Hoping is an integral part of what it is to be human, and its significance for education has been widely noted. Hope is, however, a contested category of human experience and getting to grips with its characteristics and dynamics is a difficult task. The paper argues that hope is not a singular undifferentiated experience and is best understood as a socially mediated human capacity with varying affective, cognitive and behavioural dimensions. Drawing on the philosophy, theology and psychology of hope, five (...) modes of hoping are outlined: patient, critical, sound, resolute and transformative. The key aim of the paper is to illustrate how different modes of hoping are associated with different pedagogical strategies. Phrased differently, the paper seeks to delineate a range of pedagogies of hope. The phrase ‘pedagogy of hope’ is very much associated with critical theory—one thinks instantly of, for example, Paulo Freire, Henry Giroux or bell hooks. There are many pedagogies of hope, however, and an explicitly conservative text such as William Bennett’s Book of Virtues has as strong a claim to the title as Freire’s radical and utopian ideas. A broader argument, therefore, is that there is nothing inherently radical or subversive about a pedagogy of hope. Pedagogies of hope can serve to reproduce social relations as well as to transform them. (shrink)

Husserl’s first work formulated what proved to be an algorithmically complete arithmetic, lending mathematical clarity to Kronecker’s reduction of analysis to finite calculations with integers. Husserl’s critique of his nominalism led him to seek a philosophical justification of successful applications of symbolic arithmetic to nature, providing insight into the “wonderful affinity” between our mathematical thoughts and things without invoking a pre-established harmony. For this, Husserl develops a purely descriptive phenomenology for which he found inspiration in Mach’s proposal of a “universal (...) physical phenomenology.” To account for applications to any domain, Husserl envisages a theory of all possible deductive systems, which he develops extensively in his Göttingen lectures wherein he engages with Hilbert’s work on deductive systems for geometry, real arithmetic, and physics. This leads Husserl to formulate claims of decidability and proofs of completeness for various arithmetics that result from his analysis of Kronecker’s general arithmetic. Careful attention to these proofs seem to show that Husserl was not oblivious to problems that underlie our incompleteness theorems, namely that of showing that some inversions of his algorithmic arithmetic are undefined. His growing preoccupation with the issue of a pre-established harmony between mathematical thought and reality motivate his pursuit of a “supramathematics” of all possible complete theory forms to demystify such harmony, by having such a form on hand for describing any empirical domain. He soon decides that a transcendental idealism of nature will reveal the wonderful affinity of thoughts and things comprising such harmony, to be a wonderful “parallelism of objective unities and constituted manifolds of consciousness.” But the paradoxes of logic and set theory cloud the clarity of mathematics, which Weyl would restore with Brouwer’s intuitionism and Hilbert with his metamathematics. Husserl informed Weyl that his student Becker had formulated a phenomenological foundation not only for Weyl’s generalization of relativity theory but also for the Brouwer-Weyl continuum. But Weyl eventually rejected much of Becker’s work, especially when it became clear that his phenomenological intuitionism could not account for the success of Hilbert’s transfinite mathematics in quantum physics. Becker responded to this “crisis of phenomenological method” with his mantic phenomenology celebrating the magic of mathematical mysticism, which Husserl finally rejects in favor of a pluralistic phenomenology of mathematics and nature. (shrink)

Drawing together the ideas, practices, and techniques associated with the subject, this book puts them in historical context and demonstrates their relevance to ...

A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections.

