The contributions to this volume originate from a symposium in honour of Hermann von Helmholtz. The authors are concerned with different aspects of the inverse methodology being a powerful tool in modern science. There is emphasized its role for understanding the concept of physical observation, for interpreting experimental results and for developing constructive strategies as well.

The contributions to this volume originate from a symposium in honour of Hermann von Helmholtz. The authors are concerned with different aspects of the inverse methodology being a powerful tool in modern science. There is emphasized its role for understanding the concept of physical observation, for interpreting experimental results and for developing constructive strategies as well.

Visual space can be distinguished from physical space. The first is found in visual experience, while the second is defined independently of perception. Theorists have wondered about the relation between the two. Some investigators have concluded that visual space is non-Euclidean, and that it does not have a single metric structure. Here it is argued that visual space exhibits contraction in all three dimensions with increasing distance from the observer, that experienced features of this contraction are not the same as (...) would be the experience of a perspective projection onto a fronto-parallel plane, and that such contraction is consistent with size constancy. These properties of visual space are different from those that would be predicted if spatial perception resulted from the successful solution of the inverse problem. They are consistent with the notion that optical constraints have been internalized. More generally, they are also consistent with the notion that visual spatial structures bear a resemblance relation to physical spatial structures. This notion supports a type of representational relation that is distinct from mere causal correspondence. The reticence of some philosophers and psychologists to discuss the structure of phenomenal space is diagnosed in terms of the simple materialism and the functionalism of the 1970s and 1980s. (shrink)

Many have thought that symmetries of a Lagrangian explain the standard laws of energy, momentum, and angular momentum conservation in a rather straightforward way. In this paper, I argue that the explanation of conservation laws via symmetries of Lagrangians involves complications that have not been adequately noted in the philosophical literature and some of the physics literature on the subject. In fact, such complications show that the principles that are commonly appealed to to drive explanations of conservation laws are not (...) generally correct without caveats. I hope here to give a clearer picture of the relationship between symmetries and conservation laws in Lagrangian mechanics via an examination of the bearing that results in the inverse problem in the calculus of variations have on this topic. (shrink)

Johann Bernoulli in 1710 affirmed that Newton had not proved that conic sections, having a focus in the force centre, were necessary orbits for a body accelerated by an inverse square force. He also criticized Newton's mathematical procedures applied to central forces in Principia mathematica, since, in his opinion, they lacked generality and could be used only if one knew the solution in advance. The development of eighteenth-century dynamics was mainly due to Continental mathematicians who followed Bernoulli's approach rather (...) than Newton's. The ways of thinking of the British Newtonians have, therefore, been somewhat forgotten. This paper is an attempt to assess what Bernoulli was criticizing and what were the immediate reactions of the Newtonians. In particular, I will concentrate on two papers by John Keill, submitted to the Royal Society in 1708 and 1714, in which the results on central forces achieved by the British were summarized and their methods defended. (shrink)

Although to live is to face problems, the general concept of a problem has been significantly understudied. So much so, that the publication of Polya’s delightful How to Solve It caused quite a stir. And, although the concept of a conceptual problem is philosophical because it is deep and occurs across fields, from mathematics to politics, no philosophers have produced any memorable studies of it. Moreover, the word ‘problem’ is absent from most philosophical reference works. There are (...) plenty of texts on particular problems such as those of evil and induction, but none on the general concept of a conceptual problem—as if it were not a problematic concept. Worse, we are seldom told that doing original mathematics, science or technology is to wrestle with original problems. Nor have we been told that the hardest problems are likely to be inverse, in that they go from effect to cause, or from sketch to implementation, or from conclusion to premises—as in diagnosing disease from symptoms, looking for a westward passage from Europe to Asia, and designing public policies to attack social issues. The existence of this significant gap in the philosophical literature justifies the publication of the present study. (shrink)

Let U be an initial segment of $^*{\mathbb N}$ closed under addition (such U is called a cut) with uncountable cofinality and A be a subset of U, which is the intersection of U and an internal subset of $^*{\mathbb N}$ . Suppose A has lower U-density α strictly between 0 and 3/5. We show that either there exists a standard real $\epsilon$ > 0 and there are sufficiently large x in A such that | (A+A) ∩ [0, 2x]| > (...) (10/3+ $\epsilon$ ) | A ∩ [0, x]| or A is a large subset of an arithmetic progression of difference greater than 1 or A is a large subset of the union of two arithmetic progressions with the same difference greater than 2 or A is a large subset of the union of three arithmetic progressions with the same difference greater than 4. (shrink)

The notion of quantum supports introduced by Foulis, Piron, and Randall can be used to construct combinatorial versions of contextualist hidden-variable models for finite quantum logics. The original logic can be uniquely recovered from appropriate such models as a solution of a combinatorial inverse problem. One can thus set up a classical ontology for a finite quantum logics that completely specifies it. Computer studies are used to explore the ideas.

