We use a deontic logic of collective agency to study reducibility questions about collective agency and collective obligations. The logic that is at the basis of our study is a multi-modal logic in the tradition of *stit* logics of agency. Our full formal language has constants for collective and individual deontic admissibility, modalities for collective and individual agency, and modalities for collective and individual obligations. We classify its twenty-seven sublanguages in terms of their expressive power. This classification enables us to (...) investigate reducibility relations between collective deontic admissibility, collective agency, and collective obligations, on the one hand, and individual deontic admissibility, individual agency, and individual obligations, on the other. (shrink)

abstract The moral value of distributive equality constitutes one of the most contentious debates in political philosophy. Following Frankfurt, many philosophers have claimed that the intuitive appeal of equality is illusory and that egalitarian intuitions are fundamentally intuitions about the importance of satisfying basic needs. According to this argument, our intuitions tell us that inequality ceases to matter once a certain threshold has been reached. Despite the widespread appeal to intuitions regarding this issue, few empirical studies have tried to assess (...) whether Frankfurt and his followers are right in claiming the lack of intuitiveness of equality per se. In a series of three experiments, we show that experimental evidence does not allow us to settle the intuitiveness of each theory: laypeople are divided in the consideration of the respective importance of needs and equality. While our results do show that laypeople attach special importance to needs‐fulfilment, it also seems that they are divided when it comes to the importance they grant to equality once needs are fulfilled. No theory is unanimously backed by participants, and it seems that, fundamentally, divisions among philosophers reflect deep divisions among people. (shrink)

A key argument of Dixon et al. in the target article is that prejudice reduction through intergroup contact and collective action work in opposite ways. We argue for a complementary approach focusing on extreme emotions to understand why people turn to non-normative collective action and to understand when and under what conditions extreme emotions may influence positive effects of contact on reconciliation.

In order to come to grips with Peirce's definition of truth as the ideal limit of inquiry, I give a succinct exposition of Peirce's theory of inquiry and his philosophical logic, paying attention to several types of reasoning and their interrelations. Subsequently, the arguments of a contemporary apologist of Peirce's notion of truth, C.J. Misak, are subjected to a scrutiny and found to be insufficient, as the principle of bivalence is defended improperly and, as a Peircean definition of truth, turns (...) out to be incompatible with a pragmatist epistemology. (shrink)

Individualists claim that collective obligations are reducible to the individual obligations of the collective’s members. Collectivists deny this. We set out to discover who is right by way of a deontic logic of collective action that models collective actions, abilities, obligations, and their interrelations. On the basis of our formal analysis, we argue that when assessing the obligations of an individual agent, we need to distinguish individual obligations from member obligations. If a collective has a collective obligation to bring about (...) a particular state of affairs, then it might be that no individual in the collective has an individual obligation to bring about that state of affairs. What follows from a collective obligation is that each member of the collective has a member obligation to help ensure that the collective fulfills its collective obligation. In conclusion, we argue that our formal analysis supports collectivism. (shrink)

If group members aim to fulfill a collective obligation, they must act in such a way that the composition of their individual actions amounts to a group action that fulfills the collective obligation. We study a strong sense of joint action in which the members of a group design and then publicly adopt a group plan that coordinates the individual actions of the group members. We characterize the conditions under which a group plan successfully coordinates the group members' individual actions, (...) and study how the public adoption of a plan changes the context in which individual agents make a decision about what to do. (shrink)

Cette introduction invite à décadrer et à recadrer la thématique de l’effondrement, popularisée et médiatisée par la théorie dite « collapsologie », vers le plan des acteurs, des terrains, des temporalités, et des régimes d’énonciation. Nous appelons à documenter empiriquement ce que fait l’effondrement, et ce qu’en font celles et ceux à qui cette idée « fait » quelque chose. En effet, l’effondrisme pose la question des façons de se positionner non pas uniquement par rapport à une théorie, mais également (...) par rapport à des expériences individuelles et collectives. Le dossier vise à comprendre comment la réception de la « collapsologie » donne lieu à des jeux complexes entre désemparement et capacités d’agir. L’atterrissage sur un sol anthropocénique de plus en plus critique mérite une décisive discussion collective. L’hypothèse de cette majeure est que les expériences effondristes ont une valeur d’expérimentation à cet égard, notamment en créant un zone discursive et praxique où des cultures et des expériences politiques différentes sont amenées à se rencontrer et à collaborer. (shrink)

