This essay is a contribution to a symposium on Anja Jauernig's excellent book, The World According to Kant. I discuss Jauernig's account of how Kant conceives the empirical reality of appearances.

I consider an epistemological, methodological dispute between Nietzsche and Kant about the possibility of rational self-critique: an activity where the intellect reflects on its cognitive powers, demarcates the proper use and limitations of these powers, and thereby achieves a systematically complete insight into what we can and cannot know. Kant affirms whereas Nietzsche denies that we can successfully conduct such a self-directed rational enquiry. By reconstructing the central argumentative moves that Nietzsche and Kant do or could make to defend their (...) respective position, I trace their disagreement to starkly diverging models of philosophical enquiry, of what philosophy is and ought to be all about. (shrink)

I discuss the difference and the connections between Kant’s notions of cognition (Erkenntnis) and knowledge (Wissen). Unlike knowledge, cognition is a representational state which need not have the propositional structure of a judgments. Even cognitions that have such a structure need not coincide with knowledge, because they might rather have the doxastic status of opinion or faith, or they might be false (whereas knowledge is a certain recognition of truth). I argue that while Kant distinguishes between many different species of (...) cognition, he uses the term ‘knowledge’ univocally across his theoretical and practical philosophy. All knowledge is based upon some kind of cognition that provides the sufficient objective, certain ground for a knowing assent to a proposition. However, not all knowledge must be based upon the demanding type of cognition that is central to Kant’s overall argument in the first Critique, which requires a synthesis of concepts and sensible intuition. We have a lot of determinate knowledge, including knowledge that we possess transcendental freedom of will, that is based upon purely conceptual practical cognition. We can also have some indeterminate philosophical knowledge (e.g. knowledge that there are non-sensible, noumenal beings) that is based upon purely conceptual theoretical cognition. (shrink)

I argue that Kant acknowledges two models of spontaneous self-determination that rational beings are capable of. The first model involves absolute unconditional necessity and excludes any form of contingency. The second model involves (albeit not as a matter of definition) a form of contingency which entails alternative possibilities for determining oneself. The first model would be exhibited by a divine being; the second model is exhibited by human beings. Human beings do, however, partake in the divine model up to an (...) extent, namely, as far as the legislative spontaneity of their law-giving faculties are concerned. I conclude by suggesting that for Kant, the mechanistic principle that we are exclusively determined by natural causes poses a twofold threat for human agency. In one respect (in relation to the second model), it threatens us with the obliteration of contingency, or with the universality of hypothetical necessity. But in another respect (in relation to the first model), it threatens us (and our putative "laws") with the obliteration of absolute necessity, or with the universality of contingency. (shrink)

“Naturrecht Feyerabend” is a collection of student notes taken on a lecture that Kant gave around the time he was working on the Groundwork. I show that these notes portray Kant as proposing a defense of morality and freedom whose “subjectivism” is unparalleled by anything that we find in his major published works. Kant here traces both the normativity of the moral principle that we must treat humanity as an end in itself and the legitimacy of regarding ourselves as free (...) agents to the subjective needs of finite human reason that he discusses in the Transcendental Dialectic of the Critique of Pure Reason. I argue that this subjectivist defense of morality and freedom does not withstand the critical scrutiny that is suggested by Kant’s considered (published) views on these topics. (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)

In the Metaphysics of Morals, Kant declares that virtue “can and must be taught.” This claim raises two problems. First, it is in tension with Kant’s emphasis on the absolute moral responsibility that each individual agent owes to her transcendental freedom. Second, it raises the question of how the empirical events that constitute moral education can have an impact on atemporal moral choices. Concerning the second issue, I argue that Kant has a coherent framework for representing how empirical conditions can (...) influence (“affect”) the noumenal will without determining it to action. Regarding the first problem, I argue that although a good moral education is mostly only a facilitating rather than a strictly necessary condition for moral virtue, there is one moral capacity that does require good moral teaching: namely, the practical power of judgment that correctly applies wide, general duties of virtue to particular cases. (shrink)

