We examine changing production relations in the Mexican tequila industry to explore the ways in which large industrial firms are using “reverse leasing arrangements,” a form of contract farming, to extend their control over small agave farmers. Under these arrangements, smallholders rent their parcels to contracting companies who bring in capital, machinery, labor, and other agricultural inputs. Smallholders do not have access to their land, nor do they make any of the management decisions. We analyze the factors that have led (...) some producers to participate in reverse leasing arrangements, while allowing other producers to continue farming independently. In addition, we look at the ways in which farmers are responding to these new production relations and constraints and the strategies that they are using to regain control over the production process. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic in character and (...) are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

The relationship of Grundy and chromatic numbers of graphs in the context of Reverse Mathematics is investi-gated.

Reverse mathematics is a program in mathematical logic that seeks to give precise answers to the question of which axioms are necessary in order to prove theorems of "ordinary mathematics": roughly speaking, those concerning structures that are either themselves countable, or which can be represented by countable "codes". This includes many fundamental theorems of real, complex, and functional analysis, countable algebra, countable infinitary combinatorics, descriptive set theory, and mathematical logic. This entry aims to give the reader a broad introduction to (...) the history, methodology, and results of the reverse mathematics program, with a particular focus on its connections to foundational programs such as finitism, constructivism, and predicativism. (shrink)

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

Reverse mathematics is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the minimal axioms needed to prove a theorem of ordinary, that is, non-set-theoretic, mathematics. As suggested by the title, this paper deals with the study of the topological notions of dimension and paracompactness, inside Kohlenbach’s higher-order RM. As to splittings, there are some examples in RM of theorems A, B, C such that A (...) ↔, that is, A can be split into two independent parts B and C, and the aforementioned topological notions give rise to a number of splittings involving highly natural A, B, C. Nonetheless, the higher-order picture is markedly different from the second-one: in terms of comprehension axioms, the proof in higher-order RM of, for example, the paracompactness of the unit interval requires full second-order arithmetic, while the second-order/countable version of paracompactness of the unit interval is provable in the base theory RCA 0. We obtain similarly “exceptional” results for the Urysohn identity, the Lindelöf lemma, and partitions of unity. We show that our results exhibit a certain robustness, in that they do not depend on the exact definition of cover, even in the absence of the axiom of choice. (shrink)

Reverse mathematics is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the minimal axioms needed to prove a theorem of ordinary, that is, non-set-theoretic, mathematics. As suggested by the title, this paper deals with two RM-phenomena, namely, splittings and disjunctions. As to splittings, there are some examples in RM of theorems A, B, C such that A↔, that is, A can be split into two (...) independent parts B and C. As to disjunctions, there are examples in RM of theorems D, E, F such that D↔, that is, D can be written as the disjunction of two independent parts E and F. By contrast, we show in this paper that there is a plethora of splittings and disjunctions in Kohlenbach’s higher-order RM. (shrink)

We use methods of reverse mathematics to analyze the proof theoretic strength of a theorem involving the notion of coloring number. Classically, the coloring number of a graph $G=$ is the least cardinal $\kappa$ such that there is a well-ordering of $V$ for which below any vertex in $V$ there are fewer than $\kappa$ many vertices connected to it by $E$. We will study a theorem due to Komjáth and Milner, stating that if a graph is the union of $n$ (...) forests, then the coloring number of the graph is at most $2n$. We focus on the case when $n=1$. (shrink)

In this paper, we investigate the logical strength of completeness theorems for intuitionistic logic along the program of reverse mathematics. Among others we show that is equivalent over to the strong completeness theorem for intuitionistic logic: any countable theory of intuitionistic predicate logic can be characterized by a single Kripke model.

