Philosophers agree that scientific explanations aim to produce understanding, and that good ones succeed in this aim. But few seriously consider what understanding is, or what the cues are when we have it. If it is a psychological state or process, describing its specific nature is the job of psychological theorizing. This article examines the role of understanding in scientific explanation. It warns that the seductive, phenomenological sense of understanding is often, but mistakenly, viewed as a cue of genuine understanding. (...) The article closes with a discussion of several new paths of research that tie the psychology of scientific explanation to cognate notions of learning, testimony, and understanding. (shrink)

Scientists and laypeople alike use the sense of understanding that an explanation conveys as a cue to good or correct explanation. Although the occurrence of this sense or feeling of understanding is neither necessary nor sufficient for good explanation, it does drive judgments of the plausibility and, ultimately, the acceptability, of an explanation. This paper presents evidence that the sense of understanding is in part the routine consequence of two well-documented biases in cognitive psychology: overconfidence and hindsight. In light of (...) the prevalence of counterfeit understanding in the history of science, I argue that many forms of cognitive achievement do not involve a sense of understanding, and that only the truth or accuracy of an explanation make the sense of understanding a valid cue to genuine understanding. (shrink)

This article focuses on the role of statistical concepts in both experiment and theory in various scientific disciplines, especially physics, including astronomy, and psychology. In Sect. 1 the concept of uncertainty in astronomy is analyzed from Ptolemy to Laplace and Gauss. In Sect. 2 theoretical uses of probability and statistics in science are surveyed. Attention is focused on the historically important example of radioactive decay. In Sect. 3 the use of statistics in biology and the social sciences is examined, with (...) detailed consideration of various Chi-square statistical tests. Such tests are essential for proper evaluation of many different kinds of scientific hypotheses. (shrink)

ArgumentTextual and material evidence suggests that early Byzantine architects, known asmechanikoi, were comprehensively educated in the mathematical sciences according to contemporary standards. This paper explores the significance of the astronomical and optical sciences for the working methods of the twomechanikoiof Hagia Sophia in Constantinople, Anthemios of Tralles and Isidoros of Miletus. It argues that one major concern in the sixth-century architectural design of the Great Church was the visual effect of its sacred interior, particularly the luminosity within. Anthemios and Isidoros (...) seem to have been thoroughly conversant with the ancient corpus of astronomical and optical writings and, as will be shown, implemented their theoretical knowledge in the design of Hagia Sophia. Specifically, the paper demonstrates that the orientation of the building's longitudinal axis coincides with the sunrise on the winter solstice according to ancient computations, implying that the orientation was intentionally calculated in order to secure an advantageous natural illumination of the interior. Light and visual effects served to reinforce the symbolic significance of the sacred space that furthermore provides evidence for optical considerations with respect to late antique concepts of light and vision. (shrink)

What is the relationship between observations, predictions, texts, and instruments in ancient astrology? By distinguishing between two distinct kinds of observation claim in astrological texts, I show on the one hand the rhetorical and theoretical importance of each kind of observation claim to ancient astrological traditions, and on the other hand how practices of ancient astrology break from observation once astronomical phenomena become reliably predictable. We thus see a shift in practice from observationally derived predictions to a reliance on textual (...) and instrumental authority, even though the rhetoric of ancient astrology still tries to maintain an emphasis on observation.Author Keywords: Astrology; Astrometeorology; Astronomy; Divination; Instruments; Observation; Parapegmata; Prediction; Rhetoric; Signs; Weather. (shrink)

The attempt to narrow the general discourse of the problem of error and to focus it on the specific problem of experimental error may be approached from different directions. One possibility is to establish a focusing process from the standpoint of history; such an approach requires a careful scrutiny of the history of science with a view to identifying the juncture when the problem of experimental error was properly understood and accounted for. In a study of this kind one would (...) have to examine the evolution of the method of experimentation and related topics so that clear criteria would underlie the analysis. (shrink)

► I present an intellectual history of Ptolemy’s accounts of the human soul. ► I assess the accounts for consistency. ► I argue that disparities in the psychological accounts are significant. ► I argue that the disparities demonstrate the maturation of his scientific method.

