This paper summarizes (in German) recent tendencies in the philosophy of the life sciences.

The current humanitarian use of drones is focused on two applications: disaster mapping and medical supply delivery. In response to the growing interest in drone deployment in the aid sector, we sought to develop a resource to support value sensitivity in humanitarian drone activities. Following a bottom-up approach encompassing a comprehensive literature review, two empirical studies, a review of guidance documents, and consultations with experts, this work illuminates the nature and scope of ethical challenges encountered by humanitarian organizations embarking upon (...) innovation programmes. The Framework for the Ethics Assessment of Humanitarian Drones (FEAHD) identifies five values and five key questions related to ethical considerations along the decision chain of humanitarian drone activities. It fills a gap between high-level, principle-based guidance related to humanitarian innovation, and detailed operation-oriented checklists for projects involving the use of drones. In this way, the FEAHD contributes to support value sensitivity in the humanitarian use of drones. (shrink)

Many philosophers of science think that most laws of nature (even those of fundamental physics) are so called ceteris paribus laws, i.e., roughly speaking, laws with exceptions. Yet, the ceteris paribus clause of these laws is problematic. Amongst the more infamous difficulties is the danger that 'For all x: Fx ⊃ Gx, ceteris paribus' may state no more than a tautology: 'For all x: Fx ⊃ Gx, unless not'. One of the major attempts to avoid this problem (and others concerning (...) ceteris paribus laws) is to claim that the subject matter of laws are ascriptions of dispositions, powers, capacities etc., and not the regular behaviour we find in nature. That we do not know whether the cetera are paria in a specific situation does not matter to the dispositionalist because the objects have the disposition regardless of the circumstances. The defence of the latter claim is that dispositions can be instantiated without being manifested. Hence, the laws that ascribe dispositions are strict and it looks as if they do not face the above mentioned problems of ceteris paribus laws. In this essay I attempt to show that these assumptions are wrong. I hope to illustrate that not only does the ceteris paribus clause reoccur inside the dispositions, moreover, there are laws—laws about non-fundamental entities with instable dispositions—which bear a ceteris paribus clause that cannot be hidden in a disposition. (shrink)

The role that need plays in dealing with problems of distributive justice is examined in a series of vignette studies. Among other things, it becomes clear that impartial observers make gradual assessments of justice that depend on the extent to which the observed individuals are endowed with a good. If it is known how high their need for that good is, the assessments are made relative to this reference point. In addition, impartial decision-makers make hypothetical distribution decisions that take into (...) account need, productivity, and accountability. The need of individuals is partially compensated even if they have contributed less to the available amount than they themselves require. However, the willingness to do so decreases if they are accountable for needing more than others or for having contributed less than others. Lastly, both impartial observers and impartial decision-makers distinguish between different types of needs, the fulfillment of which is given different levels of importance. (shrink)

Distributive justice deals with allocations of goods and bads within a group. Different principles and results of distributions are seen as possible ideals. Often those normative approaches are solely framed verbally, which complicates the application to different concrete distribution situations that are supposed to be evaluated in regard to justice. One possibility in order to frame this precisely and to allow for a fine-grained evaluation of justice lies in formal modelling of these ideals by metrics. Choosing a metric that is (...) supposed to map a certain ideal has to be justified. Such justification might be given by demanding specific substantiated axioms, which have to be met by a metric. This paper introduces such axioms for metrics of distributive justice shown by the example of needs-based justice. Furthermore, some exemplary metrics of needs-based justice and a three dimensional method for visualisation of non-comparative justice axioms or evaluations are presented. Therewith, a base worth discussing for the evaluation and modelling of metrics of distributive justice is given. (shrink)

Although artificial intelligence has been given an unprecedented amount of attention in both the public and academic domains in the last few years, its convergence with other transformative technologies like cloud computing, robotics, and augmented/virtual reality is predicted to exacerbate its impacts on society. The adoption and integration of these technologies within industry and manufacturing spaces is a fundamental part of what is called Industry 4.0, or the Fourth Industrial Revolution. The impacts of this paradigm shift on the human operators (...) who continue to work alongside and symbiotically with these technologies in the industry bring with it novel ethical issues. Therefore, how to design these technologies for human values becomes the critical area of intervention. This paper takes up the case study of robotic AI-based assistance systems to explore the potential value implications that emerge due to current design practices and use. The design methodology known as Value Sensitive Design (VSD) is proposed as a sufficient starting point for designing these technologies for human values to address these issues. (shrink)