In his remarkable paper Formalism 64, Robinson defends his eponymous position concerning the foundations of mathematics, as follows:Any mention of infinite totalities is literally meaningless.We should act as if infinite totalities really existed. Being the originator of Nonstandard Analysis, it stands to reason that Robinson would have often been faced with the opposing position that ‘some infinite totalities are more meaningful than others’, the textbook example being that of infinitesimals. For instance, Bishop and Connes have made such claims regarding infinitesimals, (...) and Nonstandard Analysis in general, going as far as calling the latter respectively a debasement of meaning and virtual, while accepting as meaningful other infinite totalities and the associated mathematical framework. We shall study the critique of Nonstandard Analysis by Bishop and Connes, and observe that these authors equate ‘meaning’ and ‘computational content’, though their interpretations of said content vary. As we will see, Bishop and Connes claim that the presence of ideal objects in Nonstandard Analysis yields the absence of meaning. We will debunk the Bishop–Connes critique by establishing the contrary, namely that the presence of ideal objects in Nonstandard Analysis yields the ubiquitous presence of computational content. In particular, infinitesimals provide an elegant shorthand for expressing computational content. To this end, we introduce a direct translation between a large class of theorems of Nonstandard Analysis and theorems rich in computational content, similar to the ‘reversals’ from the foundational program Reverse Mathematics. The latter also plays an important role in gauging the scope of this translation. (shrink)

This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse (...) Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics. (shrink)

A theory is usually said to be time reversible if whenever a sequence of states S 1, S 2, S 3 is possible according to that theory, then the reverse sequence of time reversed states S 3 T, S 2 T, S 1 T is also possible according to that theory; i.e., one normally not only inverts the sequence of states, but also operates on the states with a time reversal operator T. David Albert and Paul Horwich have suggested that (...) one should not allow such time reversal operations T on states. I will argue that time reversal operations on fundamental states should be allowed. I will furthermore argue that the form that time reversal operations take is determined by the type of fundamental geometric quantities that occur in nature and that we have good reason to believe that the fundamental geometric quantities that occur in nature correspond to irreducible representations of the Lorentz transformations. Finally, I will argue that we have good reason to believe that space-time has a temporal orientation. (shrink)

Reverse analyses of three proofs of the Sylvester-Gallai theorem lead to three different and incompatible axiom systems. In particular, we show that proofs respecting the purity of the method, using only notions considered to be part of the statement of the theorem to be proved, are not always the simplest, as they may require axioms which proofs using extraneous predicates do not rely upon.

One of the earliest applications of Cantor's Normal Form Theorem is Jacobstahl's proof of the existence of prime factorizations of ordinals. Applying the techniques of reverse mathematics, we show that the full strength of the Normal Form Theorem is used in this proof.

We analyze three applications of Ramsey’s Theorem for 4-tuples to infinite traceable graphs and finitely generated infinite lattices using the tools of reverse mathematics. The applications in graph theory are shown to be equivalent to Ramsey’s Theorem while the application in lattice theory is shown to be provable in the weaker system RCA0.

This article attempts to identify, in the context of the contemporary debate on discrimination, the meanings attributed to the term ‘reverse sexism’, which concerns the broader social phenomenon of sexism. It examines how the rhetoric of reverse sexism has been shaped historically, highlights aspects of the criticism that it has received, and describes the field in which it is currently being reproduced. Upon this basis, it is proposed that ‘reverse sexism’ should be rejected as an inadequate conceptualization for describing discrimination (...) against men. At the same time, it is suggested that it could be replaced by the concept of ‘sexist offsetting’. (shrink)

Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be fruitfully applied in the (...) evaluation of major foundational approaches by a careful examination of two case studies: a partial realization of Hilbert’s program due to Simpson [1988], and predicativism in the extended form due to Feferman and Schütte. -/- Shore [2010, 2013] proposes that equivalences in reverse mathematics be proved in the same way as inequivalences, namely by considering only omega-models of the systems in question. Shore refers to this approach as computational reverse mathematics. This paper shows that despite some attractive features, computational reverse mathematics is inappropriate for foundational analysis, for two major reasons. Firstly, the computable entailment relation employed in computational reverse mathematics does not preserve justification for the foundational programs above. Secondly, computable entailment is a Pi-1-1 complete relation, and hence employing it commits one to theoretical resources which outstrip those available within any foundational approach that is proof-theoretically weaker than Pi-1-1-CA0. (shrink)

