Some irrational states can be avoided in more than one way. For example, if you believe that you ought to A you can avoid akrasia by intending to A or by dropping the belief that you ought to A. This supports the claim that some rational requirements are wide-scope. For instance, the requirement against akrasia is a requirement to intend to A or not believe that you ought to A. But some writers object that this Wide-Scope view ignores asymmetries between (...) the different ways of avoiding irrationality. In this paper I defend the Wide-Scope view against recent objections of this sort from Mark Schroeder and Niko Kolodny. I argue that once we are clear about what the Wide-Scope view is committed to—and, importantly, what it is not—we can see that Schroeder and Kolodny’s objections fail. (shrink)

Presentation and discussion of two new experimental studies surveying intuitions about cases of moral ignorance due to childhood deprivation. Discussion of resulting asymmetry between negative and positive cases and proposal of speculative hypothesis to explain results, The Difficulty Hypothesis.

The Principle of Indifference (POI) is a rule for rationally assigning precise degrees of confidence to possibilities among which we have no reason to discriminate. Despite criticism of the principle stemming from Bertrand's paradox, many have recently come to the defense of POI or adopted some restricted version of that principle, especially in discussions of self-locating belief. I argue that POI in both unrestricted and restricted forms is untenable, and that arguments for the more restricted principles are hostage to problems (...) similar to those that bedevil arguments for traditional POI. (shrink)

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the (...) Weyl’s system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)

It may be a myth that Plato wrote over the entrance to the Academy “Let no-one ignorant of geometry enter here.” But it is a well-chosen motto for his view in the Republic that mathematical training is especially productive of understanding in abstract realms, notably ethics. That view is sound and we should return to it. Ethical theory has been bedevilled by the idea that ethics is fundamentally about actions (right and wrong, rights, duties, virtues, dilemmas and so on). That (...) is an error like the one Plato mentions of thinking mathematics is about actions (of adding, constructing, extracting roots and so on). Mathematics is about eternal relations between universals, such as the ratio of the diagonal of a square to the side. Ethics too is about eternal verities, such as the equal worth of persons and just distributions. Mathematical and ethical verities do both constrain actions, such as the possibility of walking over the seven bridges of Königsberg once and once only or of justly discriminating between races. But they are not themselves about action. In principle, neither mathematical nor ethical verities are subject to historical forces or disagreement among tribes (though they can be better understood as time goes on). Plato is right: immersion in mathematics induces an understanding of the necessities underpinning reality, an understanding that is essential for distinguishing objective ethics from tribal custom. Equality, for example, is an abstract concept which is foundational for both mathematics and ethics. (shrink)

A brief historical comment on scientific knowledge as Socratic ignorance -- Some critical comments on the text of this book, particularly on the theory of truth Exposition [1933] -- Problem of Induction (Experience and Hypothesis) -- Two Fundamental Problems of the Theory of Knowledge -- Formulation of the Problem -- The problem of induction and the problem of demarcation -- Deductivtsm and Inductivism -- Comments on how the solutions are reached and preliminary presentation of the solutions -- Rationalism and (...) empiricism-deductivism and inductivism -- The possibility of a deductivist psychology of knowledge -- The Problem of Induction -- The infinite regression (Hume's argument) --The inductivist positions -- The Normal-Statement Positions -- The normal-statement positions: naive inductivism, strict positivism and apriorism -- Critique of strict positivism - twofold transcendence of natural laws -- The transcendental method - presentation of apriorism -- Critique of apriorism -- Kant and Fries -- Supplement to the critique of apriorism. (Psychologism and transcendentalism in Kant and Fries.-On the question of the empirical basis.) -- Probability Positions -- The probability positions - subjective belief in probability -- Statements about the objective probability of events -- Probability as an objective degree of validity of universal empirical statements -- One way of more closely defining the concept of the probability of a hypothesis (primary and secondary probability of hypotheses). The concept of simplicity -- The concept of the corroboration of a hypothesis - positivist, pragmatist and probabilistic interpretations of the concept of corroboration -- The infinite regression of probability statements -- Pseudo-Statement Positions -- The pseudo-statement positions: new formulation of the problem -- Natural laws as "instructions for the formation of statements" -- "True - false" or "useful - useless"? Consistent pragmatism --Difficulties of consistent pragmatism -- Tool and schema as purely pragmatic constructs -- Natural laws as propositional functions -- Conventionalism -- The pseudo-statement positions will temporarily be put away: conventionalism -- The three interpretations of axiomatic systems. (The circle of problems surrounding conventionalism) -- Conventionalist implicit and explicit definitions Propositional function and propositional equation -- Conventionalist propositional equations as tautological general implications -- Can axiomatic-deductive systems also be understood as consequence classes of pure propositional functions (of pseudo-statements)? -- The coordinative definitions of empiricism: synthetic general implications -- Conventionalist and empiricist interpretations, illustrated by the example of applied geometry -- Strictly Universal Statements and Singular Statements -- Implication and general implication -- General implication and the distinction between strictly universal and singular statements -- Universal concept and individual concept-class and element -- Strictly universal statements-the problem of induction and the problem of universals -- Comments on the problem of universals -- Back to the Pseudo-Statement Positions -- Return to the discussion of the pseudo-statement positions -- Symmetry or asymmetry in the evaluation of natural laws? -- The negative evaluation of universal statements. Critique of the strictly symmetrical interpretation of pseudo-statements -- An infinite regression of pseudo-statements -- An apriorist pseudo-statement position -- Interpretation of the critique up to this point; comments on the unity of theory and practice -- A last chance for the pseudo-statement positions -- Pseudo-Statement Positions and the Concept of Meaning -- The concept of meaning and logical positivism -- The concept of meaning and the demarcation problem-the fundamental thesis of inductivism -- Critique of the inductivist dogma of meaning -- Fully decidable and partially decidable empirical statements-the antinomy of the knowability of the world. (Conclusion of the critique of the pseudo-statement positions.) -- The dialectical and the transcendental corroboration of the solution -- Is the problem of induction solved? (shrink)

