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)

The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect, Itanoet al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations, we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss how far the experiment of (...) Itanoet al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to take the corrections into account. (shrink)

In the last decade, the notion of triad was reintroduced by Eric Scerri, who suggested it as a possible categorical criterion to represent chemical periodicity. In particular, he reformulated the notion of triad in terms of atomic number instead of atomic weights; in this way, the value of the intermediate term of the triad became the exact average of the values of the two extremes. Following the inspiration of Scerri’s work, the main purpose of this article is to (...) obtain a representation where all the relations among the chemical elements that form the groups of the periodic system can be reconstructed on the basis of triads, without using electronic configurations. (shrink)

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)

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 philosophical vision of the world and the consequent methodology behind the book are clarified. The perspective used is the systemic one, but since today this term has assumed a wide and diversified meaning in the literature, this introduction will clarify the specific meaning of our approach, starting from the meaning of the term "system". Our idea of system is based on three key assertions that may seem contradictory, but are necessary and complementary to its definition. In particular, (...) we considered the usual idea that the system is more and less than the sum of its juxtaposed parts, highlighting the role of emergencies and constraints. In our idea of a system, however, we must consider a third fundamental characteristic: its dynamism, the dual nature of the system as an entity and as a process, its role as a "dynamic entity". Afterwards, the holistic and reductionist approaches were analysed in detail, and both the specific merits and the fact that these two opposing worldviews, considered individually, cannot give a complete and balanced description of reality, were taken into account. For us, only the systemic approach provides a balanced description of both the parts and the whole and must, therefore, be preferred. Finally, the differences between our approach and the approaches mentioned above have been considered in detail in this introduction. (shrink)

기존의 증명론적 의미론은 대부분 논리상항의 의미에 대한 증명론적 규명에 그 초점이 맞추어져왔다. 그러나 원자문장의 의미에 대한 증명론적 규명이 이루어지지 않는 한 증명론적 의미론은 불완전한 이론에 머무르게 된다. 이 글에서는 증명론적 의미론의 원자적 기반에 관한 문제가 검토되고 그 해결책이 모색될 것이다. 증명론적 의미론의 대표적인 형태인 프라위츠와 덤밋의 증명론적 타당성개념의 핵심 사항들에 대해 논의하고, 이 이론에 대한 원자적 기반의 문제를 제기한 후, 최소한 귀납적으로 정의된 술어에 관해서는 만족스런 원자적 기반이 마련될 수 있음을 보일 것이며, 이를 넘어서 보다 포괄적인 원자적 기반을 제시하는 문제가 (...) 검토되고 그 해결책이 모색될 것이다. (shrink)

Contemporary arguments for forms of psycho-physical dualism standardly depart from phenomenal aspects of consciousness. Conceptual aspects of conscious experience, as opposed to phenomenal or visual/perceptual ones, are often taken to be within the scope of functionalist, reductionist, or physicalist theories. I argue that the particular conceptual structure of human consciousness makes this asymmetry unmotivated. The argument for a form of dualism defended here proceeds from the empirical premise that conceptual structure in a linguistic creature like us is a combinatorial and (...) compositional system that implicates a distinction between simple and complex, or 'atomic' and 'molecular' concepts. The argument is that conceptual atoms, qua atoms, are irreducible to anything else. If so, and if the atoms are essentially semantic, a form of dualism follows: though positively inviting naturalistic inquiry into the semantic and mental aspects of nature, it requires that we look at the mental as a primitive domain of nature. Schematically, then, the argument is as follows: Human consciousness/thought is conceptually structured. The human conceptual system is a 'particulate' system at a syntactic and semantic level of representation. This implies the existence of conceptual 'particles', concepts that have no further semantic decomposition. A conceptual atom cannot be explained in terms of anything that does not involve its own intrinsic properties. Physicalism as normally conceived is inconsistent with and. (shrink)

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)

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)

"The time-honored dualism of the mutually exclusive systems of thought, mechanistic biology on the one hand and vitalism on the other, expresses a pair of theoretical approaches which are both inadequate. We shall show how they can be replaced by an abstractly descriptive system of a different type that is far better adapted to the nature of biology"--Preface.