We present a vignette study conducted with a quota sample of the German population (n = 400). Subjects had to redistribute a good between two hypothetical persons who contributed equally to the available amount but differed in quantity needed and the reason for their neediness. On a within-subjects level, we tested for the effects of need, accountability, and resource availability on their third-party distribution decisions. Between subjects, we further varied the kinds of needs: The persons either needed the good as (...) a means to survive, to live a decent life, to participate in society, or to be autonomous. Despite equal productivity, the mean share allocated to the needier person was significantly higher than an equal share. However, this share turned out significantly smaller when the needier person was accountable for needing more than the other. Nonetheless, even if accountable, the needier person still got a share larger than their contribution would suggest. When there was a surplus of resources, the needier person got an even higher share than when resources were scarce. (shrink)

In Pantsar (2014), 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 (...) ... (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)

Der Aufsatz beschäftigt sich am Beispiel des deutschen "Kopftuchstreits" mit der rechtlich-politischen Auseinandersetzung um subjektive Rechte innerhalb des liberalen Rechtsstaats. Wie Christoph Menke in seiner Deutung der für den politischen Liberalismus wesentlichen politischen Konflikte gezeigt hat, bezieht sich diese Auseinandersetzung vorrangig auf zwei Fragen: Wer sollte Anspruch darauf genießen, ein politisches Subjekt zu sein, das heißt, als Gleiche oder Gleicher berücksichtigt zu werden? Welche Ansprüche politischer Subjekte könneen als schützenswerte Verwirklichung subjektiver Rechte gelten? Der vorliegende Beitrag beschäftigt sich vorwiegend mit (...) der Frage, wie die politischen Konflikte des letztgenannten Typs auf die rechtliche Auseinandersetzung um Grundrechte abfärben. Damit wende ich mich gegen ein Verständnis der Grundrechte, das diese als Garant der ethischen Neutralität eines liberalen Gemeinwesens ansieht. Ich möchte zeigen, dass der Sinn subjektiver Rechte in der liberalen Demokratie zwar unter anderem genau darin besteht, dass sie partikulare ethische Wertvorstellungen neutralisieren und die Bürgerinnen und Bürger innerhalb eines vernünftigen Rahmens vor Unterdrückung schützen. Wie eine Analyse der Entscheidungen des Bundesverfassungsgerichts (BVerfG) zum "Kopftuchstreit" zeigt, wird diese Funktion aber stets zugleich durch die partikulare Interpretation gleicher Rechte unterminiert. Dies bezeichne ich als die Dekonstruktion der Neutralität, die sich im Recht vollzieht. (shrink)

Previous research in Explainable Artificial Intelligence (XAI) suggests that a main aim of explainability approaches is to satisfy specific interests, goals, expectations, needs, and demands regarding artificial systems (we call these “stakeholders' desiderata”) in a variety of contexts. However, the literature on XAI is vast, spreads out across multiple largely disconnected disciplines, and it often remains unclear how explainability approaches are supposed to achieve the goal of satisfying stakeholders' desiderata. This paper discusses the main classes of stakeholders calling for explainability (...) of artificial systems and reviews their desiderata. We provide a model that explicitly spells out the main concepts and relations necessary to consider and investigate when evaluating, adjusting, choosing, and developing explainability approaches that aim to satisfy stakeholders' desiderata. This model can serve researchers from the variety of different disciplines involved in XAI as a common ground. It emphasizes where there is interdisciplinary potential in the evaluation and the development of explainability approaches. (shrink)

The link is to an expanded, English version of this essay.

In this paper, I study how mathematicians are presented in western popular culture. I identify five stereotypes that I test on the best-known modern movies and television shows containing a significant amount of mathematics or important mathematician characters: (1) Mathematics is highly valued as an intellectual pursuit. (2) Little attention is given to the mathematical content. (3) Mathematical practice is portrayed in an unrealistic way. (4) Mathematicians are asocial and unable to enjoy normal life. (5) Higher mathematics is ...