C.S. Peirce's and Isaac Levi's accounts of the belief-doubt-belief model are discussed and evaluated. It is argued that the contemporary study of belief change has metamorphosed into a branch of philosophical logic where empirical considerations have become obsolete. A case is made for reformulations of belief change systems that do allow for empirical tests. Last, a belief change system is presented that (1) uses finite representations of information, (2) can adequately deal with inconsistencies, (3) has finite operations of change, (4) (...) can do without extra-logical elements, and (5) only licenses consistent beliefs. (shrink)

This book is a major contribution to the study of the philosopher F. H. Bradley, the most influential member of the nineteenth-century school of British Idealists. It offers a sustained interpretation of Bradley's Principles of Logic, explaining the problem of how it is possible for inferences to be both valid and yet have conclusions that contain new information. The author then describes how this solution provides a basis for Bradley's metaphysical view that reality is one interconnected experience and how this (...) gives rise to a new problem of truth. (shrink)

I apply Kooi and Tamminga's (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting natural (...) deduction systems is sound and complete with respect to its particular semantics. Among other things, I thus obtain a new proof system for Lukasiewicz's three-valued logic. (shrink)

Quine's holistic empiricist account of scientific inquiry can be characterized by three constitutive principles: *noncontradiction*, *universal revisability* and *pragmatic ordering*. We show that these constitutive principles cannot be regarded as statements within a holistic empiricist's scientific theory of the world. This claim is a corollary of our refutation of Katz's [1998, 2002] argument that holistic empiricism suffers from what he calls the Revisability Paradox. According to Katz, Quine's empiricism is incoherent because its constitutive principles cannot themselves be rationally revised. Using (...) Gärdenfors and Makinson's logic of belief revision based on epistemic entrenchment, we argue that Katz wrongly assumes that the constitutive principles are *statements* within a holistic empiricist's theory of the world. Instead, we show that constitutive principles are best seen as *properties* of a holistic empiricist's theory of scientific inquiry and we submit that, without Katz's mistaken assumption, the paradox cannot be formulated. We argue that our perspective on the status of constitutive principles is perfectly in line with Quinean orthodoxy. In conclusion, we compare our findings with van Fraassen's [2002] argument that we should think of empiricism as a stance, rather than as a doctrine. (shrink)

Two groups of agents, G1 and G2, face a *moral conflict* if G1 has a moral obligation and G2 has a moral obligation, such that these obligations cannot both be fulfilled. We study moral conflicts using a multi-agent deontic logic devised to represent reasoning about sentences like "In the interest of group F of agents, group G of agents ought to see to it that phi". We provide a formal language and a consequentialist semantics. An illustration of our semantics with (...) an analysis of the Prisoner’s Dilemma follows. Next, necessary and sufficient conditions are given for (1) the possibility that a single group of agents faces a moral conflict, for (2) the possibility that two groups of agents face a moral conflict within a single moral code, and for (3) the possibility that two groups of agents face a moral conflict. (shrink)

