The lowest order processes described within quantum electrodynamics are free from the problems of infinites in the theory, and can be dealt with disregarding the need for charge and mass renormalization. This might indicate that the space-time description of these processes is not only consistent but also could give a privileged insight to the functioning of models provided by the theory. The Møller scattering is as R. P. Feynman considered, a prototype for the development of his rules of quantum electrodynamics (...) and his overall space-time approach. The study of Møller scattering might then provide the must straightforward way to the understanding of the space-time description of interactions provide by quantum electrodynamics. This method is much less powerful than might be expected at first, pointing to the intrinsic limitations of the theory in what regards the modelling of the temporality in interaction processes. (shrink)

Discussions of the metaphysical status of spacetime assume that a spacetime theory offers a causal explanation of phenomena of relative motion, and that the fundamental philosophical question is whether the inference to that explanation is warranted. I argue that those assumptions are mistaken, because they ignore the essential character of spacetime theory as a kind of physical geometry. As such, a spacetime theory does notcausally explain phenomena of motion, but uses them to construct physicaldefinitions of basic geometrical structures by coordinating (...) them with dynamical laws. I suggest that this view of spacetime theories leads to a clearer view of the philosophical foundations of general relativity and its place in the historical evolution of spacetime theory. I also argue that this view provides a much clearer and more defensible account of what is entailed by realism concerning spacetime. (shrink)

The present work is focussed on the completeness of physics, or what is here called the Completeness Thesis: the claim that the domain of the physical is causally closed. Two major questions are tackled: How best is the Completeness Thesis to be formulated? What can be said in defence of the Completeness Thesis? My principal conclusions are that the Completeness Thesis can be coherently formulated, and that the evidence in favour if it significantly outweighs that against it. In opposition to (...) those who argue that formulation is impossible because no account of what is to count as physical can be provided, I argue that as long as the purpose of the argument in which the account is to be used are borne in mind there are no significant difficulties. The account of the physical which I develop holds as physical whatever is needed to fix the likelihood of pre-theoretically given physical effects, and hypothesises in addition that no chemical, biological or psychological factors will be needed in this way. The thus formulated Completeness Thesis is coherent, and has significant empirical content. In opposition to those who defend the doctrine of emergentism by means of philosophical arguments I contend that those arguments are flawed, setting up misleading dichotomies between needlessly attenuated alternatives and assuming the truth of what is to be proved. Against those who defend emergentism by appeal to the evidence, I argue that the history of science since the nineteenth century shows clearly that the empirical credentials of the view that the world is causally closed at the level of a small number of purely physical forces and types of energy is stronger than ever, and the credentials of emergentism correspondingly weaker. In opposition to those who argue that difficulties with reductionism point to the implausibility of the Completeness Thesis I argue that completeness in no way entails the kinds of reductionism which give rise to the difficulties in question. I argue further that the truth of the Completeness Thesis is in fact compatible with a great deal of taxonomic disorder and the impossibility of any general reduction of non-fundamental descriptions to fundamental ones. In opposition to those who argue that the epistemological credentials of fundamental physical laws are poor, and that those laws should in fact be seen as false, I contend that truth preserving accounts of fundamental laws can be developed. Developing such an account, I test it by considering cases of the composition of forces and causes, where what takes place is different to what is predicted by reference to any single law, and argue that viewing laws as tendencies allows their truth to be preserved, and sense to be made of both the experimental discovery of laws, and the fact that composition enables accurate prediction in at least some cases. (shrink)

We motivate and develop a perspectival A-theory of time (future/present/past) and probe its implied interpretation of quantum mechanics. It will emerge that, as a first take, the time of relativity is a B-series (earlier-times to later-times) and the time of quantum mechanics is an A-series. There is philosophical motivation for the idea that mutual quantum measurement happens when and only when the systems’ A-series become one mutual A-series, as in the way qualia work in the Inverted Spectrum. This seems to (...) account for certain quantum phenomena, including that the electrons of a Bell pair do not have definite spins until measurement, as ‘until’ here is a (perspectival) A-series notion. Various issues in the foundations of quantum mechanics are canvassed. (shrink)