As we have seen in the transition form Part I to Part II of this book, the inductive riskiness of doxastic methods applied in testimonial uptake or prescribed as exemplary of religious faith, helpfully operationalizes the broader social scientific, philosophical, moral, and theological interest that people may have with problems of religious luck. Accordingly, we will now speak less about luck, but more about the manner in which highly risky cognitive strategies are correlated with psychological studies of bias studies and (...) human cognitive ecology. Chapter Four is concerned with connections between psychological study of biases and heuristics, and the comparative study of fundamentalism. The first section looks at work by psychologists and philosophers on our bias blind spot. Later sections ask, ‘In what ways might biases and heuristics play a special role in aiding our understanding of, and response to, fundamentalist orientation?’. The judgments we make in ignorance of our own biases Montaigne calls our importunate presumptions, and he suggests a host of practical factors that make them appealing. Montaigne, as I discuss in the first section, associates many of our errors with one or another kind of presumption, often about our similarity or differences from others, or from God. Our obvious psychographic diversity, and the polemical ground dynamics involved in our ‘culture wars’ are compounded on the agential side by the invisibility of our biases to ourselves. A number of person and social biases are described that plausibly affect all of our beliefs in domains of controversial views, religious views included. The second section continues to study of how etiological symmetry (similar patterns of belief-uptake) gives rise to religious contrariety (diverse narratives and theologies) in testimonial faith traditions, and what the implications of this are for philosophy of religion, generally, and for an improved comparative study of fundamentalism, in particular. Utilizing the work of philosophers such as Rachel Fraser and psychologists such as Emily Pronin and her co-authors, I offer a four-step genealogical account for how etiological symmetry so easily gives rise to religious contrariety. This account begins with the narrative nature of testimony in the Abrahamic family of religions, and how narrative content confounds our “source monitoring.” My genealogy also introduces what I term biased-closure inferences (BCI) as one of the key enablers of religious exclusivism and absolutism. These are the seemingly ‘logical’ but actually very self-serving inferences people often make, inferences from their own belief being true, to any belief contrary to it being false. Those who claim unique truth, epistemic access, and/or virtue and religious value for the home religion are no exception to the broad pertinence of bias studies across domains of controversial view. The proximate causes of belief are all that we can study, and in these there may be significant etiological symmetries. Yet those groups themselves, especially to the extent that they are exclusivist, are tunnel-visioned on claims of doctrinal uniqueness: on content differences of a theological sort. Comparative philosophy is met with the puzzlement that symmetric or essentially similar doxastic strategies should give rise not just to cognitive diversity, but to what we can call polarized or polemical contrariety, contrariety of a kind where each view adamantly rejects all others. Arguably, the more that theologies offer explanations of a counter-inductive sort, or profess counter-inductive thinking as exemplary of faith, the better evidential ground there for inferring that bias involved in the acquisition or maintenance of beliefs. This provides more substance to the question of when censure, and etiological challenges to faith-based beliefs are philosophically well-motivated. (shrink)

The semigroup of trajectories in Minkowski space-time and its induced representations are constructed as a generalization of the Galilei case. They describe relativistic pointlike particles and yield the free propagator as a path integral in the space of trajectories parametrized by a fifth parameter. This non physical propagator in a five-dimensional space is integrated over the fifth parameter to yield the physical propagator in Minkowski space. Thereafter, this notion is applied to a model of extended particles with internal Poincaré (...) class='Hi'>symmetry and moving in an external Minkowski space. The geometrical structure is of Hilbert bundles and the interaction is introduced as a connection. The propagator is a path integral with respect to either the internal and external trajectories and reduces to a product of an internal and an external propagator when the interaction is ignored, just as has been found in a previous work with representations of the group rather than those of the semigroup. (shrink)

