The Mellin transform is the Fourier transform of scale. This elementary sentence is the kinematical center of the shadow framework. A positive variable is not naturally additive; it is multiplicative. Its invariant measure is Haar measure d×x = dx/x, its time coordinate is u = log x, its translation group is dilation, and its spectral transform is Mellin analysis. This paper develops that statement as a precise spectral principle. The logarithm identifies L²(R⁺, d×x) with L²(R, du); after the half-density passage (...) to the classical Mellin convention on L²(R⁺, dx), the unitary spectral axis becomes Re(s) = 1/2, and the self-adjoint dilation generator is −i(x∂ₓ + 1/2). In celestial holography, the same positive scale appears as the boost energy ω, and conformal primary wavefunctions are Mellin transforms in ω with dimension Δ. The paper proves a uniqueness theorem for the scale bridge: among homogeneous positive scale laws x = ω^α (proved to be the unique continuous group homomorphisms of (R⁺, ×)), compatibility of the arithmetic half-density axis Re(s) = 1/2 with the four-dimensional celestial principal axis Re(Δ) = 1 forces α = 2. Thus x = ω², and the arithmetic kernel x^{s-1} dx transports to the celestial kernel ω^{Δ-1} dω precisely when Δ = 2s. Consequently the celestial principal series Δ = 1 + iλ is the critical line s = 1/2 + iλ/2, and the celestial shadow Δ → 2 - Δ is the arithmetic reflection s → 1 - s. The result is not a convention but a rigidity statement: once scale, Haar measure, half-densities, and four-dimensional celestial unitarity are fixed, the factor of two is forced. The paper also clarifies the relationship between Mellin spectral parameters (principal-series labels λ ∈ R) and physical conformal dimensions (Δ ∈ R⁺), which are distinct objects arising from the same dilation structure in different contexts. (shrink)

The companion paper—On Self-Dual Measure and Finite Quantum Gravity—on the Plancherel loop measure established a structural factorization of celestial loop amplitudes into a spectral factor, governed by the measure P(λ) = πλ/sinh(πλ) on the principal series, and a kinematic factor, the conformal block evaluated on the unit circle of cross-ratio. This paper develops the kinematic factor. Four exact structures are established. First, the chiral block k_h(z) = z^h ₂F₁(h,h;2h;z) on the principal series h = ½(1+iλ) reduces exactly to a conical (...) Legendre function, k_h(z) = [2Γ(2h)/Γ(h)²] Q_{h−1}(2/z−1). Second, the shadow involution is the classical Legendre degree symmetry ν ↦ −ν−1, and the connection formula Q_{−ν−1} − Q_ν = iπ tanh(πτ) P_ν exhibits the shadow-symmetric part of the block as the Mehler–Fock kernel and the shadow-antisymmetric part as the carrier of the Mehler–Fock spectral density. Third, the Temperedness Theorem: on physical kinematics z̄ = z*, |z| = 1, the exponential growth rates of the two chiral factors are conjugate-odd and cancel identically, and |g_{1+iλ}(z, z̄)| = |1−z|^{−1/2} (1 + O(λ^{−1})) uniformly on compact subsets of the circle away from z = 1; the shadow spectral integrand therefore decays at the full Plancherel rate e^{−πλ}. Fourth, under the dictionary Δ = 2s the spectral weight is P(λ) = |Γ(2s)|² on the critical line, the logarithmic singularity of the block at z = 1 carries the coefficient ψ(s) evaluated on the critical line, the logarithmic derivative of the archimedean factor at the complex place, and the first moment of this transcendentality engine is evaluated in closed form: (1/2π) ∫ P(λ) Re ψ(½ + iλ/2) dλ = 1/8 + ¼ψ(½), the one-loop measure plus a quarter of the digamma at the shadow fixed point. A Mellin bridge is proved realizing (1−2^{−s})Γ(s)ζ(s) as the transform of the spectral kernel (2 sinh t)^{−1}, with the vanishing of its analytic continuation at the first nontrivial zeros verified to twenty-nine digits. The program for the closed-form one-loop kinematic factor is formulated with these tools and its target identified. Every exact claim is verified in a computational companion; the status of each statement is labeled. (shrink)

