We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.

We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.

Tarski [5] showed that for any set X, its set w(X) of well-orderable subsets has cardinality strictly greater than that of X, even in the absence of the axiom of choice. We construct a Fraenkel-Mostowski model in which there is an infinite strictly descending sequence under the relation |w (X)| = |Y|. This contrasts with the corresponding situation for power sets, where use of Hartogs' ℵ-function easily establishes that there can be no infinite descending sequence under the relation |P(X)| = (...) |Y|. (shrink)

We propose Rhythmic Relating for autism: a system of supports for friends, therapists, parents, and educators; a system which aims to augment bidirectional communication and complement existing therapeutic approaches. We begin by summarizing the developmental significance of social timing and the social-motor-synchrony challenges observed in early autism. Meta-analyses conclude the early primacy of such challenges, yet cite the lack of focused therapies. We identify core relational parameters in support of social-motor-synchrony and systematize these using the communicative musicality constructs: pulse; quality; (...) and narrative. Rhythmic Relating aims to augment the clarity, contiguity, and pulse-beat of spontaneous behavior by recruiting rhythmic supports and relatable vitality; facilitating the predictive flow and just-ahead-in-time planning needed for good-enough social timing. From here, we describe possibilities for playful therapeutic interaction, small-step co-regulation, and layered sensorimotor integration. Lastly, we include several clinical case examples demonstrating the use of Rhythmic Relating within four different therapeutic approaches. These clinical case examples are introduced here and several more are included in the Supplementary Material. A suite of pilot intervention studies is proposed to assess the efficacy of combining Rhythmic Relating with different therapeutic approaches in playful work with individuals with autism. Further experimental hypotheses are outlined, designed to clarify the significance of certain key features of the Rhythmic Relating approach. (shrink)

It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-permutation-models of assertions which have perfectly sensible ZF-style meanings, such as: the existence of wellfounded sets of great size or rank, or the nonexistence of small counterexamples to the wellfoundedness of ∈. Everything here holds also for NFU if the permutations are taken to fix all urelemente.

There is an interesting problem concerning component causes posed by Cartwright (1983) in her book How the Laws of Physics Lie, which is easily explained in terms of a simple example. Consider a cup sitting on the table. Why doesn’t it move? The explanation given by Newtonian mechanics is that the cup is experiencing two forces-the downward force of gravity and the upward ‘elastic’ force of the table-and these two forces exactly cancel to produce a zero resultant force. This zero (...) resultant force then produces a zero acceleration, which ‘explains’ why the cup doesn’t move. This rather simple, yet typical, example of theoretical explanation raises a surprisingly deep puzzle: What justification is there for believing in the existence of the component forces if they are redundant to the explanation? For it does not really matter what size the component forces are so long as their resultant is zero. (shrink)

Leitfaden zu einer künftigen Geschichte der Menschheit.--Über die Humanität des Künstlers.--Über historische Glaubwürdigkeit.--Über den gelehrten Zunftzwang.--Fragment einer Rede, gehalten in Mainzer Jakobiner klub.--Anrede an die Gesellschaft der Freunde der Freiheit und Gleichheit am Neujahrstage 1793.--Parisische Umrísse.

This book is remarkable for what it does not do. It purports to be about Peirce's opposition to nominalism, but it never states clearly what nominalism is and says little about Peirce's realist alternative. It contains no historical discussion of nominalism and thus does not explain the relation of Peirce's idiosyncratic use of that term to its original meaning. It ignores the secondary literature on that topic and does not even list Rosa Mayorga's highly relevant 2007 book, From Realism to (...) Realicism [sic], in its Bibliography. Nor, despite nominalism's alleged 'threat,' does it make reference to such important recent nominalists as Nelson Goodman or W.V.O. Quine. Indeed, after page one, there is hardly any.. (shrink)

"...T S Eliot was unimpressed by Freud. Eliot preferred the more approachable Roger Vittoz. It was only Scofield Thayer, who in his prolonged therapy with Sigmund Freud can be said to have brought anything Freudian in the classically psychoanalytic sense to Modernism." This is from the review. The review of the book is contrarian as the book under review is. The salient points of the book are interrogated in this review.

Recent years have seen a wave of new scholarship on Georg Forster. At least five books substantially concerned with Forster have been published since 2017.1 This interest is hardly surprising. He t...

This book not only sets the historical record straight but also champions the Herderian tradition for its philosophical depth and breadth.

Scientific discovery is often regarded as romantic and creative - and hence unanalyzable - whereas the everyday process of verifying discoveries is sober and more suited to analysis. Yet this fascinating exploration of how scientific work proceeds argues that however sudden the moment of discovery may seem, the discovery process can be described and modeled. Using the methods and concepts of contemporary information-processing psychology (or cognitive science) the authors develop a series of artificial-intelligence programs that can simulate the human thought (...) processes used to discover scientific laws. The programs - BACON, DALTON, GLAUBER, and STAHL - are all largely data-driven, that is, when presented with series of chemical or physical measurements they search for uniformities and linking elements, generating and checking hypotheses and creating new concepts as they go along. "Scientific Discovery examines the nature of scientific research and reviews the arguments for and against a normative theory of discovery; describes the evolution of the BACON programs, which discover quantitative empirical laws and invent new concepts; presents programs that discover laws in qualitative and quantitative data; and ties the results together, suggesting how a combined and extended program might find research problems, invent new instruments, and invent appropriate problem representations. Numerous prominent historical examples of discoveries from physics and chemistry are used as tests for the programs and anchor the discussion concretely in the history of science. Pat Langley is an Associate Professor in the Department of Information and Computer Science at the University of California, Irvine.Herbert Simon is a Professor in the Departments of Psychology, Computer Science, and Philosophy at Carnegie-Mellon University. Gary L. Bradshaw is an Assistant Professor in the Department of Psychology and Institute of Cognitive Science at the University of Colorado, Boulder. Jan M. Zytkow is an Associate Professor in the Computer Science Department at Wichita State University. (shrink)

We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$ , except trivially. We derive this as a corollary of a more general result concerning variable sharing.

The Afterword reevaluates Isaiah Berlin’s highly influential collection of essays, Russian Thinkers, and suggests that some of Berlin’s views are either somewhat dated or tendentious. It sketches out a new vision of the Russian intellectual tradition as perceived from the twenty-first-century Anglophone perspective.