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 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)

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 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)

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)

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)

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)

This volume covers a great range of topics within general metaphysics, featuring contributions by experts in the respective areas. The information contained is suitable for introductory as well as research purposes. The book equally targets laymen, students, and experts in their own right. Subjects range from the history of metaphysics, properties, objects, modality, structure, truth, etc. to methodological concerns of metaphysics.

In their recent book Every Thing Must Go, Ladyman and Ross claim: (i) Physics is analytically complete since it is the only science that cannot be left incomplete. (ii) There might not be an ontologically fundamental level. (iii) We should not admit anything into our ontology unless it has explanatory and predictive utility. In this discussion note I aim to show that the ontological commitment in implies that the completeness of no science can be achieved where no fundamental level exists. (...) Therefore, if claim requires a science to actually be complete in order to be considered as physics,, and if Ladyman and Ross's “tentative metaphysical hypothesis ... that there is no fundamental level” is true,, then there simply is no physics. Ladyman and Ross can, however, avoid this unwanted result if they merely require physics to ever strive for completeness rather than to already be complete. (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)

I argue for the possibility of a proprioceptive art in addition to, for example, visual or auditory arts, where aspects of some martial arts will serve as examples of that art form. My argument is inspired by a thought of Ted Shawn’s, one of the pioneers of American modern dance: "Dance is the only art wherein we ourselves are the stuff in which it is made.” In a first step, I point out that in some practices of martial arts (in (...) the paper I will introduce “hyongs” & “katas”), we are, too, the stuff these performances are made of. Second, I show that we, as martial arts practitioners, are not in the first place visual or auditorial observers (as common in painting or music or ballet) but introspective, proprioceptive perceivers of our bodies and their movements. (As a corollary we get that we are, in such a case, necessarily our exclusive audience.) In an third crucial step, I show that the martial arts practices referred to, hyongs & katas, and especially the proprioceptive aspects thereof, can indeed count as art. Thus, proprioceptive art is possible because some practices of some martial arts are actual existing examples of that art form. (shrink)

The Philosophy ofLanguage belongs to the foundations of philosophical reflexion. In this volume, its central problems and strategies are explained, and the nature of sentences and other elements of language are analysed. The didactical exposition of the most important schools and thinkers makes the volume particularly interesting for readers new to the subject.

The verification theory of meaning aims to characterise what it is for a sentence to be meaningful and also what kind of abstract object the meaning of a sentence is. A brief outline is given by Rudolph Carnap, one of the theory's most prominent defenders: If we knew what it would be for a given sentence to be found true then we would know what its meaning is. [...] thus the meaning of a sentence is in a certain sense identical (...) with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. [4: 420] In short, the verification theory of meaning claims that the meaning of a sentence is the method of its verification. (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)

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)

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)

This paper presents a series of studies (total N=579) which demonstrate that folk judgments concerning the reasonableness of decisions and actions depend strongly on whether they engender positive or negative consequences. A particular decision is deemed more reasonable in retrospect when it produces beneficial consequences than when it produces harmful consequences, even if the situation in which the decision was taken and the epistemic circumstances of the agent are held fixed across conditions. This finding is worrisome for the law, where (...) the reasonable person standard plays a prominent role. The legal concept of reasonableness is outcome-insensitive: whether the defendant acted in a reasonable fashion or not depends exclusively on her context of action, no matter how things play out. Folk judgments of reasonableness are thus inconsistent with the legal concept of reasonableness. Problematically, in common law jurisdictions, the decision whether a defendant’s behavior was reasonable or not is frequently (though not necessarily) delegated to a lay jury. (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)

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)

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)

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)

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)

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)

Fogelin’s neo-Pyrrhonism is skepticism about epistemology and philosophy more generally. Philosophical reflection on ordinary epistemic practices leads us to deny the possibility of knowledge and justified belief. However, instead of accepting the dogma that knowledge and justified beliefs are impossible, a neo-Pyrrhonist rejects the philosophical premises that lead to this conclusion. Fogelin argues in particular that contemporary theories of justification cannot avoid dogmatic skepticism, because they are committed to the premises of the skeptical argument deriving from the modes of Agrippa. (...) It is argued against Fogelin that those theories can and typically do deny one or another of the premises and thus can avoid the skeptical conclusion. Neo-Pyrrhonism should rather be defended by arguing that the premises of the Agrippan argument are intuitively plausible and that neo-Pyrrhonism provides the best resolution of the resulting paradox. Only neo-Pyrrhonism both explains the intuitive plausibility of the premises and avoids dogmatic skepticism. (shrink)

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

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)

While philosophers hold that it is patently absurd to blame robots or hold them morally responsible [1], a series of recent empirical studies suggest that people do ascribe blame to AI systems and robots in certain contexts [2]. This is disconcerting: Blame might be shifted from the owners, users or designers of AI systems to the systems themselves, leading to the diminished accountability of the responsible human agents [3]. In this paper, we explore one of the potential underlying reasons for (...) robot blame, namely the folk's willingness to ascribe inculpating mental states or "mens rea" to robots. In a vignette-based experiment (N=513), we presented participants with a situation in which an agent knowingly runs the risk of bringing about substantial harm. We manipulated agent type (human v. group agent v. AI-driven robot) and outcome (neutral v. bad), and measured both moral judgment (wrongness of the action and blameworthiness of the agent) and mental states attributed to the agent (recklessness and the desire to inflict harm). We found that (i) judgments of wrongness and blame were relatively similar across agent types, possibly because (ii) attributions of mental states were, as suspected, similar across agent types. This raised the question - also explored in the experiment - whether people attribute knowledge and desire to robots in a merely metaphorical way (e.g., the robot "knew" rather than really knew). However, (iii), according to our data people were unwilling to downgrade to mens rea in a merely metaphorical sense when given the chance. Finally, (iv), we report a surprising and novel finding, which we call the inverse outcome effect on robot blame: People were less willing to blame artificial agents for bad outcomes than for neutral outcomes. This suggests that they are implicitly aware of the dangers of overattributing blame to robots when harm comes to pass, such as inappropriately letting the responsible human agent off the moral hook. (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)

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.

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 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)

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)

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)

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)

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)

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)

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)

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)

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)

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)