In this paper I examine whether representationalism can account for various thought experiments about colour inversions. Representationalism is, at minimum, the view that, necessarily, if two experiences have the same representational content then they have the same phenomenal character. I argue that representationalism ought to be rejected if one holds externalist views about experiential content and one holds traditional exter- nalist views about the nature of the content of propositional attitudes. Thus, colour inver- sion scenarios are more damaging to externalist (...) representationalist views than have been previously thought. More specifically, I argue that representationalists who endorse externalism about experiential content either have to become internalists about the content of propositional attitudes or they have to adopt a novel variety of externalism about the content of propositional attitudes. This novel type of propositional attitude externalism is investigated. It can be seen that adopting it forces one to reject Putnam. (shrink)

Does the claimed fine-tuning of the constants of nature for life give reason to think that there are many other universes in which the constants have different values? Or does the inference from fine-tuning to a multiverse commit what Hacking calls the inverse gambler’s fallacy? The present paper considers two fine-tuning problems that seem promising to consider because they are in many respects analogous to the problem of the fine-tuned constants. Reasoning that parallels the inference from fine-tuning to (...) a multiverse seems prima facie adequate in these problems. However, it turns out that in both cases there are independent empirical reasons to believe the hypotheses that are analogous to the multiverse hypothesis. In the absence of such evidence, it would be coherent to raise the inverse gambler’s fallacy charge against the inference from fine-tuning to these multiverse-type hypotheses. In response to this finding, I suggest taking the possibility seriously that established standards of rationality may not allow us to decide whether the inference from fine-tuning to a multiverse is fallacious or not. The paper concludes by sceptically assessing the prospects for obtaining independent empirical evidence for concrete multiverse theories. (shrink)

Charles S. Peirce introduced in the late 19th century the notion of abduction as inference from effects to causes, or from observational data to explanatory theories. Abductive reasoning has become a major theme in contemporary logic, philosophy of science, and artificial intelligence. This paper argues that the new growing branch of applied mathematics called inverse problems deals successfully with various kinds of abductive inference within a variety of scientific disciplines. The fundamental theorem about the inverse reconstruction of plane (...) functions from their line integrals was proved by Johann Radon already in 1917. The practical applications of Radon’s theorem and its generalizations include computerized tomography which became a routine imaging technique of diagnostic medicine in the 1970s.Keywords: Abduction; Inference to the best explanation; Inverse problems; Peirce; Radon’s theorem; Tomography. (shrink)

Philosophical (p-) zombies are constructs that possess all of the behavioral features and responses of a sentient human being, yet are not conscious. P-zombies are intimately linked to the hard problem of consciousness and have been invoked as arguments against physicalist approaches. But what if we were to invert the characteristics of p-zombies? Such an inverse (i-) zombie would possess all of the behavioral features and responses of an insensate being yet would nonetheless be conscious. While p-zombies are (...) logically possible but naturally improbable, an approximation of i-zombies actually exists: individuals experiencing what is referred to as “anesthesia awareness.” Patients under general anesthesia may be intubated (preventing speech), paralyzed (preventing movement), and narcotized (minimizing response to nociceptive stimuli). Thus, they appear—and typically are—unconscious. In 1-2 cases/1000, however, patients may be aware of intraoperative events, sometimes without any objective indices. Furthermore, a much higher percentage of patients (22% in a recent study) may have the subjective experience of dreaming during general anesthesia. P-zombies confront us with the hard problem of consciousness—how do we explain the presence of qualia? I-zombies present a more practical problem—how do we detect the presence of qualia? The current investigation compares p-zombies to i-zombies and explores the “hard problem” of unconsciousness with a focus on anesthesia awareness. (shrink)

