Humboldts texttheoretischer Ansatz, dessen Einfluß auf die moderne (Text-)Linguistik größer ist als bisher wahrgenommen, wird im ersten Teil dieses Bandes erstmals zusammenhängend nachgewiesen.

Gottfried Wilhelm Leibniz leitete die Bibliothek der Hannoveraner Welfen vierzig Jahre lang bis zu seinem Tod 1716.

In the first part of chapter 2 of book II of the Physics Aristotle addresses the issue of the difference between mathematics and physics. In the course of his discussion he says some things about astronomy and the ‘ ‘ more physical branches of mathematics”. In this paper I discuss historical issues concerning the text, translation, and interpretation of the passage, focusing on two cruxes, the first reference to astronomy at 193b25–26 and the reference to the more physical branches at 194a7–8. In (...) section I, I criticize Ross’s interpretation of the passage and point out that his alteration of has no warrant in the Greek manuscripts. In the next three sections I treat three other interpretations, all of which depart from Ross's: in section II that of Simplicius, which I commend; in section III that of Thomas Aquinas, which is importantly influenced by a mistranslation of, and in section IV that of Ibn Rushd, which is based on an Arabic text corresponding to that printed by Ross. In the concluding section of the paper I describe the modern history of the Greek text of our passage and translations of it from the early twelfth century until the appearance of Ross's text in 1936. (shrink)

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)

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)

Hempel and Giere contend that the existence of provisos poses grave difficulties for any regularity account of physical law. However, Hempel and Giere rely upon a mistaken conception of the way in which statements acquire their content. By correcting this mistake, I remove the problem Hempel and Giere identify but reveal a different problem that provisos pose for a regularity account — indeed, for any account of physical law according to which the state of affairs described by a law-statement presupposes (...) a Humean regularity. These considerations suggest a normative analysis of law-statements. On this view, law-statements are not distinguished from accidental generalizations by the kind of Humean regularities they describe because a law-statement need not describe any Humean regularity. Rather, a law-statement says that in certain contexts, one ought to regard the assertion of a given type of claim, if made with justification, as a proper way to justify a claim of a certain other kind. (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.

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

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)

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.

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.

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

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)

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)

The merits of David Lewis’s Best System Account of natural law are frequently debated. But to my knowledge, the prospects for extending the BSA to cover meta-laws have never been examined. I shall identify two obstacles facing the most natural way of extending the BSA to cover meta-laws. The BSA’s fans should consider how these obstacles are to be overcome. Meta-laws are laws about laws. For example, Einstein’s special theory of relativity incorporates a meta-law: The content of the [special] relativity (...) theory can … be summarized in one sentence: all natural laws must be so conditioned that they are covariant with respect to Lorentz transformations. [The special theory of relativity] is not a theory in the usual sense but is better regarded as a second-level theory, or a theory of theories that constrains first-level theories. The principle of relativity is an example of a symmetry principle: a principle requiring that the first-order laws be unchanged under a given transformation. Long before Einstein proposed the principle of relativity, other spacetime symmetries were widely believed to be meta-laws: that the first-order laws are covariant under arbitrary spatial displacements, temporal displacements and spatial rotations. These spacetime symmetries require the laws to treat all spatial locations and directions alike and all moments alike. For instance, symmetry under temporal displacements rules out a fundamental force law specifying that a given force declines with the inverse-square of the distance before a given moment but with the inverse-cube of the distance at and after that moment. Wigner characterizes such a symmetry principle as ‘a superprinciple which is in …. (shrink)

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)

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)

has offered a lovely example to motivate the intuition that a successful prediction has a kind of confirmatory significance that an accommodation lacks. This paper scrutinizes Maher's example. It argues that once the example is tweaked, the intuitive difference there between prediction and accommodation disappears. This suggests that the apparent superiority of prediction to accommodation is actually a side effect of an important difference between the hypotheses that tend to arise in each case.