Contemporary debate over laws of nature centers around Humean supervenience, the thesis that everything supervenes on the distribution of non-nomic facts. The key ingredient of this thesis is the idea that nomic-like concepts—law, chance, causation, etc.—are expressible in terms of the regularities of non-nomic facts. Inherent to this idea is the tacit conviction that regularities, “constant conjunctions” of non-nomic facts do supervene on the distribution of non-nomic facts. This paper raises a challenge for this conviction. It will be pointed out (...) that the notion of regularity, understood as statistical correlation, has a necessary conceptual component not clearly identified before—I shall call this the “conjunctive relation” of the correlated events. On the other hand, it will be argued that there exists no unambiguous, non-circular way in which this relation could be determined. In this regard, the notion of correlation is similar to that of distant simultaneity where the necessary conceptual component is the one-way speed of light, whose value doesn’t seem to be determined by matters of facts. (shrink)

Although logical empiricism is now mostly decried, their naturalist claim that the content of a theory can be read off from its structure, without any philosophical considerations needed, still supports traditional strategies to escape cases of underdetermination. The appeal to theoretical equivalence or to theoretical virtues, for instance, both assume that there is a neutral standpoint from which the structure of the theories can be analyzed, the physically relevant from the superfluous separated, and a comparison made between their theoretical content (...) and virtues. In my dissertation, I examine the presuppositions upon which such strategies depend. I argue that the methodological principle underlying them, according to which theories with no superfluous structure should be preferred, is unpractical, for what constitutes relevant structure is determined by epistemic considerations about the aim of scientific theories. In chapter 1, I analyze the claim that theories with ordinary bosons and fermions are theoretically equivalent to theories with exotic `paraparticles'. I argue that this claim does not do justice to the latter, as the proof is formulated in a vocabulary parochial to the former and thus favors one of the theory while giving an impoverished version of the second. In chapter 2, I examine recent arguments to the effects that any interpretation of Quantum Mechanics that can offer a no-go theorem against paraparticles possesses an explanatory advantage over other interpretations and should, as such, be favored over others. Given that most physicists consider paraparticles as surplus structure whose non-observation does not require an explanation, I evaluate arguments of both sides and suggest a third way to approach the question. Finally, in chapter 3, I turn my attention to methods for excluding another kind of unphysical structure, mathematical artifacts, from rival dark matter models. Simulations are our only window into what rival models predict about the universe’s structure. But for them to play a useful role in generating knowledge, we need to distinguish reliably between real predictions and artifacts. I argue that robustness analysis fails to fulfill this task. I propose in its place another methodology, that of crucial simulations. (shrink)

In Part 3, I will discuss the problems of inertia and gravity in Leibniz, and present three conjectures: If Leibniz were really ready to insist on relativity, he would have to assert the relativity of inertial motion. In Leibniz’s theories of dynamics and geometry, there was a struggle between his predilection for straight line and his adherence to an optimality principle. Gravity, as well as inertia, can be considered as a universal feature of the world, so that the foundation of (...) both may have a common root. Further, drawing on the results in Part 1 and Part 2, I will argue for the need of a unified interpretation of Leibniz’s metaphysics and dynamics. My three conjectures as regards Leibniz’s possible treatment of inertia and gravity are proposed along a unified interpretation, in terms of my informational reconstruction of Leibniz’s philosophy. Finally, the most important features of the informational interpretation are summarized. The synopsis of the whole paper is added. (shrink)

Theory and Reality is about the connection between true theories and the world. A mathematical framefork for such connections is given, and it is shown how that framework can be used to infer facts about the structure of reality from facts about the structure of true theories, The book starts with an overview of various approaches to metaphysics. Beginning with Quine's programmatic "On what there is", the first chapter then discusses the perils involved in going from language to metaphysics. It (...) criticises contemporary intuition-driven metaphysics, comments on naturalistic approaches, and then presents the main proposition put forward in the thesis: we should base metaphysics on model theory. In chapters 2 to 5, mathematical treatments are given of concepts that we need: theories, metaphysics, necessitation and semantics. These are used in chapters 6 and 7 to prove that, seen from a certain informative view point, any true theory will give rise to an isomorphism between that theory and the world. This conclusion is similar to Wittgenstein's in the Tractatus, but differs in that it places the structural relationship on the level of whole theories, rather than single propositions. (shrink)

