In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets (...) of higher-order values. This method is based on the concept of a multilattice. If the method is applied to the set of truth values of Belnap's “useful four-valued logic”, one obtains a trilattice, and, more generally, structures here called Belnap-trilattices. As in Priest's case, it is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic. Whereas Priest's construction in terms of designated truth values always results in his Logic of Paradox, the present construction in terms of truth and falsity orderings always results in First Degree Entailment. However, it is observed that applying the multilattice-approach to Priest's initial set of truth values leads to an interesting algebraic structure of a “bi-and-a-half” lattice which determines seven-valued logics different from Priest's Logic of Paradox. (shrink)

As a unique method of philosophical argument, performative contradiction attracted general attention after the change in direction of pragmatics in the twentieth century. Hintikka used this method to conduct an in-depth analysis of Descartes’ proposition “I think, therefore I am,” providing a proof which is a model in the philosophical history; Apel absorbed performative contradiction into his own framework of a priori pragmatics; and Habermas introduced it into the theory of formal pragmatics and rendered it an effective weapon of (...) debate. Wittgenstein, who had fallen into the trap of performative contradiction in Tractatus Logico-Philosophicus, later managed to extract himself from it and indeed used the methodology of performative contradiction to cure the ills of philosophy, making it a general philosophical method. Through analysis of its connotations and classic examples of its use we can see that it is crucial in refuting extreme relativism and skepticism, and hence provides methodological support for a new foundation for philosophical paradigms. (shrink)

Kant’s most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the 'universalizability' of one's maxims and described in terms of the distinction between 'contradictions in conception' and 'contradictions in the will'. Focusing on the underappreciated significance of the simultaneity condition included in the (...) FUL, I argue, by contrast, that the principle is better read as requiring that one be able to will two things simultaneously without self-contradiction, namely, that a maxim be one's own and that it be a universal law. This amounts to a new interpretation of the FUL with significant interpretive and philosophical advantages. (shrink)

This project explores the "contradiction" that critics contend lies at the heart of the Supreme Court's capital sentencing jurisprudence. The doctrine of "guided discretion," represents the Court's attempt to achieve both consistency and individuation in capital sentencing. Guided discretion rejects the unbridled sentencing discretion of an earlier era that resulted in sentencing decisions that were "arbitrary and capricious." At the same time, guided discretion requires juries to give individualized consideration to the facts and circumstances of individual defendants. Critics contend that (...) consistency and individuation are mutually exclusive, and that "guided discretion" is a contradiction in terms. ;The analysis first attempts to isolate the moral dimension of the capital punishment debate, arguing that such analytical clarity is essential to any defensible view of capital punishment. Second, it sets forth and defends the coherence approach to moral and legal justification, according to which the specific moral and legal principles relevant to capital sentencing are evaluated for their compatibility with the principles of the legal system more generally. Third, the analysis canvasses the traditional justifications for punishment, as well as the development of the Court's capital sentencing jurisprudence, and identifies retribution and deterrence as the most promising rationales for the death penalty. Fourth, the claim of contradiction is considered in the context of legal liberalism, which, contrary to critics, has ample resources to accommodate the doctrinal balancing act that guided discretion entails. Moreover, examination of a typical capital sentencing statute establishes that the doctrine of guided discretion is compatible with at least some forms of retributivism and with traditional principles of deterrence. Finally, the analysis recognizes the limits of philosophical consistency. The capital sentencing process presents daunting practical challenges that a theoretical defense of guided discretion cannot fully address. Substantial reforms are needed before the theoretical coherence of guided discretion can be translated into a constitutionally defensible capital sentencing process. (shrink)

This paper explores the concept of digital modernity, the extension of narratives of modernity with the special affordances of digital networked technology. Digital modernity produces a new narrative which can be taken in many ways: to be descriptive of reality; a teleological account of an inexorable process; or a normative account of an ideal sociotechnical state. However, it is understood that narratives of digital modernity help shape reality via commercial and political decision-makers, and examples are given from the politics and (...) society of the United Kingdom. The paper argues that digital modernity has two dimensions, of progression through time and progression through space, and these two dimensions can be in contradiction. Contradictions can also be found between ideas of digital modernity and modernity itself, and also between digital modernity and some of the basic pre-modern concepts that underlie the whole technology industry. Therefore, digital modernity may not be a sustainable goal for technology development. (shrink)

Modern trends in social development are defined not only as an information society, but increasingly as a knowledge society. To understand its content and strategy of implementation, an important aspect is to understand the contradictions that are increasingly manifested and are of a general socioanthropological nature. In particular, this is the problem of the correlation between a knowledge society and objective scientific knowledge; this is the question of the correlation between the available knowledge and experience reflected in the (...) cultural tradition and the rapidly changing information flow; this is the question of the social role of education and the social status of an educated person, as well as the problem of human self-determination in the context of situational relations and a configurative society, etc.The widespread mythologeme of a knowledge society as a society of intellectuals supports a rather one-sided view of it. Therefore, understanding the paradoxical combination of elements of a knowledge society system, their contradictions, and complementarities, makes it possible to understand the risks and develop tools to avoid them. The research methodology. The study is based on an interdisciplinary and comprehensive analysis of contemporary socio-cultural processes in the context of the formation of a knowledge society and information pedagogy. Research results: The interpretation of modern society as a knowledge society raises a number of theoretical questions and discussions concerning the definition of knowledge (scientific/non-scientific, useful/unsuitable, etc.), and the definition of its social and anthropological characteristics and human status (educated person, informed person, professional person, successful person). The challenges of the processes of informatization of society lead to the formation of «e-didactics» and «information pedagogy» of a new educational paradigm, the effectiveness of which should resolve a number of contradictions. These include, in particular, the discrepancy between learning tools (openness and mobility) and reproductive learning models; between distance asynchronous learning and the classical stability of the structure and forms of organization of the educational process, etc. Discussions. The analysis of knowledge as the fundamental basis of the new social reality and changes in its historical status allows us to identify problematic issues of the worldview picture of the world that is formed in the conditions of intensive production of information and a certain devaluation of knowledge, actualization of innovations, and devaluation of cultural tradition. The knowledge society is often characterized as an education society. Although such a generalization is debatable, educational technologies of knowledge production and transmission are an important component of the development of a knowledge society and include the destruction of stereotypes and attitudes of the industrial society’s education paradigm. This explains why interdisciplinary discussions about the content and forms of organization of modern education are becoming increasingly acute. The problem of rethinking the established models of teacherstudent relations and the requirements for the subjects of the educational process is important among the many aspects of changes. A student is transformed from an object of pedagogical influence into a subject of the educational process, where a teacher plays the role of a mentor, a tutor, since knowledge must be «extracted» by a student because of his or her own intellectual efforts and cognitive search.The change in social role also includes a change in worldview, way of thinking, and value priorities. Conclusion. The analysis of the socio-cultural mechanisms and practices of the knowledge society reveals its ambivalence and risks, which are its inherent characteristics. Knowledge as the fundamental basis of the new social reality is defined not only as a tool for understanding the world but also as a factor of civilizational development that produces new forms of activity and relationships, new worldview orientations, and value priorities. The transformation of the phenomenon of knowledge and the rapidity of the information flow raises the question of the relevance of existing knowledge and experience to the needs of a given situation, thus actualizing the demand not for the depth of knowledge and understanding, but for the ability to combine and choose a practical (useful) option, to put together puzzles and mosaics, forming a clip thinking. Challenges of the processes of society informatization lead to the formation of “e-didactics”, information pedagogy as a tool for adaptation and a new educational paradigm, the effectiveness of which should resolve the identified contradictions.However, the transformation of modern educational practices involves not only rethinking their content, technologies, and teaching methods, changing the status relations of the subjects of the educational process, but also a general change in models of thinking and personal behavior, and a change in the human world. The correlation of the modes of human definition: educated, intellectual, erudite, and specialist becomes an important issue of the anthropological dimension of the knowledge society, where the problem of human self-determination is becoming more acute. (shrink)

