Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, machine learning results (...) in solving mathematical tasks have shown early promise that deep artificial neural networks could learn symbolic mathematical processing. In this paper, I analyze the theoretical prospects of such neural networks in proving mathematical theorems. In particular, I focus on the question how such AI systems could be incorporated in practice to theorem proving and what consequences that could have. In the most optimistic scenario, this includes the possibility of autonomous automated theorem provers (AATP). Here I discuss whether such AI systems could, or should, become accepted as active agents in mathematical communities. (shrink)

I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...) that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects. (shrink)

Linnebo in 2018 argues that abstract objects like numbers are “thin” because they are only required to be referents of singular terms in abstraction principles, such as Hume's principle. As the specification of existence claims made by analytic truths (the abstraction principles), their existence does not make any substantial demands of the world; however, as Linnebo notes, there is a potential counter-argument concerning infinite regress against introducing objects this way. Against this, he argues that vicious regress is avoided in the (...) account of arithmetic based on Hume's principle because we are specifying numbers in terms of the concept of equinumerosity, or its ordinal equivalent. But far from being only a matter for philosophy, this implies a distinct empirical prediction: in cognitive development, the principle of equinumerosity is primary to number concepts. However, by analysing and expanding on the bootstrapping theory of Carey in 2009, I argue in this paper that there are good reasons to think that the development could be the other way around: possessing numerosity concepts may precede grasping the principle of equinumerosity. I propose that this analysis of early numerical cognition can also help us understand what numbers as thin objects are like, moving away from Platonist interpretations. (shrink)

Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...) any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system. Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge. (shrink)

The causal theory of action has been the standard view in the philosophy of action and mind. In this chapter, I will present responses to two challenges to the theory. The first says, basically, that there is no positive argument in favour of the causal theory, as the only reason that supports it consists in the apparent lack of tenable alternatives. The second challenge says that the theory fails to capture the phenomenon of agency, as it reduces activity to mere (...) happenings (events and event-causal processes). This is often referred to as the problem of "disappearing agency". My main aim is to show that there is no problem of disappearing agency, and we will see that my response to the first challenge will be conducive to this end. I will present a positive argument for the causal theory on the basis of considerations concerning the metaphysics of agency, and I will suggest that we "own" the agency that springs from our mental states and events "by default". (shrink)

Why would we want to develop artificial human-like arithmetical intelligence, when computers already outperform humans in arithmetical calculations? Aside from arithmetic consisting of much more than mere calculations, one suggested reason is that AI research can help us explain the development of human arithmetical cognition. Here I argue that this question needs to be studied already in the context of basic, non-symbolic, numerical cognition. Analyzing recent machine learning research on artificial neural networks, I show how AI studies could potentially shed (...) light on the development of human numerical abilities, from the proto-arithmetical abilities of subitizing and estimating to counting procedures. Although the current results are far from conclusive and much more work is needed, I argue that AI research should be included in the interdisciplinary toolbox when we try to explain the development and character of numerical cognition and arithmetical intelligence. This makes it relevant also for the epistemology of mathematics. (shrink)

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez, I propose one particular conceptual metaphor, the Process → Object Metaphor, as a key element in understanding the development of mathematical thinking.

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...) models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order (classical) systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

Following Marr’s famous three-level distinction between explanations in cognitive science, it is often accepted that focus on modeling cognitive tasks should be on the computational level rather than the algorithmic level. When it comes to mathematical problem solving, this approach suggests that the complexity of the task of solving a problem can be characterized by the computational complexity of that problem. In this paper, I argue that human cognizers use heuristic and didactic tools and thus engage in cognitive processes that (...) make their problem solving algorithms computationally suboptimal, in contrast with the optimal algorithms studied in the computational approach. Therefore, in order to accurately model the human cognitive tasks involved in mathematical problem solving, we need to expand our methodology to also include aspects relevant to the algorithmic level. This allows us to study algorithms that are cognitively optimal for human problem solvers. Since problem solving methods are not universal, I propose that they should be studied in the framework of enculturation, which can explain the expected cultural variance in the humanly optimal algorithms. While mathematical problem solving is used as the case study, the considerations in this paper concern modeling of cognitive tasks in general. (shrink)

