The Heythrop Journal, Volume 63, Issue 1, Page 3-4, January 2022.

Contemporary discussions of skepticism often frame the skeptic's argument around an instance of the closure principle. Roughly, the closure principle states that if a subject knows p, and knows that p entails q, then the subject knows q. The main contention of this paper is that the closure argument for skepticism is defective. We explore several possible classifications of the defect. The closure argument might plausibly be classified as begging the question, as exhibiting transmission failure, or as structurally inefficient. Interestingly, (...) perhaps, each of these has been proposed as the correct classification of Moore's proof of an external world. (shrink)

In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many less familiar numbers including $-\omega, \,\omega/2, \,1/\omega, \sqrt{\omega}$ and $\omega-\pi$ to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered fields—be individually definable in terms of sets of NBG, it may be said to contain (...) “All Numbers Great and Small.” In this respect, No bears much the same relation to ordered fields that the system ℝ of real numbers bears to Archimedean ordered fields. In Part I of the present paper, we suggest that whereas $\mathbb{R}$should merely be regarded as constituting an arithmetic continuum, No may be regarded as a sort of absolute arithmetic continuum, and in Part II we draw attention to the unifying framework No provides not only for the reals and the ordinals but also for an array of non-Archimedean ordered number systems that have arisen in connection with the theories of non-Archimedean ordered algebraic and geometric systems, the theory of the rate of growth of real functions and nonstandard analysis. In addition to its inclusive structure as an ordered field, the system No of surreal numbers has a rich algebraico-tree-theoretic structure—a simplicity hierarchical structure—that emerges from the recursive clauses in terms of which it is defined. In the development of No outlined in the present paper, in which the surreals emerge vis-à-vis a generalization of the von Neumann ordinal construction, the simplicity hierarchical features of No are brought to the fore and play central roles in the aforementioned unification of systems of numbers great and small and in some of the more revealing characterizations of No as an absolute continuum. (shrink)

This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik, with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework.

Encountering the North. Cultural Geography, International Relations and Northern Landscapes. Edited by Frank Möller and Samu Pehkonen, xiii + 294 pp. $89.95/50.00 cloth. The Nordic Peace. Edited by Clive Archer and Pertti Joenniemi, x + 217 pp. $79.95/46.50 cloth. Sweden and the “Third Way”: A Macroeconomic Evaluation. By Philip Whyman, xi + 251 pp. $94.95/52.50 cloth.

The following syllogism is considered: a string is not an expression unless it is tokenable; no one can utter, write, or in anyway token an infinite string; so no infinite string is an expression. The second premise is rejected. But the tokenability of an infinite sentence is not sufficient for it being an infinite expression. A further condition is that no finite sentence expresses that sentence’s truth-conditions. So it is an open question whether English contains infinite expressions.

This essay describes and compares three attempts to provide accounts of the nature of historical consciousness, along with accompanying explanations of how one comes to have historical knowledge. It explores, compares, and contrasts the views of the late Qing dynasty Chinese philosopher Zhang Xuecheng 章學誠 and two Western philosophers – R.G. Collingwood and Louis O. Mink . These three thinkers all present historical understanding as a distinctive type of knowledge and share the aim of defending the discipline of history as (...) a special, independent field of intellectual endeavor. Aside from analyzing these aspects of their respective theories, this essay aims to stimulate extensive and nuanced comparisons between Chinese and more recent Western forms of historical consciousness. While the comparison presented here is but one way forward, it not only seeks to offer specific insights generated by the comparative project but also to set forth a range of themes worthy of future study. For example, the analysis presented here shows that Zhang’s reflections on how historians relate to the past can contribute to current discussions of epistemic virtues. (shrink)

According to a posteriori physicalism, phenomenal properties are physical properties, despite the unbridgeable cognitive gap that holds between phenomenal concepts and physical concepts. Current debates about a posteriori physicalism turn on what I call “the perspicuity principle”: it is impossible for a suitably astute cognizer to possess concepts of a certain sort—viz., narrow concepts—without being able to tell whether the referents of those concepts are the same or different. The perspicuity principle tends to strike a posteriori physicalists as implausibly rationalistic; (...) further, a posteriori physicalists maintain that even if the principle is applicable to many narrow concepts, phenomenal concepts have unique features that render them inferentially isolated from other narrow concepts ). I argue, on the contrary, that the case for the perspicuity principle is quite strong. Moreover, not only have versions of the PCS repeatedly failed, likely, all versions will, given the strange combination of lucidity and opacity that the PCS has to juggle. I conclude that a posteriori physicalists currently lack a principled objection to classic anti-physicalist arguments. (shrink)

"_Heidegger and Modernity_ is an intervention in the Heidegger debate in France which many may see as decisive. Its central claim is that the responses of left Heideggerians to continuing disclosures regarding Heidegger's Nazi affiliations fail to come to terms with central ambiguities in his philosophical responses, both early and late, to modernity and technology.... Incisive and hard hitting, Luc Ferry and Alain Renault have condensed in a short and tightly organized book both a judicious and well-informed account of the (...) Heidegger question and an implicit defence of humanism which has a strong political resonance."—Liam O'Sullivan, _Political Studies_. (shrink)

The present account, based on introspective comments, deals with motivation and hedonic tone as subjective factors which affect continuous work at high speeds. Actual introspective reports are given. The earlier papers in the series described the experimental procedure and presented objective data.

Engaging variously with the legacy of Paul L. Lehmann, these essays argue for a reorientation in Christian theology that better honours the formative power of ...

One of the deepest problems in philosophical theology is that of divine causality and human freedom. The analogy between God and the author of a work of fiction can shed light on this and many other thorny problems in philosophical and dogmatic theology.

I review three problems that have historically motivated pessimism about artificial intelligence: (1) the Problem of Consciousness, according to which artificial systems function without the right sort of conscious oversight; (2) The Problem of Global Relevance, according to which artificial systems cannot solve fully general theoretical and practical problems; (3) The Problem of Semantic Irrelevance, according to which artificial systems cannot be guided by semantic comprehension. I connect the dots between all three problems by drawing attention to non-syntactic inferences—inferences that (...) are made on the basis of insight into the rational relationships among thought-contents. Consciousness alone affords such insight, I argue, and such insight alone confers positive epistemic status on the execution of the inferences. Only when artificial systems can execute inferences that are rationally guided by phenomenally conscious states will such systems count as intelligent in a literal sense. (shrink)