Proper interpretation of the problem of contradiction in motion has acquired pressing importance in recent years in conjunction with the development of dialectical materialist concepts of motion, space and time, continuity and discontinuity, infinity, and the like, and also in relations to problems of dialectical logic. In a number of writings , we have attempted to demonstrate that internal contradiction is inherent in motion that inseparably connected with it are such contradictory factors as variability and stability, movement and rest, with (...) variability playing the leading role. Moreover, generally speaking, the concept of preservation, stability or rest means the preservation or maintenance of the very state of motion. (shrink)

What happens when well-defined disciplines meet or are confronted with transdisciplinary discourses and concepts, where transdisciplinary concepts are analytical tools rather than specifications of a field of objects or a class of entities? Or, if disciplines reject transdisciplinary discourses and concepts as having no part to play in their practice, why do they so reject them? This essay addresses these questions through a discussion of the relationship between philosophy – the most tightly policed discipline in the humanities – and what (...) I will argue is the emblematically transdisciplinary practice of feminist theory, via a discussion of interdisciplinarity and related terms in gender studies. It argues that the tendency of philosophy to reject feminist theory in fact correctly intuited that the two defining features of feminist theory – its constitutive tie to a political agenda for social change and the transdisciplinary character of many of its central concepts – are indeed at odds with, and pose a threat to, the traditional insularity of the discipline of philosophy. It argues, further, that feminist theory operates with what we should now recognise as a set of transdisciplinary concepts – including, sex, gender, woman, sexuality and sexual difference – and that the use of these concepts in feminist philosophy has been the most far-reaching continuation in the late 20th/early 21st centuries of the critique of philosophy initiated by Marx and pursued by ‘critical theory’. This puts feminist philosophy in a difficult position: its transdisciplinary aspects open it up to an unavoidable contradiction. Nonetheless, this is a contradiction that can and must be endured and made productive. In order to draw out the specificity of the concept of transdisciplinarity at issue the essay begins with a discussion of attempts to define inter- and transdisciplinarity, particularly in gender studies. Arguing for the transdisciplinary origin of the concept of gender, it then suggests one way of understanding its function as a critical concept, before making explicit how this leads to the historical antagonism between traditional philosophy and the critical, transdisciplinary concept of gender and with feminist theory more generally. (shrink)

The problem considered in the article that follows has a long and complicated history. The many different solutions proposed reflect the process of development, deepening, and broadening of knowledge as a whole. They correspond to particular levels of knowledge, determining the character of thought both of the times and of particular individuals. Specifically, it is the understanding of the essence of contradiction that governs the entire theoretical exposition that follows, its substance and approximation to truth. Here we shall consider for (...) analysis only one aspect of this fundamental theme — dialectical contradiction in the evolution of knowledge. Thus, for the most part the discussion will be of the laws of thought; only when necessary will we turn to analysis of contradictions in the objective world. It is quite understandable that the process of thought should occur according to the same, more general laws that are operative in the objective world; nevertheless, the manifestation of these laws has its own special features. Therefore, the questions posed by philosophers of antiquity concerning the degree to which reality itself corresponds to the understanding thereof in terms of the exactness, comprehensiveness, and depth of reflection of the objective world by a subject have not lost their timeliness. Such questions include those associated with the phenomenon of contradiction. For example, is contradiction in thought adequate to the contradictions among things ? How does contradiction in thought take shape, and what are its forms and structures? Is the relationship between opposites always a contradiction? Is it possible to solve antinomies, and so forth? An extensive literature has been published on these subjects. There is hardly a philosopher who can avoid them and not express his attitude toward them. As it is impossible, within the confines of an article, to adduce a full list of published works on contradictions, the authors, with an eye to what has been achieved in this sphere, also regard it as undesirable to analyze the diversity of points of view, and will confine themselves to presenting their own understanding of the problem under consideration. (shrink)

A common and much-explored thought is Łukasiewicz's idea that the future is ‘indeterminate’—i.e., ‘gappy’ with respect to some claims—and that such indeterminacy bleeds back into the present in the form of gappy ‘future contingent’ claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future—one which is ‘glutty’ with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simply to sketch (...) and briefly explore an alternative glutty-future view, one that is conservative—indeed, entirely classical—with respect to the present. The structure of the paper runs as follows. §1 briefly sketches the target gap picture of an indeterminate future yielding gappy claims at the present. §2 presents the direct dual idea—a glut picture of an overdeterminate future yielding glutty claims at present. §3 sketches the central idea, a more interesting glut picture in which the future contains contradictory states but the present remains entirely classical. §4 contains a general defence of the idea, leaving it open as to whether the gappy-future view enjoys substantive virtues over the proposed glutty-future view of §3. (shrink)