Embodied cognition postulates a bi-directional link between the human body and its cognitive functions. Whether this holds for higher cognitive functions such as problem solving is unknown. We predicted that arm movement manipulations performed by the participants could affect the problem-solving solutions. We tested this prediction in quantitative reasoning tasks that allowed two solutions to each problem. In two studies with healthy adults, we found an effect of problem-congruent movements on problem solutions. Consistent with embodied cognition, sensorimotor information gained via (...) right or left arm movements affects the solution in different types of problem-solving tasks. (shrink)

How is knowledge of geometry developed and acquired? This central question in the philosophy of mathematics has received very different answers. Spelke and colleagues argue for a “core cognitivist”, nativist, view according to which geometric cognition is in an important way shaped by genetically determined abilities for shape recognition and orientation. Against the nativist position, Ferreirós and García-Pérez have argued for a “culturalist” account that takes geometric cognition to be fundamentally a culturally developed phenomenon. In this paper, I argue that (...) when understood as moderate versions supported by the state-of-the-art research, the nativist and culturalist views are in fact possible to reconcile. While Ferreirós and García-Pérez present the work of Spelke and colleagues as implying that geometric cognition is genetically determined, I argue that they fail to appreciate the role that Spelke and colleagues see for cultural factors. On this basis, I provide theoretical and terminological clarifications and show that moderate versions of the nativist and culturalist view are in fact consistent with each other. I then propose a unifying theoretical framework for future study that can integrate the two accounts in ontogeny by moving beyond the crude nature (nativism) vs. nurture (culturalism) dichotomy. (shrink)

Dass wir durch Wahrnehmung einen Zugang zur materiellen Welt haben, scheint selbstverständlich zu sein. Und dass die visuelle Wahrnehmung dabei einen prominenten Platz einnimmt, scheint ebenfalls selbstverständlich zu sein. Doch was genau sehen wir: die Gegenstände selbst oder bloß ihre wahrnehmbaren Eigenschaften? Wie gelingt es uns überhaupt, etwas zu sehen? Können wir allein aufgrund von optischen und physiologischen Vorgängen etwas sehen, oder setzt das Sehen bereits Begriffe voraus, mithilfe derer wir etwas als etwas sehen können? -/- Diese Fragen, die in (...) der gegenwärtigen Wahrnehmungs- und Erkenntnistheorie ausgiebig erörtert werden, waren bereits in der Frühen Neuzeit Gegenstand intensiver Debatten. In vielfacher Hinsicht legten die Diskussionen im 17. und 18. Jahrhundert sogar die Grundlage für heutige Theorien, da sie zum einen die Probleme in aller Schärfe benannten, zum anderen aber auch Lösungsstrategien vorlegten, die auch heute noch von Bedeutung sind. -/- Der Band soll diese Debatten (von Descartes bis Reid) neu erschließen und einem breiten philosophisch interessierten Publikum zugänglich machen. Es soll gezeigt werden, dass die Frühe Neuzeit kein ehrwürdiges Museum der Philosophiegeschichte ist, sondern eine äußerst produktive und anregende philosophische Epoche, die zu einem Dialog einlädt. (shrink)

Advanced old age has been characterized as a biologically highly vulnerable life phase. Biological, morbidity-, and cognitive impairment-related factors play an important role as mortality predictors among very old adults. However, it is largely unknown whether previous findings confirming the role of different wellbeing domains for mortality translate to survival among the oldest-old individuals. Moreover, the distinction established in the wellbeing literature between hedonic and eudaimonic wellbeing as well as the consideration of within-person variability of potentially relevant mortality predictors has (...) not sufficiently been addressed in prior mortality research. In this study, we examined a broad set of hedonic and eudaimonic wellbeing indicators, including their levels, their changes, as well as their within-person variability, as predictors of all-cause mortality in a sample of very old individuals. We used data from the LateLine study, a 7-year longitudinal study based on a sample of n = 124 individuals who were living alone and who were aged 87–97 years at baseline. Study participants provided up to 16 measurement occasions between 2009 and 2016. Dates of death were available for 118 individuals who had deceased between 2009 and 2021. We ran longitudinal multilevel structural equation models and specified between-person level differences, within-person long-term linear change trends, as well as the “detrended” within-person variability in three indicators of hedonic and four indicators of eudaimonic wellbeing as all-cause mortality predictors. Controlling for age, gender, education, and physical condition and testing our sets of hedonic and eudaimonic indictors separately in terms of their mortality impact, solely one eudaimonic wellbeing indicator, namely, autonomy, showed significant effects on survival. Surprisingly, autonomy appeared “paradoxically” related with mortality, with high individual levels and intraindividual highly stable perceptions of autonomy being associated with a shorter residual lifetime. Thus, it seems plausible that accepting dependency and changing perceptions of autonomy over time in accordance with objectively remaining capabilities might become adaptive for survival in very old age. (shrink)

