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)

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 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)

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)

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.

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)

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)

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)

The striking difference between the orthodox nomological necessitation view of laws and the claims made recently by Scientific Essentialism is that on the latter interpretation laws are metaphysically necessary while they are contingent on the basis of the former. This shift is usually perceived as an upgrading: essentialism makes the laws as robust as possible. The aim of my paper—in which I contrast Brian Ellis’s Scientific Essentialism and David Armstrong’s theory of nomological necessity—is threefold. (1) I first underline the familiar (...) fact that metaphysical necessity (of Kripkean “water is necessarily H2O” kind) is not a stronger kind of necessity than nomological necessity but an entirely different kind of thing: nomological, but not metaphysical necessity, is an intra-world necessitation which Armstrong (almost) identifies with causation; metaphysical, but not nomological necessitation, has a canonical link to possible world considerations and counterfactual reasoning. Hence, the change from one necessity to the other is not an upgrading but a substantial shift. (2) I will explain how the essentialists, who promote this shift, are nonetheless able to retain the features of nomological necessity. (3) I also explore, for both the essentialist and the Armstrongian, whether they could extract a modal force from intra-world nomological necessity which it does not have per se. I argue that such a modal force is, indeed, obtainable for them. I will close the paper with some remarks and questions about the relation between Kripkean metaphysical necessity and the modal version of nomological necessity as defined in (3). (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)

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)

It is widely believed that at least two developments in the last third of the 20th century have given dispositionalism—the view that powers, capacities, potencies, etc. are irreducible real properties—new credibility: (i) the many counterexamples launched against reductive analyses of dispositional predicates in terms of counterfactual conditionals and (ii) a new anti-Humean faith in necessary connections in nature which, it is said, owes a lot to Kripke’s arguments surrounding metaphysical necessity. I aim to show in this paper that necessity is, (...) in fact, of little help for the dispositionalists. My argument makes use of one of the above mentioned counterexamples against Humean reduction: antidotes. Turning the tables, I ask how the dispositionalists themselves can deal with antidotes. The result will be to show that if the dispositionalists are to demystify antidote cases, they must make plausible a conceptualisation of dispositions that does not invoke any kind of necessity. I will cautiously suggest that the anti-Humean link dispositions bring to the world has to be thought of in terms of (Newtonian) forces. (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)

Hume glaubte, die Kausalverknüpfung sei eine „secret connection“, also eine Verknüpfung, die mindestens unerkennbar, wenn nicht sogar inexis- tent ist. Einige moderne Gegner Humes halten dem entgegen, dass apos- teriorisch entdeckte, metaphysische Notwendigkeit, wie wir sie bei- spielsweise von Kripke und Putnam kennen, diejenige objektiv-reale Verknüpfung in der Welt ist, die auch die Rolle einer kausalen Verknüp- fung in der Welt spielen kann. Ich hinterfrage diese anti-Hume’sche Identifizierung kausaler mit me- taphysischer Notwendigkeit, zeige aber auch einen anderen Weg auf, kausale (...) Kräfte zu postulieren: Wenn unsere willentlichen Handlungen auf Widerstände in der Welt stoßen, haben wir (direkten) Beobachtungszu- gang zu einer Verknüpfung in der Welt, die mindestens einen essentiellen Teil kausaler Kraft ausmacht. (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)

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)

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)

Alfred Mele’s zygote argument is widely considered to be the strongest version of the manipulation argument against compatibilism (about free will and determinism). Opponents have focused largely on the first of its two premises and on the overall dialectic. My focus here will be on the underlying thought experiment—the Diana scenario—and on the second premise of the argument. I will argue that reflection on the Diana scenario shows that the second premise does not hold, and we will see that my (...) objection to the second premise helps to defend the claim that manipulation arguments face, in general, a dilemma. (shrink)

This paper combines two ideas: (1) That the Lewisian best system analysis of lawhood (BSA) can cope with laws that have exceptions (cf. Braddon-Mitchell in Noûs 35(2):260–277, 2001; Schrenk in The metaphysics of ceteris paribus laws. Ontos, Frankfurt, 2007). (2) That a BSA can be executed not only on the mosaic of perfectly natural properties but also on any set of special science properties (cf., inter alia, Schrenk 2007, Selected papers contributed to the sections of GAP.6, 6th international congress of (...) the society for analytical philosophy. Mentis, Paderborn/Münster, 2008; Cohen and Callender in Philos Stud 145:1–34, 2009, Erkenntnis 73:427–447, 2010). Bringing together (1) and (2) results in an analysis of special science ceteris paribus laws. (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.