Ernst Mach is the only person whom Einstein included on both the list of physicists he considered his true precursors, and the list of the philosophers who had most affected him. Einstein scholars have been less generous in their estimation of Mach's contributions to Einstein's work, and even amongst the more generous of them, Mach's great achievements in physics are seldom mentioned in this context. This is odd, considering Mach was nominated for the Nobel Prize in Physics three times. In (...) this paper, I examine some of Mach's work in physics that bears conceptually on Einstein's 1905 paper on Special Relativity ("On The Electrodynamics of Moving Bodies"). Mach was the first to give the correct explanation of the Doppler Effect, and he presented it in a way that Einstein echoes in his 1905 paper: laying out two apparently contradictory principles and showing how both can be retained. It is also notable that Mach's explanation was explicit about not relying on the existence of a medium of transmission for the propagation of light waves. In his work on supersonic shock waves, Mach invokes the constancy of the velocity of sound (i.e., its independence of the motion of the sound source) , just as he had invoked the constancy of the velocity of light in his work on the Doppler Effect for Light. I examine the analogies between light and sound that were drawn upon by Einstein and Mach, as well as one analogy that Einstein could have, but did not make: Cherenkov radiation, or "singing electrons", i.e., cases in which the sound of light in the medium of transmission is exceeded, which results in an optical analogue of supersonic shock waves. (shrink)

(1987). Einstein's brand of verificationism. International Studies in the Philosophy of Science: Vol. 2, No. 1, pp. 33-54. doi: 10.1080/02698598708573301.

In this paper I examine Quine''s indispensability argument, with particular emphasis on what is meant by ''indispensable''. I show that confirmation theory plays a crucial role in answering this question and that once indispensability is understood in this light, Quine''s argument is seen to be a serious stumbling block for any scientific realist wishing to maintain an anti-realist position with regard to mathematical entities.

There is good reason to suppose that our best physical theories are false: In addition to its own internal problems, the standard formulation of quantum mechanics is logically incompatible with special relativity. I will also argue that we have no concrete idea what it means to claim that these theories are approximately true.

We explore the significance of physical theories set in Euclidean spacetimes. In particular, we explore the use of these theories in contemporary physics at large, and the sense in which there can be a notion of temporal evolution in these theories. Having achieved these tasks, we proceed to reflect on the lessons that one can take from such theories for Knox’s ‘inertial frame’ version of spacetime functionalism, which seems to issue incorrect verdicts in the case of theories with Euclidean metrical (...) structure. (shrink)

Throughout the twentieth and twenty-first centuries, artists and scholars have pursued connections between modern art movements and scientific exploration and expertise. Particularly in discussions of Cubism and Futurism, artists and historians have employed the terms ‘fourth dimension’, ‘simultaneity’, and ‘space-time’ in their artistic theories. Select scholars have connected the use of these terms with Albert Einstein’s theories of relativity. This paper presents brief notes on this perceived intersection between Western science and art during the early to mid-twentieth century. It focuses (...) on the Bauhaus master Laszlo Moholy-Nagy, for whom ideas of “space-time” offered new and dynamic possibilities for art and perception. Rather than solely trying to interpret or represent Einstein’s theories in art, Moholy-Nagy considered the artistic implications of a theory that challenged the notion of absolute time and space. His writing on technology and the use of projected light to produce spatial modulation greatly impacted subsequent generations of artists. Moholy-Nagy also viewed greater collaboration within the disciplines of science and art as necessary. He argued that in order to best respond to the twentieth century a new generation of artists must be equipped with both technical and scientific expertise. (shrink)

Is freedom compatible with determinism? Davidson famously rephrased this question by replacing “freedom” with “anomaly of the mental”, that is, failure to fall under a law. In order to prove that the anomaly of the mental is compatible with other conjectures he makes, in particular that: there is psycho-physical causation; “where there is causality, there must be a law” ; and the mental supervenes on the physical, Davidson proposed a model, that came to be known as anomalous monism. Accepting all (...) of Davidson’s conjectures, we compare the structure of Davidson’s argument with that of Einstein’s argument for the special theory of relativity. This leads us to an exposition of Davidson’s ontology in terms that are inspired by recent results in the philosophy of physics, that is, in terms of fundamental ontology and high-level coarse-grained descriptions. We explain in what sense Davidson’s model is a principle theory and discuss some requirements that the constructive theory underlying Davidson's principle approach must satisfy. We propose two constructive theories of description that may underlie Davidson's approach and this deeper structure leads us to formulating a dilemma according to which Davidson's approach entails either a non-physicalist type-identity reductive and monistic structure of events; or else it entails a structure of events that requires what we call token-substance dualism. We consider some issues which seem to suggest that the first horn of this dilemma collapses into a reductive type-identity physicalist theory, contrary to Davidson's intent. Finally, we show how Davidson's achievement of accounting for some freedom of the mental from the physical and the anomaly of the mental within anomalous monism can be achieved in a fully reductive type-identity physicalist theory. (shrink)