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)

Musical ensemble performances provide an ideal environment to gain knowledge about complex human interactions. Network structures of synchronization can reflect specific roles of individual performers on the one hand and a higher level of organization of all performers as a superordinate system on the other. This study builds on research on joint singing, using hyperscanning of respiration and heart rate variability from eight professional singers. Singers performed polyphonic music, distributing their breathing within the same voice and singing without and with (...) physical contact: that is touching each other's shoulder or waist. The idea of singing with touch was motivated by historical depictions of ensemble performances that showed singers touching each other. It raises the question of the potential benefit of touch for group performances. From a psycho-physiological point of view, physical contact should increase the synchronization of singing coordination. The results confirm previous findings on synchronization of respiration and HRV during choir singing and extend those findings to a non-homophonic musical repertoire while also revealing an increase in synchronization in respiration during physical contact. These effects were significant across different frequency ranges. The effect of physical contact was stronger when all singers were singing in comparison to the partial ensemble. Importantly, the synchronization could not be fully explained by the singing action or by the standing position or touch. This finding suggests a higher level of organization of all singers, forming a superordinate system. (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)

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)

Many philosophers argue that explanatoriness plays no special role in confirmation – that “inference to the best explanation” (IBE) incorrectly demands giving hypotheses extra credit for their potential explanatory qualities beyond the credit they already deserve for their predictive successes. This paper argues against one common strategy for responding to this thought – that is, for trying to fit IBE within a Bayesian framework. That strategy argues that a hypothesis’ explanatory quality (its “loveliness”) contributes either to its prior probability or (...) to its likelihood. This paper argues that this strategy fails because it must give different treatments to two hypotheses that are unlovely for the very same reason. The strategy therefore loses the insight into scientific reasoning that its reconstruction in terms of IBE is supposed to provide. The paper then provides a Bayesian account of the confirmatory role of explanatoriness that represents explanatory quality as having an impact in the same place for two hypotheses that are unlovely for the very same reason. This approach works by “putting explanation back into IBE” – that is, by invoking hypotheses that refer explicitly to scientific explanation and by invoking the agent's background opinions regarding the kind of explanation that the evidence is liable to have. On this approach, there is no list of “explanatory virtues” the possession of which always helps to make an explanation better. Rather, for different facts, there are different characteristics that our background knowledge of other explanations gives us some reason to expect the given fact's explanation to possess. (shrink)

Batterman and Rice offer an account of “minimal model explanations” and argue against “common features accounts” of those explanations. This paper offers some objections to their proposals and arguments. It argues that their proposal cannot account for the apparent explanatory asymmetry of minimal model explanations. It argues that their account threatens ultimately to collapse into a “common features account.” Finally, it argues against their motivation for thinking that an explanation appealing to “common features” would have to explain the common features’ (...) own prevalence. (shrink)

Why do forces compose according to the parallelogram of forces? This question has been controversial; it is one episode in a longstanding, fundamental dispute regarding which facts are not to be explained dynamically. If the parallelogram law is explained statically, then the laws of statics are separate from and “transcend” the laws of dynamics. Alternatively, if the parallelogram law is explained dynamically, then statical laws become mere corollaries to the dynamical laws. I shall attempt to trace the history of this (...) controversy in order to identify what it would be for one or the other of these rival views to be correct. I shall argue that various familiar accounts of natural law not only make it difficult to see what the point of this dispute could have been, but also improperly foreclose some serious scientific options. I will sketch an alternative account of laws that helps us to understand what this dispute was all about. (shrink)

Roche and Sober have offered a new argument for the view that a hypothesis H is not confirmed by its capacity to explain some observation O. Their argument purports to work by showing that O screens H off from the fact that H would explain O. This paper offers several objections to this argument. Firstly, the screening-off test cannot identify whatever evidential contribution Hs explanatoriness may make. Secondly, that H would explain O may be logically necessary, eluding the screening-off test. (...) Thirdly, the test cannot detect an important difference that Hs explanatoriness often makes to Hs confirmation. (shrink)

Erich Frauwallners Buch "Die Philosophie des Buddhismus" ist längst zu einem,Klassiker' geworden. Die Form der Darstellung ist glücklich gewählt; sie verknüpft allgemeine Überblicke, Einführungen in das Denken individueller buddhistischer Philosophen und lange Exzerpte aus philosophischen Werken des südasiatischen Buddhismus in wörtlicher Übersetzung. Das Buch bewegt sich also zwischen einem Einführungswerk und einer Anthologie. Die knappen Einleitungen zu den repräsentativen Texten sind informativ und klar und rücken die philosophischen Inhalte in das Licht ihrer historischen Entwicklung; die Übersetzungen aus den relevanten (...) Sprachen (Pali, Sanskrit, Tibetisch, Chinesisch) wiederum sind außerordentlich verlässlich. Der Neuauflage des Bandes wurde ein Vorwort von Eli Franco und Karin Preisendanz zu Frauwallners Leben und Schaffen beigefügt, ergänzt durch eine Bibliographie seiner Schriften und eine kommentierte Liste weiterführender Literatur zum südasiatischen Buddhismus. (shrink)

