Freely falling point-like objects converge toward the center of the Earth. Hence the gravitational field of the Earth is inhomogeneous, and possesses a tidal component. The free fall of an extended quantum mechanical object such as a hydrogen atom prepared in a high principal-quantum-number state, i.e. a circular Rydberg atom, is predicted to fall more slowly than a classical point-like object, when both objects are dropped from the same height above the Earth’s surface. This indicates that, apart (...) from transitions between quantum states, the atom exhibits a kind of quantum mechanical incompressibility during free fall in inhomogeneous, tidal gravitational fields like those of the Earth.A superconducting ring-like system with a persistent current circulating around it behaves like the circular Rydberg atom during free fall. Like the electronic wavefunction of the freely falling atom, the Cooper-pair wavefunction is quantum mechanically incompressible. The ions in the lattice of the superconductor, however, are not incompressible, since they do not possess a globally coherent quantum phase. The resulting difference during free fall in the response of the nonlocalizable Cooper pairs of electrons and the localizable ions to inhomogeneous gravitational fields is predicted to lead to a charge separation effect, which in turn leads to a large Coulomb force that opposes the convergence caused by the tidal gravitational force on the superconducting system.A “Cavendish-like” experiment is proposed for observing the charge separation effect induced by inhomogeneous gravitational fields in a superconducting circuit. The charge separation effect is determined to be limited by a pair-breaking process that occurs when low frequency gravitational perturbations are present. (shrink)

In recent decades historians of science have argued that observation became something of a way of life in the early modern period. This article expands this analysis by shifting focus from observational practices within natural and experimental philosophy to a number of discourses and practices of self-examination and self-observation in eighteenth-century Germany. While the initial aim of these was therapeutic rather than scientific, therapeutic connotations were partly replaced by epistemic virtues and techniques adopted from natural and experimental philosophy toward the (...) end of the century. The article further argues that the subordination of self-observation to scientific modes of procedure reflected the increasingly radical interest in human subjectivity and, by extension, the emergence of a modern civic and individual self. (shrink)

This article contributes to the historiography of scientific objectivity as well as to the broader attempt to historicize basic epistemic categories by examining the case of empirical psychology in eighteenth-century Germany. From the time when the philosopher Christian Wolff first presented empirical psychology in the late 1720s until Kantian philosophers elaborated on the topic towards the end of the century, the discourse hinged on discussions of how to obtain scientific knowledge of the soul. Whereas the work of Wolff and his (...) followers reflected established epistemic techniques for accomplishing this, from the early 1770s philosophers highlighted a new category of difficulties connected to the development of a systematic method of psychological self-observations. These difficulties, I argue, both complement and complicate the picture of how the subject became an obstacle to knowledge first in the mid-nineteenth century. (shrink)

We examine the process of the emission of light from an atom that is in a relative translational motion with respect to the medium at rest in which the electromagnetic excitations propagate. The effect of Lorentz contraction of the of electron orbits on the emitted frequency is incorporated in the Rydberg formula, as well as the emitter’s Doppler effect is acknowledged. The result is that the frequency of the emitted light is modified by a factor that is identical (...) with what is called the ‘relativistic Doppler effect’. The new emission formula is applied for reinterpretation of the Ives-Stilwell experiment and shown that within the second order of approximation with respect to the speeds of the atom and the ‘absolute speed’ (Earth’s speed relative to the medium), the absolute motion does not affect the interference. The expression for the modification of the frequency involves both a first and a second-order term with respect to the speed of the atoms in the cathode tube. The latter turns out to be quantitatively the same as if the time would have changed its rate in the frame moving with the atoms. Thus, a new interpretation of the results of this famous experiment is provided without stipulating time dilation. (shrink)

This short account summarizes our recent achievements in ultrafast coherent control of isolated molecules in the gas phase, and its ongoing applications to an ensemble of ultracold Rydberg atoms to explore quantum many-body dynamics.