Richard Jeffrey regarded the version of Bayesian decision theory he floated in ‘The Logic of Decision’ and the idea of a probability kinematics—a generalisation of Bayesian conditioning to contexts in which the evidence is ‘uncertain’—as his two most important contributions to philosophy. This paper aims to connect them by developing kinematical models for the study of preference change and practical deliberation. Preference change is treated in a manner analogous to Jeffrey’s handling of belief change: not as mechanical outputs of (...) combinations of intrinsic desires plus information, but as a matter of judgement and of making up one’s mind. In the first section Jeffrey’s probability kinematics is motivated and extended to the treatment of changes in conditional belief. In the second, analogous kinematical models are developed for preference change and in particular belief-induced change that depends on an invariance condition for conditional preference. The two are the brought together in the last section in a tentative model of pratical deliberation. (shrink)

The so-called "non-commutativity" of probability kinematics has caused much unjustified concern. When identical learning is properly represented, namely, by identical Bayes factors rather than identical posterior probabilities, then sequential probability-kinematical revisions behave just as they should. Our analysis is based on a variant of Field's reformulation of probability kinematics, divested of its (inessential) physicalist gloss.

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant Λ is discussed by using Inönü–Wigner contractions of the de Sitter groups and spaces. When Λ→∞, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c→∞ is further considered, the kinematical group in this case being a modified Galilei (...) group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology. (shrink)

Every physical theory has two different forms of mathematical equations to represent its target systems: the dynamical and the kinematical. Kinematical constraints are differentiated from equations of motion by the fact that their particular form is fixed once and for all, irrespective of the interactions the system enters into. By contrast, the particular form of a system's equations of motion depends essentially on the particular interaction the system enters into. All contemporary accounts of the structure and semantics of physical theory (...) treat dynamics, i.e., the equations of motion, as the most important feature of a theory for the purposes of its philosophical analysis. I argue to the contrary that it is the kinematical constraints that determine the structure and empirical content of a physical theory in the most important ways: they function as necessary preconditions for the appropriate application of the theory; they differentiate types of physical systems; they are necessary for the equations of motion to be well posed or even just cogent; and they guide the experimentalist in the design of tools for measurement and observation. It is thus satisfaction of the kinematical constraints that renders meaning to those terms representing a system's physical quantities in the first place, even before one can ask whether or not the system satisfies the theory's equations of motion. (shrink)

Richard Jeffrey regarded the version of Bayesian decision theory he floated in ‘The Logic of Decision’ and the idea of a probability kinematics—a generalisation of Bayesian conditioning to contexts in which the evidence is ‘uncertain’—as his two most important contributions to philosophy. This paper aims to connect them by developing kinematical models for the study of preference change and practical deliberation. Preference change is treated in a manner analogous to Jeffrey’s handling of belief change: not as mechanical outputs of (...) combinations of intrinsic desires plus information, but as a matter of judgement and of making up one’s mind. In the first section Jeffrey’s probability kinematics is motivated and extended to the treatment of changes in conditional belief. In the second, analogous kinematical models are developed for preference change and in particular belief-induced change that depends on an invariance condition for conditional preference. The two are the brought together in the last section in a tentative model of pratical deliberation. (shrink)

Probability kinematics is studied in detail within the framework of elementary probability theory. The merits and demerits of Jeffrey's and Field's models are discussed. In particular, the principle of maximum relative entropy and other principles are used in an epistemic justification of generalized conditionals. A representation of conditionals in terms of Bayesian conditionals is worked out in the framework of external kinematics.

