Certain scientific explanations of physical facts have recently been characterized as distinctively mathematical –that is, as mathematical in a different way from ordinary explanations that employ mathematics. This article identifies what it is that makes some scientific explanations distinctively mathematical and how such explanations work. These explanations are non-causal, but this does not mean that they fail to cite the explanandum’s causes, that they abstract away from detailed causal histories, or that they cite no natural laws. Rather, in these explanations, (...) the facts doing the explaining are modally stronger than ordinary causal laws or are understood in the why question’s context to be constitutive of the physical arrangement at issue. A distinctively mathematical explanation works by showing the explanandum to be more necessary than ordinary causal laws could render it. Distinctively mathematical explanations thus supply a kind of understanding that causal explanations cannot. 1 Introduction2 Some Distinctively Mathematical Scientific Explanations3 Are Distinctively Mathematical Explanations Set Apart by their Failure to Cite Causes? 4 Distinctively Mathematical Explanations do not Exploit Causal Powers5 How these Distinctively Mathematical Explanations Work6 Conclusion. (shrink)

Parenting our biological children is a centrally important matter, but how, if it all, can it be justified? According to a contemporary influential line of thinking, the acquisition by parents of a moral right to parent their biological children should be grounded by appeal to the value of the intimate emotional relationship that gestation facilitates between a newborn and a gestational procreator. I evaluate two arguments in defence of this proposal and argue that both are unconvincing.

Not all scientific explanations work by describing causal connections between events or the world's overall causal structure. In addition, mathematicians regard some proofs as explaining why the theorems being proved do in fact hold. This book proposes new philosophical accounts of many kinds of non-causal explanations in science and mathematics.

It is often presumed that the laws of nature have special significance for scientific reasoning. But the laws' distinctive roles have proven notoriously difficult to identify--leading some philosophers to question if they hold such roles at all. This study offers original accounts of the roles that natural laws play in connection with counterfactual conditionals, inductive projections, and scientific explanations, and of what the laws must be in order for them to be capable of playing these roles. Particular attention is given (...) to laws of special sciences, levels of scientific explanation, natural kinds, ceteris-paribus clauses, and physically necessary non-laws. (shrink)

It has often been argued that Humean accounts of natural law cannot account for the role played by laws in scientific explanations. Loewer (Philosophical Studies 2012) has offered a new reply to this argument on behalf of Humean accounts—a reply that distinguishes between grounding (which Loewer portrays as underwriting a kind of metaphysical explanation) and scientific explanation. I will argue that Loewer’s reply fails because it cannot accommodate the relation between metaphysical and scientific explanation. This relation also resolves a puzzle (...) about scientific explanation that Hempel and Oppenheim (Philosophy of Science 15:135–75, 1948) encountered. (shrink)

Laws form counterfactually stable sets -- Natural necessity -- Three payoffs of my account -- A world of subjunctives.

Partiality is the special concern that we display for ourselves and other people with whom we stand in some special personal relationship. It is a central theme in moral philosophy, both ancient and modern. Questions about the justification of partiality arise in the context of enquiry into several moral topics, including the good life and the role in it of our personal commitments; the demands of impartial morality, equality, and other moral ideals; and commonsense ideas about supererogation. This paper provides (...) an overview of the debate on the ethics of partiality through the lens of the domains of permissible and required partiality. After outlining the conceptual space, I first discuss agent-centred moral options that concern permissions not to do what would be impartially optimal. I then focus on required partiality, which concerns associative duties that go beyond our general duties to others and require us to give special priority to people who are close to us. I discuss some notable features of associative duties and the two main objections that have been raised against them: the Voluntarist and the Distributive objections. I then turn to the justification of partiality, focusing on underivative approaches and reasons-based frameworks. I discuss the reductionism and non-reductionism debate: the question whether partiality is derivative or fundamental. I survey arguments for ‘the big three’, according to which partiality is justified by appeal to the special value of either projects, personal relationships, or individuals. I conclude by discussing four newly emerging areas in the debate: normative transitions of various personal relationships, relationships with AI, epistemic partiality, and negative partiality, which concerns the negative analogue of our positive personal relationships. (shrink)

Buch 1. Geschichte des Materialismus bis auf Kant.--Buch 2. Geschichte des Materialismus seit Kant.