We study an alternative embedding of IPC into atomic system F whose translation of proofs is based, not on instantiation overflow, but instead on the admissibility of the elimination rules for disjunction and absurdity. As compared to the embedding based on instantiation overflow, the alternative embedding works equally well at the levels of provability and preservation of proof identity, but it produces shorter derivations and shorter simulations of reduction sequences. Lambda-terms are employed in the technical development so that (...) the algorithmic content is made explicit, both for the alternative and the original embeddings. The investigation of preservation of proof-reduction steps by the alternative embedding enables the analysis of generation of “administrative” redexes. These are the key, on the one hand, to understand the difference between the two embeddings; on the other hand, to understand whether the final word on the embedding of IPC into atomic system F has been said. (shrink)

In this stimulating investigation, Gideon Freudenthal has linked social history with the history of science by formulating an interesting proposal: that the supposed influence of social theory may be seen as actual through its co herence with the process of formation of physical concepts. The reinterpre tation of the development of science in the seventeenth century, now widely influential, receives at Freudenthal's hand its most persuasive statement, most significantly because of his attention to the theoretical form which is charac teristic. (...) of classical Newtonian mechanics. He pursues the sources of the parallels that may be noted between that mechanics and the dominant philosophical systems and social theories of the time; and in a fascinating development Freudenthal shows how a quite precise method - as he descriptively labels it, the 'analytic-synthetic method' - which underlay the Newtonian form of theoretical argument, was due to certain interpretive premisses concerning particle mechanics. If he is right, these depend upon a particular stage of con ceptual achievement in the theories of both society and nature; further, that the conceptual was generalized philosophically; but, strikingly, Freudenthal shows that this concept-formation itself was linked to the specific social relations of the times of Newton and Hobbes. (shrink)

ABSTRACT Despite the increasing interest in science exhibitions, there has been hardly any work on mobile science exhibitions and their role within science diplomacy – a gap this thematic issue is meant to fill. Atomic mobile exhibitions are seen here not only as cultural sites but as multifaceted strategic processes of transnational nuclear history. We move beyond the bipolar Cold War history that portrays propagandist science exhibitions as instances of a one-way communication employed to promote the virtues of the (...) two major and conflicting political powers. Instead, Science Diplomacy on Display follows mobile atomic exhibitions as they move across national borders and around the world, functioning as spaces for diplomatic encounters. Exhibitions play a vital role not only in the production of knowledge and the formation of political worldviews but also as assets in diplomatic negotiations and as promoters of a new worldview in which nuclear stands at the centre. They are powerful iconic diplomatic devices, that is systems of representations that capture the diplomatic processes in action and make the nitty-gritty details of international relations visible. This issue seeks to trace the multiple and often contradictory meanings that mobile exhibitions took on for various actors. (shrink)

The periodic table is one of the best-known systems of classification in science. Because of the information it contains, it raises explanation-seeking questions. Quantum mechanical models of the behaviour of electrons may be seen as providing explanations in response to these questions. In this paper we first address the question ‘Do quantum mechanical models of atoms provide legitimate explanations?’ Because our answer is positive, our next question is ‘Are the explanations provided by quantum mechanical models of atoms mechanistic explanations?’. This (...) question is motivated by the fact that in many scientific disciplines, mechanistic explanations are abundant. Because our answer to the second question is negative, our last question is ‘What kind of explanation do quantum mechanical models of atom provide?’ By addressing these questions, we shed light on the nature of an important type of chemical explanation. (shrink)

Atoms and molecules are particular kinds of restricted n-body systems, which generally behave as quasi-separable, unlike other n-body systems, e.g., Newtonian ones. The Coulomb repulsion and the Pauli exclusion principle in atoms and molecules are responsible for that separability. Additionally, chemical bonds, especially covalent bonds, enhance the separability of molecules. Independent particle models do not describe atoms and molecules since first-order energy corrections are high. However, these corrections obtained by the first-order perturbation or mean-field strongly converge, implying a one-electron effective (...) potential description. Consequently, stable states of atoms and molecules can be reasonably described by one-electron effective potentials, which strongly differ from other n-body problems. We discuss the peculiarities of the correlation motion of generic systems in the context of the four fundamental forces. In particular, we have shown that the two components (attraction and repulsion) of the electromagnetic force confer a relatively low correlation motion to atoms and molecules. We discuss the physical and chemical nature of atoms and molecules, comparing the degrees of separability between different systems. For example, the separability of Newtonian systems is generally possible in particular classes of restricted systems due to relative mass differences. However, for atoms and molecules, the separability is much broader. (shrink)

The ground state of the driven three-level atomic system becomes unstable as a result of its spontaneous decay to the dynamic Stark level when the last one falls below this state. Different peculiarities of the atomic response may appear depending on the intensity and detuning of the driving field providing such level crossing.