Husserl’s lifelong interest in Kant eventually becomes a preoccupation in his later years when he finds his phenomenology in competition with Neokantianism for the title of transcendental philosophy. Some issues that Husserl is concerned with in Kant are bound up with the works of Lambert. Kant believed that the role played by principles of sensibility in metaphysics should be determined by a “general phenomenology” on which Lambert had written. Kant initially believed that man is capable only of symbolic cognition, not (...) intellectual intuition. Lambert saw an increasing need in mathematics for symbolic cognition as exemplified in his proofs of the irrationality of π and e. Kant takes from Leibniz and Lambert an unrestricted notion of construction, allowing him to view mathematics as constructing its concepts in intuition, while Lambert’s proofs convince him that all mathematical problems are eventually solvable. Husserl criticizes Kant’s intuitionism for its inadequate accommodation of meaning to intuition, which he redresses with his theory of categorial intuition. This may improve on Kant’s intuition of the axiom of parallels but not so clearly on his spatial intuition. Husserl opposes Kant’s view of space as the form of outer intuition with his own view of it as the form of things. Husserl’s exploration of the geometry of visual space, which involves his earliest uses of epoché and reduction, converges however with Hilbert’s logical analysis of Kantian spatial intuition in leading to Euclidean spatial judgments. Hilbert’s analysis leads him to affirm the solvability of all well posed mathematical problems, a thesis complicated by the outbreak of logical paradoxes. Untroubled by such paradoxes, Husserl develops a supramathematics of all possible deductive systems whose completeness implicitly would also provide solutions of all such problems. Husserl’s full transcendental turn coincides with his realization that in effecting his Copernican turn, Kant was really the first to detect the “secret longing” of modern philosophy for a phenomenological clarification of being. Husserl now finds that Kant’s transcendental deductions presuppose a pure ego not adequately analyzed by Kant that survives the phenomenological reduction. Husserl’s idealism leads him to develop his own intuitionism, which adds to Kant’s, a “method of clarification” of mathematical concepts intended to clarify difficult impossibility proofs, but neither Husserl nor Kant base arithmetic on time. Husserl’s critique of the room left in Kant’s idealism, for things in themselves, leads to his own monadological solution of the problem of intersubjectivity. Husserl’s final judgment on Kant is that his form of transcendental idealism did not enable him to achieve absolute subjectivity through a genuine transcendental reduction. (shrink)

This chapter attempts to give a brief overview of nonclassical (-logic) theories of truth. Due to space limitations, we follow a victory-through-sacrifice policy: sacrifice details in exchange for clarity of big-picture ideas. This policy results in our giving all-too-brief treatment to certain topics that have dominated discussion in the non-classical-logic area of truth studies. (This is particularly so of the ‘suitable conditoinal’ issue: §4.3.) Still, we present enough representative ideas that one may fruitfully turn from this essay to the more-detailed (...) cited works for further study. Throughout – again, due to space – we focus only on the most central motivation for standard non-classical-logic-based truth theories: namely, truth-theoretic paradox (specifically, due to space, the liar paradox). (shrink)

We say that a sentence A is a permissive consequence of a set X of premises whenever, if all the premises of X hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the (...) requisite of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference. (shrink)

For some reason, participants hold agents more responsible for their actions when a situation is described concretely than when the situation is described abstractly. We present examples of this phenomenon, and survey some attempts to explain it. We divide these attempts into two classes: affective theories and cognitive theories. After criticizing both types of theories we advance our novel hypothesis: that people believe that whenever a norm is violated, someone is responsible for it. This belief, along with the familiar workings (...) of cognitive dissonance theory, is enough to not only explain all of the abstract/concrete paradoxes, but also explains seemingly unrelated effects, like the anthropomorphization of malfunctioning inanimate objects. (shrink)

Corporate social responsibility (CSR) is a dramatically expanding area of activity for managers and academics. Consumer demand for responsibly produced and fair trade goods is swelling, resulting in increased demands for CSR activity and information. Assets under professional management and invested with a social responsibility focus have also grown dramatically over the last 10 years. Investors choosing social responsibility investment strategies require access to information not provided through traditional financial statements and analyses. At the same time, a group of mainstream (...) institutional investors has encouraged a movement to incorporate environmental, social, and governance information into equity analysis, and multi-stakeholder groups have supported enhanced business reporting on these issues. The majority of research in this area has been performed on European and Australian firms. We expand on this literature by exploring the CSR disclosure practices of a size- and industry-stratified sample of 50 publicly traded U.S. firms, performing a content analysis on the complete identifiable public information portfolio provided by these firms during 2004. CSR activity was disclosed by most firms in the sample, and was included in nearly half of public disclosures made during that year by the sample firms. Areas of particular emphasis are community matters, health and safety, diversity and human resources (HR) matters, and environmental programs. The primary venues of disclosure are mass media releases such as corporate websites and press releases, followed closely by disclosures contained in mandatory filings. Consistent with prior research, we identify industry effects in terms of content, emphasis, and reporting format choices. Unlike prior research, we can offer only mixed evidence on the existence of a size effect. The disclosure frequency and emphasis is significantly different for the largest one-fifth of the firms, but no identifiable trends are present within the rest of the sample. There are, however, identifiable size effects with respect to reporting format choice. Use of websites is positively related to firm size, while the use of mandatory filings is negatively related to firm size. Finally, and also consistent with prior literature, we document a generally self-laudatory tone in the content of CSR disclosures for the sample firms. (shrink)

