This paper investigates modular combinations of temporal logic systems. Four combination methods are described and studied with respect to the transfer of logical properties from the component one-dimensional temporal logics to the resulting combined two-dimensional temporal logic. Three basic logical properties are analyzed, namely soundness, completeness, and decidability. Each combination method comprises three submethods that combine the languages, the inference systems, and the semantics of two one-dimensional temporal logic systems, generating families of two-dimensional temporal languages with varying expressivity and varying (...) degrees of transfer of logical properties. The temporalization method and the independent combination method are shown to transfer all three basic logical properties. The method of full join of logic systems generates a considerably more expressive language but fails to transfer completeness and decidability in several cases. So a weaker method of restricted join is proposed and shown to transfer all three basic logical properties. (shrink)

Nesta entrevista, conduzida por Gonçalo Marcelo e Maria Luísa Portocarrero, Daniel Frey, professor de filosofia da religião na Universidade de Estrasburgo e Presidente do Conselho Científico do Fonds Ricoeur, apresenta alguns aspetos centrais da sua investigação filosófica, do seu desenvolvimento intelectual e das atividades desenvolvidas no Fonds Ricoeur. Daniel Frey expõe a sua teoria hermenêutica da leitura, influenciada por Gadamer e Ricoeur, mostrando a especificidade da abordagem hermenêutica da leitura. Na entrevista, o autor também explora a importância da filosofia (...) do jovem Ricoeur dos anos 1950‑1960, e a evolução da relação entre filosofia e religião em Ricoeur. Fazendo uma breve descrição do estatuto das obras que se tornam “clássicas” e dos projetos recentes do Fonds Ricoeur, como a digitalização dos arquivos de Ricoeur, esta entrevista de Daniel Frey mostra‑nos até que ponto o trabalho de Ricoeur se encontra hoje aberto a novas leituras e interpretações. (shrink)

Robert Brandom propõe um modelo de interação social no qual defende que as atitudes práticas dos usuários da linguagem instituem os conteúdos semânticos e as normas inferenciais que determinam seus usos. Assim, o que ele descreve é uma prática linguística, caracterizado por asserções, que mostra como as atitudes dos agentes, diante das asserções sendo produzidas e consumidas, devem ser entendidas para que instituam conteúdos inferencialmente articulados. Ademais, Brandom relaciona a prática assertiva e o entendimento inferencial do conteúdo semântico a um (...) paradigma racionalista, sugerindo que os conteúdos que aparecem em asserções são aquilo que podem ser oferecidos ou exigidos, dentro da prática de uso da linguagem, como razões. Considerando estas ideias, o objetivo deste trabalho é desenvolver e relacionar os conceitos de "asserção", "inferência" e "razão", tais como Brandom os compreende. (shrink)

La presente nota crítica tiene como finalidad exponer y comentar las ideas fundamentales de la edición española del primer escrito de Jacques Derrida, El problema de la génesis en la filosofía de Husserl. Asimismo, hacemos algunas aclaraciones sobre el origen y significado de este escrito. Al concluir, añadimos algunas observaciones sobre la traducción y sobre el estudio final del editor y traductor Javier Bassas Vila sobre la filosofía del joven Derrida.

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and (...) offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses the history of paraconsistent logic; language, negation, contradiction, consistency and inconsistency; logics of formal inconsistency and the main paraconsistent propositional systems; many-valued companions, possible-translations semantics and non-deterministic semantics; paraconsistent modal logics; first-order paraconsistent logics; applications to information processing, databases and quantum computation; and applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning. (shrink)

In the recent debate between conceptualists and nonconceptualists about perceptual content, Kant’s notion of intuition has been invoked on both sides. Conceptualists claim Kant as a forerunner of their position, arguing that Kantian intuitions have the same kind of content as conceptual thought. On the other hand, nonconceptualists claim Kant as a forerunner of their own position, contending that Kantian intuitions have a distinctly nonconceptual kind of content. In this paper, I argue first, that both sides are wrong about Kant, (...) secondly, that neither side can properly account for the epistemic function of intuition, and thirdly, that Kant’s own notion of intuition contains the resources for a third alternative. The epistemic function of an intuition for Kant is to furnish the sensory representation of an object of cognition. Conceptualism cannot account for this function because it construes perception as a species of thought. As a proper appreciation of Kant’s reasons for insisting upon the heterogeneity of thought and perception puts one in a position to see, any view that does this will fail to do justice to the distinctly sensory nature of intuition. Nonconceptualism, on the other hand, cannot account for the epistemic function of intuition because it views intuition as self-standing, and thus as completely independent from thought. As a consequence, nonconceptualism is not entitled to claim that an intuition is itself a cognitive state. I show that Kant’s actual view avoids both these extremes because it involves a different way of conceiving how perception is informed by conceptual thought. Building on this conception, Kant is able to preserve the distinctly sensory nature of intuition, while also securing proper cognitive standing for it. As a result, Kant’s notion of intuition provides the resources for an alternative account of how thought relates to the senses – one that avoids the shortcomings of the positions staked out in the contemporary debate. (shrink)