We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang’s quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, λ and R, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, we find a (...) certain kind of kinematical holographic relation in YSTA, which may be regarded as a primordial form of the holographic principle suggested so far in the framework of the present quantum theory that appears now in the contraction limit of YSTA, λ→0 and R→∞. (shrink)

Dance plays a vital role in human societies across time and culture, with different communities having invented different systems for artistic expression through movement (genres). Differences between genres can be described by experts in words and movements, but these descriptions can only be appreciated by people with certain background abilities. Existing dance notation schemes could be applied to describe genre-differences, however they fall substantially short of being able to capture the important details of movement across a wide spectrum of genres. (...) Our knowledge and practice around dance would benefit from a general, quantitative and human-understandable method of characterizing meaningful differences between aspects of any dance style; a computational kinematics of dance. Here we introduce and apply a novel system for encoding bodily movement as 17 macroscopic, interpretable features, such as expandedness of the body or the frequency of sharp movements. We use this encoding to analyze Hip Hop Dance genres, in part by building a low-cost machine-learning classifier that distinguishes genre with high accuracy. Our study relies on an open dataset (AIST++) of pose-sequences from dancers instructed to perform one of ten Hip Hop genres, such as Breakdance, Popping, or Krump. For comparison we evaluate moderately experienced human observers at discerning these sequence's genres from movements alone (38% where chance = 10%). The performance of a baseline, Ridge classifier model was fair (48%) and that of the model resulting from our automated machine learning pipeline was strong (76%). This indicates that the selected features represent important dimensions of movement for the expression of the attitudes, stories, and aesthetic values manifested in these dance forms. Our study offers a new window into significant relations of similarity and difference between the genres studied. Given the rich, complex, and culturally shaped nature of these genres, the interpretability of our features, and the lightweight techniques used, our approach has significant potential for generalization to other movement domains and movement-related applications. (shrink)

A general framework for the explanation of perceptual phenomena as internalizations of external regularities was developed by R. N. Shepard. A particular example of this framework is his account of perceived curvilinear apparent motions. This paper contains a brief summary of the relevant psychophysical data, some basic kinematical considerations and examples, and several criticisms of Shepard's account. The criticisms concern the feasibility of internalization of critical motion types, the roles of simplicity and uniqueness, the contrast between classical physics and kinematic (...) geometry, the import of perceived path curvilinearity, and the relation of perceptual and scientific knowledge. Key Words: internalization of regularities; kinematic geometry; simplicity. (shrink)

Contextualism is the view that knowledge ascriptions – utterances of sentences containing the word “knows” - express different propositions in different contexts of utterance. But what features of context determine the propositions expressed by knowledge ascriptions? According to a version of contextualism I call conversational contextualism, the conversational dynamics or kinematics determine the propositions expressed by knowledge ascriptions. In this paper I argue that the most sophisticated version of conversational contextualism, which is the view defended by Michael Blome-Tillmann (2009; (...) 2014), faces serious problems. My (very) tentative conclusion will be that conversational contextualism should be abandoned because of these problems. (shrink)

A kinematic description of mass state transitions is derived within the context of parametrized relativistic quantum mechanics (PRQM). It is shown that a collision between two bradyons can result in the formation of a tachyon. Conversely, the formation of a bradyon following the interaction of a tachyon with a bradyon is also possible. The PRQM kinematics is used to describe the role of tachyons in particle beam-thin foil scattering experiments and counter-circulating beam experiments. Conditions under which tachyons may be (...) experimentally created and detected at meson factories such as LAMPF and TRIUMF are determined. Several numerical examples are given, and many technical details are included in the appendices. (shrink)

Kinematic properties of reaching movements reflect constraints imposed on the joint angles. Contemporary models present solutions to the redundancy problem by a pseudoinverse procedure (Whitney 1969) or without any inversion (Berkenblit et al. 1986). Feldman & Levin suggest a procedure based on a regular inversion. These procedures are considered as an outcome of a more general approach.

