This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

The surviving sources on the Stoic theory of division reveal that the Stoics, particularly Chrysippus, believed that bodies, places and times were such that all of their parts themselves had proper parts. That is, bodies, places and times were composed of gunk. This realisation helps solve some long-standing puzzles about the Stoic theory of mixture and the Stoic attitude to the present.

This paper considers what function—if any—colocation of bodies may have in the Stoic theory of blending (κρᾶσις), by examining (1) whether colocation is part of the definition of what blending is; and (2) whether colocation is posited by the Stoics as a requirement necessary for the definition to be satisfied. I reconstruct the standard, Chrysippean definition of blending, and I show that the answer to (1) is ‘no’; further, I argue that the evidence gives no reason to affirm (2). Thus, (...) it appears that colocation does not have a central function in the Stoic theory of blending. (shrink)

In Stoic physics, blending (κρᾶσις) is the relation between active pneuma and passive matter; natural bodies from rocks and logs to plants, animals and the cosmos itself are blends of pneuma and matter. Blending structures the Stoic cosmos. I develop a new interpretation of the Stoic theory of blending, based on passages from Hierocles. The theory of blending, I argue, has been misunderstood. Hierocles allows us to see in detail how the theory is supposed to work and how it fits (...) into Stoic physics. (shrink)

According to the Feigl–Reichenbach–Salmon–Schurz pragmatic justification of induction, no predictive method is guaranteed or even likely to work for predicting the future; but if anything will work, induction will work—at least when induction is employed at the meta-level of predictive methods in light of their track records. One entertains a priori all manner of esoteric prediction methods, and is said to arrive a posteriori at the conclusion, based on the actual past, that object-level induction is optimal. Schurz’s refinements largely solve (...) the notorious short-run problem. A difficulty is noted, however, related to short-run worries but based on localized disagreement about the past, a feature characteristic of real debates (especially early modern) involving induction in intellectual history. Given the evidence about past events, _unfiltered by induction_, meta-induction might support a partly non-inductive method—especially as judged by proponents of esoteric prediction methods, who presumably believe that their methods have worked. Thus induction is justified meta-inductively in contexts where it was uncontroversial, while not obviously justified in key contexts where it has been disputed. This objection, momentarily sensed by Reichenbach regarding clairvoyance, is borne out by the Stoics’ use of meta-induction to justify both science and divination and by ancient Hebrew examples of meta-induction. Schurz’s recently introduced criteria for acceptance of testimony play a crucial role in arriving at object-level induction using meta-induction, but one might question them. Given the need for judgment in accepting testimony, it is unclear that the subjectivity of Howson’s Bayesian answer to Hume’s problem is overcome. (shrink)

Quantum technologies can be presented to the public with or without introducing a strange trait of quantum theory responsible for their non-classical efficiency. Traditionally the message was centered on the superposition principle, while entanglement and properties such as contextuality have been gaining ground recently. A less theoretical approach is focused on simple protocols that enable technological applications. It results in a pragmatic narrative built with the help of the resource paradigm and principle-based reconstructions. I discuss the advantages and weaknesses of (...) these methods. To illustrate the importance of new metaphors beyond the Schrödinger cat, I briefly describe a non-mathematical narrative about entanglement that conveys an idea of some of its unusual properties. If quantum technologists are to succeed in building trust in their work, they ought to provoke an aesthetic perception in the public commensurable with the mathematical beauty of quantum theory experienced by the physicist. The power of the narrative method lies in its capacity to do so. (shrink)

This essay analyzes the ways in which, in his Nova de Universis Philosophia, Francesco Patrizi uses, adopts, and, in some cases, rejects the Stoic philosophical tradition. Although, at first glance, most of Patrizi’s remarks on Stoicism and Stoic understanding of nature are critical – as this article demonstrates – he widely relied on Stoic teaching that he sought to combine with Neoplatonism and the prisca theologia doctrine.