Periodic tables (PTs) are the ‘ultimate paper tools’ of general and inorganic chemistry. There are three fields of open questions concerning the relation between PTs and physics: (i) the relation between the chemical facts and the concept of a periodic system (PS) of chemical elements (CEs) as represented by PTs; (ii) the internal structure of the PS; (iii)␣The relation between the PS and atomistic quantum chemistry. The main open questions refer to (i). The fuzziness of the concepts of chemical properties (...) and of chemical similarities of the CE and their compounds guarantees the autonomy of chemistry. We distinguish between CEs, Elemental Stuffs and Elemental Atoms. We comment on the basic properties of the basic elements. Concerning (ii), two sharp physical numbers (nuclear charge and number of valence electrons) and two coarse fuzzy ranges (ranges of energies and of spatial extensions of the atomic orbitals, AOs) characterize the atoms of the CEs and determine the two-dimensional structure of the PS. Concerning (iii), some relevant ‘facts’ about and from quantum chemistry are reviewed and compared with common ‘textbook facts’. What counts in chemistry is the whole set of nondiffuse orbitals in low-energy average configurations of chemically bonded atoms. Decisive for the periodicity are the energy gaps between the core and valence shells. Diffuse Rydberg orbitals and minute spin–orbit splittings are important in spectroscopy and for philosophers, but less so in chemical science and for the PS. (shrink)

A new theory of particles proposed in an earlier paper is now applied to explain energy. Having earlier derived the Rydberg formula for atomic spectra without using the Pauli principle, the authors now derive the photoelectric effect, deflection of light by gravitation, and Planck's law for blackbody radiation without using Planck's assumption on energy quanta or Einstein's theory of general relativity.

Introductory survey -- Atomic theory and mechanics -- The quantum postulate and the recent development of atomic theory -- The quantum of action and the description of nature -- The atomic theory and the fundamental principles underlying the description of nature.

These articles and speeches by the Nobel Prize-winning physicist date from 1934 to 1958. Rather than expositions on quantum physics, the papers are philosophical in nature, exploring the relevance of atomic physics to many areas of human endeavor. Includes an essay in which Bohr and Einstein discuss quantum and_wave equation theories. 1961 edition.

Although continued investments in nanotechnology are made, atomically precise manufacturing (APM) to date is still regarded as speculative technology. APM, also known as molecular manufacturing, is a token example of a converging technology, has great potential to impact and be affected by other emerging technologies, such as artificial intelligence, biotechnology, and ICT. The development of APM thus can have drastic global impacts depending on how it is designed and used. This paper argues that the ethical issues that arise from APM (...) - as both a standalone technology or as a converging one - affects the roles of stakeholders in such a way as to warrant an alternate means furthering responsible innovation in APM research. This paper introduces a value-based design methodology called Value Sensitive Design (VSD) that may serve as a suitable framework to adequately cater to the values of stakeholders. Ultimately, it is concluded that VSD is a strong candidate framework for addressing the moral concerns of stakeholders during the preliminary stages of technological development. (shrink)

The quantum theory of atoms in molecules (QTAIM) uses physics to define an atom and its contribution to observable properties in a given system. It does so using the electron density and its flow in a magnetic field, the current density. These are the two fields that Schrödinger said should be used to explain and understand the properties of matter. It is the purpose of this paper to show how QTAIM bridges the conceptual gulf that separates the observations of (...) chemistry from the realm of physics and do so in a manner that is both rigorous and conceptually simple. Since QTAIM employs real measurable fields, it enables one to present the findings of complex quantum mechanical calculations in a pictorial manner that isolates the essential physics. The time has arrived for a sea change in our attempts to predict and classify the observations of chemistry, time to replace the use of simplified and arbitrary models with the full predictive power of physics, as applied to an atom in a molecule. (shrink)

This book reexamines the birth of quantum mechanics, in particular examining the development of crucial and original insights of Bohr. In particular, it gives a detailed study of the development and the interpretation given to Bohr's Principle of Correspondence. It also describes the role that this principle played in guiding Bohr's research over the critical period from 1920 to 1927.

This paper argues that the field of chemistry underwent a significant change of theory in the early twentieth century, when atomic number replaced atomic weight as the principle for ordering and identifying the chemical elements. It is a classic case of a Kuhnian revolution. In the process of addressing anomalies, chemists who were trained to see elements as defined by their atomic weight discovered that their theoretical assumptions were impediments to understanding the chemical world. The only way to normalize the (...) anomalies was to introduce new concepts, and a new conceptual understanding of what it is to be an element. In the process of making these changes, a new scientific lexicon emerged, one that took atomic number to be the defining feature of a chemical element. (shrink)