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$ sentence of a certain form is provable using E-HA ${}^\omega$ along with the axiom of choice and an independence of premise principle, the sequential form of the statement is provable in the classical system RCA. We obtain this and similar results using applications of modified realizability and the Dialectica interpretation. (...) These results allow us to use techniques of classical reverse mathematics to demonstrate the unprovability of several mathematical principles in subsystems of constructive analysis. (shrink)

The Jordan decomposition theorem states that every function $f \colon \, [0,1] \to \mathbb {R}$ of bounded variation can be written as the difference of two non-decreasing functions. Combining this fact with a result of Lebesgue, every function of bounded variation is differentiable almost everywhere in the sense of Lebesgue measure. We analyze the strength of these theorems in the setting of reverse mathematics. Over $\mathsf {RCA}_{0}$, a stronger version of Jordan’s result where all functions are continuous is equivalent to (...) $\mathsf {ACA}_0$, while the version stated is equivalent to ${\textsf {WKL}}_{0}$. The result that every function on $[0,1]$ of bounded variation is almost everywhere differentiable is equivalent to ${\textsf {WWKL}}_{0}$. To state this equivalence in a meaningful way, we develop a theory of Martin–Löf randomness over $\mathsf {RCA}_0$. (shrink)

Perceptual learning can be defined as practice-induced improvement in the ability to perform specific perceptual tasks. We previously proposed the Reverse Hierarchy Theory as a unifying concept that links behavioral findings of visual learning with physiological and anatomical data. Essentially, it asserts that learning is a top-down guided process, which begins at high-level areas of the visual system, and when these do not suffice, progresses backwards to the input levels, which have a better signal-to-noise ratio. This simple concept has proved (...) powerful in explaining a broad range of findings, including seemingly contradicting data. We now extend this concept to describe the dynamics of skill acquisition and interpret recent behavioral and electrophysiological findings. (shrink)

This article compares the growth trajectories of Catholicism and Protestantism in modern China and tackles a puzzle: Why did Catholicism, which maintained a substantial numerical advantage in Chinese converts over Protestantism before 1949, come to lag so far behind Protestantism today? The article identifies three crucial differences in the institutional features of Catholicism and Protestantism, but shows that an institutional argument alone is insufficient to explain their reversal of fortune. It argues that the growth trajectories of Catholicism and Protestantism changed (...) less because their institutional features have experienced major changes, but more because their institutional features played out differently in the sociopolitical contexts of pre-1949 China, Maoist China, and post-Mao China. The article advances a new approach that combines the currently dominant institutional argument with a historical perspective that stresses the importance of political forces in order to understand the growth dynamics of religions. It concludes by making some preliminary observations on the generalized patterns of how institutional features of Catholicism and Protestantism play out under different kinds of political structures, shaping their waxing and waning in a global context. (shrink)

We investigate the reverse-mathematical status of several theorems to the effect that the natural number system is second-order categorical. One of our results is as follows. Define a system to be a triple A,i,f such that A is a set and i∈A and f:A→A. A subset X⊆A is said to be inductive if i∈X and ∀a ∈X). The system A,i,f is said to be inductive if the only inductive subset of A is A itself. Define a Peano system to be (...) an inductive system such that f is one-to-one and i∉the range of f. The standard example of a Peano system is N,0,S where N={0,1,2,…,n,…}=the set of natural numbers and S:N→N is given by S=n+1 for all n∈N. Consider the statement that all Peano systems are isomorphic to N,0,S. We prove that this statement is logically equivalent to WKL0 over RCA0⁎ source. From this and similar equivalences we draw some foundational/philosophical consequences. (shrink)

This article deals with the question of what time reversal means. It begins with a presentation of the standard account of time reversal, with plenty of examples, followed by a popular non-standard account. I argue that, in spite of recent commentary to the contrary, the standard approach to the meaning of time reversal is the only one that is philosophically and physically viable. The article concludes with a few open research problems about time reversal.