The Turing test has a peculiar status in the artificial intelligence (AI) research community. On the one hand, it is presented as an important topic in virtually every AI textbook, and the research direction focused on developing AI systems that behave in human-like fashion is standardly called the “Turing test approach”. On the other hand, reports of computer programs passing the Turing test have had relatively little effect. Does this mean that the Turing test is no longer relevant as a (...) test, doomed to be a theoretical notion with little connection to AI practice? In this paper, I argue that there is one problem in particular with common traditional versions of the Turing test, namely their focus on deception. The criterion for passing the Turing test is standardly connected to an AI system’s ability to deceive the interrogator about its identity. But why should we connect intelligence to the ability deceive? Here I present a revised version of an intelligence test that is not based on deception. In what I call the Community-based intelligence test (CBIT), an AI is introduced to a community of human subjects. If after a sufficient number of interactions within that community the humans are not able to identify the AI system as a computer, it is considered to have passed CBIT. I discuss whether that should be enough to ascribe intelligence to the AI, and if not, what more would be needed? (shrink)

How do we acquire the notions of cardinality and cardinal number? In the (neo-)Fregean approach, they are derived from the notion of equinumerosity. According to some alternative approaches, defended and developed by Husserl and Parsons among others, the order of explanation is reversed: equinumerosity is explained in terms of cardinality, which, in turn, is explained in terms of our ordinary practices of counting. In their paper, ‘Cardinality, Counting, and Equinumerosity’, Richard Kimberly Heck proposes that instead of equinumerosity or counting, cardinality (...) is derived from a cognitively earlier notion of _just as many_. In this paper, we assess Heck’s proposal in terms of contemporary theories of number concept acquisition. Focusing on bootstrapping theories, we argue that there is no evidence that the notion of _just as many_ is cognitively primary. Furthermore, since the acquisition of cardinality is an enculturated process, the cognitive primariness of these notions, possibly including _just as many_, depends on various external cultural factors. Therefore, being possibly a cultural construction, _just as many_ could be one among several notions used in the acquisition of cardinality and cardinal number concepts. This paper thus challenges those accounts which seek for a fundamental concept underlying all aspects of numerical cognition. (shrink)

In Pantsar, an outline for an empirically feasible epistemological theory of arithmetic is presented. According to that theory, arithmetical knowledge is based on biological primitives but in the resulting empirical context develops an essentially a priori character. Such contextual a priori theory of arithmetical knowledge can explain two of the three characteristics that are usually associated with mathematical knowledge: that it appears to be a priori and objective. In this paper it is argued that it can also explain the third (...) one: why arithmetical knowledge appears to be necessary. A Kripkean analysis of necessity is used as an example to show that a proper analysis of the relevant possible worlds can explain arithmetical necessity in a sufficiently strong form. (shrink)

Upregulation of implicit positive affect (PA) can act as a mechanism to deal with negative affect. Two studies tracked temporal changes in positive and negative affect (NA) assessed by self-report and the Implicit Positive and Negative Affect Test (IPANAT; Quirin, Kazén, & Kuhl, 2009). Study 1 observed the predicted increases in implicit PA after exposure to a threat-related film clip, which correlated positively with the speed of recognising a happy face among an angry crowd. Study 2 replicated increases in implicit (...) PA after exposition to the same film clip, and showed that such increases were enhanced by priming self-referential stimuli. The findings are discussed against the background of personality systems interaction (PSI) theory (Kuhl, 2000, 2001), which emphasises the role of the implicit self in affect regulation. (shrink)

Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support the radical enactivist view. (...) I argue that although more research is needed, it is at least possible to develop the REC position consistently with the state-of-the-art empirical research on the development of arithmetical cognition. After this, I move the focus to the question whether the radical enactivist account can explain the objectivity of arithmetical knowledge. Against the realist view suggested by Hutto, I argue that objectivity is best explained through analyzing the way universal proto-arithmetical abilities determine the development of arithmetical cognition. (shrink)

One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. I will (...) show that since the development of arithmetic is (partly) determined by biologically evolved proto-arithmetical abilities, arithmetical knowledge can be understood as maximally intersubjective. This maximal intersubjectivity, I argue, can lead to the experience of objectivity, thus providing a solution to the problem of reconciling non-platonist philosophy of mathematics with the (apparent) objectivity of mathematical knowledge. (shrink)

In this conceptual analysis contribution to the special issue on radical embodied cognition, we discuss how embodied cognition can exist with and without representations. We explore this concept through the lens of judgment and decision making in sports (JDMS). Embodied cognition has featured in many investigations of human behavior, but no single approach has emerged. Indeed, the very definitions of the concepts “embodiment” and “cognition” lack consensus, and consequently the degree of “radicalism” is not universally defined, either. In this paper (...) we address JDMS not from a rigid theoretical perspective, but from two embodied cognition approaches: one that assumes there is mediation between the athlete and the environment through mental representation, and another that assumes direct contact between the athlete and the environment and thus no need for mental representation. Importantly, our aim was not to arrive at a theoretical consensus or set up a competition between approaches, but rather to provide a legitimate scientific discussion about how to explain empirical results in JDMS from contrasting perspectives within embodied cognition. For this, we first outline the definitions and constructs of embodied cognition in JDMS. Second, we detail the theory underlying the mental representation and direct contact approaches. Third, we comment on two published research papers on JDMS, one selected by each of us: (1) Correia et al. (2012) and (2) Pizzera (2012). Fourth, following the interpretation of the empirical findings of these papers, we present a discussion on the commonalities and divergences of these two perspectives and the consequences of using one or the other approach in the study of JDMS. (shrink)

Eating disorders are evolutionarily novel conditions that lead to some of the highest mortality rates of all psychiatric disorders. Several evolutionary hypotheses have been proposed for eating disorders, but only the intrasexual competition hypothesis is extensively supported by evidence. We present the mismatch hypothesis as a necessary extension to the current theoretical framework of eating disorders. This hypothesis explains the evolutionarily novel adaptive metaproblem that has arisen when mating motives and readily available food rewards conflict with one another. This situation (...) is exacerbated in contemporary environments characterized by sedentary lifestyles, caloric surplus and the ubiquity of social comparisons that take place via social media. Our psychoneuroimmunological model connects ultimate-level causation with proximate mechanisms by showing how the adaptive metaproblem between mating motives and food rewards leads to chronic stress and, further, to disordered eating. Chronic stress causes neuroinflammation, which increases susceptibility to OCD-like behaviors that typically co-occur with eating disorders. Chronic stress upregulates the serotonergic system and causes dysphoric mood in patients with restricting-type anorexia nervosa. Dieting, however, reduces serotonin levels and dysphoric mood, leading to a vicious serotonergic-homeostatic stress/starvation cycle whereby cortisol and neuroinflammation increase through stringent dieting. Between-individual and within-individual variation in eating disorders partially arises from (co)variation in gut microbiota and stress responsivity, which influence neuroinflammation and the serotonergic system. In binge-related eating disorders, even a short period of fasting drops serotonin levels, a state alleviated by binge eating. Eating disorder treatments should aim to reduce the chronic stress, neuroinflammation, stress responsivity and gut dysbiosis that fuel the disorders. We review the advances that have been made in recent years in understanding how to best treat eating disorders, outlining directions for future clinical research. Connecting ultimate causes with proximate mechanisms and treating biopsychosocial causes rather than manifest symptoms will enable more effective and sophisticated long-term interventions for the millions of people who suffer from eating disorders. (shrink)