The human propensity to take an ethical stance toward oneself and others is found in every known society, yet we also know that values taken for granted in one society can contradict those in another. Does ethical life arise from human nature itself? Is it a universal human trait? Or is it a product of one's cultural and historical context? Webb Keane offers a new approach to the empirical study of ethical life that reconciles these questions, showing how ethics (...) arise at the intersection of human biology and social dynamics. Drawing on the latest findings in psychology, conversational interaction, ethnography, and history, Ethical Life takes readers from inner city America to Samoa and the Inuit Arctic to reveal how we are creatures of our biology as well as our history--and how our ethical lives are contingent on both. Keane looks at Melanesian theories of mind and the training of Buddhist monks, and discusses important social causes such as the British abolitionist movement and American feminism. He explores how styles of child rearing, notions of the person, and moral codes in different communities elaborate on certain basic human tendencies while suppressing or ignoring others."--Publisher's Web site. (shrink)

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.

The ability to generate diverse ideas is valuable in solving creative problems ; yet, however advantageous, this ability is insufficient to solve the problem alone and requires the ability to logically deduce an assessment of correctness of each solution. Positive schizotypy may help isolate the aspects of divergent thinking prevalent in insight problem solving. Participants were presented with a measure of schizotypy, divergent and convergent thinking tasks, insight problems, and non-insight problems. We found no evidence for a relationship between schizotypy (...) and insight problem solving. Relationships between divergent thinking and insight problem solving were also surprisingly weak; however, measures of convergent thinking had a stronger relationship with problem solving. These results suggest that convergent thinking is more important than divergent thinking in problem solving. (shrink)

Three leading philosopher-logicians present a clear and concise overview of formal theories of truth, explaining key logical techniques. Truth is as central topic in philosophy: formal theories study the connections between truth and logic, including the intriguing challenges presented by paradoxes like the Liar.

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends classical (...) logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but the (...) other does not.). (shrink)

Recent years have featured a spate of regulatory action pertaining to the development and/or disclosure of corporate governance structures in response to financial scandals resulting in part from governance failures. During the same period, corporate governance activists and institutional investors increasingly have called for increased voluntary governance disclosure. Despite this attention, there have been relatively few comprehensive studies of governance disclosure practices and response to the regulation. In this study, we examine a sample of 50 U.S. firms and their public (...) disclosure packages from 2004. We find a high degree of variability in the presentation and reporting format choices for many elements of the governance structure. This variability includes several items for which disclosure is mandated by regulators or legislative action. In particular, smaller firms offer fewer disclosures pertaining to independence, board selection procedures, and oversight of management (including whistleblowing procedures). There are also trends associated with board characteristics: boards that are less independent offer fewer disclosures of independence and management oversight matters. Moreover, large firms provide more disclosures of independence standards, board selection procedures, audit committee matters, management control systems, other committee matters, and whistleblowing procedures but do not appear to have a strictly superior information environment when compared to smaller firms. The findings raise questions about compliance with regulatory requirements and the degree to which conflicts of interest between managers and directors are being controlled. While there have been notable improvements in the information environment of governance disclosures, there remain structural issues that may possess negative ramifications for stakeholders. (shrink)

ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K3+. We clarify the distinction between internal and external logic and (...) argue that while ST+’s nonclassicality can be granted, its self-dual character does not tie it to LP+ more closely than to K3+. (shrink)

Where has the Western attraction to the study and practice of shamanic techniques brought us? Where might it take us? In what ways have our Western biases and philosophical underpinnings influenced and changed how shamanism is practiced, both in the West and in the traditional cultures out of which they emerged? Is it time to stop using the umbrella term “shamanism” to refer to such diverse cross-cultural practices? What are our responsibilities, both as researchers and as spiritual seekers? In this (...) conversation, researcher-authors Stephan Beyer, Stanley Krippner, and Hillary S. Webb discuss their work in field and consider some of the ramifications of the Western world's intellectual and spiritual fascination with shamanic practices. Special attention is paid to the language used to describe these techniques and their practitioners, the developing relationship between researchers and cultural participants, and the ethical implications of merging what are often very distinct worldviews. (shrink)

We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with classical logic.