Dynamical collapse models embody the idea of a physical collapse of the wave function in a mathematically well-defined way. They involve modifications to the standard rules of quantum theory in order to describe collapse as a physical process. This appears to introduce a time reversal asymmetry into the dynamics since the state at any given time depends on collapses in the past but not in the future. Here we challenge this conclusion by demonstrating that, subject to specified model constraints, collapse (...) models can be given a structurally time symmetric formulation in which the collapse events are the primitive objects of the theory. Three different examples of time asymmetries associated with collapse models are then examined and in each case it is shown that the same dynamical rule determining the collapse events works in both the forward and backward in time directions. Any physically observed time asymmetries that arise in such models are due to the asymmetric imposition of initial or final time boundary conditions, rather than from an inherent asymmetry in the dynamical law. This is the standard explanation of time asymmetric behaviour resulting from time symmetric laws. (shrink)

In the last decade, experimental philosophers have documented systematic asymmetries in the attributions of mental attitudes to agents who produce different types of side effects. We argue that this effect is driven not simply by the violation of a norm, but by salient-norm violation. As evidence for this hypothesis, we present two new studies in which two conflicting norms are present, and one or both of them is raised to salience. Expanding one’s view to these additional cases presents, we argue, (...) a fuller conception of the side-effect effect, which can be reversed by reversing which norm is salient. (shrink)

Reverse inference in cognitive neuropsychology has been characterized as inference to ‘psychological processes’ from ‘patterns of activation’ revealed by functional magnetic resonance or other scanning techniques. Several arguments have been provided against the possibility. Focusing on Machery’s presentation, we attempt to clarify the issues, rebut the impossibility arguments, and propose and illustrate a strategy for reverse inference. 1 The Problem of Reverse Inference in Cognitive Neuropsychology2 The Arguments2.1 The anti-Bayesian argument3 Patterns of Activation4 Reverse Inference Practiced5 Seek and Ye Shall (...) Find, Maybe6 Conclusion. (shrink)

In Manipulated Agents: A Window to Moral Responsibility, Alfred Mele invokes radical reversal cases in which one agent is covertly manipulated to be just like another agent in relevant respects to defend a version of the following “externalist” thesis: how agents acquire their springs of action, such as desires and beliefs, bears on whether they are morally responsible for their actions. I assess proposed rationales for the crucial verdict that agents in such cases are not responsible for their germane actions. (...) I argue for the superiority of Mele’s rationale and propose that these cases also support accepting an externalist constraint on other normative appraisals, such as those of practical rationality. Key words: Moral obligation; practical rationality; radical reversal cases; ultimate origination; zygote argument. (shrink)

Daniel C. Dennett ha dedicado una parte considerable de su obra a concebir una aplicación de la ingeniería inversa y el adaptacionismo para explicar la evolución de la mente humana. Dennet considera esta perspectiva como una posibilidad prometedora en el desarrollo de una psicología científica, en contraposición al "materialismo eliminacionista" de la neurociencia. En este artículo se expone una aproximación conceptual y se examina un antecedente filosófico en las discusiones sobre el adaptacionismo en biología y psicología evolutiva: la intencionalidad o (...) teoría de los sistemas intencionales. Daniel C. Dennett has dedicated a great part of his work to the conception of an application of reverse engineering and adaptationism in order to explain the evolution of the human mind. Dennett sees this perspective as a promising possibility in the development of a scientific psychology, in contrast to the "eliminative materialism" of neuroscience. The article provides a conceptual approach and examines a philosophical precedent in the discussions regarding adaptationism in biology and evolutionary psychology: intentionality or the theory of intentional systems. Daniel C. Dennett dedicou uma parte considerável de sua obra a conceber uma aplicação da engenharia inversa e do adaptacionismo para explicar a evolução da mente humana. Dennett considera essa perspectiva como uma possibilidade prometedora no desenvolvimento de uma psicologia científica, em contraposição ao "materialismo eliminacionista" da neurociência. Neste artigo, expõe-se uma aproximação conceitual e examina-se um antecedente filosófico nas discussões sobre o adaptacionismo em biologia e psicologia evolutiva: a intencionalidade ou teoria dos sistemas intencionais. (shrink)