What, if anything, would be wrong with replacing the light postulate in Einstein’s 1905 formulation of special relativity with a ‘sound postulate’, stating that the speed of sound is independent of the speed of the source? After reviewing the historical reasons underlying the particular focus on light in the special theory, we consider the circumstances under which such a theory of ‘sonic relativity’ would be justified on empirical grounds. We then consider the philosophical upshots of ‘sonic relativity’ for four contemporary (...) areas of investigation in the philosophy of spacetime: global versus subsystem symmetries, dynamical versus geometrical approaches to spacetime, the possibility of a preferred frame in theories of quantum gravity, and spacetime functionalism. (shrink)

Computer simulation and thought experiments seem to produce knowledge about the world without intervening in the world. This has called for a comparison between the two methods. However, Chandrasekharan et al. argue that the nature of contemporary science is too complex for using TEs. They suggest CS as the tool for contemporary sciences and conclude that it will replace TEs. In this paper, by discussing a few TEs from the history of science, I show that the replacement thesis about TE (...) is a failure. The paper is divided into three sections. The first section discusses the arguments of Chandrasekharan et al. and demonstrates the three distinct aspects of the replacement thesis. The second section examines the argument against TE and shows that they are inadequate to prove the withering of TE from science. The third section discusses Albert Einstein’s Magnet and Conductor TE and demonstrates that replacing such TE with CS yield no advantage. (shrink)

While there is a longstanding discussion about the interpretation of the extended, general principle of relativity, there seems to be a consensus that the special principle of relativity is absolutely clear and unproblematic. However, a closer look at the literature on relativistic physics reveals a more confusing picture. There is a huge variety of, sometimes metaphoric, formulations of the relativity principle, and there are different, sometimes controversial, views on its actual content. The aim of this paper is to develop a (...) precise language in order to provide a precise formulation of the principle. In view of the fact that the special relativity principle is considered as a universal meta-law, which must be valid for all physical laws in all situations, we try to keep the formalism as general as possible. The benefit of the formal reconstruction is that it makes explicit all the necessary conceptual components of the principle; it brings out many subtle details and the related conceptual problems. (shrink)

My thesis concerns the fate of the spiritual capacities of human beings in the time of digital media systems in relation to the work of Bernard Stiegler. Stiegler’s framing of the problem is situated within his ambigious, or pharmacological, approach to technology, in which it is simultaneously poison and cure. It is also founded on his notion of ‘originary technicity’, in which humanity and technology ‘invent’ each other. Both avoid a reductive reading of human-technological relations. Stiegler’s account of subjectivity is (...) one founded on the linguistic, philosophical and sociological notions of agency whereby the self is conceived as a performance within the symbolic and aesthetic order of culture. This performance necessitates a public stage akin to that of the Greek tragic age that allows its audience to reflect upon and question their society in order for the society to remain ethically reflexive. Yet, the growth of mass culture and global consumerism threatens this reflexivity and must be recovered. The generalized proletarianization of the consumer age is one that compromises the acting out of spirit due to the exhaustion of human drives. Furthermore, the social fabric, as with the fabric of the self, is a composition of tendencies, a ‘weaving’ of social bonds that is created by society and its individuals. Therefore, as with the reflexive public stage, society must have the requisite knowledge and ability to interpret and create this production of the social. In a digital age, this must now be a society of ‘image-readers’. By looking at Stiegler’s theorizing of a new contributive economy, I examine the elevating possibilities that can come out of the disindividuating processes of hyper-industrial, consumer-driven technology, and, therefore, what spiritually expressive and transformative performances of self, and society, digital media enable. I argue the aesthetic performance of the self must be one in which the individual is an amateur artist aware of the reflexive social stage that digital platforms provide. (shrink)