The institution of the family and its importance have recently received considerable attention from political theorists. Leading views maintain that the institution’s justification is grounded, at least in part, in the non-instrumental value of the parent-child relationship itself. Such views face the challenge of identifying a specific good in the parent-child relationship that can account for how adults acquire parental rights over a particular child—as opposed to general parental rights, which need not warrant a claim to parent one’s biological progeny. (...) I develop a view that meets this challenge. This Project View identifies the pursuit of a parental project as a distinctive non-instrumentally valuable good that provides a justification for the family and whose pursuit is necessary and sufficient for the acquisition of parental rights. This view grounds moral parenthood in a normative relation as opposed to a biological one, supports polyadic forms of parenting, and provides plausible guidance in cases of assisted reproduction. (shrink)

Really statistical explanation is a hitherto neglected form of noncausal scientific explanation. Explanations in population biology that appeal to drift are RS explanations. An RS explanation supplies a kind of understanding that a causal explanation of the same result cannot supply. Roughly speaking, an RS explanation shows the result to be mere statistical fallout.

Several foundational documents of bioethics mention the special obligation researchers have to vulnerable research participants. However, the treatment of vulnerability offered by these documents often relies on enumeration of vulnerable groups rather than an analysis of the features that make such groups vulnerable. Recent attempts in the scholarly literature to lend philosophical weight to the concept of vulnerability are offered by Luna and Hurst. Luna suggests that vulnerability is irreducibly contextual and that Institutional Review Boards (Research Ethics Committees) can only (...) identify vulnerable participants by carefully examining the details of the proposed research. Hurst, in contrast, defines the vulnerable as those especially at risk of incurring the wrongs to which all research ethics participants are exposed. We offer a more substantive conception of vulnerability than Luna but one that gives rise to a different rubric of responsibilities from Hurst's. While we understand vulnerability to be an ontological condition of human existence, in the context of research ethics, we take the vulnerable to be research subjects who are especially prone to harm or exploitation. Our analysis rests on developing a typology of sources of vulnerability and showing how distinct sources generate distinct obligations on the part of the researcher. Our account emphasizes that the researcher's first obligation is not to make the research participant even more vulnerable than they already are. To illustrate our framework, we consider two cases: that of a vulnerable population involved in international research and that of a domestic population of people with diminished capacity. (shrink)

Unlike explanation in science, explanation in mathematics has received relatively scant attention from philosophers. Whereas there are canonical examples of scientific explanations, there are few examples that have become widely accepted as exhibiting the distinction between mathematical proofs that explain why some mathematical theorem holds and proofs that merely prove that the theorem holds without revealing the reason why it holds. This essay offers some examples of proofs that mathematicians have considered explanatory, and it argues that these examples suggest a (...) particular account of explanation in mathematics. The essay compares its account to Steiner's and Kitcher's. Among the topics that arise are proofs that exploit symmetries, mathematical coincidences, brute-force proofs, simplicity in mathematics, merely clever proofs, and proofs that unify what other proofs treat as separate cases. (shrink)

A conservation law in physics can be either a constraint on the kinds of interaction there could be or a coincidence of the kinds of interactions there actually are. This is an important, unjustly neglected distinction. Only if a conservation law constrains the possible kinds of interaction can a derivation from it constitute a scientific explanation despite failing to describe the causal/mechanical details behind the result derived. This conception of the relation between “bottom-up” scientific explanations and one kind of “top-down” (...) scientific explanation is motivated by several examples from classical and modern physics. (shrink)