We provide a detailed history of the concepts of atomic number and isotopy before the discovery of protons and neutrons that draws attention to the role of evolving interplays of multiple aims and criteria in chemical and physical research. Focusing on research by Frederick Soddy and Ernest Rutherford, we show that, in the context of differentiating disciplinary projects, the adoption of a complex and shifting concept of elemental identity and the ordering role of the periodic table led to a relatively (...) coherent notion of atomic number. Subsequent attention to valency, still neglected in the secondary literature, and to nuclear charge led to a decoupling of the concepts of elemental identity and weight and allowed for a coherent concept of isotopy. This concept received motivation from empirical investigations on the decomposition series of radioelements and their unstable chemical identity. A new model of chemical order was the result of an ongoing collaboration between chemical and physical research projects with evolving aims and standards. After key concepts were considered resolved and their territories were clarified, chemistry and physics resumed autonomous projects, yet remained bound by newly accepted explanatory relations. It is an episode of scientific collaboration and partial integration without simple, wholesale gestalt switches or chemical revolutions. (shrink)

Philosophers routinely invoke self‐control in their theorizing, but major questions remain about what exactly self‐control is. I propose a componential account in which an exercise of self‐control is built out of something more fundamental: basic intrapsychic actions called cognitive control actions. Cognitive control regulates simple, brief states called response pulses that operate across diverse psychological systems (think of one's attention being grabbed by a salient object or one's mind being pulled to think about a certain topic). Self‐control ostensibly seems quite (...) different because it regulates complex, temporally extended states such as emotions and cravings. But critically, these complex states also exhibit important componential structure: They rely on response pulses as a key means by which they bring about action. The overall picture is that self‐control consists of skilled sequences of cognitive control directed against extended streams of response pulses that arise from states such as emotions and cravings, thus preventing these states from being effective in action. The account clarifies the “atoms” of self‐control—the elemental units that get combined in complex ways to produce different kinds of self‐control actions. Surprisingly, the account, which is derived from research in cognitive science, aligns nicely with the commonsense conception of self‐control. (shrink)

The intention of Atomic Order is to encourage and contribute to the dialogue between philosophers and scientists by discussing a concrete example of scientific discovery according to a method acceptable and understandable to both sides. This discussion takes simultaneously into account the scientific and philosophical methodologies and mentalities. By regarding "pure" science or "pure" philosophy as limiting cases, it becomes evident that basic questions are best posed and answered by emphasiz ing the deeply embedded complementary relationship between the two. The (...) example chosen is atomic physics, and a systematic method is developed to illuminate the philosophical structure of this science--and science generally--from within.The book consists of two parts. The first part is devoted to the problem of atomic order as discovered and verified by physics, from the speculations of Dalton to the consequences of modern quantum mechanics. These chapters will afford a telescopic, historical review to the scientific reader and a reliable, understandable account of the physical discoveries and theories to the nonscientist. The second part analyzes the presuppositions, guiding principles, and implications that made possible the development of atomic physics and that impart a humanistic meaning to it. In separate chapters are discussed the epistemological structure of atomic physics, the new conception of matter implicit in the quantum theory, and the ontological implications of atomic order. It is seen that, in this area, science and philosophy are inextricably interpenetrated. A philosophic problematic is immanent in creative atomic science, as is evidenced by the numerous reflections and speculations of scientists that are quoted in the book. Conversely, an interest in scientific research is indispensable for a modern philosopher, and the philosopher may well be surprised and encouraged on recognizing the role already being played by philosophy in the supposedly pragmatic world of science.Dr. Cantore brings an ecumenical cast Lof mind to the healing of the bjcultural split between the humanists and the scientists. The recipient of a doctorate in physics and another in philosophy, he has drawn from both fields in a book dedicated to "making the educated public more aware of the need and method for a new synthesis between the two cultures.". (shrink)

In this paper I discuss some consequences and manifestations of a mereology of structured wholes in chemistry, with particular reference to the concept of atoms in molecules.

Research into learners' ideas aboutscience suggests that school and collegestudents often hold alternative conceptionsabout `the atom'. This paper discusses whylearners acquire ideas about atoms which areincompatible with the modern scientificunderstanding. It is suggested that learners'alternative ideas derive – at least in part –from the way ideas about atoms are presented inthe school and college curriculum. Inparticular, it is argued that the atomicconcept met in science education is anincoherent hybrid of historical models, andthat this explains why learners commonlyattribute to atoms (...) properties (such as beingthe constituent particles of all substances, orof being indivisible and conserved inreactions) that more correctly belong to otherentities (such as molecules or sub-atomicparticles). Bachelard suggested that archaicscientific ideas act as `epistemologicalobstacles', and here it is argued thatanachronistic notions of the atom survive inthe chemistry curriculum. These conceptualfossils encourage learners to develop an`atomic ontology' (granting atoms `ontologicalpriority' in the molecular model of matter); tomake the `assumption of initial atomicity' whenconsidering chemical reactions; and to developan explanatory framework to rationalisechemical reactions which is based on thedesirability of full electron shells. Theseideas then act as impediments to thedevelopment of a modern chemical perspective onthe structure of matter, and an appreciation ofthe nature of chemical changes at the molecularlevel. (shrink)