As was first pointed out by Gercke, there are close parallels, which clearly suggest a common source, between Apuleius, de Platone 1.12, the treatise On Fate falsely attributed to Plutarch, Calcidius' excursus on fate in his commentary on Plato's Timaeus, and certain sections of the treatise de Natura hominis by Nemesius. Gercke traced the doctrines common to these works to the school of Gaius; recently however Dillon has pointed out that, while Albinus shares with these works the characteristic Middle-Platonic notion (...) of fate as conditional or hypothetical – our actions are free, but once we have acted the consequences of our actions are fated and inevitable – he does not share certain other common features, such as the identification of fate as substance with the world-soul and the hierarchy of three providences. (shrink)

This article aims to show that it is impossible to put Cicero’s testimonies regarding The Fabius Argument in a consistent inferential order. Either we must suppose that additional premises are tacitly assumed in the text or we must com-pare it with other sources, which leads to inconsistencies in the proof’s reconstruction. Cicero’s reconstruction of the progression of the argument has formal shortcomings, and the paper draws attention to some of these deficiencies. He interpreted sources in a revised and intentionally simplified (...) way, with the aim of undermining the views of his opponents, casting them as inconsistent and similar to views held by Diodorus. Rather than being a consistently interpreted argument faithfully transcribed from the Stoic sources, Cicero’s Fabius Argument is ultimately anti-Stoic. (shrink)

Thinkers from the Chinese and Greco-Roman traditions posit that disparate objects throughout the cosmos have mutual affinities. In the Stoic tradition, such affinities are explained through “sympathy.” In the Chinese tradition, the explanatory principle is often called ganying 感應 (resonance). In addition, both traditions use similar philosophical strategies when discussing these concepts. Thinkers cite natural correspondences, placing them in parallel lists as evidence for philosophical truths. On the surface, the analogous concepts and strategies hint that these thinkers share similar philosophical (...) goals. However, analysis of the role natural correspondences play in argumentation discovers fundamental differences between the two traditions. The focus on particular arguments instead of broader cosmological trends offers a different perspective for comparative research, and the conclusions raise questions concerning how scholarship should analyze philosophical trends in early China. (shrink)

R. Saadia Ga'on, which is known to have been substantially influenced by Saadia, in fine is also indebted to Stoic philosophy and physics.

The pantheon of seventeenth-century European philosophy includes some remarkably heterodox deities, perhaps most famously Spinoza’s deus-sive-natura. As in ethics and natural philosophy, early modern philosophical theology drew inspiration from classical sources outside the mainstream of Christianized Aristotelianism, such as the highly immanentist, naturalistic theology of Greek and Roman Stoicism. While the Stoic background to Spinoza’s pantheist God has been more thoroughly explored, I maintain that Hobbes’s corporeal God is the true modern heir to the Stoic theology. The Stoic and Hobbesian (...) gods are necessitarian, entirely corporeal, and thoroughly intermixed with ordinary bodies, while also supremely intelligent, providential, and good. And both gods serve as the ultimate source of diversity and change in a material world divested of Aristotelian forms and causes. Unfortunately, scholars on both sides of the long debate about the sincerity of Hobbes’s theism have not taken very seriously his late articulation of a corporeal theology. One probable reason for this dismissive attitude is a lack of thorough investigation of the historical precedents for such an unusual godhead available to Hobbes. The first part of this article attempts to establish a close congruence between the Stoic and Hobbesian gods. The second part traces the likely sources for Hobbes’s Stoic theology in his intellectual context. (shrink)

Some notes discussing some of the ancient and medieval background to the absolute-relational debate. Final version appears as Appendix C in my book, Geometric Possibility.

The causes of tidal motions were widely debated from antiquity up to the eighteenth century. These discussions got a second wind in the early modern period, in the wake of a growing number of cosmological alternatives that challenged the dominant Aristotelian-Ptolemaic stance. The 1687 publication of Isaac Newton’s Principia Mathematica was a defining moment in the discussions and consequently made universal gravitation the most credible and generally accepted explanation. This paper investigates the aftermath of Newton’s discovery and demonstrates how his (...) understanding of tidal motion crowded out competing theories within a broader European context. My main point of reference is Roger Boscovich’s De aestu maris (1747). In his work, the leading Jesuit scholar of the time contrasted Newton’s interpretation to those of other major authorities, namely Johannes Kepler, Galileo Galilei, and René Descartes, and went on to claim the superiority of the British scientist’s achievements over anything written prior to the Principia. As this essay argues, alongside a significant body of literature produced under the umbrella of the Jesuit order, Boscovich’s De aestu maris subsequently contributed to the formation of the popular image of Newton as a “scientific hero.”. (shrink)