Abstract Die moderne Physik besteht nicht nur aus neuen Entdeckungen und Erfindungen durch die Relativitätstheorie und durch die Quantenphysik. Sie besteht auch aus völlig neuen Sichtweisen und flexiblen Denkweisen von Zusammenhängen und Verschränkungen zwischen den Dingen. Die moderne Physik hat sich von dem Klischee des Schwarz-Weiß-Denkens verabschiedet, für das es nur getrennte Dinge, ohne fließende Übergänge gibt. Solche unbeweglichen, dogmatischen schwarzweißen Denkweisen können wir zurückverfolgen bis zu dem griechischen Philosophen Aristoteles. In der Zeit der Klassischen Mechanik hatten sie einen überwältigenden (...) Erfolg. Galilei behauptete, das Buch der Natur sei in der Sprache der Mathematik geschrieben. Das war die sehr kurzgefasste Formulierung der Klassischen Mechanik. Die moderne Physik hat sich keineswegs von der Mathematik verabschiedet, ganz und gar nicht. Doch der heilige Ernst und der starre und absolute Dogmatismus hat nachgelassen. Moderne Denkweisen in der Physik können mit den Begriffen von fließenden Übergängen, von Zwischenstufen, von Zusammenhängen zwischen den Dingen und von Schwingungen gekennzeichnet werden. Seit Faraday und Maxwell hat sich eine Verschiebung der Untersuchungsobjekte ergeben: Seit der Mitte des 19. Jahrhunderts, seit ca 1850, drehen sich die Denkmodelle der modernen Physik nicht mehr um getrennte, isolierten Körper, die im Nichts schwimmen, sondern um die Zwischenräume zwischen den Körpern und um die flexiblen Beziehungsgeflechte zwischen den Dingen und um die Netzwerke, die die Dinge umgeben. Das sind ganz neue physikalische Denkweisen, die durchaus Dunkelzonen und Zweifel und Ungewissheiten kennen, die den Bereich der Exaktheit überschatten. Neue Beiträge der physikalischen Denkweisen sind auch durch eine Flexibilität bei der Bildung von Begriffen gekennzeichnet. Sie lassen sich nicht auf einige wenige Begriffe oder auf eine starre und exakte Festlegung der Wortwahl festnageln. -/- „Jede Philosophie bezieht ihre Farbe von der geheimen Lichtquelle eines Vorstellungshintergrunds, der niemals ausdrücklich in ihrenGedankenketten auftaucht“ (Whitehead) (1) . (shrink)

Like all causal theories in philosophy, the causal theory of action is plagued by the problem of deviant causal chains. I have proposed a solution on the basis of the assumption that mental states and events are causally efficacious in virtue of their contents. This solution has been questioned by Torbjörn Tännsjö (2009). First, I will reply to the objection, and then I will discuss Tännsjö’s alternative.

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)

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)

Recent research shows – somewhat astonishingly – that people are willing to ascribe moral blame to AI-driven systems when they cause harm [1]–[4]. In this paper, we explore the moral- psychological underpinnings of these findings. Our hypothesis was that the reason why people ascribe moral blame to AI systems is that they consider them capable of entertaining inculpating mental states (what is called mens rea in the law). To explore this hypothesis, we created a scenario in which an AI system (...) runs a risk of poisoning people by using a novel type of fertilizer. Manipulating the computational (or quasi-cognitive) abilities of the AI system in a between-subjects design, we tested whether people’s willingness to ascribe knowledge of a substantial risk of harm (i.e., recklessness) and blame to the AI system. Furthermore, we investigated whether the ascription of recklessness and blame to the AI system would influence the perceived blameworthiness of the system’s user (or owner). In an experiment with 347 participants, we found (i) that people are willing to ascribe blame to AI systems in contexts of recklessness, (ii) that blame ascriptions depend strongly on the willingness to attribute recklessness and (iii) that the latter, in turn, depends on the perceived “cognitive” capacities of the system. Furthermore, our results suggest (iv) that the higher the computational sophistication of the AI system, the more blame is shifted from the human user to the AI system. (shrink)

Der Artikel beschäftigt sich mit dem englischen Philosophen Alfred North Whitehead und mit dem Vorstellungshintergrund, der seiner Philosophie zugrundeliegt. Der direkte Hintergrund seiner Philosophie ist die moderne Physik seit Michael Faraday und Maxwell, die als erste auf die elektromagnetischen Wellen und Schwingungen und Beziehungsgeflechte hingewiesen haben, die zwischen den Dingen liegen und die von Albert Einstein "Felder" genannt wurden. Wie sie aussehen, wissen wir bis heute nicht so genau, weil es Modellvorstellungen sind, deren Realität eigentlich nur durch Messungen belegt ist. (...) Das was zwischen den Dingen passiert ist später zu einer Hauptidee von Albert Einstein geworden, man denke nur an die Gravitationswellen, die erst vor wenigen Jahren entdeckt wurden. Einstein hatte sie vorausgesehen oder vorhergesagt. Die Quantenphysik ist voll von Wechselwirkungen zwischen den Objekten und von Verschränkungen, von Quantenverschränkungen. Deshalb spricht der Quantenphysiker Carlo Rovelli seit dem Jahre 2000 von einer "relationalen Quantenphysik". Diese Art von Relationen stellen den Hintergrund der Philosophie Whiteheads dar. (shrink)

