Probabilistic Regresses and the Availability Problem for Infinitism

Recent work by Peijnenburg, Atkinson, and Herzberg suggests that infinitists who accept a probabilistic construal of justification can overcome significant challenges to their position by attending to mathematical treatments of infinite probabilistic regresses. In this essay, it is argued that care must be taken when assessing the significance of these formal results. Though valuable lessons can be drawn from these mathematical exercises (many of which are not disputed here), the essay argues that it is entirely unclear that the form of infinitism that results meets a basic requirement: namely, providing an account of infinite chains of propositions qua reasons made available to agents.     

Introduction

This introduction presents selected proceedings of a two‐day meeting on the regress problem, sponsored by the Netherlands Organization for Scientific Research (NWO) and hosted by Vanderbilt University in October 2013, along with other submitted essays. Three forms of research on the regress problem are distinguished: metatheoretical, developmental, and critical work.     

The Astounding Assumption of Infinite Life

The multimillennial philosophical discussion about life after death has received a recent boost in the prospect of immortality attained via technologies. In this newer version, humans generally are considered mortal but may develop means of making themselves immortal. If “immortal” means not mortal, thus existing for infinity, and if the proposed infinite‐existing entity is material, it must inhabit an infinite material universe. If the proposed entity is not material, there must be means by which it can shed its material substance and exist nonmaterially. The article examines arguments for how an infinite life would be possible given current physical understanding. The paper considers a Pascalian‐style wager weighing the likelihood of adjusting to existence wholly within a finite universe versus betting on there being some way to construe the universe(s) as a viable medium for infinite beings. Conclusion: the case for a finite being to exist infinitely has little viable support.     

Fisher与Neyman–Pearson的分歧与心理统计中的假设检验争议

假设检验思想的提出者Fisher与Neyman–Pearson在统计模型的方法论基础、两类错误的性质、显著性水平的理解、以及假设检验的功能等方面存在诸多分歧, 使得心理统计中最常用的原假设显著性检验模式呈现出隐含的各种矛盾, 从而引发了应用上的争议。心理统计不仅需要检讨现有检验模型的模糊之处和提出其他补充性的统计推论方式,更应注重反思心理统计的教育传统, 以建立更加开放和多元的统计应用视野, 使心理统计为更好地心理学研究服务。     

Symmetric frenzy and catastrophic change: A consideration of primitive mental states in the wake of Bion and Matte Blanco

The author explores the connections between Matte Blanco's notion of symmetric frenzy, i.e. the turbulence characteristic of the deepest levels of mental functioning, and Bion's concept of catastrophic change. For Bion, mental links are retrieved from the formless darkness of infinity. With catastrophic change, emotional violence and the confining nature of representation come into conflict, leaving the subject prey to an explosiveness that paralyses mental resources. Matte Blanco identifies indivisibility as the abyss in which all differentiation ceases; he bases his model on the conflict between symmetry and asymmetry. Infinity, he maintains, is where the first forms of mentalization develop. Both Bion and Matte Blanco emphasize the contrast between the immensity of mental space and the spatio-temporal order introduced by the activation of thinking functions. The author presents clinical material from the analysis of a psychotic patient, stressing the need to encourage both working through the defect of thinking (Bion) and 'unfolding' manifestations of symmetry (Matte Blanco) so as to foster the activation of the resources of thought, meanwhile postponing transference interpretation. He concludes with two later sessions, in which recognition of the analyst in the transference allows the analysand to develop his capacity for containment and asymmetric differentiation.     

From Inexactness to Certainty: The Change in Hume's Conception of Geometry

Although Hume's analysis of geometry continues to serve as a reference point for many contemporary discussions in the philosophy of science, the fact that the first Enquiry presents a radical revision of Hume's conception of geometry in the Treatise has never been explained. The present essay closely examines Hume's early and late discussions of geometry and proposes a reconstruction of the reasons behind the change in his views on the subject. Hume's early conception of geometry as an inexact non-demonstrative science is argued to be a consequence of his attempt to discredit geometrical proofs of infinite divisibility of extension by anchoring the meaning of geometrical concepts in inherently inexact qualitative measurement procedures. This measurement-based attack on the exactness and certainty of geometry is analyzed and shown to be both self-refuting and inconsistent with the general epistemological framework of the Treatise. The revised conception of geometry as a demonstrative science in the first Enquiry is then interpreted as Hume's response to the failure of his earlier attempt to discredit geometrical proofs of infinite divisibility of extension. This revised version was published online in August 2006 with corrections to the Cover Date.     

Infinite Epistemic Regresses and Internalism

This article seeks to state, first, what traditionally has been assumed must be the case in order for an infinite epistemic regress to arise. It identifies three assumptions. Next it discusses Jeanne Peijnenburg's and David Atkinson's setting up of their argument for the claim that some infinite epistemic regresses can actually be completed and hence that, in addition to foundationalism, coherentism, and infinitism, there is yet another solution (if only a partial one) to the traditional epistemic regress problem. The article argues that Peijnenburg and Atkinson fail to address the traditional regress problem, as they don't adopt all of the three assumptions that underlie the traditional regress problem. It also points to a problem in the notion of making probable that Peijnenburg and Atkinson use in their account of justification.     

Boring Infinite Descent

In formal ontology, infinite regresses are generally considered a bad sign. One debate where such regresses come into play is the debate about fundamentality. Arguments in favour of some type of fundamentalism are many, but they generally share the idea that infinite chains of ontological dependence must be ruled out. Some motivations for this view are assessed in this article, with the conclusion that such infinite chains may not always be vicious. Indeed, there may even be room for a type of fundamentalism combined with infinite descent as long as this descent is “boring,” that is, the same structure repeats ad infinitum. A start is made in the article towards a systematic account of this type of infinite descent. The philosophical prospects and scientific tenability of the account are briefly evaluated using an example from physics.     

The First Antinomy and Spinoza

Scholars commonly assume that Kant never seriously engaged with Spinoza or Spinozism. However, in his later writings Kant argues several times that Spinozism is the most consistent form of transcendental realism. In the first part of the paper, I argue that the first Antinomy, debating the age and size of the world, already reflects Kant's confrontation with Spinozist metaphysics. Specifically, the position articulated in the Antithesis – according to which the world is infinite and uncreated – is Spinozist, not Leibnizian, as commonly assumed. In the second part of the paper, I raise the chief Spinozist challenge to the Antinomy, arising from Spinoza's reliance on a cosmological `totum analyticum' – an infinite whole which is prior to its parts. In conclusion, I begin to elaborate a defence of the Kantian position, confronting Spinoza's infinite whole with Kant's account of the absolutely infinite in his discussion of the sublime.