The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in the world. For (...) example, there are certain constraints as to what kind of properties an object can have, and especially: some of these properties are mutually exclusive. Given this characterisation, I will advance to examine what kind of challenges the law of non-contradiction faces; the main opponent here is Graham Priest. I will consider these challenges and conclude that they do not threaten the truth of the law of non-contradiction understood as a metaphysical principle. (shrink)

I argue that there is nothing about the structure of inference to the best explanation (IBE) that prevents it from establishing a contradiction in general, though there are some potential limitations on when it can be used for this purpose. Studying the relationship between IBE and contradictions is worthwhile for three reasons. First, it enhances our understanding of IBE. We see that, in many cases, IBE does not require explanations to be consistent, though there are some cases where (...) consistency may be required. Second, the argument has implications for the debate over scientific realism. Many scientific theories appear to be inconsistent. The best argument for scientific realism, however, appeals to IBE. My argument thus shows that a certain kind of realist faces a threat from inconsistent theories. Third, the argument is important for dialetheism. Dialetheists maintain that some contradictions are true. Many of the arguments in favour of dialetheism appeal to explanatory considerations. What I say here provides support for defending dialethism using an IBE-based methodology. (shrink)

Epistemic contradictions are now a well-known and often discussed phenomenon among those who study epistemic modals. These contradictions are expressed by sentences like ‘It is raining and it might not be raining’ whose oddness to the common ear demands an explanation. However, it has turned out to be a rather controversial enterprise to provide such an explanation in a sufficiently precise and general manner. According to pragmatic explanations, epistemic contradictions are semantically consistent but pragmatically defective. According (...) to semantic explanations, one should regard epistemic contradictions as plain semantic inconsistencies. Endorsing such a semantic solution is, however, tantamount to rejecting classical logic, which predicts the consistency of epistemic contradictions. After arguing that all existing solutions to this problem face as yet unmet challenges, I will present a new solution that adequately overcomes these challenges. I will propose to view epistemic contradictions as semantically consistent but epistemically defective sentences. The main thesis emerging will be that we need neither abandon the inference rules of classical logic nor the classical truth-conditional approach to semantics to deal adequately with epistemic contradictions. (shrink)

Towards the end of Analysis, Knowledge, and Valuation, C. I. Lewis remarks that when a Cyrenaic espouses his philosophy of life, “Have no concern for the future,” he contradicts himself. Lewis hastens to add that the contradiction is not formal but “pragmatic.”.

In In Contradiction, Graham Priest shows, as clearly as anything like this can be shown, that it is coherent to maintain that some sentences can be both true and false at the same time. As a consequence, some contradictions are true, and an appreciation of this possibility advances our understanding of the nature of logic and language.

Philanthropy is typically hierarchically constructed with an imbalance of power between funders and grantees. While this seems inherent in philanthropic relationships where funders inevitably control resources that grantees need, some women’s funds have sought to construct less hierarchical and thus more feminist relationships with the organizations they support. Based on many years of insider access to a local women’s fund, this article describes and explains the organization’s efforts to develop interactive dialogues with its grantees, which led to a change in (...) grants guidelines that were more inclusive of women’s methods of community organizing. A small survey of women’s community groups, done as background to this research, provides data on challenges and obstacles these groups face when seeking monies to support their work. Some attention is given to implications for general theories of organizations, for funder-grantee dialogues leading to increased accountability in philanthropy, and for support of women’s community organizations. (shrink)

IN THE FOURTH AND FINAL SECTION of Maimonides’s preface to his Guide of the Perplexed, in the section labeled “Introduction”, the author lists seven “causes... for the contradictory or contrary statements in any book or composition.” The best known and most significant of these is the seventh cause. Its subject, according to most classical and modern interpreters of the Guide, is intentional contradictions the purpose of which is to hide the author’s true opinion from the multitude. Maimonides tells us (...) that contradictions of the seventh type are to be found in the Guide, and in fact he delivers on that promise: in many topics touched upon in that work, we find contradictory statements that give the reader a sense of entrapment and prevent him not only from understanding the issue at hand but also from being able to grasp related matters as well. (shrink)

Chapter VI discusses a few assumptions which underlie the proposed reconstruction of Hegel's procedures. It is shown that certain equivalents of such assumptions are either explicitly accepted by Hegel, or they are consequences of theses he subscribed to. Finally, it is suggested that some of these assumptions envisage a conception of language and philosophy which has an interesting parallel in Wittgenstein's later work. Such a conception sets philosophy sharply apart from the sciences, and deemphasizes the formation of contradictions. The (...) general relationship between vagueness and contradiction is briefly explored to show that some familiar contradiction-generating procedures can be seen to be based on vagueness of the relevant theoretical expressions. ;Chapter V deals with the Aufhebung. After an examination of Hegel's own theory of sublation, and an analysis of some textual examples, it is shown that some Aufhebung-procedures can be modelled by certain patterns of argument concerning simple algebraic structures. A few Hegelian concepts, such as "opposition," "unity," "passing over," "reflection," are partially explicated in the process. ;Chapter IV plays a pivotal role in the dissertation. It explains the generation of dialectical contradictions as stemming from syntactic and intensional indeterminacy of the theoretical terms. It is shown that Hegel's conceptual terms have no well-determined sense, so that their senses can be identified in different and possibly inconsistent ways. It is also shown that they can be made to play different syntactic roles, for no rigid determination of their syntactic function is assumed. This, again, may create contradictions. Both kinds of indeterminacy are related to Hegel's borrowing of his conceptual terms from a "natural" philosophical koine. ;Chapter III is an analysis of Hegel's language in the Logic. It tries to determine the grammatical and semantical status of Hegel's conceptual terms and to explicate the Hegelian use of the copula as occurring in certain typical sentential forms. ;The presence of the so-called "dialectical contradictions" is the most evident logico-linguistic peculiarity of Hegel's text. After a discussion of Hegel's theory of contradiction, and of some of its interpretations, it is argued that any satisfactory account of the dialectical method must explain the formation of contradictions on the basis of other logico-linguistic features of Hegel's text. ;Chapter II deals with a few such explanations which have been offered by modern interpreters of Hegel. Use of contemporary analytic concepts in the logical and linguistic analysis of Hegel's text is justified with reference to the Carnapian categories of "explication" and "rational reconstruction." ;The literature on Hegel's dialectic has made important contributions to an understanding of its nature both as a metaphysical theory of reality and as a philosophical attitude towards the human world. However, many recent interpreters agree that no satisfactory progress has been made in understanding dialectic as a method. This dissertation identifies the dialectical method as the specific form of Hegel's philosophical discourse, and tries to bring out its basic logico-linguistic features. The Science of Logic is chosen as the field of inquiry, because of its crucial position among Hegel's mature works. (shrink)