Although all mathematical truths are necessary, mathematicians take certain combinations of mathematical truths to be ‘coincidental’, ‘accidental’, or ‘fortuitous’. The notion of a ‘ mathematical coincidence’ has so far failed to receive sufficient attention from philosophers. I argue that a mathematical coincidence is not merely an unforeseen or surprising mathematical result, and that being a misleading combination of mathematical facts is neither necessary nor sufficient for qualifying as a mathematical coincidence. I argue that although the components of a mathematical coincidence (...) may possess a common explainer, they have no common explanation ; that two mathematical facts have a unified explanation makes their truth non-coincidental. I suggest that any motivation we may have for thinking that there are mathematical coincidences should also motivate us to think that there are mathematical explanations, since the notion of a mathematical coincidence can be understood only in terms of the notion of a mathematical explanation. I also argue that the notion of a mathematical coincidence plays an important role in scientific explanation. When two phenomenological laws of nature are similar, despite concerning physically distinct processes, it may be that any correct scientific explanation of their similarity proceeds by revealing their similarity to be no mathematical coincidence. (shrink)

Among the niftiest arguments for scientific anti-realism is the ‘pessimistic induction’ (also sometimes called ‘the disastrous historical meta-induction’). Although various versions of this argument differ in their details (see, for example, Poincare 1952: 160, Putnam 1978: 25, and Laudan 1981), the argument generally begins by recalling the many scientific theories that posit unobservable entities and that at one time or another were widely accepted. The anti-realist then argues that when these old theories were accepted, the evidence for them was quite (...) persuasive – roughly as compelling as our current evidence is for our best scientific theories positing various unobservable entities. Nevertheless, the anti-realist argues, most of these old theories turned out to be incorrect in the unobservables they posited. Therefore, the anti-realist concludes that with regard to the theories we currently accept, we should believe that probably, most of them are likewise incorrect in the unobservable entities they posit. (This argument appeals to what our best current theories say about unobservables in order to show that the entities posited by some earlier theory are not real. So the argument takes the form of a reductio of the view that the apparent success of some scientific theory justifies our believing in its accuracy regarding unobservables.) Of course, this argument has been criticized on many grounds. Some have argued, for instance, that the scientific theories we currently accept are much better supported than were earlier scientific theories at the time they were accepted. In addition, some have argued that many scientific theories accepted justly in the past were in fact accurate.. (shrink)

Many philosophers endorse the Transparency Thesis, the claim that by introspection one cannot become aware of one's experience. Recently, some authors have suggested that the Transparency Thesis is challenged by introspective states reached under mindfulness. We label this the Mindfulness Opacity Hypothesis. The present paper develops the hypothesis in important new ways. First, we motivate the hypothesis by drawing on recent clinical psychology and cognitive science of mindfulness. Secondly, we develop the hypothesis by describing the implied shift in experiential perspective, (...) the scope of introspectable qualities, and the level of skill. Thirdly, we defend the hypothesis against various philosophical arguments. We conclude that the Mindfulness Opacity Hypothesis is empirically and theoretically well motivated and supported. (shrink)

Philosophers who regard some mathematical proofs as explaining why theorems hold, and others as merely proving that they do hold, disagree sharply about the explanatory value of proofs by mathematical induction. I offer an argument that aims to resolve this conflict of intuitions without making any controversial presuppositions about what mathematical explanations would be.

Digital duplicates reduce the scarcity of individuals and thus may impact their instrumental and intrinsic value. I here expand upon this idea by introducing the notion of collective scarcity, which pertains to the limitations faced by social groups in maintaining their size, cohesion, and function.