This paper suggests that the cases made for atoms and the aether in nineteenth-century physical science were analogous, with the implication that the case for the atom was less than compelling, since there is no aether. It is argued that atoms did not play a productive role in nineteenth-century chemistry any more than the aether did in physics. Atoms and molecules did eventually find an indispensable home in chemistry but by the time that they did so they were different (...) kinds of entities to those figuring in the speculations of those natural philosophers who were atomists. Advances in nineteenth-century chemistry were a precondition for rather than the result of the productive introduction of atoms into chemistry. (shrink)

In this paper I shall explore a novel alternative to these familiar views. In his recent book Sub ects of Ex erience, E. J. Lowe argues, as many others have done before, that you and I are not animals. It follows from this, he says, that we must be simple substances without parts. That may sound like Cartesian dualism. But Lowe is no Cartesian. He argues from premises that many present-day materialists accept. And he claims that our being mereologically simple (...) is consistent with our having such paradigmatically physical properties as being six feet tall and weighing 160 pounds. You and I, he claims, are mereological atoms shaped like human beings. (shrink)

The concepts of atoms and bonds in molecules which appeared in chemistry during the nineteenth century are unavoidable to explain the structure and the reactivity of the matter at a chemical level of understanding. Although they can be criticized from a strict reductionist point of view, because neither atoms nor bonds are observable in the sense of quantum mechanics, the topological and statistical interpretative approaches of quantum chemistry (quantum theory of atoms in molecules, electron localization function and maximum probability domain) (...) provide consistent definitions which accommodate chemistry and quantum mechanics. (shrink)

"Atom," "byte" and "gene" are metonymies for techno-scientific developments of the 20th century: nuclear power, computing and genetic engineering. Resistance continues to challenge these developments in public opinion. This book traces historical debates over atoms, bytes and genes which raised controversy with consequences, and argues that public opinion is a factor of the development of modern techno-science. The level and scope of public controversy is an index of resistance, examined here with a "pain analogy" which shows that just as (...) pain impacts movement, resistance impacts techno-scientific mobilization: it signals that something is wrong, and this requires attention, elaboration and a response to the challenge. This analysis shows how different fields of enquiry deal with the resistance of social-psychological mentalities in the face of industrial, scientific and political activities inspired by projected futures. (shrink)

In this paper I address two important objections to the theory called ‘ Composition as Identity’ : the ‘wall-bricks-and-atoms problem’, and the claim that CAI entails mereological nihilism. I aim to argue that the best version of CAI capable of addressing both problems is the theory I will call ‘Atomic Composition as Identity’ which consists in taking the plural quantifier to range only over proper pluralities of mereological atoms and every non-atomic entity to be identical to the plurality of atoms (...) it fuses. I will proceed in three main steps. First, I will defend Sider’s Composition as identity. Oxford University Press, Oxford, pp 211–221, 2014) idea of weakening the comprehension principle for pluralities and I will show that :219–235, 2016a) it can ward off both the WaBrA problem and the threat of mereological nihilism. Second, I will argue that CAI-theorists should uphold an ‘atomic comprehension principle’ which, jointly with CAI, entails that there are only proper pluralities of mereological atoms. Finally, I will present a novel reading of the ‘one of’ relation that not only avoids the problems presented by Yi Composition as identity. Oxford University Press, Oxford, pp 169–191, 2014) and Calosi :429–443, 2016b, Am Philos Q 55:281–292, 2018) but can also help ACAI-theorists to make sense of the idea that a composite entity is both one and many. (shrink)

: This paper examines the debate in the late 19th and early 20th centuries over the acceptability of atomic and molecular physics. It focuses on three prominent figures: Maxwell, who defended atomic physics, Ostwald, who initially rejected it but changed his mind as a result of experiments by Thomson and Perrin, and Duhem, who never accepted it. Each scientist defended the position he did in the light of strongly held methodological views concerning empirical evidence. The paper critically evaluates each of (...) these methodological positions. (shrink)

although mostly known to specialists nowadays, Kenelm Digby was a remarkable figure on the intellectual scene of the early seventeenth century. He has been described as “one of the most influential natural philosophers” of his time,1 and corresponded with many of the great scholars of his days, including Descartes, and the French pioneer of atomism, Pierre Gassendi. In the later years of his life, Digby, alongside men like Robert Boyle, became one of the founding members of the Royal Society.2Digby authored (...) one major work of philosophy: the Two Treatises of 1644. This work consisted of a long First Treatise on bodies, and a shorter, Second Treatise on the human soul. In the First Treatise, Digby argued... (shrink)

