First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Some mathematical proofs explain why the theorems they prove hold. This paper identifies several challenges for any counterfactual account of explanation in mathematics (that is, any account according to which an explanatory proof reveals how the explanandum would have been different, had facts in the explanans been different). The paper presumes that countermathematicals can be nontrivial. It argues that nevertheless, a counterfactual account portrays explanatory power as too easy to achieve, does not capture explanatory asymmetry, and fails to specify why (...) certain proofs are explanatory and others are not. Greater informativeness about counterfactual dependence can even yield less explanatory power. (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)

Myrvold (2003) has proposed an attractive Bayesian account of why theories that unify phenomena tend to derive greater epistemic support from those phenomena than do theories that fail to unify them. It is argued, however, that "unification" in Myrvold's sense is both too easy and too difficult for theories to achieve. Myrvold's account fails to capture what it is that makes unification sometimes count in a theory's favor.

For theologians, to conceive of God in terms of light has some undeniable advantages, allowing a middle-of-the road position between the two extremes of thinking about God in terms of a purely disembodied, unfathomable, unsensible being, and of crediting Him with a body, possibly even a human body. This paper first reviews the reasons why God, in early medieval Islam, was never fully theorized in terms of light. It then proceeds to discuss light-related narratives in two major, late-medieval compilations of (...) hadiths about the afterlife, by al-Suyuti and al-Majlisi, suggesting that eschatology was the area in which God’s light continued to shine in Islam, and the backdoor through which a theology of light, in the thought of al-Suhrawardi and his followers, made a triumphant re-entry into Islamic thought. (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)

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)

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)

Philosophers frequently refer to ‘flow’ when discussing skill and expertise. This is especially clear when considering the ‘flow argument’ advocated by the Automatic view. Although the Automatic view is a minority position today, many philosophers and scientists endorse the flow argument or central parts of it. The present paper argues that the argument is implausible in the light of current psychological research. It proceeds in two steps. First, the paper argues that the psychological research does _not_ suggest that flow is (...) the only type of psychological state characteristic of optimal expert performance. Experts undergo different states, notably the state of clutch. Second, the paper argues that the psychological research does _not_ suggest that flow states are devoid of conscious supervision in the form of conscious control, self-awareness, or task-related thoughts. Experts execute multiple conscious operations involved in attention control, motivational self-talk, and certain psychological mindsets while being in flow. These considerations oppose the two premises of the flow argument. Moreover, they correct misunderstandings of flow in the broader philosophical and scientific literature. (shrink)

Let K be a family of structures, closed under isomorphism, in a fixed computable language. We consider effective lists of structures from K such that every structure in K is isomorphic to exactly one structure on the list. Such a list is called a computable classification of K, up to isomorphism. Using the technique of Friedberg enumeration, we show that there is a computable classification of the family of computable algebraic fields and that with a 0'-oracle, we can obtain similar (...) classifications of the families of computable equivalence structures and of computable finite-branching trees. However, there is no computable classification of the latter, nor of the family of computable torsion-free abelian groups of rank 1, even though these families are both closely allied with computable algebraic fields. (shrink)

With the rise and public accessibility of AI-enabled decision-support systems, individuals outsource increasingly more of their decisions, even those that carry ethical dimensions. Considering this trend, scholars have highlighted that uncritical deference to these systems would be problematic and consequently called for investigations of the impact of pertinent technology on humans’ ethical decision-making. To this end, this article conducts a systematic review of existing scholarship and derives an integrated framework that demonstrates how intelligent decision-support systems (IDSSs) shape humans’ ethical decision-making. (...) In particular, we identify resulting consequences on an individual level (i.e., deliberation enhancement, motivation enhancement, autonomy enhancement and action enhancement) and on a societal level (i.e., moral deskilling, restricted moral progress and moral responsibility gaps). We carve out two distinct methods/operation types (i.e., processoriented and outcome-oriented navigation) that decision-support systems can deploy and postulate that these determine to what extent the previously stated consequences materialize. Overall, this study holds important theoretical and practical implications by establishing clarity in the conceptions, underlying mechanisms and (directions of) influences that can be expected when using particular IDSSs for ethical decisions. (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)

This paper challenges the traditional notions of ‘Monophysitism’ and ‘Nestorianism’ or ‘The Nestorian Church’. With regard to ‘Monophysitism’, it argues that two interpretations of the basic ‘Alexandrian’ Christological formula of the ‘one nature of the God-Logos incarnate’ need to be distinguished. One, according to which the individual properties of the two ‘natures’ of Christ were lost and mixed, and which can, indeed, be referred to as ‘Monophysitism’ – in contrast to another interpretation which insisted that the individual characteristics of the (...) two ‘natures’ were preserved and the ‘God-Logos incarnate’ remained consubstantial with human beings (homoousios hēmin). This second approach might be better referred to as ‘Miaphysitism’. Similarly, this contribution suggests that it seems necessary to differentiate between what Nestorius of Constantinople himself taught and what his opponent Cyrill of Alexandria imputed to him. When analyzing Nestorius’ own writings, it becomes clear that Nestorius neither challenged the true union between the God-Logos and the ‘Man’ nor assumed a time in which the ‘Man’ existed prior to his unification with the God-Logos. Therefore, Nestorius taught no ‘Nestorianism’ in the sense in which Cyrill of Alexandria introduced it. Likewise, the Christology of the Apostolic Church of the East is based on the views of Theodore of Mopsuestia. It is not before the 6th century that representatives of this Church discovered Nestorius as a martyr for the ‘orthodox belief’ who was persecuted by the Egyptian ‘Pharaoh’, just as had been John Chrysostom before him. Because of its loyalty to the Christology of Theodore of Mopsuestia, it seems rather fitting to abandon the inappropriate title ‘Nestorian Church’ – a polemical title that has been pinned on the ‘Church of the East’ by its theological opponents from the 6th century onwards. (shrink)

O presente trabalho apresenta os bastidores de uma pesquisa realizada sobre a Faculdade Católica de Filosofia de Rio Grande (1960- 1969), cuja criação marcou o início dos cursos superiores voltados à formação docente na cidade. Para destacar sua história, recorre-se a diferentes fontes, como documentos institucionais, jornais locais e relatos orais, cuja utilização será aqui abordada. Nesse sentido, tem-se como base os caminhos abertos pela História Cultural as quais vêm propiciando a ampliação de problemas, objetos e temas de pesquisa histórica. (...) Constata-se que a multiplicidade de histórias e memórias sobre essa instituição educacional só foram descortinadas devido à ampliação do olhar sobre as diferentes fontes de pesquisa. (shrink)