This paper analyzes the logical truths as (very roughly) those truths that would still have been true under a certain range of counterfactual perturbations.What’s nice is that the relevant range is characterized without relying (overtly, at least) upon the notion of logical truth. This approach suggests a conception of necessity that explains what the different varieties of necessity (logical, physical, etc.) have in common, in virtue of which they are all varieties of necessity. However, this approach places the counterfactual conditionals (...) in an unfamiliar foundational role. (shrink)

We say a countable model ������ has a 0-basis if the types realized in ������ are uniformly computable. We say ������ has a (d-)decidable copy if there exists a model ������ ≅ ������ such that the elementary diagram of ������ is (d-)computable. Goncharov, Millar, and Peretyat'kin independently showed there exists a homogeneous model ������ with a 0-basis but no decidable copy. We extend this result here. Let d ≤ 0' be any low₂ degree. We show that there exists a homogeneous (...) model ������ with a 0-basis but no d-decidable copy. A degree d is 0-basis homogeneous bounding if any homogenous ������ with a 0-basis has a d-decidable copy. In previous work, we showed that the nonlow₂ $\Delta _{2}^{0}$ degrees are 0-basis homogeneous bounding. The result of this paper shows that this is an exact characterization of the 0-basis homogeneous bounding $\Delta _{2}^{0}$ degrees. (shrink)

In 1984, Danecki proved that satisfiability in IPDL, i.e., Propositional Dynamic Logic (PDL) extended with an intersection operator on programs, is decidable in deterministic double exponential time. Since then, the exact complexity of IPDL has remained an open problem: the best known lower bound was the ExpTime one stemming from plain PDL until, in 2004, the first author established ExpSpace-hardness. In this paper, we finally close the gap and prove that IPDL is hard for 2-ExpTime, thus 2-ExpTime-complete. We then sharpen (...) our lower bound, showing that it even applies to IPDL without the test operator interpreted on tree structures. (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)

Fine and Rosen have argued that normative necessity is distinct from and weaker than metaphysical necessity. The first aim of this paper is to specify what it would take for this view to be true—that is, what normative necessity would have to be like. The author argues that in order for normative necessity to be weaker than metaphysical necessity, the metaphysical necessities must all be preserved under every counterfactual antecedent with which they are all collectively logically consistent—even when their preservation (...) requires that a normative necessity fail to be preserved. By exhibiting some examples that fail to display this pattern of counterfactual invariance, the author argues against the view that normative necessity is weaker than metaphysical necessity. To give this argument is the second aim of this paper. (shrink)

I offer an argument regarding chances that appears to yield a dilemma: either the chances at time t must be determined by the natural laws and the history through t of instantiations of categorical properties, or the function ch(•) assigning chances need not satisfy the axioms of probability. The dilemma's first horn might seem like a remnant of determinism. On the other hand, this horn might be inspired by our best scientific theories. In addition, it is entailed by the familiar (...) view that facts about chances at t are ontologically reducible to facts about the laws and the categorical history through t. However, that laws are ontologically prior to chances stands in some tension with the view that chances are governed by laws just as categorical-property instantiations are. The dilemma's second horn entails that if chances are in fact probabilities, then this is a matter of natural law rather than logical or conceptual necessity. I conclude with a suggestion for going between the horns of the dilemma. This suggestion involves a generalization of the notion that chances evolve by conditionalization. Introduction "Chances evolve by conditionalization" How might the lawful magnitude principle be defended? A historical interlude What if chances failed to be determined by the laws and categorical facts? (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)

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)

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)

Cognitive failures are lapses in attention, cognition, and actions that everybody experiences in everyday life. Self-reports are mainly used for assessment but those instruments are memory-biased and more related to personality aspects than to actual behavior. Ambulatory assessment is already used for capturing emotions or addictive behavior, but not yet for cognitive failures. The newly developed Questionnaire for Cognitive Failures in Everyday Life was applied via mobile phones wherein an acoustic signal asked participants 4 times daily to answer 13 questions (...) for 1 week. The new instrument showed satisfying reliability and was compared with a self-report method in terms of correlations with cognitive abilities , personality traits, and demographical aspects. Although further validation is needed, first results are promising and eKFA enriches cognitive failures research. (shrink)