We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 34.3 (2001) 245-259 [Access article in PDF] Virtue in Aristotle's Rhetoric: A Metaphysical and Ethical Capacity Susan K. Allard-Nelson It has been argued that Aristotle's description of excellence (aretê) as a capacity (dynamis) in Rhetoric 1.9 is inconsistent with his treatment of excellence in Nicomachean Ethics 2.5, where he specifically argues that aretê is not a dynamis, but a hexis (i.e., a state or condition). (...) 1 Certainly, the word that Aristotle uses throughout the Nicomachean Ethics to both describe and categorize aretê is hexis, and he uses this word at Rhetoric 1.6.1362b13, where he says that several of the virtues, and all other such states (kai hai allai hai toiautai hexeis), are excellences of the soul. However, as part of his discussion of the ethical aspects of oratory, Aristotle states that aretê is "a capacity (dynamis) of providing and preserving good things, and a capacity of conferring many great benefits (euergetikê)" (Rh. 1.9.1366a36-1366b1). 2 This discussion is set in language similar to that used to discuss excellence and goodness in Rhetoric 1362b2-4 and 1361a28-30; this suggests that Aristotle intentionally identifies aretê with dynamis in this text, and, to some degree at least, with the dynamis to benefit others. In the former passage, Aristotle claims that "the excellences, too, must be a good thing, for those who possess them are in a good condition, and they are productive of good things and good actions" (Rh. 1.6.1362b2-4). In the latter passage, Aristotle states that honor (timê) can be paid, not only to those who have already done good, but also to those who have the capacity to do good (dynamenos euergetein) in the future. Indeed, in the Rhetoric 1.9.1366b3-7, Aristotle further unites the concepts of excellence, capacity, and beneficence by stating, "If excellence is the capacity of conferring benefits (dynamis euergetikê), then the greatest virtues must be those which are the most useful to others, and, for this reason, justice and courage are the most honored; for the latter is useful to others in war, and the former both in war and in peace" (1366b3-7). [End Page 245]Based on an understanding of this apparent inconsistency in terminology as intentional on Aristotle's part, I intend to argue here that Aristotle's identification of aretê with dynamis in Rhetoric can be understood within the highly specific context of rhetoric as an art as more appropriate, both metaphysically and ethically, than would have been an identification of aretê with hexis. I also intend to argue that, while certain tensions and difficulties are created by the classification of aretê as a dynamis in the Rhetoric and as a hexis in the Nicomachean Ethics, 3 Aristotle can be defended against the charge of inconsistency.To this end, then, I begin by examining the implications of defining rhetoric as an art (technê) that has persuasion (pistis) as its end (telos) and function (ergon). 1. Rhetoric is an art, and, as we know from EN 6.4, art is identical to a state of reasoned capacity to make, and all art is concerned with the coming into being of something that is capable of either being or not being, and whose origin is in the maker (1140a1-23). Art is a rational capacity, or a potency that moves according to, and involves, a rational formula (kai ta men kata logon dynatai kinein kai hai dynameis auton meta logou), and, as such, it is capable of producing contrary effects (Met. 9.5.1047b31-1048a24). For this reason, and to negate the impossibility of contrary effects being produced simultaneously, Aristotle states that a rational capacity involves not only the elements of agent and patient, but also a desire or choice on the part of the agent that moves her 4 to act (Met. 9.5.1048a10). This necessary desire or choice, in fact, explains why an inference in the case of the arts (or of any rational capacity) can be made in one direction... (shrink)

Baumard suggests that the advent, through phenotypic plasticity mechanisms, of future-oriented preferences and creative mindsets in eighteenth-century Great Britain explains the wave of innovations that drove the British Industrial Revolution. We argue that, although this approach is promising, Baumard's model would benefit from being supplemented by demographic, economic, and sociological explanations independent of Life History Theory.

This paper offers a revised political conception of human rights informed by legal pluralism and epistemic considerations. In the first part, I present the political conception of human rights. I then argue for four desiderata that such a conception should meet to be functionally applicable. In the rest of the first section and in the second section, I explain how abstract human rights norms and the practice of specification prevent the political conception from meeting these four desiderata. In the last (...) part of the paper, I argue that full-fledged tolerance in the international order – that is tolerance-as-non-intervention and tolerance-as-respect – should be attached to (1) compliance with jus cogens norms and to; (2a) a political community recognizably organized as a community of inquiry that is; (2b) committed to the specification and incorporation or expression of the idea of human rights within its local legal system. (shrink)