The translation of Newton’s geometrical Propositions in the Principia into the language of the differential calculus in the form developed by Leibniz and his followers has been the subject of many scholarly articles and books. One of the most vexing problems in this translation concerns the transition from the discrete polygonal orbits and force impulses in Prop. 1 to the continuous orbits and forces in Prop. 6. Newton justified this transition by lemma 1 on prime and ultimate ratios which was (...) a concrete formulation of a limit, but it took another century before this concept was established on a rigorous mathematical basis. This difficulty was mirrored in the newly developed calculus which dealt with differentials that vanish in this limit, and therefore were considered to be fictional quantities by some mathematicians. Despite these problems, early practitioners of the differential calculus like Jacob Hermann, Pierre Varignon, and Johann Bernoulli succeeded without apparent difficulties in applying the differential calculus to the solution of the fundamental problem of orbital motion under the action of inverse square central forces. By following their calculations and describing some essential details that have been ignored in the past, I clarify the reason why the lack of rigor in establishing the continuum limit was not a practical problem. (shrink)

The existence of White Hole (WH) has been suggested by Schwarzschild solution to the Einstein field equation as a time-reversed Black Hole (BH), besides there has not been observational evidence for their existence yet. Our idea of the “inverse universe”, in which we introduce the time-reversed kinematics as another geometric state, can explain that WH should appear in such a geometry after a matter falls into a BH. In this work, we present a new operation for WH conversion from (...) BH, and by using it the nearly infinity point on the universe, for instance the inside of BH, is geometrically connected to the inside of WH on the inverse universe. Such a conversion is useful to provide the simple solution to the problem of “information loss” in BH. Furthermore, we find another conversion point as the prior geometric state to the Big Bang, and we propose a new cosmology of cyclic universe. (shrink)

A physical mechanical sequence is proposed representing measurement interactions ‘hidden' within QM's proverbial ‘black box'. Our ‘beam splitter' pairs share a polar angle, but head in opposite directions, so ‘led' by opposite hemisphere rotations. For orbital ‘ellipticity', we use the inverse value momentum ‘pairs' of Maxwell's ‘linear' and ‘curl' momenta, seen as vectors on the Poincare spherical surface. Values change inversely from 0 to 1 over 90 degrees, then ± inverts.. Detector polarising screens consist of electrons with the same (...) vector distributions, but polar angles set independently by A & B. The absorption/re-emission interaction process is modelled as surface vector additions at the angle of polar latitude of each interaction. This ‘collapse' of characteristic ‘wave values' is really then simply ‘re-polarisation', with new ellipticity. We then obtain the relation Cosθ at polarisers. We may simplify this to new ellipses with major/minor axis values. Considering as spherical orbital angular momentum rotation we invoke the unique quality of spheres to rotate concurrently on three axes! Rotating on y or z axes concurrent with x axis spin can return surface points to starting positions with non-integer x axis rotations, from half to infinity!. Second interactions at photomultiplier/ analysers are identical but at two orthogonal ‘channels'. Vector addition interactions at BOTH channel orientations normally produce a vector value of adequate amplitude to give a *click* from the MAJOR axis direction. At the ‘crossover' points at near circular polarity the orthogonal ‘certainty' is ~ 50:50, so both or neither channels may produce a ‘click'. The apparently unphysical but proved ‘Malus' law' relation; Cos2θ emerges physically from the 2nd set of interactions. The main departure from QM's assumptions are; That the original pair members each actually possessed two inverse momenta sets; ‘curl' and ‘linear'. Also that complex ‘vector additions' of those pairs occurs. Vector quantities allow A & B to reverse their OWN finding by reversing dial setting, reproducing experimental outputs without problematic ‘non-locality'. (shrink)

This paper takes issue with a recent proposal due to Shogenji (Synthese 184:29–48, 2012). In his paper, Shogenji introduces J, a normatively motivated formal measure of justification (and of confirmation), and then proceeds to recruit it descriptively in an explanation of the conjunction fallacy. We argue that this explanation is undermined by the fact that it cannot be extended in any natural way to the inverse conjunction fallacy, a more recently discovered, closely related fallacy. We point out that since (...) the inverse conjunction fallacy occurs in the absence of any form of explicit evidence, formal measures of confirmation such as J, are hard pressed to apply to it at all. We then proceed to argue that this problem with Shogenji’s measure is actually quite difficult to come to terms with; even if the situations where people commit the inverse conjunction fallacy are understood in such a way that the measure is applicable, it doesn’t seem possible to reasonably interpret these situations in such a way that the measure can explain the found response pattern. (shrink)