The purpose of this essay is to shed some light on a certain type of sentence, which I call a borderline contradiction. A borderline contradiction is a sentence of the form F a ∧ ¬F a, for some vague predicate F and some borderline case a of F , or a sentence equivalent to such a sentence. For example, if Jackie is a borderline case of ‘rich’, then ‘Jackie is rich and Jackie isn’t rich’ is a borderline contradiction. Many theories (...) of vague language have entailments about borderline contradictions; correctly describing the behavior of borderline contradictions is one of the many tasks facing anyone offering a theory of vague language. Here, I first briefly review claims made by various theorists about these borderline contradictions, attempting to draw out some predictions about the behavior of ordinary speakers. Second, I present an experiment intended to gather relevant data about the behavior of ordinary speakers. Finally, I discuss the experimental results in light of several different theories of vagueness, to see what explanations are available. My conclusions are necessarily tentative; I do not attempt to use the present experiment to demonstrate that any single theory is incontrovertibly true. Rather, I try to sketch the auxiliary hypotheses that would need to be conjoined to several extant theories of vague language to predict the present result, and offer some considerations regarding the plausibility of these various hypotheses. In the end, I conclude that two of the theories I consider are better-positioned to account for the observed data than are the others. But the field of logically-informed research on people’s actual responses to vague predicates is young; surely as more data come in we will learn a great deal more about which (if any) of these theories best accounts for the behavior of ordinary speakers. (shrink)

In a previous paper (see ‘Tolerant, Classical, Strict’, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can use (...) these notions of satisfaction to define mixed consequence relations that capture non-transitive tolerant reasoning. Although we gave some empirical motivation for the use of strict and tolerant extensions, making use of them commits us to the view that sentences of the form ‘ p∨¬p ’ and ‘ p∧¬p ’ are not automatically valid or unsatisfiable, respectively. Some philosophers might take this commitment as a negative outcome of our previous proposal. We think, however, that the general ideas underlying our previous approach to vagueness can be implemented in a variety of ways. This paper explores the possibility of defining mixed notions of consequence in the more classical super/sub-valuationist setting and examines to what extent any of these notions captures non-transitive tolerant reasoning. (shrink)

This paper consider Prior's connective Tonk from a particular bilateralist perspective. I show that there is a natural perspective from which we can see Tonk and its ilk as perfectly well-defined pieces of vocabulary; there is no need for restrictions to bar things like Tonk.

In an interesting article on Kierkegaard and the “Existential” Philosophy, contributed to the number of Philosophy for July 1941, Miss Dorothy Emmet counselled her readers to make themselves acquainted with the Journals of the famous Danish thinker, now rendered accessible to Englishmen ignorant of his language by the translation of Mr. Dru. I have taken her advice and am grateful to her for it. I am not indeed convinced that this self-revelation of a remarkable personality can be ranked among the (...) great autobiographies of the world. It seems to me to fall, if only on account of its lack of unity as a work of literary art, below the standard which such an estimate of it would imply. But it is undoubtedly both impressive in itself and important in view of the influence which its author, little known in his lifetime beyond a circle of the parochial narrowness of which he was painfully conscious, has come, long after his death, to exert upon the spiritual and intellectual life of Europe to-day. The present article, however, will not be concerned with the exposition or criticism of this or other writings of Kierkegaard, but with thoughts, more or less suggested by my reading of him, respecting the notion of God and its significance for philosophy. (shrink)

In the first part of this article I propose to describe two strongly contrasted situations in the world of thought, one of fifty years ago and the other of to-day. In the second I shall submit to my readers some reflections suggested by the contrast between the two.