Intellectual humility is an interesting but underexplored disposition. The claim “I am (intellectually) humble” seems paradoxical in that someone who has the disposition in question would not typically volunteer it. There is an explanatory gap between the meaning of the sentence and the meaning the speaker expresses by uttering it. We therefore suggest analyzing intellectual humility semantically, using a psycholexical approach that focuses on both synonyms and antonyms of ‘intellectual humility’. We present a thesaurus-based method to map the semantic space (...) of intellectual humility as a heuristic to support philosophical and psychological analysis of this disposition. We find three semantic clusters that compose intellectual humility: the sensible self, the discreet self, and the inquisitive self; likewise, we find three clusters that compose its contraries: the overrated self, the underrated other, and the underrated self. (shrink)

Sind die Menschenrechte primär Ausdruck einer politischen Praxis und die Idee der Menschenrechte eine Art „Überbau“, den die Praxis epiphänomenal hervorbringt? Oder ist die Praxis der Menschenrechte das Ergebnis der Verwirklichung einer normativen Idee, die unabhängig von ihr existiert? Ist die Idee der Menschenrechte die Bedingung dafür, dass es die Praxis der Menschenrechte geben kann? Oder gibt es einen Vorrang der Praxis vor der Idee? In meinem Aufsatz argumentiere ich für zwei These: 1. These: Menschenrechte sind prinzipiell unabhängig von jeder (...) bestehenden rechtlichpolitischen Praxis und sind zugleich untrennbar an bestimmte rechtlich-politische Praktiken geknüpft. Darin besteht der konstitutive Widerspruch der Menschenrechte. 2. These: Aus diesem Widerspruch folgt nicht, dass wir aufhören sollten über Menschenrechte nachzudenken und eine Politik der Menschenrechte anzustreben. Der Widerspruch hat keine lähmende Wirkung, sondern ist theoretisch und praktisch produktiv. Um diese Thesen zu plausiblisieren, werde ich zunächst einige Grundzüge von Arendts Diskussion der Menschenrechte rekapitulieren (Abschnitt 2) und ihr Postulat eines den Menschenrechten vorgelagerten „Rechts, Rechte zu haben“ diskutieren (Abschnitt 3). Ausgehend von einer kritischen Diskussion der diskurstheoretischen Weiterentwicklung von Arendts These zu einem „Recht auf Rechtfertigung“ im diskurstheoretischen Konstruktivismus von Seyla Benhabib und Rainer Forst (Abschnitt 4) werde ich einen rechtfertigungstheoretischen Dekonstruktivismus vorstellen, der das Verhältnis von Praxis und Idee der Menschenrechte als produktiven Widerspruch fasst (Abschnitt 5). (shrink)

Abstract In the new millennium there have been important empirical developments in the philosophy of mathematics. One of these is the so-called “Empirical Philosophy of Mathematics”(EPM) of Buldt, Löwe, Müller and Müller-Hill, which aims to complement the methodology of the philosophy of mathematics with empirical work. Among other things, this includes surveys of mathematicians, which EPM believes to give philosophically important results. In this paper I take a critical look at the sociological part of EPM as a case study of (...) ... (shrink)

I examine the extent to which God is inscrutable to human reason in Kant's critical philosophy. I argue that Kant's view here is much more radical than the rationalist commonplace that we cannot grasp how divine perfection is compatible with the existence of (apparent) imperfections. In Kant's considered view, we are absolutely incapable of accurately representing God's nature in any minimally determinate way: when we try to go beyond the empty idea of a mere 'something', we inevitably distort the nature (...) of God in an anthropomorphic fashion. The reason for this radical inscrutability of God is that our discursive intellect with its finite conceptual resources cannot capture the nature of a supremely perfect being. Our only way to form a legitimate, positive notion of God is by means of an analogy with the features that we objectively cognize in finite beings. (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)