Reintroduction programs in which captive-bred or reared animals are released into natural habitats are considered a key approach for conservation; however, success rates have generally been low. Accounting for factors that enable individual animals to have a greater chance of survival can not only improve overall conservation outcomes but can also impact the welfare of the individual animals involved. One such factor may be individual personality, and personality research is a growing field. This type of research presents animal welfare scientists (...) with the opportunity to develop behavior profiles that may predict how particular individuals cope with challenges. This has direct implications for both in situ and ex situ populations and can bridge the gap between animal welfare and conservation. We designed a project to ascertain the presence of personality traits in Blanding’s turtles (Emydoidea blandingii), a species of special concern in the state of Michigan, and assess potential links between traits and post-release success. As hypothesized, the Blanding’s turtles in this study displayed behavioral responses to modified open field tests indicative of distinct personality traits: exploration, boldness and aggression. Additionally, the personality traits were correlated differently with survival and behavior patterns when the turtles were released into the Shiawassee National Wildlife Refuge. More exploratory turtles had higher survival rates, while neither boldness nor aggression were related to survival. Exploratory turtles were also more likely to travel longer distances after release. The use of muskrat dens was related to increased survival, and both bolder and more exploratory turtles made higher use of this feature. Exploratory and aggressive turtles were found basking outside of water more often, while bold turtles were more likely to be found at the water surface. Both of these basking behaviors may increase the risk of predation and may be reflective of a trade-off between risk and behaviors related to physiological health. Understanding how personality affects behavior and survival post-release can be a critical tool for improving reintroduction success. Zoo animal welfare scientists and practitioners can implement approaches that improve the welfare of individuals within the context of conservation initiatives. (shrink)

This article provides an exploration of the relationships between a procedural account of epistemic democracy, illegitimate laws and judicial review. I first explain how there can be illegitimate laws within a procedural account of democracy. I argue that even if democratic legitimacy is conceived procedurally, it does not imply that democracy could legitimately undermine itself or adopt grossly unjust laws. I then turn to the legitimacy of judicial review with regard to these illegitimate laws. I maintain that courts do not (...) have a moral privilege on the overthrow of illegitimate laws; in this respect the refusal of royal assent has the same status. I also explain how the rule of the clear mistake fails to restrict the action of courts to only illegitimate laws. Finally, I argue for the positive epistemic inputs of weak judicial review. (shrink)

Although T. H. Green is primarily remembered today as a moral and political philosopher, many of his philosophical concerns owe their origins to the Victorian crisis of faith in which a widespread belief in the literal truth of Scripture confronted seemingly incompatible scientific theories. Green attributed this crisis to the inability of science and religion to find accommodation in the popular version of empiricism widely accepted by educated men and women of his day. In his 371-page introduction to Hume’s Treatise, (...) Green argued that this philosophy was unacceptable, even on its own terms, and that it needed to be replaced with a new philosophy of life, one recognizing that both knowledge and human action are .. (shrink)

En 1534, le grand chancelier d'Angleterre, sir Thomas More, refuse de prêter serment à l'Acte de Suprématie par lequel Henri VIII d'Angleterre, s'opposant à l'Eglise de Rome, se proclame chef de l'Eglise anglicane. Condamné par le tribunal royal à la décapitation publique, Thomas More demeure pourtant fidèle : fidèle au roi, fidèle à la foi, et fidèle à sa conscience au prix de sa vie. En effet, s'il ne reconnaît pas le roi comme chef de l'Eglise nationale, il n'a jamais (...) remis en cause son autorité temporelle. Sir Thomas More, humaniste, juriste, théologien, diplomate, homme d'Etat et finalement martyr, est devenu un modèle pour ceux qui se dévouent au bien commun. L'Europe troublée du XVIe siècle n'est pas sans rappeler notre époque soumise à la difficile gestion des affaires publiques, aux scandales financiers et à l'avidité de quelques puissants. Ce livre, qui présente la vie de Thomas More et les valeurs fondatrices de son action, peut nous aider à trouver de nouveaux repères pour devenir ferment dans la pâte du monde. Le lecteur saisira alors toute la vérité des paroles adressées par l'humaniste anglais Roger Ascham à la petite- fille de More : "Par cet homme seul, c'est toute l'Angleterre qui s'est trouvée anoblie.". (shrink)

There is a growing discourse on “new sincerity,” and related terms like “quirky” and “metamodernism,” as a movement or sensibility in contemporary cinema developing from the late 1990s onward, exemplified by the work of filmmakers such as Wes Anderson and Charlie Kaufman. However, what this new concept means in the context of cinema has so far remained under-defined and requires further philosophical analysis. This article provides such an analysis by offering a reconceptualization of Jean-Paul Sartre's existentialist-phenomenological notions of good faith (...) and sincerity, which will be connected to developments in film and elaborated in relation to Frances Ha (Noah Baumbach, 2012). I propose, against Sartre's own preference for the problematic term “authenticity,” to understand sincerity as the reflective resumption of good faith's pre-reflective acceptance of human-reality. This conception of sincerity as reflective allows us to accurately understand the combination of self-awareness and affirmation that characterizes new sincerity cinema: its self-awareness does not serve the postmodernist strategy of endless self-ironization; instead, its portrayals affirm the meaningfulness of its filmic reality, while also being aware of film as a medium. An analysis of Frances Ha illustrates how this concept of sincerity might be seen to function both on the level of story world, characters and themes, and on that of narrative structure and audio-visual style, thereby showing how we can meaningfully speak of sincerity in and of film. (shrink)