I discuss the problem of whether true contradictions of the form “x is P and not P” might be the expression of an implicit relativization to distinct respects of application of one and the same predicate P. Priest rightly claims that one should not mistake true contradictions for an expression of lexical ambiguity. However, he primarily targets cases of homophony for which lexical meanings do not overlap. There exist more subtle forms of equivocation, such as the relation of (...) privative opposition singled out by Zwicky and Sadock in their study of ambiguity. I argue that this relation, which is basically a relation of general to more specific, underlies the logical form of true contradictions. The generalization appears to be that all true contradictions really mean “x is P in some respects/to some extent, but not in all respects/not to all extent”. I relate this to the strict-tolerant account of vague predicates and outline a variant of the account to cover one-dimensional and multidimensional predicates. (shrink)

I articulate a classical-Marxist theory of technical change in the capitalist labour process, highlighting two contradictions. The management contradiction is the conflict managers experience between coordination (to increase efficiency) and discipline (to ensure valorisation). The workforce contradiction is the tension workers experience between productive socialisation and alienation. I submit that both contradictions were substantially muted from the earliest stages of capitalism through the Fordist stage but have become intensified in the postfordist period. Under postfordism, the basis of efficiency (...) is economies of scope and flexibility, and thus there is a real efficiency advantage to empowering workers, via both multiskilling and employee involvement in problem-solving and decision-making. Postfordist capitalism has thus initiated an intensification of the management and workforce contradictions. In response, capitalist management is increasingly impeding the growth of the productive forces by failing to empower workers. (shrink)

How can we reconcile two claims that are now both widely accepted: Kretschmann's claim that a requirement of general covariance is physically vacuous and the standard view that the general covariance of general relativity expresses the physically important diffeomorphism gauge freedom of general relativity? I urge that both claims can be held without contradiction if we attend to the context in which each is made.

We provide a number of simplified and improved separations between pairs of Resolution-with-bounded-conjunction refutation systems, Res, as well as their tree-like versions, Res⁎. The contradictions we use are natural combinatorial principles: the Least number principle, LNPn and an ordered variant thereof, the Induction principle, IPn.LNPn is known to be easy for Resolution. We prove that its relativization is hard for Resolution, and more generally, the relativization of LNPn iterated d times provides a separation between Res and Res. We prove (...) the same result for the iterated relativization of IPn, where the tree-like variant Res⁎ is considered instead of Res.We go on to provide separations between the parameterized versions of Res and Res. Here we are able again to use the relativization of the LNPn, but the classical proof breaks down and we are forced to use an alternative. Finally, we separate the parameterized versions of Res⁎ and Res⁎. Here, the relativization of IPn will not work as it is, and so we make a vectorizing amendment to it in order to address this shortcoming. (shrink)

In Metaphysics Γ, Aristotle argues against those who seem to accept contradictions. He distinguishes between the Sophists, who deny the principle of non-contradiction through arguments, and the Natural Philosophers, whose physical investigations lead to the acceptance of objective contradictions. Heraclitus’ name appears throughout the discussion. Usually, he is associated with the discussion against the Sophists. In this paper, I explore how the discussion with the Natural Philosophers may illuminate both the interpretation of Heraclitus by Aristotle and Heraclitus’ own (...) worldview. To refute the Natural Philosophers, Aristotle proposes a general reconstruction of their reasoning. Roughly, relying on sensory evidence (A1), they see that the same thing changes from one opposite to another (A2). Such a change appears to characterize a generation out of non-being, which a Natural Philosopher does not accept (A3). To solve the problem, despite their different worldviews, Natural Philosophers hint at a state in which opposites co-occur, characterizing an objective contradiction (C). Looking at the discussion in Metaphysics Γ and Heraclitus fragments, sections 1–3 show how assumptions A1, A2, and A3 easily apply to Heraclitus. The case of the conclusion is more challenging. In the case of the Pluralists, the co-existence of opposites characterizes a state in which there is no generation. Such a view does not fit Heraclitus’ mobilism. To argue that Aristotle’s argument is general enough to encompass dynamic views, I examine his problematization of accepting the change of change in Metaphysics K and Physics V. There, after re-stating several points that appear in Metaphysics Γ, Aristotle argues that accepting the becoming of another becoming leads to a state of contradiction in which the becoming is perishing. Heraclitus’ B8, cited in Nicomachean Ethics, gives evidence that, for Aristotle, Heraclitus puts a process at the origin of an opposite process. Moreover, after examining the expression ‘living the death/dying the life’ in B62, I argue that Heraclitus was aware that his worldview implied a dynamic objective contradiction. Finally, an analysis of elemental changes in B36 proves that accepting objective contradictions does not make Heraclitus’ worldview less attractive. (shrink)

There have been many discussions on problems of logic over the past several years. While the problem of the nature of the law of contradiction, one of the laws of formal logic, has received particular attention by everyone, the question has not been posed very precisely in the arguments. Actually, the question is not whether the movement, change, and development of things can be reflected in consciousness by use of the methods of formal logic, or in distinguishing the effectiveness of (...) the law of contradiction in disputation, proofs, or theoretical systems from its effectiveness in the general process of cognition, when applied to phenomena. If the development of reality cannot at all be reflected by the use of the logical tools of formal logic, what use do they have? No one denies that formal logic does not suffice as a method of cognition. If, in disputations and proofs, or in the establishment of theoretical systems, one relies only on the logical tools of formal logic, this is also not enough. The scope of applicability of the laws of formal logic, as laws that are studied by a concrete science, is necessarily limited. It is impossible for them to be all-powerful; it is of course impossible, relying on the law of contradiction, to know and grasp the contradictions in reality — the unity and conflict of opposites. All disputations and proofs, and the establishment of theoretical systems, are, in fact, efforts to know real objects, efforts of the subjective to grasp the objective. In principle, the use of formal logic in disputations and proofs and in the establishment of theoretical systems, and its use in knowing an object, should be no different. What, then, is the question? The question should be posed as follows: can thought contravene the law of contradiction? (shrink)