Logische Studien - Ein Beitrag zur Neubegrundung der formalen Logik und der Erkenntnisstheorie ist ein unveranderter, hochwertiger Nachdruck der Originalausgabe aus dem Jahr 1894. Hansebooks ist Herausgeber von Literatur zu unterschiedlichen Themengebieten wie Forschung und Wissenschaft, Reisen und Expeditionen, Kochen und Ernahrung, Medizin und weiteren Genres.Der Schwerpunkt des Verlages liegt auf dem Erhalt historischer Literatur.Viele Werke historischer Schriftsteller und Wissenschaftler sind heute nur noch als Antiquitaten erhaltlich. Hansebooks verlegt diese Bucher neu und tragt damit zum Erhalt selten gewordener Literatur und (...) historischem Wissen auch fur die Zukunft bei.". (shrink)

Sober 2011 argues that, contrary to Hume, some causal statements can be known a priori to be true—notably, some ‘would promote’ statements figuring in causal models of natural selection. We find Sober's argument unconvincing. We regard the Humean thesis as denying that causal explanations contain any a priori knowable statements specifying certain features of events to be causally relevant. We argue that not every ‘would promote’ statement is genuinely causal, and we suggest that Sober has not shown that his examples (...) of ‘would promote’ statements manage to achieve a priori status without sacrificing their causal character. (shrink)

We propose a ‘Moral Imagination’ methodology to facilitate a culture of responsible innovation for engineering and product teams in technology companies. Our approach has been operationalized over the past two years at Google, where we have conducted over 50 workshops with teams from across the organization. We argue that our approach is a crucial complement to existing formal and informal initiatives for fostering a culture of ethical awareness, deliberation, and decision-making in technology design such as company principles, ethics and privacy (...) review procedures, and compliance controls. We characterize some distinctive benefits of our methodology for the technology sector in particular. (shrink)

Why do relationships of friendship and love support partiality, but not relationships of hatred or commitments of racism? Where does partiality end and why? I take the intuitive starting point that important cases of partiality are meaningful. I develop a view whereby meaning is understood in terms of transcending self-limitations in order to connect with things of external value. I then show how this view can be used to distinguish central cases of legitimate partiality from cases of illegitimate partiality and (...) how it puts pressure on the traditional way of thinking about partiality. (shrink)

This paper explores whether there is any relation between mathematical proofs that specify the grounds of the theorem being proved and mathematical proofs that explain why the theorem obtains. The paper argues that a mathematical fact’s grounds do not, simply by virtue of grounding it, thereby explain why that fact obtains. It argues that oftentimes, a proof specifying a mathematical fact’s grounds fails to explain why that fact obtains whereas any explanation of the fact does not specify its ground. The (...) paper offers several examples from mathematical practice to illustrate these points. These examples suggest several reasons why explaining and grounding tend to come apart, including that explanatory proofs need not exhibit purity, tend not to be brute force, and often unify separate cases by identifying common reasons behind them even when those cases have distinct grounds. The paper sketches an account of what makes a proof explanatory and uses that account to defend the morals drawn from the examples already given. (shrink)

Explanation in mathematics has recently attracted increased attention from philosophers. The central issue is taken to be how to distinguish between two types of mathematical proofs: those that explain why what they prove is true and those that merely prove theorems without explaining why they are true. This way of framing the issue neglects the possibility of mathematical explanations that are not proofs at all. This paper addresses what it would take for a non-proof to explain. The paper focuses on (...) a particular example of an explanatory non-proof: an argument that mathematicians regard as explaining why a given theorem holds regarding the derivative of an infinite sum of differentiable functions. The paper contrasts this explanatory non-proof with various non-explanatory proofs of the same theorem. The paper offers an account of what makes the given non-proof explanatory. This account is motivated by investigating the difficulties that arise when we try to extend Mark Steiner’s influential account of explanatory proofs to cover this explanatory non-proof. (shrink)