Each of Kant’s three Critiques offers an account of the nature of a mental faculty and arrives at this account by means of a procedure I call ‘faculty analysis’. Faculty analysis is often regarded as among the least defensible aspects of Kant’s position; as a consequence, philosophers seeking to inherit Kantian ideas tend to transpose them into a different methodological context. I argue that this is a mistake: in fact faculty analysis is a live option for philosophical inquiry today. My (...) argument is as follows: Faculty analysis is a live option for certain kinds of philosophical theories if so-called “agentialist” views about the nature of belief are correct. There are good reasons for thinking that such views are correct. So faculty analysis should not be dismissed out of hand. Since the first premise in this argument bears a lot of weight, a large part of the paper is devoted to clarifying and defending it, in part by arguing that Kant himself holds a version of agentialism about belief. (shrink)

The human visual system is amazing in its ability to guide us in a wide range of tasks - driving, reading, playing ball games, or reading music. Somehow our eyes just manage to find the information we need to perform such tasks. This book explores how our eyes process and communicate the data needed for us to negotiate the world around us.

The requirement of gauge invariance for the Schwinger-DeWitt equations, interpreted as a manifestly covariant quantum theory for the evolution of a system in spacetime, implies the existence of a five-dimensional pre-Maxwell field on the manifold of spacetime and “proper time” τ. The Maxwell theory is contained in this theory; integration of the field equations over τ restores the Maxwell equations with the usual interpretation of the sources. Following Schwinger's techniques, we study the Green's functions for the five-dimensional hyperbolic field equations (...) for both signatures ± [corresponding to O(4, 1) or O(3, 2) symmetry of the field equations] of the proper time derivative. The classification of the Green's functions follows that of the four-dimensional theory for “massive” fields, for which the “mass” squared may be positive or negative, respectively. The Green's functions for the five-dimensional field are then given by the Fourier transform over the “mass” parameter. We derive the Green's functions corresponding to the principal part ΔP and the homogeneous function Δ 1 ; all of the Green's functions can be expressed in terms of these, as for the usual field equations with definite mass. In the O(3, 2) case, the principal part function has support for x2⩾τ2, corresponding to spacelike propagation, as well as along the light cone x2=0 (for τ=0). There can be no transmission ofinformation in spacelike directions, with this propagator, since the Maxwell field, obtained by integration over τ, does not contain this component of the support. Measurements are characterized by such an integration. The spacelike field therefore can dynamically establish spacelike correlations. (shrink)

I raise three objections for Gava’s thesis that the primary task of the Critique of Pure Reason is to develop a doctrine of method for metaphysics, understood as an account of the special kind of unity that a body of cognitions must exhibit to count as a science. First, I argue that this thesis has difficulty accommodating Kant’s concern with explaining the possibility of synthetic a priori judgements. This concern is motivated by a question that is prior to the issue (...) of scientific unity. Second, I argue that the context of the passage in which Kant calls the Critique a treatise on method makes clear that the remark concerns the Copernican Turn. This suggests that the method treated in the book is the procedure required by the Copernican Turn. Third, I dispute Gava’s claim that the idea that confers unity on metaphysics is the cosmopolitan concept of philosophy. (shrink)

In this paper I argue that Kant’s theory of spatial representation supports a Moderate Conceptualist view of his theory of intuition, according to which Kantian intuitions depend for their objective purport on actualizations of spontaneity in a particular kind of synthesis. In making the case for this I focus on three aspects of the theory of spatial representation: the distinction Kant draws between what he calls the original representation of space and the representations of determinate spaces; the doctrine of the (...) productive imagination; and the related doctrine of the a priori determination of sensibility by understanding. I introduce Moderate Conceptualism, explain why these three aspects support it, and consider a number of objections. (shrink)

Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical. Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics with evolution paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical (...) equations of motion, for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical levels. We then offer a new model of the particle current—as a certain distribution of the event currents on the worldline—which eliminates these difficulties and permits comparison of classisical off-shell electrodynamics with the standard Maxwell theory. In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions, and are seen to coincide when λ≳10−6 seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics. (shrink)

Examines the development iun the period between Descartes and the mid 19th century of the concept of form in semantics.