In the 1930s, several members of the Vienna Circle set out to incorporate psychology in the unity of science, by showing that all cognitively significant sentences of psychology can be translated into the language of physics. This epistemological analysis of psychology has become known as logical behaviourism. Carnap was the first logical empiricist to expound this programme in considerable detail. Relying on his particular notion of protocol languages, Carnap develops a view on the philosophy of psychology that not only is (...) thoroughly physicalistic, but also shows due appreciation to 'introspection' as a purely subjective, but reliable way to verify sentences about one's own mind. Second, contrary to the received view on logical behaviourism, Carnap's philosophy of psychology not only takes into account overt behaviour, but micro-physiological processes as well. Last, Carnap's physicalistic philosophy of mind couples full awareness of the changeability of scientific knowledge with the aspiration to develop a philosophy of psychology that really does justice to this changeability. (shrink)

Les logiciels d’aide à la décision basés sur des techniques d’intelligence artificielle sont de plus en plus utilisés dans le domaine de la justice. Or ces techniques nécessitent souvent d’accéder à de grandes quantités d’informations personnelles afin de réaliser un apprentissage de qualité. En France, le cadre légal semble aujourd’hui favorable à l’ouverture des jugements, pourvu que la vie privée des personnes concernées soit respectée. Cependant, la protection des données personnelles destinées à être publiées reste difficile techniquement. Cet article a (...) pour objectif de décrire une attaque minimaliste qui a été réalisée en 2014 sur un jeu de données protégé par l’application d’un algorithme de pseudonymisation. L’originalité de cette attaque réside dans sa simplicité de fonctionnement – elle ne nécessite pas d’accès à un jeu de données auxiliaire – et dans sa cible – l’algorithme de pseudonymisation. Nous présentons la famille des algorithmes de pseudonymisation, décrivons et analysons l’attaque, et concluons sur la place de la pseudonymisation dans le Règlement Général sur la Protection des Données personnelles. (shrink)

Two issues are addressed in this commentary: the universality and the “psychological reality” of locus equations as cues to place of articulation. Preliminary data collected in our laboratory suggest that locus equations do not reliably distinguish place of articulation for fricatives. Additionally, perception studies show that listeners can identify place of articulation based on much less temporal information than that required for deriving locus equations.

Levi, setting out to formalize Peirce's and Dewey's *belief-doubt-belief*-model, took the lead in defining the field of philosophical logic that has become known as *belief change*. First, Levi's theory of knowledge is placed within the context of American pragmatism. A discussion follows of Levi's criteria under which a change of belief must be judged an improvement. In the final section, a critical evaluation of Levi's logical epistemology opens new venues for logical and epistemological inquiry.

We develop a multi-agent deontic action logic to study the logical behaviour of two types of deontic conditionals: (1) conditional obligations, having the form "If group H were to perform action aH, then, in group F's interest, group G ought to perform action aG" and (2) conditional permissions, having the form "If group H were to perform action aH, then, in group F's interest, group G may perform action aG". First, we define a formal language for multi-agent deontic action logic (...) and a class of consequentialist models to interpret the formulas of the language. Second, we define a transformation that converts any strategic game into a consequentialist model. Third, we show that an outcome a* is a Nash equilibrium of a strategic game if and only if a conjunction of certain conditional permissions is true in the consequentialist model that results from the transformation of that strategic game. (shrink)