A series of experiments are described on self-reversal of magnetization in a rock containing pyrrhotite. This self-reversal was produced by heat-treatment at about 320°c. Two unusual effects were observed. First, in suitable conditions the direction of magnetization could be made to change sign twice on cooling. Second, after appropriate heat-treatment the reversal mechanism became obliterated; leaving the specimen self-reversed, but containing only a single magnetic material. The second effect is of considerable interest for palaeomagnetism.

Wigner time reversal implemented by antiunitary transformations on the wavefunctions is to be refined if we are to deal with systems with internal symmetry. The necessary refinements are formulated. Application to a number of physical problems is made with some unexpected revelations about some popular models.

ArgumentAn unusual compass, on which east and west are reversed, provides insight into the dynamics guiding our understanding of artifacts. By examining how such compasses were used in Tokugawa Japan (1600–1868), the benefits they brought, and how users knew how to read them, this article uncovers the cognitive factors that shape our interaction with technology. Building on the methodological approach of thedistributed cognitiontheory, the article claims that reverse compasses allowed the user to conserve cognitive effort, which was particularly advantageous to (...) Tokugawa-period mariners. Moreover, the article shows that even non-professional Tokugawa Japanese had a relatively easy time reading reverse compasses due to similarity between the compasses’ orientation and Tokugawa timekeeping practices. Building on the bodily and cognitive habits they had developed through the practices of keeping time, users could identify and interpret cultural cues embedded in the structure of reverse compasses. (shrink)

In terms of temporality of logic, the relation between "before" and "after" is an inverse relation, as is the relation between intension and extension. Reversal of temporality of human cognition is accompanied by corresponding reversal between intension and extension. Such reversal is based on lateral reversal of brain hemisphere locus of time information. A similar inverse relation exists between self as subject and self as object. Extreme objectification of self is associated with brain hemisphere lateral reversal of time information, indicating (...) that subject-object reversal is similar in nature to reversal of temporality of cognition. Dialectical nature of self is based on contradiction between self as subject and self as object. Synthesis arising from such contradiction may be regarded as reality of self. (shrink)

Recent events have put the acceptability of the risks of nuclear energy production technologies under the spotlight. A focus on risks, however, could lead to the neglect of other aspects of NEPT, such as their irreversibility. I argue that awareness of the socio-historical development of NEPT is helpful for understanding their irreversibility. To this end, I conceptualize NEPT development as a process of structuration in which material, institutional and discursive elements are produced and/or reproduced by purposive social actors. This conceptualization (...) is used to structure an analysis of how irreversibility arose in the first decades of NEPT development in India, France and the USA, and how some NEPT have been reversed or partially reversed. Lastly, two general conditions for reversible NEPT are formulated based on this analysis. (shrink)

_Gale_ Academic OneFile includes Reversing globalization: what Gandhi can teach us by Vandana Shiva. Click to explore.

Standard descriptions of thermodynamically reversible processes attribute contradictory properties to them: they are in equilibrium yet still change their state. Or they are comprised of non-equilibrium states that are so close to equilibrium that the difference does not matter. One cannot have states that both change and no not change at the same time. In place of this internally contradictory characterization, the term “thermodynamically reversible process” is here construed as a label for a set of real processes of change involving (...) only non-equilibrium states. The properties usually attributed to a thermodynamically reversible process are recovered as the limiting properties of this set. No single process, that is, no system undergoing change, equilibrium or otherwise, carries those limiting properties. The paper concludes with an historical survey of characterizations of thermodynamically reversible processes and a critical analysis of their shortcomings. (shrink)

