Although many researchers theorize that primitive numerosity processing abilities may lay the foundation for whole number concepts, other classes of numbers, like fractions, are sometimes assumed to be inaccessible to primitive architectures. This research presents evidence that the automatic processing of nonsymbolic magnitudes affects processing of symbolic fractions. Participants completed modified Stroop tasks in which they selected the larger of two symbolic fractions while the ratios of the fonts in which the fractions were printed and the overall sizes of the (...) compared fractions were manipulated as irrelevant dimensions. Participants were slower and less accurate when nonsymbolic dimensions of printed fractions were incongruent with the symbolic comparison decision. Results indicated a robust basic sensitivity to nonsymbolic ratios that exceeds prior conceptions about the accessibility of fraction values. Results also indicated a congruity effect for overall fraction size, contrary to findings of prior research. These findings have implications for extending theory about the nature of human number sense and mathematical cognition more generally. (shrink)

Clarke and Beck suggest that the ratio processing system may be a component of the approximate number system, which they suggest represents rational numbers. We argue that available evidence is inconsistent with their account and advocate for a two-systems view. This implies that there may be many access points for numerical cognition – and that privileging the ANS may be a mistake.

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and connections to symbolic numbers remains in its infancy. The current research aims to further explore these similarities by investigating whether the magnitudes of nonsymbolic ratios are associated with space just as symbolic (...) numbers are. In two experiments, we found that responses were faster on the left for smaller nonsymbolic ratio magnitudes and faster on the right for larger nonsymbolic ratio magnitudes. These results further elucidate the nature of nonsymbolic ratio processing, extending the literature of spatial–numerical associations to nonsymbolic relative magnitudes. We discuss potential implications of these findings for theories of human magnitude processing in general and how this general processing relates to numerical processing. (shrink)

Cognitive Science, Volume 46, Issue 6, June 2022.

We present a one per cent measurement of the cosmic distance scale from the detections of the baryon acoustic oscillations in the clustering of galaxies from the Baryon Oscillation Spectroscopic Survey, which is part of the Sloan Digital Sky Survey III. Our results come from the Data Release 11 sample, containing nearly one million galaxies and covering approximately 8500 square degrees and the redshift range 0.2 < z < 0.7. We also compare these results with those from the publicly released (...) DR9 and DR10 samples. Assuming a concordance Λ cold dark matter cosmological model, the DR11 sample covers a volume of 13 Gpc3 and is the largest region of the Universe ever surveyed at this density. We measure the correlation function and power spectrum, including density-field reconstruction of the BAO feature. The acoustic features are detected at a significance of over 7σ in both the correlation function and power spectrum. Fitting for the position of the acoustic features measures the distance relative to the sound horizon at the drag epoch, rd, which has a value of rd,fid = 149.28 Mpc in our fiducial cosmology. We find DV = at z = 0.32 and DV = at z = 0.57. At 1.0 per cent, this latter measure is the most precise distance constraint ever obtained from a galaxy survey. Separating the clustering along and transverse to the line of sight yields measurements at z = 0.57 of DA = and H =. Our measurements of the distance scale are in good agreement with previous BAO measurements and with the predictions from cosmic microwave background data for a spatially flat CDM model with a cosmological constant. © 2014 The Author Published by Oxford University Press on behalf of the Royal Astronomical Society. (shrink)

The dominant feature of eighteenth-century aesthetic is the inquiry and discussion concerning the theory of “taste.” There is material or bibliographical evidence of this in the rapid sequence of treatises, essays, inquiries, observations, and controversies on this subject, extending from the close of the seventeenth to the last years of the eighteenth century, and bearing the names, in France, of Dacier, Bellegarde, Bouhours, Rollin, Seran de la Tour, Trublet, Formey, Bitaubé, Marmontel, and, still more eminent, of Montesquieu, Voltaire, d’Alembert; in (...) England, of Addison, Hume, Gerard, Home, Burke, Priestley, Blair, Beattie, Percival, Reid, Alison; in Italy, of Muratori, Calepio, Pagano, Corniani; in Germany, of Thomasius, J. U. König, Bodmer, A. von Schlegel, Wegelin, Heyne, Herz, Eberhard, J. C. König, and, by German influence in Hungary, Szardahely; and, greatest of all, Immanuel Kant, whoseCritique of Judgmentconsists in the main of a critique of the aesthetic judgment of taste. (shrink)

Richard Dawkins tries to establish an analogy between computer viruses and theistic belief systems, analyzing the latter in terms of his concept of the meme. The underlying thrust of Dawkins' argument is to downplay the role of truth and logic in the survival of theories and to emphasize humankind's helpless liability to incurable infection by doctrines that Dawkins regards as absurd. Dawkins supplies a list of "symptoms” of mind-infection. However, on closer investigation these characteristics are found to be either rather (...) weak protection against criticism or quite virtuous. Dawkins relies on a crude justificationism that could just as well be called a mind-virus. Applying Dawkins’ own selection of the general characteristics of a good meme protector and propagator leads to the conclusion that his particular theistic examples would actually impair copyability. -/- Scientific theories are better examples of memes with high longevity, fecundity, and fidelity. A Darwinian analysis of wishful and fearful thinking as useful to hypotheses-testing and goal-seeking organisms undermines Dawkins' attribution of absolute irrational stubbornness to theists. To counterbalance Dawkins' emphasis on the propagation of the absurd, I rehabilitate the Socratic emphasis on the importance of truth and logic in rhetoric, interpreted broadly as the theory of the successful propagation of a message. I use Popper's notion of situational analysis, and an evolutionary perspective to argue that rational standards of a message enhance its copyability. I further apply Popper’s notions of World 3, 2, and 1 to memes; this helps us see the perpetuation of a doctrine as a logical task. (shrink)

Originally published in 1940, this book contains an expanded English translation of Books 8 and 9 of Aristotle's Nicomachean Ethics. These two books are devoted to a discussion on the nature of friendship and the role it played in Greek life, and Percival supplies an introduction with a background to the subject of ancient friendship prior to Aristotle's formulation. This book will be of value to anyone with an interest in ancient friendship or the philosophy of Aristotle.