Elsasser outlines in an informal but meticulous fashion an organismic biology which promises, in his opinion, to combine the best features of epigenetic vitalism and preformationist mechanism. Mechanistic reductionism is for Elsasser an unverifiable metaphysical hypothesis; i.e., if the postulate of infinite homogenous classes is dropped from the axiomatics of Van Neumann's proof that the state of any system is, in principle, Quantum Mechanically determinable, it becomes combinatorically obvious that biological systems and classes are radically inhomogenous [[sic]], a fact (...) which operationally bars the way to any complete reductionism. The door is thus opened to an open-ended theoretical biology in which all questions do not have a truth-functional equivalent answer according to the axioms and laws of the science, and prediction in the science becomes statistical in a nonabsolute way. Elsasser is a physicist with more than a casual acquaintance with biology and his argument benefits by his obvious expertise in both of these areas. Philosophically, however, he is a lightweight and relies, in particular, too much on the ontological ice that might be cut by operationalism. Theories are not verified in the stringent operational sense; they are confirmed in a way which is not logically tied to the requirement that all laws be inductively established. Elsasser, however, has so much to say on the problem of reductionism in biology that is of obvious value that the book is easily recommended over these caveats.—E. A. R. (shrink)

In a previous paper we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended equational theory for System F codifying at a syntactic level some properties found in parametric models of polymorphic type theory. A different approach to extract proof-theoretic properties of natural deduction derivations was proposed in a recent series of papers on the basis of an embedding of intuitionistic propositional logic (...) into a predicative fragment of System F, called atomic System F. In this paper we show that this approach finds a general explanation within our equational study of second-order natural deduction, and a clear semantic justification in terms of parametricity. (shrink)

A fully quantum-mechanical description of the spontaneous emission from an excited two-level atom placed in front of a two-slit interferometer is given. Global modes of the electromagnetic field in a two slit system are derived within the Kirchhoff-Huygens diffraction approximation, serving as a base for the field quantization. The standard Fermi's golden rule, supplemented by a factor coming from the nontrivial mode structure caused by the presence of the two-slit interferometer, is used to show that interference results from the (...) position-dependent coupling between the atom and different field modes of the system. (shrink)

The infinite-valued logic of ukasiewicz was originally defined by means of an infinite-valued matrix. ukasiewicz took special forms of negation and implication as basic connectives and proposed an axiom system that he conjectured would be sufficient to derive the valid formulas of the logic; this was eventually verified by M. Wajsberg. The algebraic counterparts of this logic have become know as Wajsberg algebras. In this paper we show that a Wajsberg algebra is complete and atomic (as a lattice) (...) if and only if it is a direct product of finite Wajsberg chains. The classical characterization of complete and atomic Boolean algebras as fields of sets is a particular case of this result. (shrink)

We show that the number-theoretic functions definable in the atomic polymorphic system are exactly the extended polynomials. Two proofs of the above result are presented: one, reducing the functions’ definability problem in ${\mathbf{F}}_{\mathbf{at}}$ to definability in the simply typed lambda calculus and the other, directly adapting Helmut Schwichtenberg’s strategy for definability in $\lambda ^{\rightarrow }$ to the atomic polymorphic setting. The uniformity granted in the polymorphic system, when compared with the simply typed lambda calculus, is emphasized.