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)

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)

In this paper we discuss a phenomenon we call perspectival plurality, which has gone largely unnoticed in the current debate between relativism and contextualism about predicates of personal taste. According to perspectival plurality, the truth value of a sentence containing more than one PPT may depend on more than one perspective. Prima facie, the phenomenon engenders a problem for relativism and can be shaped into an argument in favor of contextualism. We explore the consequences of perspectival plurality in depth and (...) assess several possible responses on behalf of advocates of relativism. (shrink)

INTRODUCTION I. CETERIS PARIBUS LAWS An alleged law of nature—like Newton's law of gravitation—is said to be a ceteris paribus law if it does not hold under ...

This paper explores whether it is possible to reformulate or re-interpret Lewis’s theory of fundamental laws of nature—his “best system analysis”—in such a way that it becomes a useful theory for special science laws. One major step in this enterprise is to make plausible how law candidates within best system competitions can tolerate exceptions—this is crucial because we expect special science laws to be so called “ceteris paribus laws ”. I attempt to show how this is possible and also how (...) we can thereby make the first step towards a solution for the infamous difficulties surrounding the troublesome ceteris paribus clause. The paper outlines the general ideas of the theory but also points out some of its difficulties and background assumptions. (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)

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)

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)

Since causal processes can be prevented and interfered with, law-governed causation is a challenge for necessitarian theories of laws of nature. To show that there is a problematic friction between necessity and interference, I focus on David Armstrong's theory; with one proviso, his lawmaker, nomological necessity, is supposed to be instantiated as the causation of the law's second relatum whenever its first relatum is instantiated. His proviso is supposed to handle interference cases, but fails to do so. In order to (...) be able to handle interferences, any theory which utilizes a kind of necessitation as lawmaker has to downgrade what it treats as necessity to something more akin to (Newtonian) forces. (shrink)

The luck argument raises a serious challenge for libertarianism about free will. In broad outline, if an action is undetermined, then it appears to be a matter of luck whether or not one performs it. And if it is a matter of luck whether or not one performs an action, then it seems that the action is not performed with free will. This argument is most effective against event-causal accounts of libertarianism. Recently, Franklin (Philosophical Studies 156:199–230, 2011) has defended event-causal (...) libertarianism against four formulations of the luck argument. I will argue that three of Franklin’s responses are unsuccessful and that there are important versions of the luck challenge that his defense has left unaddressed. (shrink)

Benjamin Libet's empirical challenge to free will has received a great deal of attention and criticism. A standard line of response has emerged that many take to be decisive against Libet's challenge. In the first part of this paper, I will argue that this standard response fails to put the challenge to rest. It fails, in particular, to address a recent follow-up experiment that raises a similar worry about free will (Soon, Brass, Heinze, & Haynes, 2008). In the second part, (...) however, I will argue that we can altogether avoid Libet-style challenges if we adopt a traditional compatibilist account of free will. In the final section, I will briefly explain why there is good and independent reason to think about free will in this way. (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)

Benjamin Libet’s work paved the way for the neuroscientific study of free will. Other scientists have praised this research as groundbreaking. In philosophy, the reception has been more negative, often even dismissive. First, I will propose a diagnosis of this striking discrepancy. I will suggest that the experiments seem irrelevant, from the perspective of philosophy, due to the way in which they operationalize free will. In particular, I will argue that this operational definition does not capture free will properly and (...) that it is based on a false dichotomy between internal and external causes. However, I will also suggest that this problem could be overcome, as there are no obvious obstacles to an operationalization of free will that is in accord with the philosophical conception of free will. (shrink)

Empirical evidence challenges many of the assumptions that underlie traditional philosophical and commonsense conceptions of human agency. It has been suggested that this evidence threatens also to undermine free will and moral responsibility. In this paper, I will focus on the purported threat to moral responsibility. The evidence challenges assumptions concerning the ability to exercise conscious control and to act for reasons. This raises an apparent challenge to moral responsibility as these abilities appear to be necessary for morally responsible agency. (...) I will argue that this challenge collapses once the underlying conditions on moral responsibility are specified in sufficient detail. I will argue, in other words, that the empirical evidence does not support a challenge to the assumption that we are, in general, morally responsible agents. In the final section, I will suggest that empirical research on human agency is nevertheless relevant to various questions about moral responsibility. (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)

