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)

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)

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)

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)

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)

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)

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)

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.

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)

Cet article, qui fait suite à une publication précédente (« Les apories du concept de redondance logique chez Bolzano »), poursuit un double objectif : (I) démontrer que les apories que nous avions relevées peuvent être surmontées par l’analyse des rapports extensionnels entre représentations ; (II) évaluer la contribution de Bolzano à la question classique des rapports intension/extension telle qu’elle a été posée par Port-Royal. La logique des classes, dont Bolzano pose les fondements ( Théorie de la science, 2 e (...) partie, 3 e section), permet en effet de dégager les lois de la redondance logique — auxquelles Bolzano ne cesse de faire implicitement référence sans en donner la formule — et de délimiter le champ d’application du principe classique de proportionnalité inverse entre intension et extension auquel déroge précisé­ment la redondance. La critique bolzanienne de la logique de Port-Royal prend alors tout son sens. (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 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)

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)

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)

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 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)

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)

Sydney Shoemaker has gone to great lengths to defend a repre-sentationalist view of phenomenal character, and yet he describes this view as breaking with standard representationalism in two ways. First, he thinks his representationalist position is consis- tent with the possibility of spectrum inversion, and second, he thinks there are qualia. Thus, we can think of his position in the qualia debate as moderate representationalism (or, equally, moderate qualia realism) by taking up some middle ground be- tween these two major (...) camps. This \moderate" view faces several problems. Here I will very briey explain Shoemaker's represen- tationalist account of spectrum inversion in which he appeals to the existence of a certain sort of subjective property of objects, namely, what he calls appearance properties (formerly he called these phenomenal properties). I will argue that an alternative ver- sion of representationalism provides a more plausible explanation of both inversion-type scenarios and Shoemaker's color constancy case, which he uses to motivate the existence of these subjective properties, without positing appearance properties at all. (shrink)

Sydney Shoemaker has gone to great lengths to defend a repre-sentationalist view of phenomenal character, and yet he describes this view as breaking with standard representationalism in two ways. First, he thinks his representationalist position is consis- tent with the possibility of spectrum inversion, and second, he thinks there are qualia. Thus, we can think of his position in the qualia debate as moderate representationalism by taking up some middle ground be- tween these two major camps. This \moderate" view faces (...) several problems. Here I will very briey explain Shoemaker's represen- tationalist account of spectrum inversion in which he appeals to the existence of a certain sort of subjective property of objects, namely, what he calls appearance properties. I will argue that an alternative ver- sion of representationalism provides a more plausible explanation of both inversion-type scenarios and Shoemaker's color constancy case, which he uses to motivate the existence of these subjective properties, without positing appearance properties at all. (shrink)

Los fondos de inversión se han convertido en los últimos años en un mecanismo frecuente que los clubes de fútbol utilizan para financiar el fichaje de jugadores. Aunque muchos autores han destacado sus efectos beneficiosos al permitir que los clubes adquieran jugadores que de otra manera no podrían conseguir, en este trabajo nos centramos en enfatizar dos problemas que pueden plantear. En primer lugar, hemos tratado de mostrar que pueden generar un progresivo alejamiento de los aficionados. En segundo lugar, a (...) través del dilema del prisionero nos hemos propuesto mostrar que pueden contribuir a aumentar a largo plazo la deuda de los clubes y amenazar el fair play financiero.Investment funds have become in recent years a frequent mechanism football clubs use to finance signing of football players. Although many authors have highlighted their beneficial effects by allowing clubs to acquire players who otherwise they would not get, in this paper we focus on two problems. First, we have tried to show that they can generate a progressive distancing from the fans. Secondly, through the prisoner’s dilemma we intend to show that they can contribute to increasing long-term clubs debt and threaten the financial fair play. (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)

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)

Philosophers who advocate the possibility of spectrum inversion often conclude that the qualitative content of experiential states pose a serious problem for functionalism. I argue that in order for the inversion hypothesis to support this conclusion one needs to show that it generalizes to all species of qualia. By examining features of touch, taste, and olfactory sensations, I show there is good reason to resist this generalization, in which case appeals to the possibility of spectral inversion are considerably less effective (...) than they may initially appear. (shrink)

This article tries to elucidate the Deleuzian project of the reversal of Platonism in relation to that of Nietzsche. To this aim, I have made a predominantly historiographic sketch of the question in both authors. In the case of Nietzsche, I inquired about both the relationship that the reversal of Platonism presents in his philosophy with the problem of nihilism and the evolution that the topic undergoes throughout his vast intellectual production, until it reaches its final formulation. With regard to (...) Deleuze, I offer a broad overview of his work aimed at tracing the subject, from his interpretation of the Nietzschean formulation, as opposed to that of Heidegger, to the meticulous way in which it fits into his own philosophy as a shift of the essence in favour of the event as a source of singularities. (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)

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)