A possible atomic mechanism underlying the Re- and Ru-induced strengthening effects on the n - n ' interface in Ni-based single-crystal superalloys has been investigated using the DMol3 molecular orbital package based on density functional theory. The calculation of bonding properties has been performed on a cluster designed to model Re and Ru strengthening effects within the interface. The stronger Re--Ni bonds are formed mainly as a result of d- hybridization, while the Ni--Ni bonding become weaker accompanying the Re substitution. (...) The vertical and horizontal bond orders for a local environmental cluster are proposed and developed for the description of the strengthening effect on the n - n ' interface, with larger bond order values achieving better effect. Results show that both Re and Ru significantly strengthen the interface. It is also shown that the strengthening effect of Re is better than that of Ru, and this is explained in terms of the charge transfer of electrons between orbitals of Ru atom according to Mulliken population analysis. The calculation results provide a basis for understanding the atomic mechanism of Re- and Ru-induced n - n ' interfacial strengthening. (shrink)

Event concepts are unstructured atomic concepts that apply to event types. A paradigm example of such an event type would be that of diaper changing, and so a putative example of an atomic event concept would be DADDY'S-CHANGING-MY-DIAPER.1 I will defend two claims about such concepts. First, the conceptual claim that it is in principle possible to possess a concept such as DADDY'S-CHANGING-MY-DIAPER without possessing the concept DIAPER. Second, the empirical claim that we actually possess such concepts and that they (...) play an important role in our cognitive lives. The argument for the empirical claim has the form of an inference to the best explanation and is aimed at those who are already willing to attribute concepts and beliefs to infants and nonhuman animals. Many animals and prelinguistic infants seem capable of re-identifying event-types in the world, and they seem to store information about things happening at particular times and places. My account offers a plausible model of how such organisms are able to do this without attributing linguistically structured mental states to them. And although language allows adults to form linguistically structured mental representations of the world, there is no good reason to think that such structured representations necessarily replace the unstructured ones. There is also no good reason for a philosopher who is willing to explain the behavior of an organism by appealing to atomic concepts of individuals or kinds to not use a similar form of explanation when explaining the organism's capacity to recognize events. -/- We can form empirical concepts of individuals, kinds, properties, event-types, and states of affairs, among other things, and I assume that such concepts function like what François Recanati calls ‘mental files’ or what Ruth Millikan calls ‘substance concepts’ (Recanati 2012; Millikan 1999, 2000, 2017). To possess such a concept one must have a reliable capacity to re-identify the object in question, but this capacity of re-identification does not fix the reference of the concept. Such concepts allow us to collect and utilize useful information about things that we re-encounter in our environment. We can distinguish between a perception-action system and a perception-belief system, and I will argue that empirical concepts, including atomic event concepts, can play a role in both systems. The perception-action system involves the application of concepts in the service of (often skilled) action. We can think of the concept as a mental file containing motor-plans that can be activated once the individual recognizes that they are in a certain situation. In this way, recognizing something (whether an object or an event) as a token of a type, plays a role in guiding immediate action. The perception-belief system, in contrast, allows for the formation of beliefs that can play a role in deliberation and planning and in the formation of expectations. I distinguish between two particular types of belief which I call where-beliefs and when-beliefs, and I argue that we can model the formation of such perceptual beliefs in nonlinguistic animals and human infants in terms of the formation of a link between an empirical concept and a position on a cognitive map. According to the account offered, seemingly complex beliefs, such as a baby's belief that Daddy changed her diaper in the kitchen earlier, will not be linguistically structured. If we think that prelinguistic infants possess such concepts and are able to form such beliefs, it is likely that adults do too. The ability to form such beliefs does not require the capacity for public language, and we can model them in nonlinguistic terms; thus, we have no good reason to think of such beliefs as propositional attitudes. Of course, we can use sentences to refer to such beliefs, and thus it is possible to think of such beliefs as somehow relations to propositions. But it is not clear to me what is gained by this as we have a perfectly good way to think about the structure of such beliefs that does not involve any appeal to language. (shrink)