The kinematic aspects of the rocket-borne clock experiment by Vessot and Levine are analyzed with the revised Robertson's test theory of special relativity (Found. Phys. 14, 625 (1984)). Besides the expected time-dilation, it is found that the intermediate steps of this experiment yield in principle Michelson-Morley type information (a relation between longitudinal and transverse length contractions) in the third order of the velocities involved, but no relativity-of-simultaneity related effects.The flat space-time test theory induces a family of “spherically symmetric” line elements (...) that become the Schwarzschild line element in the relativistic case and also in theabinito rest frame of the theory. These line elements represent the same space-time manifold, but pertain in a one-to-one correspondence to the different flat space-time coordinate transformations of the test theory. The conserved energy is related to the family of local energies in the tangent plane. No deviations from the orthodoxy appear at the pertinent levels of approximation. Hence the unexplained residuals of the Vessot-Levine experiment are not due in obvious ways to kinematic and gravitational frequency shifts caused by deviations of the “real” coordinate transformations from the Lorentz transformations. (shrink)

Janssen argues that special relativity is preferable to Lorentzian dynamics due to its kinematic structure. Brown, along with others, raises an objection, arguing that a dynamical understanding of special relativity is explanatorily prior and hence more fundamental than the principle theory-based kinematic structure of Minkowski spacetime. This paper challenges this objection, arguing that both Janssen and Brown miss the essential aspect of the principles of special relativity which underwrite its interpretational success. It is not its kinematic structure, but the constitutive (...) nature of the principles it employs, by providing a coherent conceptual framework, which does the foundational work. (shrink)

Richard Jeffrey developed the formula for probability kinematics with the intent that it would show that strong foundations are epistemologically unnecessary. But the reasons that support strong foundationalism are considerations of dynamics rather than kinematics. The strong foundationalist is concerned with the origin of epistemic force; showing how epistemic force is propagated therefore cannot undermine his position. The weakness of personalism is evident in the difficulty the personalist has in giving a principled answer to the question of when (...) the conditions for the application of the kinematic formula—the rigidity of the posteriors—are fulfilled, a problem made intractable by the personalist commitment to treating changes in intermediate probability as unexplained surds. Because the strong foundationalist admits changes in the intermediate probability of propositions only when there is some change in the foundations, he can avail himself of ananswer to the problem of the rigidity of the posteriors which the personalist cannot regard as complete. While probability kinematics does not make certain foundations unnecessary, the possession of certain foundations also does not make the probability kinematics formula superfluous. The formula allowsus to model the indirect routes by which the foundations influence various non-foundational propositions in the probability distribution. (shrink)

Plamondon's kinematic theory is very powerful from a descriptive point of view. Unfortunately, the fact that it neglects some fundamental features of the motor system, such as nonlinear inertial torque interactions or joint redundancies, limits its explanatory power and biological validity. As a consequence, the data presented by Plamondon & Alimi should be analyzed and interpreted with caution. There appears to be a gap between the observations reported by the authors and some of the conclusions they draw.

To improve the positioning accuracy of industrial robots and avoid using the coordinates of the end effector, a novel kinematic calibration method based on the distance information is proposed. The kinematic model of an industrial robot is established. The relationship between the moving distance of the end effector and the kinematic parameters is analyzed. Based on the results of the analysis and the kinematic model of the robot, the error model with displacements as the reference is built, which is linearized (...) for the convenience of the following identification. The singular value decomposition is used to eliminate the redundant parameters of the error model. To solve the problem that traditional optimization algorithms are easily affected by data noise in high dimension identification, a novel extended Kalman filter and regularized particle filter hybrid identification method is presented. EKF is used in the preidentification of the linearized error model. With the preidentification results as the initial parameters, RPF is used to identify the kinematic parameters of the linearized error model. Simulations are carried out to validate the effectiveness of the proposed method, which shows that the method can identify the error of the parameters and after compensation the accuracy of the robot is improved. (shrink)