A geometro-differential quantum theory of extended particles is presented. The geometrical selling is that of Hilbert fiber bundles whose base manifolds are pseudo-Riemannian space-times of points χ which are interpreted as partial aspects of physical reality (the extended particle). The fibers are carrier spaces of induced (internal configuration and momentum) representations of the structural group (the de Sitter group here). Sections of these bundles are seen as physical representations of the particle, and their values in the fibers are interpreted as (...) states of internally localized modes composing the particle. This geometrical structure is “analogous” to that of a geometro-stochastic quantization developed in recent years. The physical interpretation is a combination of those of an old functional quantum theory and of an induced representation scheme based on an interpretation of intertwining, between configuration and momentum representations, as localization, materialization, and propagation of particles. Our model is applied in two cases: (1) Induced representation is applied in both space-time and internal space: both have de Sitter symmetry whose connection is ignored. Intertwining is considered in both spaces in a composed fashion. (2) For generic spacetimes and when the connection is taken into account, intertwining is applied only in the internal space. Parallel transport is combined with intertwining for a redefinition of localization, materialization, and propagation (the latter in a path integral context inspired from geometro-stochastic quantization). (shrink)

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...) of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible. (shrink)

Sport categorization is often justified by benefits such as increased fairness or inclusion. Taking inspiration from John Rawls, Sigmund Loland’s fair equality of opportunity principle in sport (FEOPs) is a tool for determining whether the existence of an inequality ethically justifies the institution of a new category in any given sport. It is an elegant ethical normative framework, but since FEOPs does not account explicitly for athlete safety (i.e. athlete physical and mental wellbeing), we are left in an ethically dubious (...) situation where the risk of harm associated with a categorization regime might in fact prove to be greater than the risk of harm present within the sport before its introduction. To address this critical gap, I propose the ‘scales of ignorance’ ethical normative framework to weigh the relative risk of harm within a sport, crucially inserting athlete safety into the discourse surrounding ethical justification for categorization in sport. The current paper is the first explicit formulation of assessment and ethical justification of risk of harm in the familiar logic of FEOPs. The scales of ignorance framework can also be used independently of Loland’s approach. Two new concepts are also proposed: ‘insidious risk of harm’ and ‘pernicious risk of harm’. (shrink)

The question about the relation between spacetime structure and the symmetries of laws has received renewed attention in a recent discussion about the status of Minkowski spacetime in Special Relativity. In that context we find two extreme positions (either spacetime explains symmetries of laws or vice-versa) and a general assumption about the debate being mainly about explanation. The aim of this paper is twofold: first, to argue that the ontological dimension of the debate cannot be ignored; second, to claim that (...) taking ontology into account involves considering a third perspective on the relation between spacetime and symmetries of laws; one in which both terms would be somehow derived from common assumptions on the formulation of a given physical theory. (shrink)

The Secret Symmetry of Maimonides and Freud presents the parallels between The Guide of the Perplexed and The Interpretation of Dreams, considering how Maimonides might be perceived as anticipating Freud's much later work. In this volume, Nathan M. Szajnberg suggests that humankind has secrets to hide and does so by using common mechanisms and embedding revealing hints for the benefit of the true reader. Using a psychoanalytic approach in tandem with literary criticism and an in-depth assessment of Judaica, Szajnberg (...) demonstrates the similarities between these two towering Jewish intellectual pillars. Using concepts of esoteric literature from the Torah and later texts, this book analyses their ideas on concealing and revealing to gain a renewed perspective on Freud's view of dreams. Throughout, Szajnberg articulates the challenges of reading translated works and how we can address the pitfalls in such translations. The book is a vital read for psychoanalysts in training and practice, as well as those interested in Judaica, the history of ideas and early Medieval studies. (shrink)

Daniel Ellsberg presented in Ellsberg (The Quarterly Journal of Economics 75:643–669, 1961) various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage (1972). Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky (1995) an explanation of Ellsberg’s two-color problem (...) in terms of a psychological effect: ambiguity aversion . The ‘comparative ignorance’ hypothesis articulates how this effect works and explains why it is important to an understanding of the typical pattern of responses associated with Ellsberg’s two-color problem. In the first part of this article we challenge Fox and Tversky’s explanation. We present first an experiment that extends Ellsberg’s two-color problem where certain predictions of the comparative ignorance hypothesis are not confirmed. In addition the hypothesis seems unable to explain how the subjects resolve trade-offs between security and expected pay-off when vagueness is present. Ellsberg offered an explanation of the typical behavior elicited by his examples in terms of these trade-offs and in section three we offer a model of Ellsberg’s trade-offs. The model takes seriously the role of imprecise probabilities in explaining Ellsberg’s phenomenon. The so-called three-color problem was also considered in Fox and Tversky (1995). We argue that Fox and Tversky’s analysis of this case breaks a symmetry with their analysis of the two-color problem. We propose a unified treatment of both problems and we present a experiment that confirms our hypothesis. (shrink)