Aberration and radiation pressure reflected by a moving mirror are examples of the Klein, one-way Doppler shift, and Poincare', two-way Doppler shift, disc models of hyperbolic geometry, respectively. Aberration, like the Thomas precession, is related to the angular defect, and is a kinematical eect rather than relativistic. At the angle of parallelism, determined by a stationary observer looking at a moving object in the direction normal to its motion, the rotation of the object is related to its Lorentz contraction that (...) an observer sees traveling at the same speed as the object. The origin of the Lorentz contraction is the angular defect, while the angle of parallelism is an asymptotic limit, providing the unique link between circular and hyperbolic functions. The relative velocity provides an upper limit on the angle of incidence with the radiation pressure vanishing at the angle of parallelism. Two-way, second-order Doppler shifts can be used to establish experimentally the existence of an angle of parallelism. (shrink)

An important epistemological lesson can be learned from the impossibility to determine the one-way velocity of light and the immediate implication that simultaneity is conventional. The vicious circle -- to determine whether two distant events are simultaneous we need to know the one-way velocity of light between them, but to determine the one-way velocity of light we need to know that the two events are simultaneous -- is an indication of the need for a profound change of our view on (...) reality. (shrink)

Scientific risk evaluations are constructed by specific evidence, value judgements and biological background assumptions. The latter are the framework-setting suppositions we apply in order to understand some new phenomenon. That background assumptions co-determine choice of methodology, data interpretation, and choice of relevant evidence is an uncontroversial claim in modern basic science. Furthermore, it is commonly accepted that, unless explicated, disagreements in background assumptions can lead to misunderstanding as well as miscommunication. Here, we extend the discussion on background assumptions from basic (...) science to the debate over genetically modified (GM) plants risk assessment. In this realm, while the different political, social and economic values are often mentioned, the identity and role of background assumptions at play are rarely examined. We use an example from the debate over risk assessment of stacked genetically modified plants (GM stacks), obtained by applying conventional breeding techniques to GM plants. There are two main regulatory practices of GM stacks: (i) regulate as conventional hybrids and (ii) regulate as new GM plants. We analyzed eight papers representative of these positions and found that, in all cases, additional premises are needed to reach the stated conclusions. We suggest that these premises play the role of biological background assumptions and argue that the most effective way toward a unified framework for risk analysis and regulation of GM stacks is by explicating and examining the biological background assumptions of each position. Once explicated, it is possible to either evaluate which background assumptions best reflect contemporary biological knowledge, or to apply Douglas' 'inductive risk' argument. (shrink)

Since special relativity and quantum mechanics, information has become a central concept in our description and understanding of physical reality. This statement may be construed in different ways, depending on the meaning we attach to the concept of information, and on our ontological commitments. One distinction is between mind-independent ‘Shannon information’ and a traditional conception of information, connected with meaning and knowledge. Another, orthogonal, distinction is between information considered as a fundamental physical entity, and an ontological agnosticism where physics is (...) about our information of the world rather than about the world itself. Combinations of these lead to various possibilities. I argue that adopting mind-independent information as ontologically fundamental is a hitherto undefended position with important advantages. This position appears similar to Floridi’s informational structural realism, but is fundamentally different. Rather than ‘epistemically indistinguishable differences’, it requires a robust conception of information as consisting of readable and interpretable messages. (shrink)

Recently a suggestion has been made that standard textbook representations of hypersurfaces of simultaneity for the travelling twin in the twin 'paradox' are incorrect. This suggestion is false: the standard textbooks are in agreement with a proper understanding of the relativity of simultaneity.

This article deals with the question whether aesthetic considerations affected Einstein in formulating both his theories of relativity. The opinions of philosophers and historians alike are divided on this matter. Thus, Gerald Holton supports the view that Einstein employed aesthetic considerations in formulating his theory of special relativity whereas Jim Shelton opposes it, one of his reasons being that Einstein did not mention such considerations. The other theory, namely, that of general relativity, is discussed by John D. Norton. He asserts (...) that the successful completion of this theory was due to Einstein's adherence to mathematical simplicity resulting from experience, as Einstein himself stated, and not from an aesthetic drive, to which he did not refer. The present work attempts to overcome this deficiency indirectly by investigating Einstein's aesthetic awareness and its consequences for his work. It is found that this awareness was imbedded in his perception of nature and is linked to the criteria (such as simplicity) that guided him in formulating his theories. The conclusion thus reached is that aesthetic considerations did play a role in Einstein's endeavour, contrary to the assertions of Shelton and Norton. (shrink)