In the context of a covariant mechanics with Poincaré-invariant evolution parameter τ, Sa'ad, Horwitz, and Arshansky have argued that for the electromagnetic interaction to be well posed, the local gauge function of the field should include dependence on τ, as well as on the spacetime coordinates. This requirement of full gauge covariance leads to a theory of five τ-dependent gauge compensation fields, which differs in significant aspects from conventional electrodynamics, but whose zero modes coincide with the Maxwell theory. The pre-Maxwell (...) fields may exchange mass with charged particles, permitting pair annihilation even at the classical level. The total mass-energy-momentum tensor of the fields and particles is conserved. The Green's functions for the fields provide spacelike and timelike support for correlations, as well as lightlike propagation. A τ-integration of the fields—singling out the massless photons—recovers the standard Maxwell theory, which then has the character of an equilibrium limit of the underlying microscopic dynamics. The pre-Maxwell theory also turns out to be the solution of the inverse problem in variational mechanics: it is shown to be the most general local gauge theory consistent with unconstrained commutation relations in four dimensions. Posed in this framework, the extension to n-dimensions, curved background space, and non-abelian gauge symmetry becomes straightforward. (shrink)

This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrödinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the nonrelativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire (...) an imaginary part which is linear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformations on the invariant evolution parameter. (shrink)

In relativistic classical and quantum mechanics with Poincaré-invariant parameter, particle worldlines are traced out by the evolution of spacetime events. The formulation of a covariant canonical framework for the evolving events leads to a dynamical theory in which mass conservation is demoted from a priori constraint to the status of conserved Noether current for a certain class of interactions. In pre-Maxwell electrodynamics—the local gauge theory associated with this framework —events induce five local off-shell fields, which mediate interactions between instantaneous events, (...) not between the worldlines which represent entire particle histories. The fifth field, required to compensate for dependence of gauge transformations on the evolution parameter, enables the exchange of mass between particles and fields. In the equilibrium limit, these pre-Maxwell fields are pushed onto the zero-mass shell, but during interactions there is no mechanism regulating the mass that photons may acquire, even when event trajectories evolve far into the spacelike region. This feature of the off-shell formalism requires the application of some ad hoc mechanism for controlling the photon mass in two opposite physical domains: the low energy motion of a charged event in classical Coulomb scattering, and the renormalization of off-shell quantum electrodynamics. In this paper, we discuss a nonlocal, higher derivative correction to the photon kinetic term, which provides regulation of the photon mass in a manner which preserves the gauge invariance and Poincaré covariance of the original theory. We demonstrate that the inclusion of this term is equivalent to an earlier solution to the classical Coulomb problem, and that the resulting quantum field theory is renormalized. (shrink)

In this paper we propose a very general de nition of combination of logics by means of the concept of sheaves of logics. We first discuss some properties of this general definition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the first author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, since they provide a new (...) semantical account for abstract logical systems, particularly for many-valued and paraconsistent logics. (shrink)

O ceticismo acadêmico se encontra utilizado na formulação dos preceitos epistêmicos para a reformulação da ciência, nas _Règles Pour La Direction De L’Esprit _ ( 1701, Amsterdam, texto póstumo e inacabado). O probabilismo de Carnéades, compreendido como o principal vetor do ceticismo acadêmico na modernidade, fundamenta a certeza. Outras teses para a correção epistêmica do espírito parecem advir da tradição acadêmica, como a de fi nição de _science _ como _sagesse_, por exemplo ( _Règle _ _I_ ). Desse modo, a (...) busca da verdade (coordenada principal das _Règles_, como nos evidencia a _Règle _ _IV_ ) não abdica do ceticismo. Tratar-se-á, neste artigo, de compreender que o probabilismo acadêmico aparece no projeto de busca da verdade das _Règles _ de modo negativo _, _ pois Descartes ataca a modalidade do provável. Outros tópicos acadêmicos aparecem em questão, como a busca de sabedoria, a mitigação da dúvida, a disciplina do assentimento pela recusa do provável e a verdade do fi deísmo _. _ Estes tópicos se resumem ao método acadêmico, de fi nido pela recursividade epistêmica. (shrink)

Historia del derecho: un intento de definición -- Positivismo, historiograf ia positivista e historia del derecho -- Escuela de los Annales e historia del derecho -- El materialismo hist orico y la historia del derecho -- La historia en el derecho y la verdad en el proceso: el argumento de Michel Foucault -- Michel Foucault y el discurso histórico-jurídico: Estado y poder -- Walter Benjamin, la temporalidad y el derecho.