Many individuals with disabling conditions have difficulty with gait and balance control that may result in a fall. Exoskeletons are becoming an increasingly popular technology to aid in walking. Despite being a significant aid in increasing mobility, little attention has been paid to exoskeleton features to mitigate falls. To develop improved exoskeleton stability, quantitative information regarding how a user reacts to postural challenges while wearing the exoskeleton is needed. Assessing the unique responses of individuals to postural perturbations while wearing an (...) exoskeleton provides critical information necessary to effectively accommodate a variety of individual response patterns. This report provides kinematic and neuromuscular data obtained from seven healthy, college-aged individuals during posterior support surface translations with and without wearing a lower limb exoskeleton. A 2-min, static baseline standing trial was also obtained. Outcome measures included a variety of 0 dimensional measures such as center of pressure RMS, peak amplitude, velocities, pathlength, and electromyographic RMS, and peak amplitudes. These measures were obtained during epochs associated with the response to the perturbations: baseline, response, and recovery. T-tests were used to explore potential statistical differences between the exoskeleton and no exoskeleton conditions. Time series waveforms of the COP and EMG data were also analyzed. Statistical parametric mapping was used to evaluate the 1D COP and EMG waveforms obtained during the epochs with and without wearing the exoskeleton. The results indicated that during quiet stance, COP velocity was increased while wearing the exoskeleton, but the magnitude of sway was unchanged. The OD COP measures revealed that wearing the exoskeleton significantly reduced the sway magnitude and velocity in response to the perturbations. There were no systematic effects of wearing the exoskeleton on EMG. SPM analysis revealed that there was a range of individual responses; both behaviorally and among neuromuscular activation patterns. Using both the OD and 1D measures provided a more comprehensive representation of how wearing the exoskeleton impacts the responses to posterior perturbations. This study supports a growing body of evidence that exoskeletons must be personalized to meet the specific capabilities and needs of each individual end-user. (shrink)

It has been established that the kinematics of the Voigt transformation, which lacks group structure, is different from that of the Lorentz transformation, and that the apparent kinematic asymmetry of the Voigt coordinate transformations may be understood as a conformally symmetric kinematics. Phenomena such as the kinetic energy of a moving body and the Doppler effect are not quite the same under the conformal Voigt transformation as they are for the usual theory developed with respect to the Lorentz (...) group. Yet the massenergy conservation law under the Voigt coordinate transformations and the mass-energy conservation law under the group of Lorentz transformations are identically the same. (shrink)

Plamondon & Alimi's derivation of the kinematic model is mathematically flawed. By simply naming a particular parameter combination the model fails to explicate the sources of variability. As a result, the model cannot distinguish between various sources of error, such as those resulting from task demands and those resulting from movement execution.

In his book, Physical Relativity, Harvey Brown challenges the orthodox view that special relativity is preferable to those parts of Lorentz's classical ether theory it replaced because it revealed various phenomena that were given a dynamical explanation in Lorentz's theory to be purely kinematical. I want to defend this orthodoxy. The phenomena most commonly discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other phenomena of this kind that played a role in (...) the early reception of special relativity in the physics literature: the Fresnel drag effect in the Fizeau experiment, the velocity dependence of electron mass in beta-ray deflection experiments by Kaufmann and others, and the delicately balanced torques on a moving charged capacitor in the Trouton-Noble experiment. I offer historical sketches of how Lorentz's dynamical explanations of these phenomena came to be replaced by their now standard kinematical explanations. I then take up the philosophical challenge posed by the work of Harvey Brown and Oliver Pooley and clarify how those kinematical explanations work. (shrink)

Making up your mind can include making up your mind about how to change your mind. Here a suggestion for coding imputations of influence into the kinematics of judgmental probabilities is applied to the treatment of Newcomb problems in The Logic of Decision framework. The suggestion is that what identifies you as treating judgmental probabilistic covariance of X and Y as measuring an influence of X on Y is constancy of your probabilities for values of Y conditionally on values (...) of X as your judgmental probability distribution for values of X changes. (shrink)

In Plamondon & Alimi's target article, a bell-shaped velocity profile typically observed in fast movements is used as a basis for the of motor control. In our opinion, kinematics is a necessary but insufficient ground for a theory of motor control. Relationships between different kinematic characteristics are an emergent property of the system dynamics controlled by the brain in a specific way. In particular, bell-shaped velocity profiles with or without additional waves are a trivial consequence of shifts in the (...) equilibrium state of the system as suggested, for example, in the [lambda]-model of motor control. (shrink)

Generalizing the notion that muscles are positional frames of reference, a high-dimensional muscle space is defined for multi-muscle systems with an embedded low-dimensional motor manifold of functional articulators. A central representation of such a manifold is proposed as computational body schema. The example of the jaw-tongue system is presented, discussing the relation of functional articulators with kinematic invariances and control problems.