The scope of Platonism is extended by introducing the concept of a “Platonic computer” which is incorporated in metacomputics. The theoretical framework of metacomputics postulates that a Platonic computer exists in the realm of Forms and is made by, of, with, and from metaconsciousness. Metaconsciousness is defined as the “power to conceive, to perceive, and to be self-aware” and is the formless, con-tentless infinite potentiality. Metacomputics models how metaconsciousness generates the perceived actualities including abstract entities and physical and nonphysical realities. (...) It is postulated that this is achieved via digital computation using the Platonic computer. The introduction of a Platonic computer into the realm of Forms thus bridges the “inverse explanatory gap” and therefore solves the “inverse hard problem of consciousness” in the philosophy of mind. (shrink)

The scope of Platonism is extended by introducing the concept of a “Platonic computer” which is incorporated in metacomputics. The theoretical framework of metacomputics postulates that a Platonic computer exists in the realm of Forms and is made by, of, with, and from metaconsciousness. Metaconsciousness is defined as the “power to conceive, to perceive, and to be self-aware” and is the formless, con-tentless infinite potentiality. Metacomputics models how metaconsciousness generates the perceived actualities including abstract entities and physical and nonphysical realities. (...) It is postulated that this is achieved via digital computation using the Platonic computer. The introduction of a Platonic computer into the realm of Forms thus bridges the “inverse explanatory gap” and therefore solves the “inverse hard problem of consciousness” in the philosophy of mind. (shrink)

Existe-t-il une hypothèse de la servitude volontaire chez Spinoza? En partant des tensions qui naissent de l’apparente contradiction entre une telle hypothèse et l’anthropologie spinoziste, le présent article montre qu’il existe bien chez l’auteur du Traité théologico-politique des conditions politiques qui conduisent à l’inversion du conatus, au point de pousser les hommes à combattre « pour leur servitude comme s’il s’agissait de leur salut ». Spinoza tempère l’hypothèse laboétienne : un individu ou un peuple ne saurait de lui-même désirer la (...) servitude, mais peut y être conduit sous l’effet de l’adoption d’une certaine politique ou institution. Il ne s’agit pas seulement de la crainte favorisée par le régime monarchique. La fondation de la République des Hébreux, après la sortie d’Égypte du peuple juif, pose également la question de la servitude volontaire. La pensée spinoziste, ce faisant, témoigne d’un rationalisme politique inquiet, dont on peut s’inspirer aujourd’hui pour réfléchir sur les « causes extérieures cachées » qui peuvent fragiliser, voire contredire, le désir de liberté. (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.

In the pure powers ontology (PPO), basic physical properties have wholly dispositional essences. PPO has clear advantages over categoricalist ontologies, which suffer from familiar epistemological and metaphysical problems. However, opponents argue that because it contains no qualitative properties, PPO lacks the resources to individuate powers, and generates a regress. The challenge for those who take such arguments seriously is to introduce qualitative properties without reintroducing the problems that PPO was meant to solve. In this paper, I distinguish the core claim (...) of PPO: (i) basic physical properties have dispositional essences, from a hitherto unnoticed assumption: (ii) the dispositional essences of basic physical properties exclusively involve type-causal relations to other basic physical properties. I reject (ii), making room for a structuralist ontology in which all basic physical properties are pure powers, individuated by their places in a causal structure that includes not only other powers, but also physically realized qualitative properties such as shapes, patterns and structures. Such qualities individuate pure powers in the way that non-mental input and output properties individuate realized mental properties in functionalist theories of mind, except that here it is basic physical powers that are individuated by relations to realized non-powers. I distinguish one Platonic and two Aristotelian version of this theory, and argue that the Aristotelian versions require that grounding is not always a relative fundamentality relation, because the powers ground the qualities that individuate them. By considering ontic structural realism, I argue that symmetric grounding is the best way to make sense of relational individuation in structuralist ontologies, and is therefore no additional commitment of the one proposed here. (shrink)