While psychologists and political scientists have long investigated issues of interest to philosophers, the development of political experimental philosophy has remained limited. This slow progress is surprising, given that political philosophers commonly acknowledge the relevance of empirical data for normative theorizing. In this chapter, we illustrate the importance of empirical data by outlining recent developments in three domains related to theories of justice, where empirical results reinforce or endanger popular philosophical theories. Our first showcase concerns the boundaries of the concept (...) of fairness. While both libertarian thinkers and social egalitarians have united in rejecting the concept of natural injustice, we show that people do consider that unpreventable natural inequalities can be described as unfair. Second, we take the example of impartiality devices, such as the veil of ignorance or the idea of an impartial spectator, to show that such devices are efficient at shifting people’s intuitions in a more impartial manner. Third, we review empirical data on fairness intuitions to show that people conform to a pluralist theory of justice, valuing desert, needs-satisfaction, and equality at the same time. However, distribution according to desert enjoys a privileged position: people mostly care for the satisfaction of basic needs of deserving recipients, and people are willing to tolerate large inequalities in meritocratic contexts. The centrality of desert leads to dilemmas for mainstream egalitarian theorists, as theories that do not recognize the value of desert could fail to find support or legitimacy within the population. (shrink)

Considerable research evidence has accumulated indicating that there is an increased likelihood for illness and injury among employees working in long-hour schedules and schedules involving unconventional shift work. In addition, studies show that fatigue-related errors made by employees working in these kind of demanding schedules can have serious and adverse repercussions for public safety. As the result of these concerns, new protective legislation is being advocated in the United States, for instance, to restrict the hours of work among nurses and (...) other healthcare professionals. This article reviews the history of concerns about long working hours and the current scientific evidence regarding their effects on workers' health. The ethical implications of unconventional shift work and long work-hour schedules are considered. Relevant ethical considerations involve mandatory or unpaid overtime and the possibility of employer coercion, the political basis for government regulation of working hours, potential limits on voluntary assumption of risk, societal benefits accruing from the equitable distribution of available working hours, gender-based inequities related to working hours, and employer responsibilities for protecting individuals who are not employees from the spillover effects of demanding work schedules. (shrink)

In his foreword to wilderness and the heart, a collection of essays on Henry Bugbee’s philosophy, Alasdair MacIntyre commends Bugbee’s book, The Inward Morning, for the way in which it integrates form and content. How it is written and what it says, MacIntyre writes, “are to be grasped together or not at all” (xiii). “What can be learned from The Inward Morning,” MacIntyre continues, “is not primarily a set of philosophical theses and arguments—although such theses and arguments are to be (...) found in it—but rather something of the first importance about the place that philosophical theses and arguments might have in our lives, the relevance to our lived experience of the reading of philosophical texts” (xiii). In .. (shrink)

Publication date: 15 October 2018 Source: Author: Ehiosun O. Marvel NHIS was launched officially on 6th of June 2005. The Scheme is designed to provide comprehensive health care at affordable costs, covering employees of the formal sector, self-employed, as well as rural communities, the poor and the vulnerable groups. However, client satisfaction of services rendered continues to be a major concern for the improvement of NHIS. This study is designed to determine the level and causes of dissatisfaction of clients (...) accessing NHIS clinic at the Kubwa General Hospital, Kubwa, FCT, Abuja. This study employed a descriptive cross sectional survey. 279 NHIS enrollees were recruited for this study at the Kubwa General Hospital. Questionnaires were administered and the level of dissatisfaction and satisfaction of NHIS services were analyzed. The satisfaction rate was 69.2% while the dissatisfaction rate was 22.9%. The respondents were satisfied with the attitude of health workers in NHIS clinic, Kubwa. However, they were dissatisfied with waiting time, attitude of record officers and those in pharmacy department. This study found that the level of dissatisfaction with NHIS services is high despite a high satisfaction level. The Attitude of health workers may influence the dissatisfaction of enrollees. NHIS is still limited to the formal sector. (shrink)

This paper presents two systems of natural deduction for the rejection of non-tautologies of classical propositional logic. The first system is sound and complete with respect to the body of all non-tautologies, the second system is sound and complete with respect to the body of all contradictions. The second system is a subsystem of the first. Starting with Jan Łukasiewicz's work, we describe the historical development of theories of rejection for classical propositional logic. Subsequently, we present the two systems of (...) natural deduction and prove them to be sound and complete. We conclude with a ‘Theorem of Inversion’. (shrink)