According to selective, retentive, scientific realism, past empirical success may be explained only by the parts of past theories that are responsible of their successful predictions being approximately true, and thus theoretically retained, or approximated, by the parts of posterior theories responsible of the same successful predictions. In this article, we present as case study the transit from Ptolemy’s to Kepler’s astronomy, and their successful predictions for Mars’ orbit. We present an account of Ptolemy’s successful prediction of Mars’ orbit from (...) Kepler’s perspective, and scrutinize whether the theoretical elements responsible for Ptolemy’s empirical success are approximately retained in Kepler. In order to give to the realist the best chances, we try different strategies. We conclude that all fail and thereby this case constitutes a prima facie strong anomaly for selective retentive realism. Structural realists may call preservation of structure to the rescue, but the existing notions of structure do not work. In absence of a new notion that works, the burden of the proof lies on the realist side. (shrink)

ABSTRACT Throughout the early modern period, the most widely read astronomical textbooks were Johannes de Sacrobosco's De sphaera and the Theorica planetarum, ultimately in the new form introduced by Georg Peurbach. This essay argues that the images in these texts were intended to develop an “intelligent eye.” Students were trained to transform representations of specific heavenly phenomena into moving mental images of the structure of the cosmos. Only by learning the techniques of mental visualization and manipulation could the student “see” (...) in the mind's eye the structure and motions of the cosmos. While anyone could look up at the heavens, only those who had acquired the intelligent eye could comprehend the divinely created order of the universe. Further, the essay demonstrates that the visual program of the Sphaera and Theorica texts played a significant and hitherto unrecognized role in later scientific work. Copernicus, Galileo, and Kepler all utilized the same types of images in their own texts to explicate their ideas about the cosmos. (shrink)

ABSTRACT Throughout the early modern period, the most widely read astronomical textbooks were Johannes de Sacrobosco's De sphaera and the Theorica planetarum, ultimately in the new form introduced by Georg Peurbach. This essay argues that the images in these texts were intended to develop an “intelligent eye.” Students were trained to transform representations of specific heavenly phenomena into moving mental images of the structure of the cosmos. Only by learning the techniques of mental visualization and manipulation could the student “see” (...) in the mind's eye the structure and motions of the cosmos. While anyone could look up at the heavens, only those who had acquired the intelligent eye could comprehend the divinely created order of the universe. Further, the essay demonstrates that the visual program of the Sphaera and Theorica texts played a significant and hitherto unrecognized role in later scientific work. Copernicus, Galileo, and Kepler all utilized the same types of images in their own texts to explicate their ideas about the cosmos. (shrink)

In the third century b.c.e., Eratosthenes of Cyrene made a famous measurement of the circumference of the Earth. This was not the first such measurement, but it is the earliest for which significant details are preserved. Cleomedes gives a short account of Eratosthenes’ method, his numerical assumptions, and the final result of 250,000 stades. However, many ancient sources attribute to Eratosthenes a result of 252,000 stades. Historians have attempted to explain the second result by supposing that Eratosthenes later made better (...) measurements and revised his estimate or that the original result was simply rounded to 252,000 to have a number conveniently divisible by 60 or by 360. These explanations are speculative and untestable. However, Eratosthenes’ estimates of the distances of the Sun and Moon from the Earth are preserved in the doxographical literature. This essay shows that Eratosthenes’ result of 252,000 stades for the Earth’s circumference follows from a solar distance that is attributed to him. Thus it appears that Eratosthenes computed not only a lower limit for the size of the Earth, based on the assumption that the Sun is at infinity, but also an upper limit, based on the assumption that the Sun is at a finite distance. The essay discusses the consequences for our understanding of his program. (shrink)

Mathematical texts raise particular dilemmas for the translator. With its arm’s-length relation to verbal expression and long-standing “mathematics is written for mathematicians” ethos, mathematics lends itself awkwardly to textually centered analysis. Otherwise sound standards of historical scholarship can backfire when rigidly upheld in a mathematical context. Mathematically inclined historians have had more faith in a purported empathic sixth sense—and there is a case to be made that this is how mathematical authors have generally expected their works to be read—but it (...) is difficult to pin down exact evidentiary standards for this supposed instinct. This essay urges that both of these points of view, for all the tension between them, be kept in the historian’s toolbox. It illustrates these considerations with a case study from the Ptolemaic astronomical tradition on computing lunar model parameters from eclipse data. (shrink)