Dans « Games and the Art of Agency » puis dans Games : Agency as Art, Thi Nguyen introduit l’inversion motivationnelle, un état motivationnel adopté par certain·e·s agent·e·s qui ne visent la victoire que pour éprouver les défis qui se présentent dans le cadre du jeu. Celleux-ci sont amené·e·s à considérer les objectifs largables du jeu comme des fins, bien qu’iels sachent ne désirer les rencontrer que dans une perspective instrumentale. Il s’agit ici de préciser la description de ce phénomène (...) et de la comparer aux perspectives prévalentes de la duperie de soi. Si j’insiste sur les ressemblances entre ces dernières et l’état d’inversion motivationnelle, je ne tente pas de le réduire à un cas d’irrationalité. Il semble cependant que la nécessité de préciser davantage le concept d’agentivité chez Thi Nguyen se dessine pour éviter de traiter l’inversion motivationnelle comme un simple cas de duperie de soi ainsi que certaines conséquences curieuses se dégageant de leurs ressemblances. (shrink)

From the materialist stance that I find compelling, the metaproblem of consciousness -- explaining why the problem of consciousness seems hard -- is hardly distinct from the 'easy' problem of explaining how the underlying physical/computational system works, and how it gives rise to perceptions of its own functioning. I discuss several confusions that might plausibly arise in that process, and propose that these confusions could create apparent gaps, ontological and epistemic, in materialist accounts of consciousness, thereby making the (...) hard problem hard. Inversely, resolving these confusions may help solve the hard problem. (shrink)

This paper studies a fundamental mechanism by which conflicts between arguments are drawn from sentiments regarding acceptability of the arguments. Given sets of arguments, an inverse abstract argumentation problem seeks attack relations between arguments such that acceptability semantics interprets each argument in the sets of arguments as being acceptable in each of the attack relations. It is an inverse problem of the traditional problem we refer to as the forward abstract argumentation problem. Given an (...) attack relation, the forward abstract argumentation problem seeks sets of arguments such that acceptability semantics interprets each argument in the sets of arguments as being acceptable in the attack relation. We give a probabilistic model of argumentation-theoretic inference. It is a generative model formalising the process by which acceptability semantics interprets acceptability of arguments in a given attack relation. We show that it gives a broad view of solutions to the forward and inverse abstract argumentation problems. Specifically, solutions to the inverse and forward abstract argumentation problems are shown to be equivalent to a maximum likelihood estimate and maximum likelihood prediction, respectively, which are both available with the generative model. In addition, they are shown to be special cases of the posterior distribution and the evidence, respectively, which are both obtained by probabilistic inference on the generative model. We report an experiment result and application example of the generative model in the inverse problems. (shrink)

The specious present (James, 1890/1950) is the phenomenal temporal structure of the representational content of my present experience. This article is a study of the mereological structure of the specious present and what it reveals about the nature of the mind. I argue that the specious present has certain features that cannot be easily explained within the framework of physicalism about the mind — the view that consciousness is nothing over and above what is physical. In particular, the specious present (...) is a phenomenally extended (i.e.non-instantaneous) whole whose parts are conceptual abstractions and are therefore dependent on this whole. However, unlike the specious present, what is physical does not have this special property of the parts being dependent on the whole. Therefore, it is unclear how the specious present can be explained in physicalistic terms. (shrink)

Thought-expressions are not simply good; instead, they become good for us when they make sense, empower action, and support health. From time to time, we may need to consider the difference between thought-expression and discourse, or thought-expression that really makes sense, and the difference between discourse and discussion, or a discourse-situation that makes genuine agreement or disagreement possible for us. In this essay, I explore a problem that D. Z. Phillips and Randy Ramal have termed “logical inversion,” and I (...) argue that wherever logical inversions have gained a foothold in our thought-expressions, they threaten to render us incapable of authentic discourse and discussion by ensuring that we misunderstand the understandings of others such that we deceive ourselves and others by picturing the knowledge and truth of our perspective against an unreal background of conceivable falsehoods which we have falsely attributed to the perspectives of others. Where this has taken place, practices of philosophical attention and conceptual clarification are needed to help us move from a situation of endless thought expression toward authentic discourse and discussion. (shrink)

Non‐reflectivist real self views claim that people are morally responsible for all and only those bits of conduct that express their true values and cares, regardless of whether they have endorsed them or not. A phenomenon that is widely cited in support of these views is inverse akrasia, that is, cases in which a person is praiseworthy for having done the right thing for the right reasons despite her considered judgment that what she did was wrong. In this paper (...) I show that non‐reflectivist real self views are problematic by focusing on the related but neglected phenomenon of inverse enkrasia, which occurs when an agent commits wrongdoing by following a mistaken evaluative judgment that, unbeknownst to her, runs contrary to her true values and cares. Intuitively, inverse enkratics are blameworthy for their actions although the latter don't express their real selves; therefore, non‐reflectivist real self views are false. I assess the implications of this result for the viability of the quality of will paradigm and conclude that the latter survives unscathed to the problems besetting real self views. The lesson is that defenders of the quality of will paradigm should stop talking about real selves altogether. (shrink)