An increasing number of regulations propose the notion of ‘AI audits’ as an enforcement mechanism for achieving transparency and accountability for artificial intelligence (AI) systems. Despite some converging norms around various forms of AI auditing, auditing for the purpose of compliance and assurance currently have little to no agreed upon practices, procedures, taxonomies, and standards. We propose the ‘criterion audit’ as an operationalizable compliance and assurance external audit framework. We model elements of this approach after financial auditing practices, and argue (...) that AI audits should similarly provide assurance to their stakeholders about AI organizations’ ability to govern their algorithms in ways that mitigate harms and uphold human values. We discuss the necessary conditions for the criterion audit, and provide a procedural blueprint for performing an audit engagement in practice. We illustrate how this framework can be adapted to current regulations by deriving the criteria on which ‘bias audits’ for hiring algorithms can be performed, as required by the recently effective New York City Local Law 144 of 2021. We conclude by offering critical discussion on the benefits, inherent limitations, and implementation challenges of applying practices of the more mature financial auditing industry to AI auditing where robust guardrails against quality assurance issues are only starting to emerge. Our discussion as informed by experiences in performing these audits in practice highlights the critical role that an audit ecosystem plays in ensuring the effectiveness of such methodology. (shrink)

Existing discussions of partiality have primarily examined special personal relationships between family, friends, or co-nationals. The negative analogue of such relationships – for example, the relationship of enmity – has, by contrast, been largely neglected. This chapter explores this adverse relation in more detail and considers the special reasons generated by it. We suggest that enmity can involve justified negative partiality, allowing members to give less consideration to each other’s interests. We then consider whether the negative partiality of enmity can (...) be justified through projects or the value inherent in the relationship, following two influential views about the justification of positive partiality. We argue that both accounts of partiality can be conceptually extended to the negative analogue, but doing so brings into focus the problems with such accounts of the grounds of partiality. (shrink)

Humean accounts of natural law have long been charged with being unable to account for the laws’ explanatory power in science. One form of this objection is to charge Humean accounts with explanatory circularity: a fact in the Humean mosaic helps to explain why some regularity is a law (first premise), but that law, in turn, helps to explain why that mosaic fact holds (second premise). To this objection, Humeans have replied that the explanation in the first premise is metaphysical (...) whereas the explanation in the second premise is scientific, so (since these two varieties of explanation operate very differently) the two explanations cannot be chained together to yield explanatory circularity. This paper presents a new circularity argument that avoids this objection because both explanations in the premises are metaphysical. The new circularity argument also avoids the objection that the contrasts at the point where the two explanations are chained together fail to line up properly. The upshot is to leave the Humean account of law with two unattractive options: to regard scientific explanation under natural law as not constituting genuine explanation at all or to regard the Humean account as involving a vicious explanatory circularity. (shrink)

Rosenberg has recently argued that explanations supplied by (what he calls) functional biology are mere promissory notes for macromolecular adaptive explanations. Rosenberg's arguments currently constitute one of the most substantial challenges to the autonomy, irreducibility, and indispensability of the explanations supplied by functional biology. My responses to Rosenberg's arguments will generate a novel account of the autonomy of functional biology. This account will turn on the relations between counterfactuals, scientific explanations, and natural laws. Crucially, in their treatment of the laws' (...) relation to counterfactuals, Rosenberg's arguments beg the question against the autonomy of functional biology. This relation is considerably more subtle than is suggested by familiar slogans such as Laws support counterfactuals; accidents don't. (shrink)

This paper examines some recent attempts that use counterfactuals to understand the asymmetry of non-causal scientific explanations. These attempts recognize that even when there is explanatory asymmetry, there may be symmetry in counterfactual dependence. Therefore, something more than mere counterfactual dependence is needed to account for explanatory asymmetry. Whether that further ingredient, even if applicable to causal explanation, can fit non-causal explanation is the challenge that explanatory asymmetry poses for counterfactual accounts of non-causal explanation. This paper argues that several recent (...) accounts Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 117–140, 2018; Jansson and Saatsi in Br J Philos Sci, forthcoming; Jansson in J Philos 112:7–599, 2015; Saatsi and Pexton in Philos Sci 80: 613–624, 2013; French and Saatsi, in: Reutlinger and Saatsi Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 185–205, 2018) fail to meet this challenge. The paper then sketches a more positive proposal for dealing with explanatory asymmetry in non-causal explanations. (shrink)