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

I aim to illuminate foundational epistemological issues by reflecting on 'epistemic consequentialism'—the epistemic analogue of ethical consequentialism. Epistemic consequentialism employs a concept of cognitive value playing a role in epistemic norms governing belief-like states that is analogous to the role goodness plays in act-governing moral norms. A distinction between 'direct' and 'indirect' versions of epistemic consequentialism is held to be as important as the familiar ethical distinction on which it is based. These versions are illustrated, respectively, by cognitive decision-theory and (...) reliabilism. Cognitive decision-theory is defended, and various conceptual issues concerning it explored. A simple dilemma suggests that epistemic consequentialism has radical consequences. (shrink)

Hume's Reception in Early America: Expanded Edition brings together the original American responses to one of Britain's greatest men of letters, David Hume. Now available as a single volume paperback, this new edition includes updated further readings suggestions and dozens of additional primary sources gathered together in a completely new concluding section. From complete pamphlets and booklets, to poems, reviews, and letters, to extracts from newspapers, religious magazines and literary and political journals, this book's contents come from a wide variety (...) of sources published in colonial America and the early United States between 1758 and 1850. As well as classics by Thomas Jefferson, John Adams and Alexander Hamilton, it contains scores of unknown and hard-to-locate items, many of which have not been reprinted since their original publication. These responses are divided into four parts covering Hume's Essays; his Philosophical Writings; his History of England; and his Character and Death. Each of those parts has a separate introductory essay, and every selection is introduced by a short headnote that sets the piece in its historical context and provides bibliographical references. Packed with new insights into Hume and American thought and culture, Hume's Reception in Early America reveals the relevance and impact of Hume on American political, philosophical, historical, religious, and aesthetic debates. (shrink)

[Philip Percival] I aim to illuminate foundational epistemological issues by reflecting on 'epistemic consequentialism'-the epistemic analogue of ethical consequentialism. Epistemic consequentialism employs a concept of cognitive value playing a role in epistemic norms governing belief-like states that is analogous to the role goodness plays in act-governing moral norms. A distinction between 'direct' and 'indirect' versions of epistemic consequentialism is held to be as important as the familiar ethical distinction on which it is based. These versions are illustrated, respectively, by (...) cognitive decision-theory and reliabilism. Cognitive decision-theory is defended, and various conceptual issues concerning it explored. A simple dilemma suggests that epistemic consequentialism has radical consequences. /// [Robert Stalnaker] After reviewing the general ideas of the consequentialist framework, I take a critical look at two of the epistemic consequentialist projects that Philip Percival considers in his paper: the first assumes that there is a notion of acceptance that contrasts with belief and that can be evaluated by its expected epistemic utility. The second uses epis utility to evaluate beliefs and partial beliefs themselves, as well as actions, such as gathering information in the course of an inquiry. I express scepticism about the notion of acceptance required for the first project, and argue that the second kind of project can be fruitful only with a richer notion of epistemic utility than has yet been developed. (shrink)

Philip Percival; X*—Absolute Truth, Proceedings of the Aristotelian Society, Volume 94, Issue 1, 1 June 1994, Pages 189–214, https://doi.org/10.1093/aristotelia.

I aim to illuminate foundational epistemological issues by reflecting on ‘epistemic consequentialism’—the epistemic analogue of ethical consequentialism. Epistemic consequentialism employs a concept of cognitive value playing a role in epistemic norms governing belief-like states that is analogous to the role goodness plays in act-governing moral norms. A distinction between ‘direct’ and ‘indirect’ versions of epistemic consequentialism is held to be as important as the familiar ethical distinction on which it is based. These versions are illustrated, respectively, by cognitive decision-theory and (...) reliabilism. Cognitive decision-theory is defended, and various conceptual issues concerning it explored. A simple dilemma suggests that epistemic consequentialism has radical consequences. (shrink)

PaceZagzebski, there is no route from the value of knowledge to a non–reliabilist virtue–theoretic epistemology. Her discussion of the value problem is marred by an uncritical and confused employment of the notion of a “state” of knowledge, an uncritical acceptance of a “knowledge–belief” identity thesis, and an incoherent presumption that the widely held thought that knowledge is more valuable than true belief amounts to the view that knowledge is a state of true belief having an intrinsic property which a state (...) of ‘mere” true belief lacks. Her arguments against a “machine–product” conception of knowledge are undermined by these flaws, while the alternative “agent–act” model she recommends is unattractive, at odds with the knowledge–belief identity thesis she favours, and no solution to the problem of the value of knowledge she poses. I end with the observation that her version of virtue–theoretic epistemology points in the direction of cognitive decision–theoretic norms, and I briefly discuss the bearing of this fact upon her viewpoint. (shrink)