Facial emotion recognition (FER) deficits interfere with interpretation of social situations and selection of appropriate responses. Attention-Deficit/Hyperactivity Disorder (ADHD) symptoms are independently associated with social difficulties and might exacerbate the influence of deficient FER, because children with ADHD symptoms have fewer compensatory resources in social situations when they misinterpret emotions. Very few studies have tested this hypothesis in a community context, where child ADHD symptoms vary on a continuum. The current study extended this work by utilising a community sample (N (...) = 87) of boys and girls in middle childhood (M = 7.83 years) and testing for moderation of FER effects separately by ADHD symptom type (ADHD-I = inattentive, H = hyperactive/impulsive, C = combined) using linear regression. While lower FER was associated with more social problems, this relationship was qualified by the presence of ADHD symptoms. Specifically, only children with relatively high ADHD symptoms in our community sample showed this inverse relationship, which was clearest among children with elevated ADHD-C or ADHD-I symptoms. No gender differences were observed. These results support our primary hypothesis, extend prior findings to boys and girls in the community, and have implications for understanding how ADHD symptoms and FER influence youth social deficits. (shrink)

This paper raises a principled objection against the idea that Bayesian confirmation theory can be used to explain the conjunction fallacy. The paper demonstrates that confirmation-based explanations are limited in scope and can only be applied to cases of the fallacy of a certain restricted kind. In particular; confirmation-based explanations cannot account for the inverse conjunction fallacy, a more recently discovered form of the conjunction fallacy. Once the problem has been set out, the paper explores four different ways (...) for the confirmation theorist to come to terms with the problem, and argues that none of them are successful. (shrink)

The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. Still working (...) in natural deduction calculi, he formulated a general type of schematic introduction rules to be matched ? thanks to the idea supporting the inversion principle ? by a corresponding general schematic Elimination rule. This was an attempt to provide a solution to the problem suggested by the often quoted note of Gentzen. According to Gentzen ?it should be possible to display the elimination rules as unique functions of the corresponding introduction rules on the basis of certain requirements?. Many people have since worked on this topic, which can be appropriately seen as the birthplace of what are now referred to as ?general elimination rules?, recently studied thoroughly by Sara Negri and Jan von Plato. In this study, we retrace the main threads of this chapter of proof-theoretical investigation, using Lorenzen's original framework as a general guide. (shrink)

Inverted sensation arguments such as the inverted spectrum thought experiment are often criticized for relying on an unconstrained notion of 'qualia'. In reply to this criticism, 'qualia-free' arguments for inversion have been proposed, in which only physical changes happen: inversions in the world, such as the replacement of surface colors by their complements, and a rewiring of peripheral input cables to more central areas in the nervous system. I show why such constrained inversion arguments won't work. The first problem (...) is that the world lacks the symmetry required to invert physical properties in the way required. The second problem concerns 'rewiring'. Empirical evidence indicates that the rewirings are either impossible, or would not result in an inversion of sensation. I propose the deeper reason for the failure of constrained inversion arguments lies in the fact that sensations are not properties of brain states, but spread into the world and the body. (shrink)

We study inversions of the jump operator on ${\mathrm{\Pi }}_{1}^{0}$ classes, combined with certain basis theorems. These jump inversions have implications for the study of the jump operator on the random degrees—for various notions of randomness. For example, we characterize the jumps of the weakly 2-random sets which are not 2-random, and the jumps of the weakly 1-random relative to 0′ sets which are not 2-random. Both of the classes coincide with the degrees above 0′ which are not 0′-dominated. A (...) further application is the complete solution of [24, Problem 3.6.9]: one direction of van Lambalgen's theorem holds for weak 2-randomness, while the other fails. Finally we discuss various techniques for coding information into incomplete randoms. Using these techniques we give a negative answer to [24, Problem 8.2.14]: not all weakly 2-random sets are array computable. In fact, given any oracle X, there is a weakly 2-random which is not array computable relative to X. This contrasts with the fact that all 2-random sets are array computable. (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)

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)