Abstract Die moderne Physik besteht nicht nur aus neuen Entdeckungen und Erfindungen durch die Relativitätstheorie und durch die Quantenphysik. Sie besteht auch aus völlig neuen Sichtweisen und flexiblen Denkweisen von Zusammenhängen und Verschränkungen zwischen den Dingen. Die moderne Physik hat sich von dem Klischee des Schwarz-Weiß-Denkens verabschiedet, für das es nur getrennte Dinge, ohne fließende Übergänge gibt. Solche unbeweglichen, dogmatischen schwarzweißen Denkweisen können wir zurückverfolgen bis zu dem griechischen Philosophen Aristoteles. In der Zeit der Klassischen Mechanik hatten sie einen überwältigenden (...) Erfolg. Galilei behauptete, das Buch der Natur sei in der Sprache der Mathematik geschrieben. Das war die sehr kurzgefasste Formulierung der Klassischen Mechanik. Die moderne Physik hat sich keineswegs von der Mathematik verabschiedet, ganz und gar nicht. Doch der heilige Ernst und der starre und absolute Dogmatismus hat nachgelassen. Moderne Denkweisen in der Physik können mit den Begriffen von fließenden Übergängen, von Zwischenstufen, von Zusammenhängen zwischen den Dingen und von Schwingungen gekennzeichnet werden. Seit Faraday und Maxwell hat sich eine Verschiebung der Untersuchungsobjekte ergeben: Seit der Mitte des 19. Jahrhunderts, seit ca 1850, drehen sich die Denkmodelle der modernen Physik nicht mehr um getrennte, isolierten Körper, die im Nichts schwimmen, sondern um die Zwischenräume zwischen den Körpern und um die flexiblen Beziehungsgeflechte zwischen den Dingen und um die Netzwerke, die die Dinge umgeben. Das sind ganz neue physikalische Denkweisen, die durchaus Dunkelzonen und Zweifel und Ungewissheiten kennen, die den Bereich der Exaktheit überschatten. Neue Beiträge der physikalischen Denkweisen sind auch durch eine Flexibilität bei der Bildung von Begriffen gekennzeichnet. Sie lassen sich nicht auf einige wenige Begriffe oder auf eine starre und exakte Festlegung der Wortwahl festnageln. „Jede Philosophie bezieht ihre Farbe von der geheimen Lichtquelle eines Vorstellungshintergrunds, der niemals ausdrücklich in ihren Gedankenketten auftaucht“ (Whitehead) (1). (shrink)

What are the metaphysical foundations of Buddhism and modern science? Nagarjuna is not looking for a material or immaterial object which can be declared as a fundamental reality of this world. His fundamental reality is not an object. It is a relation between objects. This is a relational view of reality. This is the heart of Nagarjuna’s ideas. In the 19th century a more or less unknown Italian philosopher, Vincenzo Goberti, spoke about relations as the mean and as bonds between (...) things. Later, in quantum physics and in the philosophy of Alfred North Whitehead we are talking about interactions and entanglements. These ideas of relatedness or connections or entanglements in Eastern and Western modes of thought are the main idea of this essay. Not all entanglements are known. Just two examples: the nature of quantum entanglements is not known. Quantum entanglements should be faster than light. That's why Albert Einstein had some doubts. A second example: the completely unknown connections between the mind and the brain. Other examples are mysterious like the connections between birds in a flock. Some are a little known like gravitational forces. (shrink)

We propose a multi-step evaluation schema designed to help procurement agencies and others to examine the ethical dimensions of autonomous systems to be applied in the security sector, including autonomous weapons systems.

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)

Rudyard Kipling, the famous english author of « The Jungle Book », born in India, wrote one day these words: « Oh, East is East and West is West, and never the twain shall meet ». In my paper I show that Kipling was not completely right. I try to show the common ground between buddhist philosophy and quantum physics. There is a surprising parallelism between the philosophical concept of reality articulated by Nagarjuna and the physical concept of reality implied (...) by quantum physics. For neither is there a fundamental core to reality, rather reality consists of systems of interacting objects. Such concepts of reality cannot be reconciled with the substantial, subjective, holistic or instrumentalistic concepts of reality which underlie modern modes of thought. (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)

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)

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.