Valentin Asmus made a significant contribution to the formation of key interpretations, analyses and evaluations of Immanuel Kant’s work in the Russian-Soviet tradition of studying the “history of foreign philosophy”. This article shows precisely which principles and developmental models Asmus laid down in his interpretation of the transcendental dialectic section of Kant’s philosophical system. The article attempts to show that in his reading of Kant, Asmus actively relies on Hegel’s philosophical legacy, namely, on his theory of dialectics, the ontological status (...) of contradiction and the highly significant role of “error” in the formation and advancement of knowledge. Asmus reads Kant through the lens of Hegel’s philosophy and adheres to Hegelian philosophy as a benchmark of fidelity and heuristics, as a canon and organon, through which Kant’s thought should be evaluated. Pursuing this path, he notes the significant progress of Kant’s thought compared to the metaphysical philosophy of previous centuries, but points out the insufficiency of Kant’s determination to fully think through contradictions ontologically and dialectically. Kant confines himself to pointing out the natural origin of the principle of “appearance” in the limits of reason, but is not ready to revise the foundations of classical logic, where any contradictions should be avoided. As a consequence, he settles on the epistemological interpretation of contradiction seeing it as an error of reason, albeit a natural one, leaving Asmus deeply disenchanted with his Hegelian expectations. (shrink)

My aim in this note is to shed light on ways of interpreting Kant’s Formula of Universal Law (FUL), by looking at relevant similarities and differences between Pauline Kleingeld and Mark Timmons. I identify both their readings as a formal interpretation of Kant’s FUL, in contrast to the substantive interpretations that favor a robust conception of rational agency as a necessary requirement for moral deliberation. I highlight the benefits that arise from Kleingled’s interpretation in showing the immediacy involved in the (...) volitional self-contradiction when universalizing a maxim. Alongside Timmons, I address a question as to whether Kleingeld’s interpretation is completely free from at least a minimal set of assumptions about practical deliberation more broadly, that seem to play a role in generating the volitational self-contradiction she is defending. I close by raising some skeptical worries about the capacity of this kind of contradiction to translate into a moral judgment triggering action. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Abstract General Ideas in Hume George S. Pappas Hume followed Berkeley in rejecting abstract general ideas; that is, both of these philosophers rejected the view that one could engage in the operation or activity ofabstraction — a kind ofmental separation ofentities that are inseparable in reality —as well as the view that the alleged products of such an activity — ideas which are intrinsically general — (...) really exist. What has not been clear to commentators on either of these two philosophers has been why they each were so opposed to abstraction and abstract general ideas. The provision of an answer to this question is the main thrust of this paper. The nature of the question should be clarified at the outset. I am notasking the psychological question, whatwere BerkeleyandHume's actual intentions when they were moved to reject abstraction and abstract general ideas. Though I regard this question as one of great interest and importance, I am presently aiming to answer a somewhat different one, viz., what role, what philosophical role, does the rejection of abstraction and abstract general ideas play in the philosophies ofBerkeley and Hume? The answer to this latter question is apt to have some bearing on the right way to answer the first question; but, for present purposes, it is important to keep the two questions distinct. The maincontentionofthe paperis thattherejectionofabstraction and abstract general ideas lies at the very heart of the philosophy of Berkeley, and that pretty much the same may be said for Hume. Berkeley's defense ofa kind ofidealism stands or falls with the success ofhis attack on abstract general ideas, and Hume's critique ofinfinite divisibility in matters pertaining to space and time, along with his destructive critique ofvarious metaphysical notions, crucially depends on the successful denial of abstract general ideas. I. Berkeleyan Idealism Berkeley's most extended treatment of abstract ideas comes in the introduction to the Principles ofHuman Knowledge, first published in 1710. However, since he does not take up the topic in any systematic way later in the same book, nor in the Three Dialogues Between Hylas and Phihnous (1713), it has seemed to many commentators that Berkeley's attack on abstract ideas is a local matter, one having only to do with issues concerning language use and a somewhat isolated criticism of Locke. That this is the wrong way to look at things is Volume XV Number 2 339 GEORGE S. PAPPAS perhaps best indicated by a couple of passages from the Principles. In section 5 ofthat work Berkeley says: If we thoroughly examine this tenet it will, perhaps, be found at bottom to depend on the doctrine of abstract ideas. For can there be a nicer strain of abstraction than to distinguish the existence of sensible objects from there being perceived, so as to conceive them existing unperceived? The tenet Berkeley is here referring to is to the effect that sensible objects such as trees and chairs exist independently ofperception. This allusion is made clear when we notice that in the immediately preceding passage Berkeley says: It is indeed an opinion strangely prevailing among men that houses, mountains, rivers, and in a word all sensible objects, have an existence, natural or real, distinct from their being perceived by the understanding. But, with how great an assurance and acquiescence soever this Principle may be entertained... whoever shall find in his heart to call it in question may... perceive it to involve a manifest contradiction. For, what are the aforementioned objects but the things we perceive by sense? and what do we perceive besides our own ideas or sensations? and is it not plainly repugnant that any one of these, or any combination of them, should exist unperceived? (Principles 4) The claim that sensible objects exist independently ofall perception is the very denial of Berkeley's esse is percipi thesis regarding such objects. For the latter thesis holds that each sensible object is such that it exists if and only if it is perceived. So, in the first-quoted passage from Principles 5, Berkeley is saying that the denial of esse is percipi 'depends on' the doctrine of abstract ideas. Surely, the esse is percipi thesis is part ofthe core ofBerkeley's... (shrink)

