rule of law, and, according to Carl Schmitt, ignores the law so as to allow it to become effective. Secrecy serves to protect and stabilize the state, but at the same time it opens a space of exception from the rule of law that breeds violence, corruption and oppression. Instead of seeing secrecy as the opposite of a political culture of transparency, it is more productive to regard secrecy as transparency's complement – a counterpart, however, that is marked by the profound paradox of being both a consolidation of and a threat to democracy. (shrink)

I explore what and when hypocrisy is a moral wrong by interrogating the case of hypocrisy of Julien in Stendhal's The Red and The Black. I conclude hypocrisy is most morally vexed in those sphere where sincerity is required.

Gaze following occurs automatically in social interactions, but the degree to which gaze is followed depends on whether an agent is perceived to have a mind, making its behavior socially more relevant for the interaction. Mind perception also modulates the attitudes we have towards others, and deter-mines the degree of empathy, prosociality and morality invested in social interactions. Seeing mind in others is not exclusive to human agents, but mind can also be ascribed to nonhuman agents like robots, as long (...) as their appearance and/or behavior allows them to be perceived as intentional beings. Previous studies have shown that human appearance and reliable behavior induce mind perception to robot agents, and positively affect attitudes and performance in human-robot interaction. What has not been investigated so far is whether different triggers of mind perception have an independent or interactive effect on attitudes and performance in human-robot interaction. We examine this question by manipulating agent appearance (human vs. robot) and behavior (reliable vs. random) within the same paradigm and examine how congruent (human/reliable vs. robot/random) versus incongruent (human/random vs. robot/reliable) combinations of these triggers affect performance (i.e., gaze fol-lowing) and attitudes (i.e., agent ratings) in human-robot interaction. The results show that both ap-pearance and behavior affect human-robot interaction but that the two triggers seem to operate in iso-lation, with appearance more strongly impacting attitudes, and behavior more strongly affecting per-formance. The implications of these findings for human-robot interaction are discussed. (shrink)

6 and 14 recently proposed taxonomies that distinguish between four processing states, based on bottom-up stimulus strength and top-down attentional amplification. The aim of the present study was to empirically test these processing states using the priming paradigm. Our results showed that attention and stimulus strength significantly modulated priming effects: either receiving top-down attention or possessing sufficient bottom-up strength was a prerequisite for a stimulus to elicit priming. When both top-down attention and sufficient bottom-up strength were present, the priming effect (...) was boosted. The origins of the observed priming effects also varied between different processing states. We can conclude that our empirical study using the priming paradigm confirmed the presence of four processing states, which displayed a differential pattern of response priming effects and differential origins of the response priming effects. (shrink)

The goal of this dissertation is to demonstrate that construals of our emotional responses to fictions as irrational or merely pseudo-emotional are not the only explanations available to us, and that necessary and sufficient conditions for an emotional response to a fiction can be established without abandoning either its intentionality or the assignment of a causal role to our beliefs. ;Colin Radford's claim that our emotional responses to fictions are irrational and inconsistent is challenged in two ways. First, distinctions can (...) be drawn between our reactions to fiction and indisputably irrational emotional reactions which preclude arriving at Radford's conclusion via an argument from analogy. Further, the conditions for rationality put forward in several analyses of emotion, ranging from that of David Hume to that of Ronald de Sousa, are not violated by our emotional responses to fictions. ;Kendall Walton's contention that such affective reactions are merely quasi-emotions is contested on the ground that the absence of the existentially committed beliefs which Walton allies with all genuine emotional responses does not demonstrate an absence of cognitive content. Existentially uncommitted evaluative beliefs, thoughts, and even beliefs about the world can be linked to our emotional experience of fictions, and can serve a function necessary to the identification of the emotion, a function which Walton assigns to the existentially committed belief. ;In our experience of fictions, the objects of our emotion are various. However, a direct response to a fictional entity or event is characterized in terms of Peter Lamarque's account: as a response to the content of a thought, a response to what has been thought or imagined rather than to the thought itself. The roles played both by evaluative beliefs and beliefs about what can occur in the world are investigated and found to constitute necessary conditions for an emotional response to a fiction. An account of the role of the imagination, which borrows from Boruah, David Novitz, and Susan Feagin, provides another condition which, together with the two preceding, appears sufficient for such a response. (shrink)

Artificial intelligent (AI) systems used in medicine are often very reliable and accurate, but at the price of their being increasingly opaque. This raises the question whether a system’s opacity undermines the ability of medical doctors to acquire knowledge on the basis of its outputs. We investigate this question by focusing on a case in which a patient’s risk of recurring breast cancer is predicted by an opaque AI system. We argue that, given the system’s opacity, as well as the (...) possibility of malfunctioning AI systems, practitioners’ inability to check the correctness of their outputs, and the high stakes of such cases, the knowledge of medical practitioners is indeed undermined. They are lucky to form true beliefs based on the AI systems’ outputs, and knowledge is incompatible with luck. We supplement this claim with a specific version of the safety condition on knowledge, Safety*. We argue that, relative to the perspective of the medical doctor in our example case, his relevant beliefs could easily be false, and this despite his evidence that the AI system functions reliably. Assuming that Safety* is necessary for knowledge, the practitioner therefore doesn’t know. We address three objections to our proposal before turning to practical suggestions for improving the epistemic situation of medical doctors. (shrink)

6 and 14 recently proposed taxonomies that distinguish between four processing states, based on bottom-up stimulus strength and top-down attentional amplification. The aim of the present study was to empirically test these processing states using the priming paradigm. Our results showed that attention and stimulus strength significantly modulated priming effects: either receiving top-down attention or possessing sufficient bottom-up strength was a prerequisite for a stimulus to elicit priming. When both top-down attention and sufficient bottom-up strength were present, the priming effect (...) was boosted. The origins of the observed priming effects also varied between different processing states. We can conclude that our empirical study using the priming paradigm confirmed the presence of four processing states, which displayed a differential pattern of response priming effects and differential origins of the response priming effects. (shrink)

In this paper, we consider reducts of p-adically closed fields. We introduce a notion of shadows: sets Mf={∈K2∣|y|=|f|}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_f = \{ \in K^2 \mid |y| = |f|\}}$$\end{document}, where f is a semi-algebraic function. Adding symbols for such sets to a reduct of the ring language, we obtain expansions of the semi-affine language where multiplication is nowhere definable, thus giving a negative answer to a question posed by Marker, Peterzil and Pillay. The second (...) main result of this paper is the fact that in p-adic fields, full multiplication becomes definable if we add a rational function to the semi-affine language. (shrink)