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)

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 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)

According to the standard view in philosophy, intentionality is the mark of genuine action. In psychology, human cognition and agency are now widely explained in terms of the workings of two distinct systems (or types of processes), and intentionality is not a central notion in this dual-system theory. Further, it is often claimed, in psychology, that most human actions are automatic, rather than consciously controlled. This raises pressing questions. Does the dual-system theory preserve the philosophical account of intentional action? How (...) much of our behavior is intentional according to this view? And what is the role of consciousness? I will propose here a revised account of intentional action within the dual-system framework, and we will see that most of our behavior can qualify as intentional, even if most of it is automatic. An important lesson will be that philosophical accounts of intentional action need to pay more attention to the role of consciousness in action. (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 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)

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)

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.

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to (...) be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. -/- Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. -/- However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. -/- The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion. (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)

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)

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 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)

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)

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)

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)

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)

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)

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)

According to radical versions of embodied cognition, human cognition and agency should be explained without the ascription of representational mental states. According to a standard reply, accounts of embodied cognition can explain only instances of cognition and agency that are not “representation-hungry”. Two main types of such representation-hungry phenomena have been discussed: cognition about “the absent” and about “the abstract”. Proponents of representationalism have maintained that a satisfactory account of such phenomena requires the ascription of mental representations. Opponents have denied (...) this. I will argue that there is another important representation-hungry phenomenon that has been overlooked in this debate: temporally extended planning agency. In particular, I will argue that it is very difficult to see how planning agency can be explained without the ascription of mental representations, even if we grant, for the sake of argument, that cognition about the absent and abstract can. We will see that this is a serious challenge for the radical as well as the more modest anti-representationalist versions of embodied cognition, and we will see that modest anti-representationalism is an unstable position. (shrink)

This chapter reviews empirical research on the rules governing assertion and retraction, with a focus on the normative role of truth. It examines whether truth is required for an assertion to be considered permissible, and whether there is an expectation that speakers retract statements that turn out to be false. Contrary to factive norms (such as the influential “knowledge norm”), empirical data suggests that there is no expectation that speakers only make true assertions. Additionally, contrary to truth-relativist accounts, there is (...) no requirement for speakers to retract statements that are false at the context of assessment. We conclude by suggesting that truth still plays a crucial role in the evaluation of assertions: as a standard for evaluating their success, rather than permissibility. (shrink)

This paper concerns anti-Humean intuitions about connections in nature. It argues for the existence of a de re link that is not necessity.Some anti-Humeans tacitly assume that metaphysical necessity can be used for all sorts of anti-Humean desires. Metaphysical necessity is thought to stick together whatever would be loose and separate in a Hume world, as if it were a kind of universal superglue.I argue that this is not feasible. Metaphysical necessity might connect synchronically co-existent properties—kinds and their essential features, (...) for example—but it is difficult to see how it could also serve as the binding force for successions of events. That is, metaphysical necessity seems not to be fit for diachronic, causal affairs in which causal laws, causation, or dispositions are involved. A different anti-Humean connection in nature has to do that job.My arguments focus mainly on a debate which has been the battleground for Humean vs. anti-Humean intuitions for many decades—namely, the analysis of dispositional predicates—yet I believe (but do not argue here) that the arguments generalise to causation and causal laws straightforwardly. (shrink)

This paper proposes and defends an account of what it is to act for reasons. In the first part, I will discuss the desire-belief and the deliberative model of acting for reasons. I will argue that we can avoid the weaknesses and retain the strengths of both views, if we pursue an alternative according to which acting for reasons involves taking something as a reason. In the main part, I will develop an account of what it is to take something (...) as a reason for action. On the basis of this, I will then offer a new account of what it is to act for reasons. (shrink)

Assertions are speech acts by means of which we express beliefs. As such they are at the heart of our linguistic and social practices. Recent research has focused extensively on the question whether the speech act of assertion is governed by norms, and if so, under what conditions it is acceptable to make an assertion. Standard theories propose, for instance, that one should only assert that p if one knows that p (the knowledge account), or that one should only assert (...) that p if p is true (the truth account). In a series of four experiments, this question is addressed empirically. Contrary to previous findings, knowledge turns out to be a poor predictor of assertability, and the norm of assertion is not factive either. The studies here presented provide empirical evidence in favour of the view that a speaker is warranted to assert that p only if her belief that p is justified. (shrink)