To cover as much as possible the various questions raised by the commentators, I have divided my Response into three major sections. In section R1, I reply to the major comments and remarks dealing with the basic hypothesis upon which the kinematic theory is built (Plamondon 1993b; 1993c; 1995a; 1995b). I focus on linearity, determinism, kinematics, and the biological significance of the model parameters. I conclude this section by showing how, from a practical point of view, the delta-lognormal law (...) can be used to group similar data prior to proceeding with further statistical analysis. In section R2, I address the main comments and remarks dealing with the speed/accuracy tradeoffs. First, I focus on the origin of speed/accuracy tradeoffs and the effect of visual feedback. Then I clarify some terminology problems and mathematical misinterpretations prior to providing new support for the theory using the experiments and data referred to by some commentators. I devote section R3 to a generalization of the kinematic theory and to some potential applications. I first provide new explanations of some classical experiments; then I show how more complex movements can be analyzed using the delta-lognormal law. I focus on perturbed and oscillatory movements as well as on cursive script and signature analysis. I conclude this section and my Response by showing some possible applications to the study of movement learning in children as well as to the study of aging phenomena in movement control. I complete my Response by recalling some technical problems that still need further analysis. Throughout the text, I try to convince the reader that the kinematic theory provides a new window on old and new data in the field. (shrink)

The aim of the present study was to investigate the effect of observing other’s movements on subsequent performance in bottlenose dolphins. The imitative ability of non-human animals has intrigued a number of researchers. So far, however, studies in dolphins have been confined to intentional imitation concerned with the explicit request to imitate other agents. In the absence of instruction to imitate, do dolphins (un)intentionally replicate other’s movement features? To test this, dolphins were filmed while reaching and touching a stimulus before (...) and after observing another dolphin (i.e., model) performing the same action. All videos were reviewed and segmented in order to extract the relevant movements. A marker was inserted post hoc via software on the videos upon the anatomical landmark of interest (i.e., rostrum) and was tracked throughout the time course of the movement sequence. The movement was analyzed using an in-house software developed to perform two-dimensional (2D) post hoc kinematic analysis. The results indicate that dolphins’ kinematics is sensitive to other’s movement features. Movements performed for the “visuomotor priming” condition were characterized by a kinematic pattern similar to that performed by the observed dolphin (i.e., model). Addressing the issue of spontaneous imitation in bottlenose dolphins might allow ascertaining whether the potential or impulse to produce an imitative action is generated, not just when they intend to imitate, but whenever they watch another conspecific’s behavior. In closing, this will clarify whether motor representational capacity is a by-product of factors specific to humans or whether more general characteristics such as processes of associative learning prompted by high level of encephalization could help to explain the evolution of this ability. (shrink)

Restricted and repetitive behavior is a core symptom of autism spectrum disorder characterized by features of restrictedness, repetition, rigidity, and invariance. Few studies have investigated how restrictedness is manifested in motor behavior. This study aimed to address this question by instructing participants to perform the utmost complex movement. Twenty children with ASD and 23 children with typical development performed one-dimensional, left-right arm oscillations by demonstrating varying amplitudes and frequencies. The entropy of amplitude and velocity was calculated as an index of (...) kinematic complexity. Results showed that the velocity entropy, but not the amplitude entropy, was significantly lower in ASD than in TD, suggesting restricted kinematics. Further analysis demonstrated that a significantly higher proportion of the velocity values was allocated at a low-speed level in the children with ASD. A qualitative comparison of the complex movement with movement at preferred frequency suggested that the children with ASD might be less likely to shift away from the preferred movement. However, our study can be improved in terms of recruiting a larger sample of participants, measuring the level of motivation, and collecting both complex and preferred movements of the same participant. (shrink)

The question of coherence of rules for changing degrees of belief in the light of new evidence is studied, with special attention being given to cases in which evidence is uncertain. Belief change by the rule of conditionalization on an appropriate proposition and belief change by "probability kinematics" on an appropriate partition are shown to have like status.