: Plato’s instructions entail that the line of Republic VI is divided so that the middle two segments are of equal length. Yet I argue that Plato’s elaboration of the significance of this analogy shows he believes that these segments are of unequal length because the domains they represent are not of equally clear mental states, nor perhaps of objects of equal reality. I label this inconsistency between Plato’s instructions and his explanation the “overdetermination problem.” The overdetermination problem has been (...) a perennial concern, and a substantial amount of work has been produced which attempts to deal with it. I offer a classification of approaches to the overdetermination problem as a way of documenting the problem’s significance, and show why these approaches are all inadequate as solutions. My novel resolution of the overdetermination problem rests upon a demonstration that the contradiction is intentional. The later recapitulation of the ratio at 534a reveals that Plato was himself aware that the middle two segments are equal. I argue that this contradiction is a sophisticated device designed to lead the reader of the Republic through the four epistemic stages represented by the line itself. Most significantly, recognition of this mathematical contradiction acts as a goad, spurring independent philosophical reflection just in the way that Plato advocates in the Republic more generally. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A CONTRADICTION IN SAINT THOMAS'S TEACHING ON CREATION THEODORE J. KONDOLEON Villanova University Villanova, Pennsylvania 0 THOSE FAMILIAR with Saint Thomas's writings is generally known that the Angelic Doctor changed his position on a number of philosophical issues during the course of his relatively short professional career. For instance, there is his opinion concerning the instrumental role of higher creatures in the creation of the universe-something he allowed as (...) possible in his Commentary on the Sentences but later rejected in his Disputed Question On the Power of God and in the Summa Theologiae. Another example is Thomas's view on the possibility of an actual infinite multitude, an opinion he accepted in the early Disputed Question On Truth but argued against in the Summa Theologiae.1 However, to change one's mind on a particular issue is not to contradict oneself, since to do that is to say or hold, in the same time frame, pwhile also saying or holding not p. However, in his Treatise on Creation in the Summa Theologiae, Saint Thomas does, at least once, contradict himself in what he has to say on the question of the demonstrability of the world's temporal beginning, a contradiction which, to my knowledge, has never previous1 On the question whether higher creatures can be instrumental causes in the creation of lower creatures see In Sent. IV, d. 5, q. 5, a. 3; De potentia Dei, q. 3, a. le and Summa Theologiae, I, q, 45, a. Sc. On the issue of an actual infinite multitude see D. Q. De veritate, q. 2, a. 9 and Summa Theologiae, 1, q. 7, a. 5. However, in the De aeternitate mundi-a work possibly written after Saint Thomas completed the first part of his Summa-Aquinas asserts, towards the end of this work, that no demonstration has as yet been forthcoming that God cannot produce a multitude that is actually infinite. 51 52 THEODORE J. KONDOLEON ly been noted. In what follows I intend to expose this contradiction and to see whether there is any possible way for him to escape it. I In article 1 of Question 46 of the Prima pars, Aquinas argues that it cannot be demonstrated that the world of creatures always existed, given that the actual existence of creatures depends upon the causal will of God and the only thing which God wills necessarily is Himself.2 Consequently, whether or not the world exists, or is created eternally or with a temporal beginning, are matters entirely up to God's free will.3 In the following article he argues that neither can the world's temporal beginning be demonstrated but that this is something known only by faith.4 It cannot be demonstrated from the world itself since demonstration proceeds by way of knowledge of the universal essences of things and universals abstract from the hie et nunc, or from the question of temporal origin.5 Nor can it be proved from the world's efficient cause-the divine will-seeing that God's will cannot be investigated by reason except as regards those things which God wills necessarily (and what He wills about creatures is not among 2 " Dicendum nihil praeter Deum ab aeterno fuisse. Et hoc ponere non est impossibile. Ostensum est enim supra quad voluntas Dei est causa rerum. Sic ergo necesse est esse sicut necesse est Deum velle ilia, cum necessitatis effectus ex necessitate causae dependeat, ut dicitur in Meta. Ostensum est autem supra quod, absolute loquendo, non est necesse Deum velle aliquid nisi seipsum." ST I, q. 46, a. le. Latin quotations from Saint Thomas appearing in the footnotes are from the Leonine edition. 3 " Non est ergo necessarium Deum velle quod mundus fuerit semper. Sed eatenus mundus est quatenus Deus vult illum esse, cum esse mundi ex voluntate dependeat, sicut ex sua causa. Non est igitur necessarium mundum semper esse: Unde nee demonstrative probari potest." Ibid. 4 " Dicendum quod mundum non semper fuisse sola fidei tenetur, et demonsrtative probari non potest; sicut et supra de mysterio Trinitatis dictum est." Ibid., a. 2c. 5 "Et hujus ratio est, quia novitas mundi non potest demonstrationem recipere ex parte ipsius mundi... (shrink)

Introduction. The problem of corruption continues to be relevant in Russia. More research is needed to effectively combat corruption. Studying corruption in the context of general issues of contemporary Russian politics is particularly relevant in this regard. Purpose. The article is aimed at disclosing contradictions associated with perceiving corruption by the population of Russia and its representation in the official discourse. Methods. The author uses the following methods: analysis of statistical data, analysis of the results of public opinion (...) polls, and discourse analysis. Scientific novelty of the research. The article demonstrates the discrepancy between citizens’ perceptions of corruption and their attitudes regarding power and the political regime. The author shows the inconsistency of the official discourse on corruption in Russia. Results. The article reveals the peculiarities of perceiving corruption by the population of Russia. Citizens’ perceptions of corruption correlate with their attitudes towards power and political regime. The author shows the key features of depicting corruption in the official discourse. Conclusions. Widespread perceptions of high levels of corruption have little impact on public support for the Russian political regime. In the mass consciousness, there is no understanding of the connection between corruption, an ineffective economy and a low standard of the population’s living. Corruption is not a significant factor in protest moods, although many causes of social discontent are somehow related to corruption. Reflections of corruption in official discourse are incomplete and internally inconsistent. The approaches to combating corruption proclaimed in the official discourse are not fully implemented in the current anti-corruption policy. (shrink)

We introduce the simpler and shorter proof of Hajek’s theorem that the mathematical induction on ω implies a contradiction in the set theory with the comprehension principle within Łukasiewicz predicate logic Ł ${\forall}$ (Hajek Arch Math Logic 44(6):763–782, 2005) by extending the proof in (Yatabe Arch Math Logic, accepted) so as to be effective in any linearly ordered MV-algebra.

