For simplicity, most of the literature introduces the concept of definitional equivalence only for disjoint languages. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to non-disjoint languages and they show that their generalization is not equivalent to intertranslatability in general. In this paper, we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce another formalization of definitional equivalence due to Andréka and Németi which is equivalent to the Barrett–Halvorson (...) generalization in the case of disjoint languages. We show that the Andréka–Németi generalization is the smallest equivalence relation containing the Barrett–Halvorson generalization and it is equivalent to intertranslatability, which is another definition for definitional equivalence, even for non-disjoint languages. Finally, we investigate which definitions for definitional equivalences remain equivalent when we generalize them for theories in non-disjoint languages. (shrink)

The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic kinematics. We show that the axioms of special relativity can be interpreted in the language of classical kinematics. This means that there is a logical translation function from the language of special relativity to the language of classical kinematics which translates the axioms of special relativity into consequences of classical kinematics. We will also show that if we distinguish a class (...) of observers in special relativity and exclude the non-slower-than light observers from classical kinematics by an extra axiom, then the two theories become definitionally equivalent. Furthermore, we show that classical kinematics is definitionally equivalent to classical kinematics with only slower-than-light inertial observers, and hence by transitivity of definitional equivalence that special relativity theory extended with “Ether” is definitionally equivalent to classical kinematics. So within an axiomatic framework of mathematical logic, wee xplicitly show that the transition from classical kinematics to relativistic kinematics is the knowledge acquisition that there is no “Ether”, accompanied by a redefinition of the concepts of time and space. (shrink)

The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special relativity is (...) also studied. (shrink)

In natural sciences, the most interesting and relevant questions are the so-called why-questions. There are several different approaches to why-questions and explanations in the literature, however, most of the literature deals with why-questions about particular events, such as ``Why did Adam eat the apple?''. Even the best known theory of explanation, Hempel's covering law model, is designed for explaining particular events. Here we only deal with purely theoretical why-questions about general phenomena of physics, for instance ``Why can no observer move (...) faster than light?'' or ``Why are Kepler's laws valid?''. Here we are not going to develop a whole new theory of why-questions in physics. We will just touch upon some ideas and examples relevant to our subject. (shrink)

For simplicity, most of the literature introduces the concept of definitional equivalence only to languages with disjoint signatures. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to languages with non-disjoint signatures and they show that their generalization is not equivalent to intertranslatability in general. In this paper,we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce the Andréka and Németi generalization as one of the many equivalent formulations for (...) languages with disjoint signatures. We show that the Andréka-Németi generalization is the smallest equivalence relation containing the Barrett–Halvorson generalization and it is equivalent to intertranslatability even for languages with non-disjoint signatures. Finally,we investigate which definitions for definitional equivalences remain equivalent when we generalize them for theories with non-disjoint signatures. (shrink)

Thought experiments are widely used in the informal explanation of Relativity Theories; however, they are not present explicitly in formalized versions of Relativity Theory. In this paper, we present an axiom system of Special Relativity which is able to grasp thought experiments formally and explicitly. Moreover, using these thought experiments, we can provide an explicit definition of relativistic mass based only on kinematical concepts and we can geometrically prove the Mass Increase Formula in a natural way, without postulates of conservation (...) of mass and momentum. (shrink)

We present three natural but distinct formalisations of Einstein’s special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made equivalent by introducing a small number of additional, intuitively acceptable axioms.

This book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers (...) that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself. (shrink)

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this paper. We would like to invite the logician reader to take part in this grand enterprise of the new century. Besides general perspective and motivation, we present initial results in this direction.

In the literature, there have been several methods and definitions for working out whether two theories are “equivalent” or not. In this article, we do something subtler. We provide a means to measure distances between formal theories. We introduce two natural notions for such distances. The first one is that of axiomatic distance, but we argue that it might be of limited interest. The more interesting and widely applicable notion is that of conceptual distance which measures the minimum number of (...) concepts that distinguish two theories. For instance, we use conceptual distance to show that relativistic and classical kinematics are distinguished by one concept only. (shrink)

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of (...) accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND. (shrink)

Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and Pearce. In Example 2, uncountably many pairs of definitionally inequivalent theories are given such that their model categories are concretely isomorphic via bijections that preserve ultraproducts in the model categories up to isomorphism. Based on these results, we settle several conjectures of Barrett, (...) Glymour and Halvorson. (shrink)