In this pedagogical communication after demonstrating the legitimacy for using the quantum theory of atoms in molecules (QTAIM) to non-Coulombic systems, Hookean H2 +/H3 2+ species are used for AIM analysis. In these systems, in contrast to their Coulombic counterparts, electron density is atom-like and instead of expected two/three topological atoms, just a single topological atom emerges. This observation is used to demonstrate that what is really “seen” by the topological analysis of electron densities is the clustering of electrons. The (...) very trait of monotonic decay of electron density around the “centers” of clustering guarantees the appearance of topological atoms as basin of attraction of the gradient vector field of the electron density. Although observations with Hookean molecules may seem disappointing at first glance, a careful reasoning points to the fact that the QTAIM methodology is extendable to novel domains, by a knowledge of the morphology of underlying densities, beyond the typical Coulombic systems. (shrink)

In the past, a few researchers have presented arguments indicating that a statistical equilibrium state of classical charged particles necessarily demands the existence of a temperature-independent, incident classical electromagnetic random radiation. Indeed, when classical electromagnetic zero-point radiation is included in the analysis of problems with macroscopic boundaries, or in the analysis of charged particles in linear force fields, then good agreement with nature is obtained. In general, however, this agreement has not been found to hold for charged particles bound in (...) nonlinear force fields. The point is raised here that this disagreement arising for nonlinear force fields may be a premature conclusion on this classical theory for describing atomic systems, because past calculations have not directed strict attention to electromagnetic interactions between charges. This point is illustrated here by examining the classical hydrogen atom and showing that this problem has still not been adequately solved. (shrink)

A comment the paper by Brian McLaughlin in the same volume, this paper raises questions about whether the classicism/connectionism debate is really well-formed.

This article investigates why Lucretius does not dedicate any section of his poem to atomic size or provide a technical term to describe the concept. This absence is particularly significant because Epicurus’ Letter to Herodotus both uses the term μέγεθος to indicate atomic size and contains a passage reporting specifically on this property. First, the article argues that atomic size and shape are causally redundant in Epicurus’ ontology. Second, it demonstrates that the origin of both shape and (...) size is found in the smallest magnitudes in Epicurean physics, the minima. Drawing on these findings, it concludes that, since atomic size violates the law of parsimony, it is a superfluous entity in the Epicurean system. After analysing passages from the De rerum natura, it suggests that the absence of atomic size in Lucretius may be deliberate. Lucretius’ microphysics works perfectly without introducing a philosophical notion of atomic size, and is more economical and efficient than that of Epicurus. (shrink)

This essay will examine the polemic and poetic means through which three Indigenous Australian writers discuss the repercussions and risks associated with nuclear power, waste and weaponry as an existential and material threat to the mythopoeic creation stories, totemic systems and landforms which sustain Indigenous Australian belief. This essay will follow the establishment of a media ecology through which discourses of technological harm in Oodgeroo Noonuccal's “No More Boomerang” lay the foundation for Australian Indigenous anti-nuclear activist poetics and highlights the (...) relationship between language, belief and technology. Oodgeroo's [Kath Walker] “No More Boomerang” will be read as a precursor to the experimental expression of Lionel Fogarty's “Foot Walking and Talking – Atomic Confusion” as well as the procedural methodologies behind Natalie Harkin's “Zero Tolerance.” It will be argued that Indigenous-led representations of nuclear weaponry as an ontologic-existential threat can only be properly critiqued when framed through the constructs of race, nationhood and the history of colonization in Australia. (shrink)

A study of the history of the atomic theory of matter between the time of Democritus and that of Newton. The classical atomic theory, we are told, consisted of four central doctrines: a firm commitment to indivisible units of matter; a belief in the reality of the vacuum; a reductionist conception of forms and qualities and a mechanistic account of natural agency. The work provides a critical account of the arguments used for and against these four theses during (...) three time-periods: Antiquity, the Middle Ages and the 17th century. Atomism was a minority position in Antiquity, rejected by most natural philosophers on the strength of Aristotelian objections. But Aristotle's own disciples gradually took his system apart in the Middle Ages, thus developing - albeit in a piecemeal manner - positions strikingly akin in some respects to classical atomism. So when Gassendi and others sought to revive atomism in the 17th century, the way was already prepared for them. This study is the first to emphasise the continuity of this process and the debt owed by the 17th-century moderns to the medieval critique of Aristotle. (shrink)