Mushkil al-Qur’ān is a science of the Qur’ān in which the verses that are considered contradictory at first glance and what ways/methods are used in reconciling them. From the point of view of a commentator or even a believer, the ishkal (contradiction) cannot be attributed to the Qur’ān proper, and the supposed contradictions between verses do not appear in the Qur’ān but the mind of the subject. Therefore, in this science, it can be seen that both the recognition of (...) contradictions and the elimination of contradictions are related to the interpretive context of the tafsīr methodology. This science has emerged on a dynamic ground and has a characteristic feature that determines the interpreter’s ability to interpret. The aspect of the Mushkil al-Qur’ān that distinguishes it from other Qurʾānic Sciences relates to the practical dimension of the tafsīr rather than general determinations and statistical information about the Qur’ān. For this reason, the scope of the Mushkil al-Qur’ān may change depending on the time, culture, perspective of the commentator, knowledge, and school preferences. The fact that disciplines define the concept of mushkil in different ways, and the change in the scope of the subject in the independent works written in the early period and the Qurʾānic Sciences literature written after al-Zarkashī requires a terminological-chronological-methodological analysis of the nature and content of the Mushkil al-Qur’ān scholarship. With its pre-Zarkashī structure, Mushkil al-Qur’ān science differs from its structure that emerged in the later period, both in terms of its target audience and its content. If we look at the works of names such as Ibn Qutaybah, it becomes clear that this science is mandated to cater to the religionless. However, especially with the scope and methods in which it has been dealt with in the recent period, the Mushkil al-Qur’ān is based on the internal dynamics of the shari'a sciences. Therefore, it can be said that al-Zarkashī defined the science of Mushkil al-Qur’ān, which had a comprehensive content in the early period, with a different name and a narrowing of its content as a field fed by the internal dynamics of the tafsīr, and that this science acquired a unified form after al-Suyūṭī. This process brought about some changes in the subject matter and content of the science of the Mushkil al-Qur'ān. For the Mushkil al-Qur’ān, which in the early days had the purpose of answering the doubts and objections of the deniers of the Qur’ān, developed after al-Zarkashī into a field mainly concerned with removing the difficulties of understanding. Within this framework, the methods and classifications presented in this science with the structure defined by al-Zarkashī are the products of the effort to make sense of the Word of God. The systematization of this effort to make sense under the umbrella of shāri‘ sciences in a terminological and theoretical framework opens the science of Mushkil al-Qur'ān to the fields of kalam and fiqh/method. In the works written on Mushkil al-Qur’ān and in the literature on fiqh, the reasons for the contradictions between the verses and the ways to eliminate them are given. What these ways depend on the context in which the contradiction is dealt with. Those who treat the contradiction in a way that includes the ambiguities in the words while eliminating these ambiguities resort to other pieces of evidence such as narratives, style of expression/context, truth metaphor, reason, analogy, and custom. In case of an apparent contradiction, methods like cem‘ (gathering), preference, naskh, renunciation are used. Despite the differences in the school’s preferences as to which of these methods was used first in the classical period, there is almost a consensus as to the ways followed in eliminating contradictions between verses. In the modern period, some scholars claim that one of these methods, abrogation, is directly related to the Mushkil al-Qur’ān, and they explain that naskh is applied when the contradictions between the verses cannot be interpreted. This assertion, made in modern times, that naskh is a method that scholars resort to when they cannot remove the impression of contradictions between verses, is closely related to the definition, essence, and content of the Mushkil al-Qur’ān. In this context, it is crucial where the ways/methods used to follow the nature-content pendulum while eliminating the counterparts of the terms and the impressions of contradiction. This is because the acceptance of naskh as a contradiction solution stems from the fact that it is one of the ways to prove that there is no contradiction in the Qur’ān from the perspective of fiqh, and naskh means that two contradictory provisions were valid at different times. The contradiction arises when it is claimed that these two provisions are valid at the same time. (shrink)

In this paper I critically engage with Pauline Kleingeld’s ‘volitional self-contradiction’ interpretation of Kant’s formula of universal law. I make three remarks: first, I seek to clarify what it means for a contradiction to be volitional as opposed to logical; second, I suggest that her interpretation might need to be closer to Korsgaard’s ‘practical contradiction’ interpretation than she thinks; and third, I suggest that more work needs to be done to explain how a volitional self-contradiction generates both a ‘contradiction in (...) conception’ and a ‘contradiction in will.’. (shrink)

David Lewis has argued that impossible worlds are nonsense: if there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them; and this--Lewis argues--is preposterous. In this paper I examine a way of resisting this argument by giving up the assumption that ‘in so-and-so world’ is a restricting modifier which passes through the truth-functional connectives The outcome is a sort of subvaluational semantics which makes a contradiction ‘A & ~A’ false (...) even when both ‘A’ and ‘~A’ are true, just as supervaluational semantics makes a tautology ‘A v ~A’ true even when neither ‘A’ nor ‘~A’ are. Connections with discussive logics and complications of the account are discussed, and some general morals are drawn. (shrink)

This paper reports laboratory data for games that are played only once. These games span the standard categories: static and dynamic games with complete and incomplete information. For each game, the treasure is a treatment in which behavior conforms nicely to predictions of the Nash equilibrium or relevant refinement. In each case, however, a change in the payoff structure produces a large inconsistency between theoretical predictions and observed behavior. These contradictions are generally consistent with simple intuition based on the (...) interaction of payoff asymmetries and noisy introspection about others’ decisions. (shrink)

From the point of view of proof-theoretic semantics, it is argued that the sequent calculus with introduction rules on the assertion and on the assumption side represents deductive reasoning more appropriately than natural deduction. In taking consequence to be conceptually prior to truth, it can cope with non-well-founded phenomena such as contradictory reasoning. The fact that, in its typed variant, the sequent calculus has an explicit and separable substitution schema in form of the cut rule, is seen as a crucial (...) advantage over natural deduction, where substitution is built into the general framework. (shrink)

Peirce’s principles of excluded middle and contradiction more resembled those of Aristotle than those of contemporary logicians. While the principles themselves are simple and straightforward, many of Peirce’s comments about them have been misunderstood by commentators. In particular, his belief that the principle of excluded middle does not apply to the general and that the principle of contradiction does not apply to the vague have been mistakenly connected to his eventual rejection of the principle of bivalence and development of (...) three-valued logical connectives. An understanding of Peirce’s view of those logical principles shows that those beliefs motivated neither his rejection of bivalence nor his work in triadic logic. (shrink)

The arguments of the dialetheists for the rejection of the traditional law of noncontradiction are not yet conclusive. The reason is that the arguments that they have developed against this law uniformly fail to consider the logic of encoding as an analytic method that can resolve apparent contradictions. In this paper, we use Priest [1995] and [1987] as sample texts to illustrate this claim. In [1995], Priest examines certain crucial problems in the history of philosophy from the point of (...) view of someone without a prejudice in favor of classical logic. For each of these problems, the logic of encoding offers an alternative explanation of the phenomena---this alternative is not considered when Priest describes what options there are in classical logic for analyzing the problem at hand. -/- The argument at heart of the case that Priest develops against the law of noncontradiction (i.e., the argument based on the paradoxes of self-reference) is then reanalyzed in light of encoding logic. After showing why the argument is inconclusive, the paper concludes both with a more general discussion of logic and predication and with the suggestion that there is no need to tamper with the logic of the traditional mode of predication if there is alternative mode of predication which is well-suited to the analysis of cases involving contradictory objects. (shrink)