Two literal quotations from Chrysippus’ On Possibles, preserved in Plutarch’s On the Contradictions of the Stoics, seem to contradict the Stoic thesis of the isotropy of the void. According to this thesis the void is an infinite undifferentiated expanse whose center is marked by, and coincides with, the position of the world. Since there is nothing else outside the world, the cohesive force that pervades it is sufficient on its own to guarantee the quasi–indestructibility of the trans–cyclical διακόσμησις and the (...) eternity of the οὐσία. Conversely, in these two quotations Chrysippus maintains that there is a central διαφορά equipped with causal force. This seems to imply the anisotropy of the void. Chrysippus’s view here is also at odds with another official Stoic thesis, i.e. that the incorporeal is causally inert. In this paper it will be argued that there is in fact no contradiction, because, in those two quotations, Chrysippus consciously develops a cosmological hypothesis in order to resolve a difficulty concerning the role of fire during the universal conflagration. Chrysippus’ solution to this difficulty belongs to modal logic and consists in distinguishing between the actual universe and the possible ones. (shrink)

El trabajo se propone evaluar en qué sentido la concepción que la Estoa antigua ha sostenido sobre lo corpóreo no privilegia la dimensión espacial. Es decir, analizaremos el argumento estoico según el cual el lugar o la extensión de un cuerpo no se determina por su posición respecto de otro cuerpo, sino por su actividad o fuerza; más específicamente, por su tensión interna. Por tanto, será nuestro objetivo inicial analizar cuáles son los fundamentos que permitirían dar cuenta de la concepción (...) estoica de lo corpóreo desde un principio biológico y no desde un modelo matemático. Luego, en una segunda instancia, evaluaremos la definición en cuestión en sus articulaciones con la teoría de la causalidad y el determinismo. (shrink)

The intelectual virtue of discernment occupies a privileged position in Aristotle’s ethics, since it intervenes in judging and choosing the best option regarding our voluntary actions. As for the Stoics, the virtues are cognitions and can be reduced to only one. The person who possesses that unique virtue is called a ‘sage’ and is able to choose, for himself, the right action to reach happiness. Thus, we propose to discover if the Stoic sage can be compared to the prudent man (...) in Aristotle by examining some key ethical issues of theses philosophical schools. We conclude that the similar theses exceed the different ones, despite encountering a quite distinct vocabulary which deceives at first sight. (shrink)

Beginning the nineteenth-century and continuing down to the present, many authors writing on the history of geology and paleontology have attributed the theory that fossils were inorganic formations produced within the earth, rather than by the deposition of living organisms, to the ancient Greeks and Romans. Some have even gone so far as to claim this was the consensus view in the classical period up through the Middle Ages. In fact, such a notion was entirely foreign to ancient and medieval (...) thought and only appeared within the manifold of ‘Renaissance episteme,’ the characteristics of which have often been projected backwards by some historians onto earlier periods. This paper endeavors to correct this error, explain the development of the Renaissance view, describe certain ancient precedents thereof, and trace the history of the misinterpretation in the literature. -/- . (shrink)

This paper analyzes views of the Stoic philosopher Posidonius (1st century BC) in the light of modern Chemistry. I propose that Posidonius’ account on “generation and destruction” bears noteworthy similarities to the scientific notions of chemical elements, chemical species, nuclear reactions, and the law of conservation of mass. I find that his views compare favorably also with our understanding of chemical change at solid surfaces. Provided his thought is correctly placed in the cultural context of his day, I argue that (...) Posidonius deserves a previously un-acknowledged consideration in the historical background of modern Chemistry. (shrink)