The heart of my dissertation project is the proposal of a new updating rule for responding to learning experiences consisting of continuous streams of evidence. I suggest characterizing this kind of learning experience as a continuous stream of stipulated credal derivatives, and show that Continuous Probability Kinematics is the uniquely coherent response to such a stream which satisfies a continuous analogue of Rigidity – the core property of both Bayesian and Jeffrey conditionalization. In the first chapter, I define neighborhood (...) norms of rationality with reference to Kenny Easwaran’s definition of neighborhood properties. I summarize and comment on some of the key arguments in the dispute between time-slice epistemologists, who argue that there are no fundamentally diachronic norms of rationality, and the proponents of diachronic norms. I am sympathetic to two of the key motivations often given in support of the synchronist position: mentalist internalism and the idea that metaphysical disputes about the identity of persons in bizarre puzzle cases should not play a central role in epistemologists’ assessments of the rationality of agents. However, I argue that time-slice epistemology cannot adequately address the rationality of temporally-extended processes like reasoning and learning. Neighborhood norms present a viable third way between these two positions, capturing much of the spirit of the previously-discussed synchronist motivations while still providing just enough temporal structure to meaningfully guide and evaluate temporally-extended rational processes. Continuous Probability Kinematics is an example of one such neighborhood norm. In the second chapter, I develop my updating rule CPK and establish many of its core properties. Of special note here are the deep connections to Jeffrey’s Probability Kinematics, as well as some key differences. The net result of any CPK updating process will always be representable as a Jeffrey shift on the refined partition generated by the propositions that the agent is receiving direct evidence concerning. However, one crucial difference is that CPK provides an intuitive account of how to combine the effects of learning experiences that are each about fundamentally different underlying partitions. In CPK’s formalism, an agent can receive simultaneous evidence streams about an arbitrary (finite) number of propositions, which can themselves be evidentially related in any way. At any given instant, the result of the combination is a simple sum of the effects that learning about the individual propositions would have separately. CPK is concerned with a novel kind of learning experience and involves a novel characterization of evidence. The third and final chapter of this dissertation is concerned with explaining what this characterization of evidence means and with arguing that it can be the basis for genuine learning. I begin by characterizing learning experiences in terms of the Value of Information, and prove a Value of Information theorem for CPK learning experiences under the assumption of a Martingale constraint on the agent’s prior distribution over the signals that they might receive. I examine Timothy Williamson’s arguments that evidence must be propositional and express my skepticism. I then explore two different routes to model agents who update by CPK as if they are learning some propositional content and updating the rest of their credences by Bayesian conditionalization on this content. The second of these two routes provides a very interesting lens to reexamine the evidential commitments that underwrite updating by CPK, which I analyze. (shrink)

Starting from simple topological arguments due to Dirac on the classical rotational properties of extended rigid bodies, we abstract the concept of a finite-size spinor (FSS). The FSS is a concept distinct from both point spinors (e.g., electrons) and composite spinors (e.g., nuclei), and suggests a new model for baryons. The FSS offers a natural explanation of “threeness” for the quarks, excludes the existence of free quarks, denies the operational definition of quark spin statistics, and, moreover, leads to the dual (...) model of hadronic interactions. (shrink)

Bayesian, Jeffrey and Field conditionals are compared and it is shown why the last two cannot be reduced to the first. Maximum relative entropy is used in two kinds of justification of the Field conditional and the dispensability of entropy principles in general is discussed.