Stratified properties such as ‘happy unhappiness’, ‘ungrounded ground’, ‘fortunate misfortune’, and evidently ‘true falsity’ may generate dialetheias (true contradictions). The aim of the article is to show that if this is the case, then we will have a special, conjunctive, kind of dialetheia: a true state description of the form ‘Fa and not Fa’ (for some property F and object a), wherein the two conjuncts, separately taken, are to be held untrue. The particular focus of the article is on (...) happy unhappiness: people suffering from (or enjoying) happy unhappiness (if there is some situation or state of mind of this kind) cannot be truly said ‘happy’ or ‘unhappy’, but we can say they are both. In the first section three cases of conjunctive stratification are presented; in the second section the logic of stratified contradictions is explored. The last section focuses on eudemonistic ascriptions: stated that a is happy to be unhappy (or unhappy to be happy), should we say a is happy? unhappy? both? neither? (shrink)

RésuméCet article étudie lafaçon dont Hegel élabore sa conception des rapports entre la pensée et la nature dans la Phénoménologie de l'esprit. L'examen montre que 1) Hegel étend le concept de raison pour y inclure i'indépendance de la nature à l'endroit de la pensée rationnelle, 2) cette indépendance se révèle dans le donné contingent de l'empiricité, 3) le concept étendu de raison détermine et justifie les présuppositions de la logique hégélienne, et 4) ce même concept limite le rôle de la (...) logique dans la philosophie hégélienne prise comme un tout, de telle manière que la philosophie y dépend de la science empirique en quelque chose d'essentiel pour sa connaissance de la vérité. En étayant ces thèses, l'article analyse la procédure de preuve utilisée par Hegel, expose le rôle qu'y joue la contradiction, et discute les explications phénoménologiques qu'il propose de la perception, de l'entendement, du stoïcisme, de l'idéalisme, de la biologie, du monde moral kantien, de la religion révélée, et du savoir absolu. (shrink)

The Jaina saptabhaṅgī (seven angles of analysis or types of sentences) has drawn the attention of non-classical logicians due to its unique use of negation, contradiction, and avaktavya (‘unutterable’). In its most basic structure, the saptabhaṅgī appears as: (i) in a certain sense, P; (ii) in a certain sense, not P; (iii) in a certain sense, P and not P; (iv) in a certain sense, inexpressibility of P; (v) in a certain sense, P and inexpressibility of P; (vi) in a (...) certain sense, not P and inexpressibility of P; (vii) in a certain sense, P, not P, and inexpressibility of P. This appearance has led many (e.g., Ganeri and Priest) to claim that the saptabhaṅgī supports non-classical systems of logic, but such a reading is contested by Balcerowicz. Focusing on Vādidevasūri’s (12th c. CE) and Yaśovijaya’s (17th c. CE) accounts of the saptabhaṅgī, this paper puts forward a formalization of the saptabhaṅgī that brings together the non-classical views and Balcerowicz’s view through relating the saptabhaṅgī to the Buddhist unanswerable questions. (shrink)

The problem addressed is that of finding a sound characterization of ambiguity. Two kinds of characterizations are distinguished: tests and definitions. Various definitions of ambiguity are critically examined and contrasted with definitions of generality and indeterminacy, concepts with which ambiguity is sometimes confused. One definition of ambiguity is defended as being more theoretically adequate than others which have been suggested by both philosophers and linguists. It is also shown how this definition of ambiguity obviates a problem thought to be posed (...) by ambiguity for truth theoretical semantics. In addition, the best known test for ambiguity, namely the test by contradiction, is set out, its limitations discussed, and its connection with ambiguity's definition explained. The test is contrasted with a test for vagueness first proposed by Peirce and a test for generality propounded by Margalit. (shrink)

Kant’s Formula of Universal Law (FUL) is generally believed to require you to act only on the basis of maxims that you can will without contradiction to become universal laws. In “Contradiction and Kant’s Formula of Universal Law” (2017), I have proposed to read the FUL instead as requiring that, for any maxim on which you act, you can will two things simultaneously, without volitional self-contradiction: (1) willing the maxim as your own action principle and (2) willing that it become (...) a universal law. In the present essay, I reply to comments by Mark Timmons, Michael Walschots, Paola Romero, and Stefano Lo Re. In response to their comments concerning the application of the FUL, I expand the interpretive framework of the Volitional Self-Contradiction Interpretation. I argue that Kant also constructs the diagnostic volitional self-contradiction as a contradiction between (1) willing a tested maxim to become a universal law and (2) willing what humans, qua finite rational beings, necessarily will, namely the means to their actual and possible future ends. I also clarify how the two ways in which Kant specifies the test are related. Furthermore, I clarify the relation between the Volitional Self-Contradiction interpretation and other interpretations of the FUL, in particular the ‘Practical Contradiction’ and ‘Logical Contradiction’ interpretations, as well as its difference from the Golden Rule. I also address the objection that the volitional self-contradiction is superfluous, clarify the relation between the Formula of Universal Law and the Formula of the Law of Nature, and explain why the will of an immoral agent does not contain a volitional self-contradiction of the type at issue. (shrink)

Okasha, in Evolution and the Levels of Selection, convincingly argues that two rival statistical decompositions of covariance, namely contextual analysis and the neighbour approach, are better causal decompositions than the hierarchical Price approach. However, he claims that this result cannot be generalized in the special case of soft selection and argues that the Price approach represents in this case a better option. He provides several arguments to substantiate this claim. In this paper, I demonstrate that these arguments are flawed and (...) argue that neither the Price equation nor the contextual and neighbour partitionings sensu Okasha are adequate causal decompositions in cases of soft selection. The Price partitioning is generally unable to detect cross-level by-products and this naturally also applies to soft selection. Both contextual and neighbour partitionings violate the fundamental principle of determinism that the same cause always produces the same effect. I argue that a fourth partitioning widely used in the contemporary social sciences, under the generic term of ‘hierarchical linear model’ and related to contextual analysis understood broadly, addresses the shortcomings of the three other partitionings and thus represents a better causal decomposition. I then defend this model against the argument that because it predicts that there is some organismal selection in some specific cases of segregation distortion then it should be rejected. I show that cases of segregation distortion that intuitively seem to contradict the conclusion drawn from the hierarchical linear model are in fact cases of multilevel selection 2 while the assessment of the different partitionings are restricted to multilevel selection 1. (shrink)