This year is being celebrated by a large number of our fellow-countrymen as the centenary of a movement, associated with the name of the University of Oxford, of which, although in its first stage it might easily be mistaken—and has often been mistaken—for a mere wave of theological and ecclesiastical reaction within the Established Church of England, the attentive historian of the nineteenth century must take account as in fact a very powerful influence in the religious and, no less really (...) though to a less degree, in the social and political life of the whole nation. Considerable, however, as is the importance which may justly be attributed in other respects to what is known as the Oxford Movement, the professed student of philosophy may be excused if he is chiefly struck by the apparent remoteness of its original leaders from the currents of speculative thought characteristic of the period in which it began its course. There were perhaps among them only two who can be named as contributors to philosophical literature in the technical sense now commonly borne by the term “philosophical”; and the contributions even of these two can scarcely be said to have taken their place among the works to which an ordinary teacher of philosophy would be likely to direct the attention of his pupils. To these two, however, John Henry Newman and William George Ward, I propose to devote here a few pages which may be found not without interest to readers of Philosophy. (shrink)

This paper discusses two distinct strategies that have been adopted to provide fine-grained propositions; that is, propositions individuated more finely than sets of possible worlds. One strategy takes propositions to have internal structure, while the other looks beyond possible worlds, and takes propositions to be sets of circumstances, where possible worlds do not exhaust the circumstances. The usual arguments for these positions turn on fineness-of-grain issues: just how finely should propositions be individuated? Here, I compare the two strategies with an (...) eye to the fineness-of-grain question, arguing that when a wide enough range of data is considered, we can see that a circumstance-based approach, properly spelled out, outperforms a structure-based approach in answering the question. (Part of this argument involves spelling out what I take to be a reasonable circumstance-based approach.) An argument to the contrary, due to Soames, is also considered. (shrink)

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

Substructural theories of truth are theories based on logics that do not include the full complement of usual structural rules. Existing substructural approaches fall into two main families: noncontractive approaches and nontransitive approaches. This paper provides a sketch of these families, and argues for two claims: first, that substructural theories are better-positioned than other theories to grapple with the truth-theoretic paradoxes, and second—more tentatively—that nontransitive approaches are in turn better-positioned than noncontractive approaches.

This paper provides a defense of the full strength of classical logic, in a certain form, against those who would appeal to semantic paradox or vagueness in an argument for a weaker logic. I will not argue that these paradoxes are based on mistaken principles; the approach I recommend will extend a familiar formulation of classical logic by including a fully transparent truth predicate and fully tolerant vague predicates. It has been claimed that these principles are not compatible with classical (...) logic; I will argue, by both drawing on previous work and presenting new work in the same vein, that this is not so. We can combine classical logic with these intuitive principles, so long as we allow the result to be nontransitive. In the end, I hope the paper will help us to handle familiar paradoxes within classical logic; along the way, I hope to shed some light on what classical logic might be for. (shrink)

The quality of corporate disclosures has drawn increasing levels of criticism from Congress and the SEC. A subject of particularly intense scrutiny and action is the Management’s Discussion and Analysis (MD&A). This narrative, intended to provide an inside perspective on the reported results of the firm, is particularly important when attempting to evaluate the investment prospects of the marginal or poorly performing firm. However, managers may restrict the information content of the disclosure, raising potential concerns about ethical behavior. In this (...) study, we employ a proprietary instrument to measure the quality of MD&A disclosures for a sample of firms entering financial distress. We evaluate the disclosure behavior of these firms in an effort to determine whether changes in the disclosure appear to be motivated primarily by economic or ethical concerns. We find, on average, that firms increase disclosure quality in the year of initial distress. However, sustained increases in disclosure quality are limited to firms that subsequently recover from the distress. The results suggest that observed changes in disclosure are driven primarily by economic considerations, rather than ethical ones, especially in good economic times. (shrink)

At least since [Frege, 1960] and [Geach, 1965], there has been some consensus about the relation between negation, the speech act of denial, and the attitude of rejection: a denial, the consensus has had it, is the assertion of a negation, and a rejection is a belief in a negation. Recently, though, there have been notable deviations from this orthodox view. Rejectivists have maintained that negation is to be explained in terms of denial or rejection, rather than vice versa. Some (...) other theorists have maintained that negation is a separate phenomenon from denial, and that neither is to be explained in terms of the other. In this paper, I present and consider these heterodox theories of the relation between negation, denial, and rejection. (shrink)