In 1978, Yu. F. Borisov presented an axiom system using a few basic assumptions and four explicit axioms, the fourth being a formulation of the relativity principle; and he demonstrated that this axiom system had (up to choice of units) only two models: a relativistic one in which worldview transformations are Poincaré transformations and a classical one in which they are Galilean. In this paper, we reformulate Borisov’s original four axioms within an intuitively simple, but strictly formal, first-order logic framework, (...) and convert his basic background assumptions into explicit axioms. Instead of assuming that the structure of physical quantities is the field of real numbers, we assume only that they form an ordered field. This allows us to investigate how Borisov’s theorem depends on the structure of quantities. We demonstrate (as our main contribution) how to construct Euclidean, Galilean, and Poincaré models of Borisov’s axiom system over every non-Archimedean field. We also demonstrate the existence of an infinite descending chain of models and transformation groups in each of these three cases, something that is not possible over Archimedean fields. As an application, we note that there is a model of Borisov’s axioms that satisfies the relativity principle, and in which the worldview transformations are Euclidean isometries. Over the field of reals it is easy to eliminate this model using natural axioms concerning time’s arrow and the absence of instantaneous motion. In the case of non-Archimedean fields, however, the Euclidean isometries appear intrinsically as worldview transformations in models of Borisov’s axioms and neither the assumption of time’s arrow, nor the rejection of instantaneous motion, can eliminate them. (shrink)

A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.

I make three related proposals concerning the development of receptive communication in human infants. First, I propose that the presence of communicative intentions can be recognized in others' behaviour before the content of these intentions is accessed or inferred. Second, I claim that such recognition can be achieved by decoding specialized ostensive signals. Third, I argue on empirical bases that, by decoding ostensive signals, human infants are capable of recognizing communicative intentions addressed to them. Thus, learning about actual modes of (...) communication benefits from, and is guided by, infants' preparedness to detect infant-directed ostensive communication. (shrink)

Many argued (Accardi and Fedullo, Pitowsky) that Kolmogorov's axioms of classical probability theory are incompatible with quantum probabilities, and that this is the reason for the violation of Bell's inequalities. Szabó showed that, in fact, these inequalities are not violated by the experimentally observed frequencies if we consider the real, “effective” frequencies. We prove in this work a theorem which generalizes this results: “effective” frequencies associated to quantum events always admit a Kolmogorovian representation, when these events are collected through different (...) experimental setups, the choice of which obeys a classical distribution. (shrink)

Two experiments investigated whether infants represent goal‐directed actions of others in a way that allows them to draw inferences to unobserved states of affairs (such as unseen goal states or occluded obstacles). We measured looking times to assess violation of infants' expectations upon perceiving either a change in the actions of computer‐animated figures or in the context of such actions. The first experiment tested whether infants would attribute a goal to an action that they had not seen completed. The second (...) experiment tested whether infants would infer from an observed action the presence of an occluded object that functions as an obstacle. The looking time patterns of 12‐month‐olds indicated that they were able to make both types of inferences, while 9‐month‐olds failed in both tasks. These results demonstrate that, by the end of the first year of life, infants use the principle of rational action not only for the interpretation and prediction of goal‐directed actions, but also for making productive inferences about unseen aspects of their context. We discuss the underlying mechanisms that may be involved in the developmental change from 9 to 12 months of age in the ability to infer hypothetical (unseen) states of affairs in teleological action representations. (shrink)

This book contains an original analysis of the existential there-sentence from a philosophical-linguistic perspective. At its core is the claim that there-sentences' form is distinct from that of ordinary subject–predicate sentences, and that this fundamental difference explains the construction's unusual grammatical and discourse properties.

PurposeThe purpose of the paper is to provide an overview of the legal implications which may be relevant to the ethical aspects of emerging technologies, to explore the existing situation in the area of legal regulation at EU level, and to formulate recommendations for the lawmakers.Design/methodology/approachThe analysis is based on the premise that the law is supposed to invoke moral principles. Speculative findings are formulated on the basis of analyzing specific emerging technologies; empirical findings are based on a research conducted (...) in the whole legal corpus of the EU.FindingsIn the area of network‐based technologies the already existing and elaborated legal frameworks can be used in an extended manner; artificial intelligence‐based technologies call for alterations in several branches of law; while interface technologies show the difficulty and complexity of regulating interdisciplinary fields. The legal implications of emerging technologies have attracted only a minimal legislative attention in the competent bodies of the EU.Originality/valueThe paper provides a systemic approach towards transmitting ethical norms to the application of emerging technologies through legal regulation, and formulates detailed recommendations in various areas of such technologies. (shrink)