Excerpt from Arnold Geulincx und Seine Philosophie Die Gestalt in welcher der nachstehende Beitrag zur Geschichte der Philosophie veroffentlicht wird, erfordert eine kurze Erklarung. Als ich die Gesammtausgabe von Geulinox' Werken zum Theil beendet hatte, wurde ich von einem verehrten Herrn Col-legen in Deutschland eingeladen, mich bei einem von ihm zu leitenden literarischen Unternehmen mit einer Monographie uber den Denker zu betheiligen. Es sollte eine Reihe von gemeinverstandlichen Abhandlungen hergestellt werden, etwa deijenigen vergleichbar, welche in England unter dem Titel Philosophical (...) Classios for English Readers" erscheint. Die gute Gesellschaft, in der meine langst angefangenen Studien uber den Gegenstand in die Welt treten sollten, veranlasste mich zu einer zustimmenden Antwort. Daher mein Entschluss, nach beinahe vierzig Jahren es abermals mit dom Abfasson eines ganzen Bandes in deutscher Sprache zu versuchen. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.". (shrink)

Bodying Postqualitative Research posits the question of what happens when lived, fleshy human bodies engage in postqualitative research in education. It takes as its central concern research propositions aimed at dismantling the structures of humanism that typically govern research in education and uses postqualitative conceptions of data, methodology, and clarity in conjunction with insights from feminist science studies scholars to imagine how we might 'body' postqualitative work. This book uses the provocations offered by postqualitative research and takes these touchpoints to (...) dismantle dominant logics of research, born of neoliberalism and ongoing settler colonialism to offer alternative perspectives. Importantly, this book stays near to the body by proposing caffeine shakes, antipsychotic medications, and scars as moments to take seriously how bodies do researching practices. After each chapter, the book turns to poetry as a "fracture" or a moment of disruption to the rhythm of the text that incites readers to reconsider the previous chapter otherwise. It concludes by asking what bodying postqualitative research might mean for pedagogy and for propositions toward future inquiry. Drawing together the work of feminist science and education scholars oriented toward the biosciences and whose work has not yet been immersed into postqualitative scholarship in a sustained way, this book brings together a vein of feminist science studies theorizing that both deepens and troubles postqualitative scholarship through its focus on the politics of science and the possibilities of doing bodies with biology, culture, and life. The volume is suitable for students and scholars interested in postqualitative and embodied research methods in education, and feminist and gender studies. (shrink)

Although Maxwell theory is O(3,1)-covariant, electrodynamics only transforms invariantly between Lorentz frames for special forms of the field, and the generator of Lorentz transformations is not generally conserved. Bérard, Grandati, Lages, and Mohrbach have studied the O(3) subgroup, for which they found an extension of the rotation generator that satisfies the canonical angular momentum algebra in the presence of certain Maxwell fields, and is conserved by the classical motion. The extended generator depends on the field strength, but not the potential, (...) and so is manifestly gauge invariant. The conditions imposed on the Maxwell field by the algebra lead to a Dirac monopole solution.In this paper, we study the generalization of the Bérard, Grandati, Lages and Mohrbach construction to the full Lorentz group in N dimensions. The requirements can be maximally satisfied in a three-dimensional subspace of the full Minkowski space; this subspace can be chosen to describe either an O(3)-invariant space sector, or an O(2,1)-invariant restriction of spacetime. The field solution reduces to the Dirac monopole found in the nonrelativistic case when the O(3)-invariant subspace is selected. When an O(2,1)-invariant subspace is chosen, the field strength can be associated with a Coulomb-like potential of the type A μ(x) = n μ/ρ, where ρ = (x μ x μ)1/2, similar to that used by Horwitz and Arshansky to obtain a covariant generalization of the hydrogen-like bound state. In the presence of these fields, which are determined entirely by symmetry considerations, without reference to a source equation, the extended generator is conserved under classical relativistic system evolution. (shrink)