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)

Given some reasonable assumptions concerning the nature of mental causation, non-reductive physicalism faces the following dilemma. If mental events cause physical events, they merely overdetermine their effects (given the causal closure of the physical). If mental events cause only other mental events, they do not make the kind of difference we want them to. This dilemma can be avoided if we drop the dichotomy between physical and mental events. Mental events make a real difference if they cause actions. But actions (...) are neither mental nor physical events. They are realized by physical events, but they are not type-identical with them. This gives us non-reductive physicalism without downward causation. The tenability of this view has been questioned. Jaegwon Kim, in particular, has argued that non-reductive physicalism is committed to downward causation. Appealing to the nature of actions, I will argue that this commitment can be avoided. (shrink)

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)

In the first part I argue that Buddhism and Hinduism can be unified by a Pure Consciousness thesis, which says that the nature of ultimate reality is an unconditioned and pure consciousness and that the phenomenal world is a mere appearance of pure consciousness. In the second part I argue that the Pure Consciousness thesis can be supported by an argument from quantum physics. According to our best scientific theories, the fundamental nature of reality consists of quantum fields, and it (...) seems that quantum fields have merely particle-like appearances—particles seem to be mere epiphenomena. This interpretation can be generalized. There appear to be individual entities, small and large, and their ontological reality is precisely what it appears to be—they are mere appearances. (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)

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)

It is widely believed that at least two developments in the last third of the 20th century have given dispositionalism—the view that powers, capacities, potencies, etc. are irreducible real properties—new credibility: (i) the many counterexamples launched against reductive analyses of dispositional predicates in terms of counterfactual conditionals and (ii) a new anti-Humean faith in necessary connections in nature which, it is said, owes a lot to Kripke’s arguments surrounding metaphysical necessity. I aim to show in this paper that necessity is, (...) in fact, of little help for the dispositionalists. My argument makes use of one of the above mentioned counterexamples against Humean reduction: antidotes. Turning the tables, I ask how the dispositionalists themselves can deal with antidotes. The result will be to show that if the dispositionalists are to demystify antidote cases, they must make plausible a conceptualisation of dispositions that does not invoke any kind of necessity. I will cautiously suggest that the anti-Humean link dispositions bring to the world has to be thought of in terms of (Newtonian) forces. (shrink)

Traditional compatibilism about free will is widely considered to be untenable. In particular, the conditional analysis of the ability to do otherwise appears to be subject to clear counterexamples. I will propose a new version of traditional compatibilism that provides a conditional account of both the ability to do otherwise and the ability to choose to do otherwise, and I will argue that this view withstands the standard objections to traditional compatibilism. For this, I will assume with incompatibilists that the (...) mere possession of a general ability to do otherwise is not sufficient for having the ability that is required for free will. This concession distinguishes the view from the traditional conditional analysis and from recent dispositional accounts of the ability to do otherwise, and we will see that this concession enables a straightforward response to the counterexamples. This, in turn, will play a crucial role in my response to the strongest version of the consequence argument for incompatibilism. (shrink)

It is widely thought that philosophical behaviorism is an untenable and outdated theory of mind. It is generally agreed, in particular, that the view generates a vicious circularity problem. There is a standard solution to this problem for functionalism, which utilizes the formulation of Ramsey sentences. I will show that this solution is also available for behaviorism if we allow quantification over the causal bases of behavioral dispositions. Then I will suggest that behaviorism differs from functionalism mainly in its commitment (...) to anti-representationalism, and I will offer two new objections to anti-representationalism. The first will be based on considerations concerning the contents of desires and intentions. The second objection concerns inner speech and mental imagery. We will see that the objections are of relevance to contemporary debates, as they apply with equal force to the currently popular anti-representationalist versions of embodied and enactive cognition. (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)

Buddhism and Hinduism appear to be separated by irreconcilable differences. I argue that this apparent gulf can be overcome. The argument has three main parts. First, I argue that the Buddhist doctrine of dependent arising is not a metaphysical principle of real causation, but a principle of fabrication. Second, I argue that this interpretation of dependent arising enables a unification of the main schools of Buddhism. Third, I argue that Buddhism can be unified fully with Advaita Vedānta, the most important (...) philosophical school of Hinduism, and I argue that a substantial unity can be established between Buddhism and the three main schools of Vedānta. In particular, Buddhism and Vedānta can agree that the highest aim and good consists in the direct realization of an unconditioned and pure mind or consciousness. (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)