This article investigates the Neo-Confucian project of “reverse moral economy,” which aims to restore the ideal congruence between political power and moral virtue, by examining a political debate on the selection of the new Crown Prince and the incumbent ruler’s subsequent abdication that took place in Korea during the formative period of the Chosŏn 朝鮮 dynasty in light of the so-called “the Mencian trouble,” a compromise between Mencius’ ideal vision of Confucian virtue politics and his realistic concern with political stability. (...) After discussing how Korean Neo-Confucians were able to justify their choice of a more virtuous candidate in violation of the Lineage Law, which upheld father-son transmission as the constant norm, by judiciously balancing between the candidate’s virtue and the incumbent ruler’s recommendation, it articulates the Korean Neo-Confucian project of reverse moral economy from the standpoint of the constitutionality of the new dynasty. (shrink)

Many have suggested that the transformation standardly referred to as `time reversal' in quantum theory is not deserving of the name. I argue on the contrary that the standard definition is perfectly appropriate, and is indeed forced by basic considerations about the nature of time in the quantum formalism.

The phenomenon of disagreement has recently been brought into focus by the debate between contextualists and relativist invariantists about epistemic expressions such as ‘might’, ‘probably’, indicative conditionals, and the deontic ‘ought’. Against the orthodox contextualist view, it has been argued that an invariantist account can better explain apparent disagreements across contexts by appeal to the incompatibility of the propositions expressed in those contexts. This paper introduces an important and underappreciated phenomenon associated with epistemic expressions — a phenomenon that we call (...) reversibility. We argue that the invariantist account of disagreement is incompatible with reversibility, and we go on to show that reversible sentences cast doubt on the putative data about disagreement, even without assuming invariantism. Our argument therefore undermines much of the motivation for invariantism, and provides a new source for constraints on the proper explanation of purported data about disagreement. (shrink)

A broad evolutionary perspective is essential to fully reverse figure and ground in the rationality debate. Humans' evolved psychological architecture was designed to produce inferences that were adaptive, not normatively logical. This perspective points to several predictable sources of errors in modern laboratory reasoning tasks, including inherent, systematic biases in information-processing systems explained by Error Management Theory.

The AGM (Alchourrón-Gärdenfors-Makinson) model of belief change is extended to cover changes on sets of beliefs that are not closed under logical consequence (belief bases). Three major types of change operations, namely contraction, internal revision, and external revision are axiomatically characterized, and their interrelations are studied. In external revision, the Levi identity is reversed in the sense that one first adds the new belief to the belief base, and afterwards contracts its negation. It is argued that external revision represents an (...) intuitively plausible way of revising one's beliefs. Since it typically involves the temporary acceptance of an inconsistent set of beliefs, it can only be used in belief representations that distinguish between different inconsistent sets of belief. (shrink)

The extraordinary parallel between the psychological theory of reversals (Apter, 1982) and the anthropological theory of anti-structure (Turner, 1982)-- both derived independently and almost simultaneously from entirely different kinds of evidence and research-- would seem to point to something profound and universal in human experience which has been curiously neglected in the behavioural sciences and entirely ignored in consciousness studies. What I will do here is to introduce reversal theory, show how it applies to ritual, and then compare it with (...) Victor Turner's well-known approach to the very same topic. Reversal theory has in fact been used to elucidate many diverse social phenomena, for example criminal violence, military combat, sexual behaviour, family relationships, soccer hooliganism, organizational culture, leadership, team sports, social advocacy and classroom management (see review in Apter, 2001a). The present paper extends these ideas to ritual for the first time, and makes reference especially to the work of Turner and his idea of cultural inversions (Turner, 1969). Reversal theory is also about inversions, but the inversions in this case (i.e. reversals) occur at the level of individual psychology and are identified initially as experiential rather than behavioural or social. This paper will explore the relationship between these two kinds of reversal, psychological and anthropological. (shrink)

Modal ontological arguments argue from the possible existence of a perfect being to the actual (necessary) existence of a perfect being. But modal ontological arguments have a problem of symmetry; they can be run in both directions. Reverse ontological arguments argue from the possible nonexistence of a perfect being to the actual (necessary) nonexistence of a perfect being. Some familiar points about the necessary a posteriori, however, show that the symmetry can be broken in favour of the ontological argument.