An examination of a particular passage in Cicero's De fato—Fat. 13–17—is crucial to our understanding of the Stoic theory of the truth-conditions of conditional propositions, for it has been uniquely important in the debate concerning the kind of connection the antecedent and consequent of a Stoic conditional should have to one another. Frede has argued that the passage proves that the connection is one of logical necessity, while Sorabji has argued that positive Stoic attitudes toward empirical inferences elsewhere suggest that (...) that cannot be the right interpretation of the passage. I argue that both parties to the debate have missed a position somewhere between them which both renders a connection between antecedent and consequent that is not merely empirical and makes sense of the actual uses to which the Stoics put the conditional. This will be an account which grounds the connection between antecedent and consequent in a prolêpsis, a special kind of concept which plays a special epistemological role for the Stoics, especially in grounding scientific explanations. My contention will be that Stoic conditionals are true when there is a conceptually necessary connection between antecedent and consequent such that the former explains the latter via a prolêpsis. (shrink)

En el contexto de su crítica a la fenomenomenología husserliana Michel Henry apela a la caracterización de los errores de la perspectiva hetero-afectiva remitiéndose a sus orígenes en la tradición sintetizados en los parámetros de la “gnosis griega” y su compromiso con la racionalidad entendida como comprensión de “objetos puestos a distancia”. La revisión de los alcances de esta categoría revela, sin embargo, que existen tratamientos en el pensamiento griego que apelan a la auto-afección y la inmanencia para dar cuenta (...) de elementos que exceden la dimensión ek-stática. En este trabajo se revisa el planteo henryano para mostrar sus puntos de contacto con el estoicismo, especialmente a partir de la teoría de Hierocles a propósito de la oikeîosis. Este recorrido permitirá sugerir que entre ambos planteos existe una compatibilidad estructural que hace posible apelar a claves de interpretación similares para dar cuenta de la convivencia de mecanismos de explicación que apelan a lo auto-afectivo y lo hétero-afectivo en un conjunto coherente. (shrink)

In contrast to other ancient philosophers, Epicurus and his followers famously maintained the infinity of matter, and consequently of worlds. This was inferred from the infinity of space, because they believed that a limited amount of matter would inevitably be scattered through infinite space, and hence be unable to meet and form stable compounds. By contrast, the Stoics claimed that there was only a finite amount of matter in infinite space, which stayed together because of a general centripetal tendency. The (...) Roman Epicurean poet Lucretius tried to defend the Epicurean conception of infinity against this Stoic alternative view, but not very convincingly. One might suspect, therefore, that the Epicureans’ adherence to the infinity of matter was not so much dictated by physical arguments as it was motivated by other, mostly theological and ethical, concerns. More specifically, the infinity of atoms and worlds was used as a premise in several arguments against divine intervention in the universe. The infinity of worlds was claimed to rule out divine intervention directly, while the infinity of atoms lent plausibility to the chance formation of worlds. Moreover, the infinity of atoms and worlds was used to ensure the truth of multiple explanations, which was presented by Epicurus as the only way to ward off divine intervention in the realm of celestial phenomena. However, it will be argued that in all of these arguments the infinity of matter is either unnecessary or insufficient for reaching the desired conclusion. (shrink)

The three studies that make up this work each deal with another facet or subdiscipline of Epicurean cosmology. The first study is devoted to Epicurus’ method of multiple explanations, the second study compares the meteorological sections of Epicurus' Letter to Pythocles and Lucretius' De rerum natura with other ancient meteorological accounts as regards the range and order of subjects, and the third study investigates what shape the Epicureans assigned to the earth. [For an updated version of this thesis, see Frederik (...) A. Bakker, Epicurean Meteorology: Sources, Method, Scope and Organization, Leiden/Boston: Brill, 2016]. (shrink)

Static levitation is a form of marvel with metaphysical implications whose long history has not previously been charted. First, Pliny the Elder reports an architect’s plan to suspend an iron statue using magnetism, and the later compiler Ampelius mentions a similar-sounding wonder in Syria. When the Serapeum at Alexandria was destroyed, and for many centuries afterwards, chroniclers wrote that an iron Helios had hung magnetically inside. In the Middle Ages, reports of such false miracles multiplied, appearing in Muslim accounts of (...) Christian and Hindu idolatry, as well as Christian descriptions of the tomb of Muhammad. A Christian levitation miracle involving saints’ relics also emerged. Yet magnetic suspension could be represented as miraculous in itself, representing lost higher knowledge, as in the latest and easternmost tradition concerning Konark’s ruined temple. The levitating monument, first found in classical antiquity, has undergone many cultural and epistemological changes in its long and varied history. (shrink)