The current study investigates the effects of green advertising and a corporation’s environmental performance on brand attitudes and purchase intentions. A 3 × 3 (firm’s environmental performance and its advertising efforts as independent variables) experiment using n = 302 subjects was conducted. Results indicate that the negative effect of a firm’s low performance on brand attitudes becomes stronger in the presence of green advertising compared to general corporate advertising and no advertising. Further, when the firm’s environmental performance is high, both (...) green and general corporate advertising result in more unfavorable brand attitudes than no advertising. The study’s counter-intuitive findings are explained by attribution theory. (shrink)

According to recent work in experimental philosophy, folk intuitions concerning various metaphysical issues are heavily teleological. The experiments in question, which belong to a broader research program in psychology about ‘promiscuous teleology’, have featured prominently in debates about the methodology of metaphysics, with some authors claiming that the folk’s teleological bias debunks everyday intuitions concerning composition, persistence, and organisms. The present paper argues for a possibility that is very rarely discussed in that debate, namely the idea that the folk’s intuitions (...) could be veridical. Our argument is based on an emerging naturalistic theory of biological functions called “the organismic view”. The gist of the organismic view is that biological systems are characterized by a special circular causal regime where each part of the system contributes to the boundary conditions of some other parts, as well as of the whole. We argue that teleological folk intuitions are veridical in the biological domain under such a view, and they are veridical in the social and artefactual domains under coherent extensions of the organismic view. (shrink)

We review studies of an evolution operator ℒ for a discrete Langevin equation with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading eigenvalue of ℒ yields a physically measurable property of the dynamical system, the escape rate from the repeller. The spectrum of the evolution operator ℒ in the weak noise limit can be computed in several ways. A method using a local matrix representation of the operator allows to push the corrections to the escape rate up (...) to order eight in the noise expansion parameter. These corrections then appear to form a divergent series. Actually, via a cumulant expansion, they relate to analogous divergent series for other quantities, the traces of the evolution operators ℒn. Using an integral representation of the evolution operator ℒ, we then investigate the high order corrections to the latter traces. Their asymptotic behavior is found to be controlled by sub-dominant saddle points previously neglected in the perturbative expansion, and to be ultimately described by a kind of trace formula. (shrink)

The paper investigates and refines the proportionalist solution to the causal exclusion problem developed by Menzies and List. First and foremost, it explores the implications of their inter-level compatibility result. It is highlighted that in theory the inter-level causal compatibility of realizer and realized properties allows for scenarios where the higher-level property is multiply realized. By developing concrete illustrations, the paper proves this to be an empirically plausible option. Further non-trivial implications of the framework are unpacked to show that the (...) sensitivity of causal relations to background conditions is as important in deciding on the existence and the direction of exclusion as sensitivity to the realization of the cause. This insight also opens the way to further refinements: a richer reconceptualization of upwards exclusion and a plausible answer to a critic of the Menzies and List project. (shrink)

In a recent article “From Epistemology to Ontology,” Tihamer Margitay argues, in addition to other things, that the ontological arguments Polanyi provided for his ontological realism with respect to the levels of reality are insufficient. Although Margitay shows this correctly in the case of arguments from boundary conditions, his arguments are not that convincing against the unidentifyability thesis, the thesis that entity kinds on higher levels cannot be identified with descriptions given on lower levels. I argue that here Polányi relies (...) on a version of the multiple realizeability thesis and this argument can be reformulated in a stronger version against which the counterargument Margitay provides is insufficient. (shrink)

How does cultural knowledge shape the development of human minds and, conversely, what kind of species-specific social-cognitive mechanisms have evolved to support the intergenerational reproduction of cultural knowledge? We critically examine current theories proposing a human-specific drive to identify with and imitate conspecifics as the evolutionary mechanism underlying cultural learning. We summarize new data demonstrating the selective interpretive nature of imitative learning in 14-month-olds and argue that the predictive scope of existing imitative learning models is either too broad or too (...) narrow to account for these findings. We outline our alternative theory of a human-specific adaptation for ‘pedagogy’, a communicative system of mutual design specialized for the fast and efficient transfer of new and relevant cultural knowledge from knowledgeable to ignorant conspecifics. We show the central role that innately specified ostensive-communicative triggering cues and learner-directed manner of knowledge manifestations play in constraining and guiding selective imitation of relevant cultural knowledge that is both new and cognitively opaque to the naive learner. (shrink)