In this paper we analyse the approach to interpreting atomic spectra in the framework of classical physics from the discovery of the electron in 1897 to Bohr's atomic model of 1913. Taken as a whole, efforts in this direction are part of a remarkable intellectual endeavour in which the classical theoretical framework seems to have been exploited to its full potential. By demonstrating the limits and weaknesses of classical physics in solving the problem of spectral emissions, these attempts opened the (...) way to a complete break from traditional thought and the introduction of the new quantum ideas. (shrink)

This article examines the attempt by the Kingdom of Morocco—a country of pivotal geopolitical importance in the late 1970s and early 1980s—to secure a research reactor. It finds that by treating that reactor as a diplomatic object, we can observe the different diplomatic frameworks in which that object was conceived of, contextualized, and negotiated. The historical emergence of these frameworks occurred in close relationship with the IAEA, which acted as an intermediary linking various administrations, programs, and countries, including Morocco. In (...) the end, this history reveals that the late Cold War nuclear world involved multilateral actions and forces, some of which encouraged Morocco in its bid to acquire a reactor, but others of which left that same reactor orphaned and unfinished. (shrink)

For any finite n 3 there are two atomic n-dimensional cylindric algebras with the same atom structure, with one representable, the other, not.Hence, the complex algebra of the atom structure of a representable atomic cylindric algebra is not always representable, so that the class RCAn of representable n-dimensional cylindric algebras is not closed under completions. Further, it follows by an argument of Venema that RCAn is not axiomatisable by Sahlqvist equations, and hence nor by equations where negation can (...) only occur in constant terms.Similar results hold for relation algebras. (shrink)

We give an account of some relationships between the principles of Constant and Atom Exchangeability and various generalizations of the Principle of Instantial Relevance within the framework of Inductive Logic. In particular we demonstrate some surprising and somewhat counterintuitive dependencies of these relationships on ostensibly unimportant parameters, such as the number of predicates in the overlying language.

It is customary practice to define ‘x is composed of the ys’ as ‘x is a sum of the ys and the ys are pairwise disjoint ’. This predicate has played a central role in the debate on the special composition question and on related metaphysical issues concerning the mereological structure of objects. In this note we show that the customary characterization is nonetheless inadequate. We do so by constructing a mereological model where everything qualifies as composed of atoms even (...) though some elements in the domain are gunky, i.e., can be divided indefinitely into smaller and smaller proper parts. (shrink)

For this eighth edition he also wrote a new chapter on the quantum theory of solids.

The role of measure theoretic atomicity in common cause closedness of general probability theories with non-distributive event structures is raised and investigated. It is shown that if a general probability space is non-atomic then it is common cause closed. Conditions are found that entail that a general probability space containing two atoms is not common cause closed but it is common cause closed if it contains only one atom. The results are discussed from the perspective of the Common Cause (...) Principle. (shrink)

The words "atom laser" appearing in a science fiction magazine conjure up visions of death rays and space battles. The real device is rather different in its implications and ultimately is much less likely to be a weapon than a tool for probing the innermost secrets of Nature. Therefore, let's begin by reviewing some basic facts about quantum statistics and the ground rules for the operation of lasers.

It has been known for six years that the restriction of Girard's polymorphic system $\text{\bfseries\upshape F}$ to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait's method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each $\beta$-reduction step of the full intuitionistic propositional calculus translates into one or more $\beta\eta$-reduction steps in the restricted Girard system. As a consequence, we obtain (...) a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to $\eta$-conversions. (shrink)

SummaryJohn Dalton's atomic theory, with its postulate of compound formation through atom-to-atom combination, brought a new perspective to weight relationships in chemical reactions. A presumed one-to-one combination of atoms A and B to form a simple compound AB allowed Dalton to construct his first table of relative atomic weights from literature analyses of appropriate binary compounds. For such simple binary compounds, the atomic theory had little advantages over affinity theory as an explanation of fixed proportions by weight. For (...) ternary compounds of the form AB2, however, atomic theory made quantitative predictions that were not deducible from affinity theory. Atomic theory required that the weight of B in the compound AB2 be exactly twice that in the compound AB. Dalton, Thomas Thomson and William Hyde Wollaston all published within a few years of each other experimental data that claimed to give the predicted results with the required accuracy. There are nonetheless several experimental barriers to obtaining the desired integral multiple proportions. In this paper I will discuss replication experiments which demonstrate that only Wollaston's results are experimentally reliable. It is likely that such replicability explains why Wollaston's experiments were so influential. (shrink)