In this paper I argue that the positivist–conventionalist interpretation of the Restricted Principle of Relativity is flawed, due to the positivists’ own understanding of conventions and their origins. I claim in the paper that, to understand the conventionalist thesis, one has to diambiguate between three types of convention; the linguistic conventions stemming from the fundamental role of mathematical axioms (conceptual conventions), the conventions stemming from the coordination betweeh theoretical statements and physical, observable facts or entities (coordinative definitions), and conventions that (...) are made possible by possible revisions to theory (the thesis of empirical underdetermination). I claim that it is not possible to interpret the Principle of Relativity as based on one of these three types of convention. This renders the conventionalist interpretation of the Principle of Relativity untenable. The paper is part of a larger project that aims to understand the philosophical significance of the Principle of Relativity. (shrink)

In this paper I argue that the positivist–conventionalist interpretation of the Restricted Principle of Relativity is flawed, due to the positivists’ own understanding of conventions and their origins. I claim in the paper that, to understand the conventionalist thesis, one has to diambiguate between three types of convention; the linguistic conventions stemming from the fundamental role of mathematical axioms, the conventions stemming from the coordination betweeh theoretical statements and physical, observable facts or entities, and conventions that are made possible by (...) possible revisions to theory. I claim that it is not possible to interpret the Principle of Relativity as based on one of these three types of convention. This renders the conventionalist interpretation of the Principle of Relativity untenable. The paper is part of a larger project that aims to understand the philosophical significance of the Principle of Relativity. (shrink)

I examine a property of theories called "background-independence" that Einsteinian gravitation is thought to exemplify. This concept has figured in the work of Rovelli (2001, 2004), Smolin (2006), Giulini (2007), and Belot (2011), among others. I propose and evaluate a few candidates for background-independence, and I show that there is something chimaerical about the concept. I argue, however, that there is a proposal that clarifies the feature of Einsteinian gravitation that motivates the concept.

Is it possible to construct an alternative framework for the description of physical reality that is not based on space and time? According to Kant, because of the incorrigibility of the spatiotemporal scheme, the contents of any such alternative will be beyond our cognitive grasp. Nonetheless, the possibility of constructing such a descriptive scheme poses itself as an intriguing challenge. In this paper, we attempt to answer this challenge by exploiting an analytical tool extensively used by physicists and engineers: the (...) utilisation of multiple representations of the same data using integral transforms – for example, the Fourier transform. According to the spectral picture we propose, frequencies and wavelengths, related to time and space by the Fourier transform, form an adequate alternative basis for describing physical systems, and one that is of equal richness to the spatiotemporal picture. Furthermore, the routine use of Fourier analysis applied to familiar physical systems suggests ways in which sense organs might be constructed such that they naturally give rise to a spectral representation of the world. Although we might never be able to imagine perceiving the world in this way, we can nonetheless describe the contents of such a mode of perception and relate them precisely to our own world-view. Hence, we suggest in a Kantian spirit, that the spatiotemporal description of the world is not unique. (shrink)

The twin paradox (i.e. the reasoning made by the traveling twin, reversing the reasoning made by the earthbound twin, by which it is he who should be older) can be resolved by taking into account the relativity of simultaneity. However, simultaneity depends on a convention about the one-way velocity of light provided that the Reichenbach-Grünbaum hypothesis, is time. So far the resolution has been presented only for the Einstein convention. We show that for all possible choices of the relevant synchronization (...) parameters the calculations performed by both twins yield the same final results when carefully taking into account the relativity of simultaneity according to the conventions they have chosen. Since the final results do not depend on any of the synchronization parameters, the Reichenbach-Grünbaum hypothesis is thereby supported. (shrink)

Abstract The grammar of spatial and temporal concepts cannot, it is argued, be the same in their application to the (manifest) world as perceived and to the (nether) world of unobservable causes as modelled in physics. A parallel case is the dual meaning of colour words, for hues and for material dispositions. The keys to differentiating the two main ranges of uses of ?s? and ?t? are: differences in criteria of numerical and qualitative identity in the two ?worlds'; differences in (...) the logic of indexicals in each context; the explanatory role of powers. The differences can be illustrated in a close analysis of the concept of velocity. (shrink)