This paper argues that in at least some cases, one proof of a given theorem is deeper than another by virtue of supplying a deeper explanation of the theorem — that is, a deeper account of why the theorem holds. There are cases of scientific depth that also involve a common abstract structure explaining a similarity between two otherwise unrelated phenomena, making their similarity no coincidence and purchasing depth by answering why questions that separate, dissimilar explanations of the two phenomena (...) cannot correctly answer. The connections between explanation, depth, unification, power, and coincidence in mathematics and science are compared. (shrink)

I argue that you can be permitted to discount the interests of your adversaries even though doing so would be impartially suboptimal. This means that, in addition to the kinds of moral options that the literature traditionally recognises, there exist what I call other-sacrificing options. I explore the idea that you cannot discount the interests of your adversaries as much as you can favour the interests of your intimates; if this is correct, then there is an asymmetry between negative partiality (...) toward your adversaries and positive partiality toward your intimates. (shrink)

This paper proposes an account of why proof is the only way to acquire knowledge of some mathematical proposition’s truth. Admittedly, non-deductive arguments for mathematical propositions can be strong and play important roles in mathematics. But this paper proposes a necessary condition for knowledge that can be satisfied by putative proofs (and proof sketches), as well as by non-deductive arguments in science, but not by non-deductive arguments from mathematical evidence. The necessary condition concerns whether we can justly expect that if (...) the mathematical proposition is actually false, despite the evidence for its truth, then this fact has an explanation. (shrink)

I here settle a recent dispute between two rival theories in distributive ethics: Restricted Prioritarianism and the Competing Claims View. Both views mandate that the distribution of benefits and burdens between individuals should be justifiable to each affected party in a way that depends on the strength of each individual’s separately assessed claim to receive a benefit. However, they disagree about what elements constitute the strength of those individuals’ claims. According to restricted prioritarianism, the strength of a claim is determined (...) in ‘prioritarian’ fashion by both what she stands to gain and her absolute level of well-being, while, according to the competing claims view, the strength of a claim is also partly determined by her level of well-being relative to others with conflicting interests. I argue that, suitably modified, the competing claims view is more plausible than restricted prioritarianism. (shrink)

Counterfactuals all the way down? Content Type Journal Article DOI 10.1007/s11016-010-9437-9 Authors Jim Woodward, History and Philosophy of Science, 1017 Cathedral of Learning, University of Pittsburgh, Pittsburgh, PA 15260, USA Barry Loewer, Department of Philosophy, Rutgers University, New Brunswick, NJ 08901, USA John W. Carroll, Department of Philosophy and Religious Studies, North Carolina State University, Raleigh, NC 27695-8103, USA Marc Lange, Department of Philosophy, University of North Carolina at Chapel Hill, CB#3125—Caldwell Hall, Chapel Hill, NC 27599-3125, USA Journal Metascience (...) Online ISSN 1467-9981 Print ISSN 0815-0796 Journal Volume Volume 20 Journal Issue Volume 20, Number 1. (shrink)

This paper concerns the relation between a proof’s beauty and its explanatory power – that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical practice has long recognized that certain proofs but not others have explanatory power, and this paper (...) offers an account of what makes a proof explanatory. This account is motivated by a wide range of examples drawn from mathematical practice, and the account proposed here is compared to other accounts in the literature. The concept of a proof that explains is closely intertwined with other important concepts, such as a brute force proof, a mathematical coincidence, unification in mathematics, and natural properties. Ultimately, this paper concludes that the features of a proof that would contribute to its explanatory power would also contribute to its beauty, but that these two virtues are not the same; a beautiful proof need not be explanatory. (shrink)