Quantum mechanics exhibits inherent probabilistic behavior, violations of classical probability, and a formalism seemingly disconnected from spacetime. We show that these features naturally emerge in single-variable systems, which can encode only a single independent unit of information at a time and therefore behave probabilistically. Imposing reversibility and conservation of total probability on the generalized probability formalism leads uniquely to a quadratic probability theory, with linear unitary transformations and probabilities given by squared moduli. From this, the Hilbert-space structure, Born’s rule, and (...) unitary evolution follow directly. This first-principles derivation of quantum theory is consistent with the experimental fact that observing quantum effects requires coherence. (shrink)

While it was argued earlier in the book that no rule‐governed notion of rational opinion change could be adequate, there are certainly patterns of normal opinion change (updating in response to new data or new constraints accepted in response to experience), which have a rule‐following form. The basic example is Simple Conditionalization (often characterized as the application of Bayes's rule or Bayes's theorem, sometimes called Bayesian Conditionalization, and sometimes accepted as the sole admissible form of opinion change), but more advanced (...) patterns (beginning with Jeffrey Conditionalization) have been described in the literature, as well as challenged there, e.g. by Isaac Levi. The question of what can justify such rules is addressed using symmetry arguments, and the (hidden or explicit) premises of such arguments analysed. Probability kinematics, as formulated initially by Richard Jeffrey, is the general theory of rules for changing a (‘prior’) probability function, subject to given or imposed constraints, into a new (‘updated’, ‘posterior’) function. Such constraints can take various forms, and the rules offered for them can be limited by symmetry considerations but may not be uniquely determined. (shrink)

Dutch Book arguments have been presented for static belief systems and for belief change by conditionalization. An argument is given here that a rule for belief change which under certain conditions violates probability kinematics will leave the agent open to a Dutch Book.

Jeffrey conditionalization is generalized to the case in which new evidence bounds the possible revisions of a prior below by a Dempsterian lower probability. Classical probability kinematics arises within this generalization as the special case in which the evidentiary focal elements of the bounding lower probability are pairwise disjoint.

A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment , and the family of possible epistemic inputs . First a simple theory is examined in which the states are probability functions, and the subject of probability kinematics introduced by Richard Jeffrey is explored. Then a second theory is examined in which the state has as constituents a body of information and a recipe that determines the (...) accepted epistemic judgments on the basis of this corpus. Through an examination of several approaches to the statistical syllogism, a relation is again established with Jeffrey's generalized conditionalization. (shrink)

A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment, and the family of possible epistemic inputs. First a simple theory is examined in which the states are probability functions, and the subject of probability kinematics introduced by Richard Jeffrey is explored. Then a second theory is examined in which the state has as constituents a body of information and a recipe that determines the accepted epistemic (...) judgments on the basis of this corpus. Through an examination of several approaches to the statistical syllogism, a relation is again established with Jeffrey's generalized conditionalization. (shrink)

ABSTRACTPrevious research has revealed a stable preference for words with inward consonantal-articulation patterns, over outward-words. Following the oral approach-avoidance account suggesting that the in–out effect is due to the resemblance between consonantal-articulations patterns and ingestion/expectoration, recent findings have shown that when judging inward-outward names for objects with particular oral functions, valence did not modulate the effect while the oral function did. To replicate and examine further the role of edibility and valence in shaping the in–out effect, we asked participants to (...) rate inward and outward names for edible and non-edible products while controlling for valence. Results revealed that the motor-to-affect link was only observed for edible products, regardless of valence. (shrink)

Probability kinematics is the theory of how subjective probabilities change with time, in response to certain constraints . Rules are classified by the imposed constraints for which the rules prescribe a procedure for updating one's opinion. The first is simple conditionalization , and the second Jeffrey conditionalization . It is demonstrated by a symmetry argument that these rules are the unique admissible rules for those constraints, and moreover, that any probability kinematic rule must be equivalent to a conditionalization preceded (...) by a determination of the values x i to be given to the members of such a partition. Next two rival rules which can go beyond such conditionalization are described. INFOMIN and MTP . Their properties are investigated and compared. (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)