This paper describes the interventions by the International Committee of the Red Cross to support a hospital in Afghanistan during the mid 1990s. We present elements of the interventions introduced in Ghazni, Afghanistan, and consider a number of ethical issues stimulated by this analysis. Ethical challenges arise whenever humanitarian interventions to deal with complex political emergencies are undertaken: among those related to the case study presented are questions concerning: a) whether humanitarian support runs the risk of propping up repressive and (...) irresponsible governments; b) whether humanitarian relief activities can legitimately focus on a narrow range of interventions, or need to broaden to address the range of challenges facing the health system; and c) whether sustainability and quality of care should be routinely considered in such settings. The paper concludes by highlighting the value of case studies, suggesting mechanisms for extending transparency and accountability in humanitarian health interventions, and highlighting the need of contextualising humanitarian work if the interventions are to be successful. (shrink)

RNAs have emerged as a major target for diagnostics and therapeutics approaches. Regulatory nonprotein‐coding RNAs (ncRNAs) in particular display remarkable versatility. They can fold into complex structures and interact with proteins, DNA, and other RNAs, thus modulating activity, localization, or interactome of multi‐protein complexes. Thus, ncRNAs confer regulatory plasticity and represent a new layer of regulatory control. Interestingly, long noncoding RNAs (lncRNAs) tend to acquire complex secondary and tertiary structures and their function—in many cases—is dependent on structural conservation rather than (...) primary sequence conservation.Whereas for many proteins, structure and its associated function are closely connected, for lncRNAs, the structural domains that determine functionality and its interactome are still not well understood. Numerous approaches for analyzing the structural configuration of lncRNAs have been developed recently. Here, will provide an overview of major experimental approaches used in the field, and discuss the potential benefit of using combinatorial strategies to analyze lncRNA modes of action based on structural information. (shrink)

1. Bd. Die Grundlagen. Die spezielle Relativitätstheorie.- 2. Bd. Die allgemeine Relativitätstheorie.

In this paper, I study the kind of questions we can ask about the existence of numbers. In addition to asking whether numbers exist, and how, I argue that there is also a third relevant question: why numbers exist. In platonist and nominalist accounts this question may not make sense, but in the psychologist account I develop, it is as well-placed as the other two questions. In fact, there are two such why-questions: the causal why-question asks what causes numbers to (...) exist and the teleological why-question asks for what purpose numbers exist. I argue that in a psychologist constructivist account, in which numbers are understood to exist as referents of a particular type of culturally shared concepts, both why-questions can get plausible answers. (shrink)

Democracy has come under pressure in many countries in recent years. Authoritarian tendencies, populism and the cult of leadership threaten pluralistic societies in Europe and other parts of the world. But democracy is more than just a method of finding a majority; it is inextricably linked to the fight against oppression and injustice in all contexts of life. Especially in times of democratic crisis, it is necessary to focus on its core aspects. The political thinking of French philosopher and writer (...) Albert Camus, who died in 1960, offers the basis for a redefinition of democracy that is linked to and dependent on rebellion. From his reflections, a radical theory of democracy can be derived that is based on the absurdity of the world, its incompleteness, revolt and resistance to authoritarianism, on doubt, dialogue and foreignness. (shrink)

In this article, which is assembled from interviews, the main issues of in silico medicine, present and future, are discussed by three scientists who are directly involved in the implementation and development of in silico techniques.

This volume provides the reader with exclusive insights into Ernest Sosa’s latest ideas as well as main aspects of his philosophical work of the last 50 years. Ernest Sosa, one of the most distinguished contemporary philosophers, is best known for his ground-breaking work in epistemology, and has also contributed greatly to metaphysics, metaphilosophy and philosophy of language.

European Journal of Political Theory, Volume 21, Issue 1, Page 178-186, January 2022. Few debates in political theory are challenged as much by the constant change of their empirical subject as those about democracy in the European Union. With A Republican Europe of States, Richard Bellamy responds to the EU’s post-Lisbon era, which has been characterized by the euro crisis, conflicts over migration, the rise of Euroscepticism and Brexit. Keeping an eye on these contextual conditions and the related legal and (...) political transformations, he has developed a general theory of international democracy aimed at securing non-domination between peoples and between citizens and their representatives at the international level, and elaborated its implications for the EU. The result is a distinctive version of demoi-cracy, whose firm centring on the nation-state as the natural locus of democracy is likely to be controversially discussed. In this article, I raise some critical considerations regarding the design of demoi-cratic institutions, the adequate understanding of EU citizenship and the normative credentials of differentiated integration. (shrink)