In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five-dimensional U(1) gauge theory associated with Stueckelberg–Schrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five-dimensional theory prevents a natural generaliza tion of the Dirac monopole, since the theory is not symmetric under duality transforma tions. It is shown that the duality symmetry can be restored by generalizing the electromagnetic field strength to an element of (...) a Clifford algebra. Nevertheless, the generalized framework does not permit us to recover the phenomenological (or conventional) absence of magnetic monopoles. (shrink)

This paper discusses the discrete symmetries of off-shell electromagnetism, the Stueckelberg–Schrodinger relativistic quantum theory and its associated 5D local gauge theory. Seeking a dynamical description of particle/antiparticle interactions, Stueckelberg developed a covariant mechanics with a monotonically increasing Poincaré-invariant parameter. In Stueckelberg’s framework, worldlines are traced out through the parameterized evolution of spacetime events, which may advance or retreat with respect to the laboratory clock, depending on the sign of the energy, so that negative energy trajectories appear as antiparticles when the (...) observer describes the evolution using the laboratory clock. The associated gauge theory describes local interactions between events (correlated by the invariant parameter) mediated by five off-shell gauge fields. These gauge fields are shown to transform tensorially under under space and time reflections—unlike the standard Maxwell fields—and the interacting quantum theory therefore remains manifestly Lorentz covariant. Charge conjugation symmetry in the quantum theory is achieved by simultaneous reflection of the sense of evolution and the fifth scalar field. Applying this procedure to the classical gauge theory leads to a purely classical manifestation of charge conjugation, placing the CPT symmetries on the same footing in the classical and quantum domains. In the resulting picture, interactions do not distinguish between particle and antiparticle trajectories—charge conjugation merely describes the interpretation of observed negative energy trajectories according to the laboratory clock. (shrink)

We explore certain difficulties in the covariant classical mechanics associated with off-shell electrodynamics, through an examination of the classical Coulomb problem. We present a straightforward solution of the classical equations of motion for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution reveals the essential difficulties in the formalism at the classical level. We then offer a new model of the particle, as (...) a certain distribution of events on the worldline, which eliminates these difficulties and permits comparison of classical off-shell electrodynamics with the standard Maxwell theory In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions—they are seen to coincide when λ > 10–6 sec, providing an initial estimate of this parameter. (shrink)

In the framework of off-shell quantum electrodynamics—the quantum field theory of a covariant symplectic mechanics, in which events evolve according to a Poincaré-invariant parameter τ—we study the low-energy scattering of identical scalar particles. It is shown that exchange of mass is permitted in the formalism, and we calculate scattering cross-sections for this case. In these cross-sections, the usual forward pole of the standard scalar QED splits into two poles and a zero, slightly offset from the forward direction. As mass exchange (...) vanishes, a pole-zero pair cancel, the remaining pole moves to θ = 0, and the standard cross-section is recovered. (shrink)

C. I. Lewis’s conception of the given element in perceptual experience was one of the targets of Sellars’ famous charge that many such conceptions fall victim to the Myth of the Given. Yet exactly what makes a conception of the given mythical has remained unclear. Here I aim to clarify this issue by discussing Eric Watkins’ recent claim that a conception exactly like the one Lewis articulated in Mind and the World Order in fact avoids the Myth. Watkins motivates this (...) claim in part by raising objections for John McDowell’s account of the Myth and argues that a better account can be extracted from Kant. I defend McDowell’s position (and reject Watkins’ Kantian account) by arguing that these objections are based on a failure to appreciate an implication of the claim (which Watkins accepts) that rational thought operates in “the logical space of reasons.” Specifically, I focus on the implication that a thinker must be in a position to understand the rational significance of her perceptual experience. Along the way I explain in what ways Watkins’ conception of the given in experience mirrors the view of Lewis. (shrink)

We explore certain difficulties in the covariant classical mechanics associated with off-shell electrodynamics, through an examination of the classical Coulomb problem. We present a straightforward solution of the classical equations of motion for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution reveals the essential difficulties in the formalism at the classical level. We then offer a new model of the particle, as (...) a certain distribution of events on the worldline, which eliminates these difficulties and permits comparison of classical off-shell electrodynamics with the standard Maxwell theory In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions—they are seen to coincide when λ > 10–6 sec, providing an initial estimate of this parameter. (shrink)