Two more or less standard methods exist for the systematic, logical construction of classical mathematics, the so-called theory of types, due in the main to Russell, and the Zermelo axiomatic set theory. In systems based upon either of these, the connective of membership, “ε”, plays a fundamental role. Usually although not always it figures as a primitive or undefined symbol.Following the familiar simplification of Russell's theory, let us mean by alogical typein the strict sense any one of the following: (i) (...) the totality consisting exclusively of individuals, (ii) the totality consisting exclusively of classes whose members are exclusively individuals, (iii) the totality consisting exclusively of classes whose members are exclusively classes whose members in turn are exclusively individuals, and so on. Any entity from (ii) is said to beone type higherthan any entity from (i), any entity from (iii), one type higher than any entity from (ii), and so on. In systems based upon this simplified theory of types, the only significant atomic formulae involving “ε” are those asserting the membership of an entity in an entity one type higher. Thus any expression of the form “(x∈y)” is meaningless except where “y” denotes an entity of just one type higher than the type of the entity denoted by “x” It is by means of general type restrictions of this kind that the Russell and other paradoxes are avoided. (shrink)

Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference and Greg (...) Restall’s bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates. (shrink)

Gooddy, a British neurologist, argues that our sense of time, and relativity in general, is a function of the nervous system. Written for the general reader, the 10 essays discuss atomic, cellular, and glandular "clocks," age, government time vs. personal time, and time disorders (such as being in love). Annotation copyrighted by Book News, Inc., Portland, OR.

A novel non-classical mereological concept built up by blending the Metaphysics of Xavier Zubiri and the Quantum Theory of Atoms in Molecules of R. F. W. Bader is proposed. It is argued that this philosophical concept is necessary to properly account for what happens in a chemical reaction. From the topology of the gradient of the laplacian of the electronic charge density, \\) within the QTAIM framework, different “atomic graphs” are found for each atom depending on the molecular context, (...) reflecting how the whole molecule affects each atom. In this way, the whole molecular system imposes certain geometry onto each atom, and every atom exhibits different ontological modality. On the Metaphysical side, for X. Zubiri real things are system of different notes. The physical essence is the subsystem of essential notes with a coherence unity. Every note is grounded on the essence. The unity of the system is present somehow in every note-of beforehand, and every essential note-of turns towards the other. The essence determines the position of each note within the system, and hence is the grounding for modality of the notes. By conflating both “theories” and taking the atoms as essential notes, we propose the concept of “Molecule in atoms-of” or “atoms-of in Molecules”. Within the course of a chemical reaction the atoms-of modified their “of” as required by the new molecular unity being formed, and eventually change their modality. The validity to the Zubiri’s statements, is attained by evaluating necessity and possibility in a set-up of finite accessible “possible worlds”. (shrink)

Scientists often think of the world as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are the system of planets orbiting the sun or any other classical mechanical system, a hydrogen atom or any other quantum–mechanical system, and the earth’s atmosphere or any other statistical mechanical system. We introduce a general and unified framework for describing such systems and show how it can be used to (...) examine some familiar philosophical questions, including the following: how can we define nomological possibility, necessity, determinism, and indeterminism; what are symmetries and laws; what regularities must a system display to make scientific inference possible; how might principles of parsimony such as Occam’s Razor help when we make such inferences; what is the role of space and time in a system; and might they be emergent features? Our framework is intended to serve as a toolbox for the formal analysis of systems that is applicable in several areas of philosophy. (shrink)

The paper studies Heyting algebras within the framework of computable structure theory. We prove that the class _K_ containing all Heyting algebras with distinguished atoms and coatoms is complete in the sense of the work of Hirschfeldt et al. (Ann Pure Appl Logic 115(1-3):71-113, 2002). This shows that the class _K_ is rich from the computability-theoretic point of view: for example, every possible degree spectrum can be realized by a countable structure from _K_. In addition, there is no simple syntactic (...) characterization of computably categorical members of _K_ (i.e., structures from _K_ possessing a unique computable copy, up to computable isomorphisms). (shrink)

The second-order radial differential equations for the relativistic Dirac hydrogen atom are derived from the Dirac equation treated as a system of partial differential equations. The quantum operators which arise in the development are defined and interpreted as they appear. The splitting in the energy levels is computed by applying the theory of singularities for second-order differential equations to the Klein-Gordon and Dirac relativistic equations. In the Dirac radial equation additional terms appear containing a constant, which is shown to (...) be the “radius of the electron.” It is concluded that the minute perturbation of the radial eigenfunction in the vicinity of the proton brought about by the extension of the elementary particles, which appears naturally out of the Dirac equations, results in the prediction of the observed splitting of the hydrogen atom energy levels by the Dirac theory. The extension of the particles arises even though the Dirac hydrogen atom is originally formulated for point charges. (shrink)