Intellectual humility can be broadly construed as being conscious of the limits of one’s existing knowledge and capable to acquire more knowledge, which makes it a key virtue of the information age. However, the claim “I am (intellectually) humble” seems paradoxical in that someone who has the disposition in question would not typically volunteer it. There is an explanatory gap between the meaning of the sentence and the meaning the speaker ex- presses by uttering it. We therefore suggest analyzing intellectual (...) humility semantically, using a psycholexical approach that focuses on both synonyms and antonyms of ‘intellectual humili- ty’. We present a thesaurus-based methodology to map the semantic space of intellectual hu- mility and the vices it opposes as a heuristic to support philosophical and psychological anal- ysis of this disposition. We performed the mapping both in English and German in order to test for possible cultural differences in the understanding of intellectual humility. In both lan- guages, we find basically the same three semantic dimensions of intellectual humility (sensi- bility, discreetness, and knowledge dimensions) as well as three dimensions of its related vic- es (self-overrating, other-underrating and dogmatism dimensions). The resulting semantic clusters were validated in an empirical study with English (n=276) and German (n=406) par- ticipants. We find medium to high correlations (0.54-0.72) between thesaurus similarity and perceived similarity, and we can validate the labels of the three dimensions identified in the study. But we also find indications of the limitations of the thesaurus methodology in terms of cluster plausibility. We conclude by discussing the importance of these findings for construct- ing psychometric scales for intellectual humility. (shrink)

Moral philosophers and psychologists often assume that people judge morally lucky and morally unlucky agents differently, an assumption that stands at the heart of the Puzzle of Moral Luck. We examine whether the asymmetry is found for reflective intuitions regarding wrongness, blame, permissibility, and punishment judg- ments, whether people’s concrete, case-based judgments align with their explicit, abstract principles regarding moral luck, and what psychological mechanisms might drive the effect. Our experiments produce three findings: First, in within-subjects experiments favorable to reflective (...) deliberation, the vast majority of people judge a lucky and an unlucky agent as equally blameworthy, and their actions as equally wrong and permissible. The philosophical Puzzle of Moral Luck, and the challenge to the very possibility of systematic ethics it is frequently taken to engender, thus simply do not arise. Second, punishment judgments are significantly more outcome- dependent than wrongness, blame, and permissibility judgments. While this constitutes evidence in favor of current Dual Process Theories of moral judgment, the latter need to be qualified: punishment and blame judgments do not seem to be driven by the same process, as is commonly argued in the literature. Third, in between-subjects experiments, outcome has an effect on all four types of moral judgments. This effect is mediated by negligence ascriptions and can ultimately be explained as due to differing probability ascriptions across cases. (shrink)

The idea of levels of organization plays a central role in the philosophy of the life sciences. In this article, I first examine the explanatory goals that have motivated accounts of levels of organization. I then show that the most state-of-the-art and scientifically plausible account of levels of organization, the account of levels of mechanism proposed by Bechtel and Craver, is fundamentally problematic. Finally, I argue that the explanatory goals can be reached by adopting a deflationary approach, where levels of (...) organization give way to more well-defined and fundamental notions, such as scale and composition. (shrink)

The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical (...) ability to arithmetic proper. I argue that enculturation based on neural reuse provides a theoretically sound and fruitful framework for explaining this development. However, I show that a comprehensive explanation must be based on valid theoretical distinctions and involve several stages in the development of arithmetical knowledge. I provide an account that meets these challenges and thus leads to a better understanding of the subject of enculturation. (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)

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)

Although there is an ongoing controversy in philosophy of science about so called ceteris paribus laws that is, roughly, about laws with exceptionsóa fundamental question about those laws has been neglected (ß2). This is due to the fact that this question becomes apparent only if two different readings of ceteris paribus clauses in laws have been separated. The first reading of ceteris paribus clauses, which I will call the epistemic reading, covers applications of laws: predictions, for example, might go wrong (...) because we do not know all the relevant factors which are causally effective in relevant situation. The second reading, which I will call the metaphysical reading, is concerned with the laws themselves and their possible exceptions (ß3). It is this latter readingóand the funda- mental question associated with itówhich has been neglected due to the confusion of the two readings (ß4): if we leave epistemic issues aside is there at all conceptual space left for a notion of laws of nature which allows the laws themselves to have exceptions? I call a law with exceptions in this sense, if such there is, a real ceteris paribus law. To tackle this question, I distinguish grounded laws from non-grounded laws (ß5). A grounded law is, roughly, a law about structured entities where the properties of the parts of that structure figure themselves in laws of nature (ß6). I will claim that, since the substructure of such an entity can be damaged, grounded laws themselves can face exceptions. Hence, they are candidates to be real (metaphysical) ceteris paribus laws in the sense of my central question. I will discuss grounded laws and their exceptions in detail (ß7, ß8, ß9). For reasons of space, the further question whether we can even have a notion of fun- damental (non-grounded) laws that allows for exceptions cannot be discussed here. I will, however, give a positive answer and also outline how I have argued for that claim elsewhere (ß10). (shrink)

Tutkin tässä artikkelissa Kurt Gödelin epätäydellisyysteoreemojen tulkintoja filosofiassa. Aihepiiri kattaa valtavan määrän eri tulkintoja tekoälystä fysiikkaan ja runouteen asti. Osoitan, että kriittisesti tarkasteltuna kaikki radikaalit epätäydellisyysteoreemojen sovellukset ovat virheellisiä.

Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical (...) knowledge developed in such a way cannot be totally conceptual in the sense relevant to the philosophy of arithmetic, but neither can arithmetic understood to be empirical. Rather, we need to develop a contextual a priori notion of arithmetical knowledge that preserves the special mathematical characteristics without ignoring the roots of arithmetical cognition. Such a contextual a priori theory is shown not to require any ontologically problematic assumptions, in addition to fitting well within a standard framework of general epistemology. (shrink)

Robustness is often presented as a guideline for distinguishing the true or real from mere appearances or artifacts. Most of recent discussions of robustness have focused on the kind of derivational robustness analysis introduced by Levins, while the related but distinct idea of robustness as multiple accessibility, defended by Wimsatt, has received less attention. In this paper, I argue that the latter kind of robustness, when properly understood, can provide justification for ontological commitments. The idea is that we are justified (...) in believing that things studied by science are real insofar as we have robust evidence for them. I develop and analyze this idea in detail, and based on concrete examples show that it plays an important role in science. Finally, I demonstrate how robustness can be used to clarify the debate on scientific realism and to formulate new arguments. (shrink)

Is justice (merely) an expression of particular values or is it to be understood as a (universal) cross-cultural standard of validity? Following the ideas of Jacques Derrida, this book provides a new answer to this question: Justice is to be explained as a process of deconstruction. To arrive at this conclusion, I proceed from a critical discussion of Martin Heidegger's approach to social philosophy in Being and Time which I connect with a detailed analysis of the implications of Derrida's writings (...) on practical philosophy aspiring to provide a variety of insights, both critical and constructive, into the cultural and normative foundations of democracy. Thematically, the book bridges the frontiers between the philosophy of law, cultural and social philosophy, ethics and political theory, focusing on fundamental questions of the constitution of normativity, responsibility and justification. In this way, my reading of Heidegger and Derrida aims to shed light on the nature of the political problems that concern our societies today. The file contains the table of contents and the first two (introductory) chapters, the introductions of the remaining chapters, as well as the concluding remarks (in German). (shrink)

I show that the recent account of levels in neuroscience proposed by Craver and Bechtel is unsatisfactory since it fails to provide a plausible criterion for being at the same level and is incompatible with Craver and Bechtel’s account of downward causation. Furthermore, I argue that no distinct notion of levels is needed for analyzing explanations and causal issues in neuroscience: it is better to rely on more well-defined notions such as composition and scale. One outcome of this is that (...) apparent cases of downward causation can be analyzed away. (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.

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 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)

The relationship between psychological states and the brain remains an unresolved issue in philosophy of psychology. One appealing solution that has been influential both in science and in philosophy is Dennett’s concept of the intentional stance, according to which beliefs and desires are real and objective phenomena, but not necessarily states of the brain. A fundamental shortcoming of this approach is that it does not seem to leave any causal role for beliefs and desires in influencing behavior. In this paper, (...) I show that intentional states ascribed from the intentional stance should be seen as real causes, develop this to an independently plausible ontological position, and present a response to the latest interventionist causal exclusion worries. (shrink)

This paper focuses on the hermeneutic of reading text and hearing text.

Though ancient Pyrrhonian skepticism is apparently based on disagreement, this aspect of skepticism has been widely neglected in contemporary discussion on skepticism. The paper provides a rational reconstruction of the skeptical argument from disagreement that can be found in the books of Sextus Empiricus. It is argued that this argument forms a genuine skeptical paradox that has no fully satisfactory resolution. All attempts to resolve it make knowledge or justified belief either intuitively too easy or impossible.

In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.

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)

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)

This paper focuses on Merleau Ponty understanding that the body is the medium of the field of awareness.

This paper focuses on awareness and movement in dzogchen.

This paper focuses on the phenomenology of healing within the awareness field.

This paper focuses on the phenomenology of awareness as natural liberation.

This paper focuses on the phenomenology of desire and fixation.