Philosophers who work on time often ignore the implications their doctrines have for the common sense intuition that the past is fixed and the future not. Similarly, those who work on fatalism, and whose arguments often imply an assertion or denial of the common sense intuition, rarely take into account the implicit dependence their arguments have upon specific theories of time. I take the intuition, and its relation to the nature of time, seriously. In Part I of my thesis, I (...) investigate the relations between the dynamic and static theories of time, on the one hand, and the intuition, on the other. I argue that the so called 'pure' forms of these theories, inasmuch as they both posit an ontological temporal symmetry, cannot do justice to the intuition. The 'pure' B-Theory, with its denial of objective temporal becoming, cannot allow for a robust sense in which the future is non-fixed. The 'pure' A-Theory, according to which only the present exists, acknowledges the robustness of the asymmetry, but cannot provide a ground for it. I conclude Part I of my thesis with the claim that only a conception of time according to which the past exists and the future does not, can account for the intuition. In Part II, I discuss those fatalistic arguments which rely upon the determinateness of future truth as their key premise, and argue that these fail either because they rely on an illegitimate modal concept, or because they rely on a key undefended assumption. Finally, in the Epilogue, I provide a more detailed sketch of the account of time posited at the end of Part I, and suggest that it can also provide a more thoroughgoing rejection of the logical fatalistic argument. (shrink)

Contemporary evolutionary theory, derived from the intellectual marriage of Darwin's and Mendel's discoveries, leads us to view organisms as successful, but essentially ad hoc, responses to chance and necessity. Biological universals, the code, the pentadactyl limb, are frozen accidents shared by descent. The source of biological order has come to be seen as selection itself. This paper argues that this view is fundamentally inadequate. It ignores those underlying sources of biological order which derive from the generic self-organizing properties of the (...) biological building blocks. Among these generic properties are almost universal aspects of phase resetting responses in biological rhythmic systems, fascinating properties of continuity, symmetry and handedness seen in pattern regeneration across distant phyla; and statistically robust properties expected of eukaryotic gene regulatory systems persistently subject to mutations which "scramble" regulatory interactions. These examples suggest that many properties in organisms reflect a balance between selection, and the rich generic properties which would occur in the absence of selection. Where the balance is "close" to generic, a new pattern of evolutionary inference, and an ahistorical source of biological universals may be found: Those properties reflect, not selection, but the self-organizing features of the building blocks. (shrink)

It is widely held among philosophers that the conservation of energy is true and important, and widely held among philosophers of science that conservation laws and symmetries are tied together by Noether's first theorem. However, beneath the surface of such consensus lie two slights to Noether's first theorem. First, there is a 325+-year controversy about mind-body interaction in relation to the conservation of energy and momentum, with occasional reversals of opinion. The currently popular Leibnizian view, dominant since the late 19th (...) century, claims to find an objection to broadly Cartesian views in their implication of energy non-conservation. Here energy conservation is viewed as an oracle, an unchallengeable black box. But Noether's first theorem and its converse show that conservation and symmetry of the laws stand or fall together. Absent some basis for expecting conservation in brains that has a claim on the Cartesian, the objection is circular. An empirically based argument is possible, but is a different argument with little force except insofar as it is rooted in neuroscience. Second, General Relativity has a 100+-year-long controversy about whether gravitational energy exists and is objectively localized. The usual view is that gravitational energy exists but is not objectively localized, though some deny its existence. Without positive answers to both questions, generally applicable conservation laws do not exist: energy is not conserved. This conclusion is startling in itself and a problem for conserved quantity theories of causation. Yet Noether's first theorem applies to General Relativity, which has uncountably many symmetries of its laws and so has conservation laws, indeed uncountably many of them. Many authors downplay these laws due to their quirky properties; some authors even attempt to explain the laws' supposed nonexistence in terms of an absence of symmetries of the geometry, which is a distraction. Thus Noether's first theorem is widely ignored, left uninterpreted, or distorted in relation to General Relativity. Taking the theorem seriously seems possible, however, restoring the conservation of energy, or rather, energies. How do these controversies relate? One sometimes finds claims that General Relativity's supposed lack of conservation laws answers Leibniz on behalf of Descartes. Taking seriously the superabundance of formal conservation laws in General Relativity, however, suggests that General Relativity resists mind-to-body causation. This conclusion can be proven apart from interpretive controversies. The resistance is, however, finite and tends to be swamped by larger world-view considerations. (shrink)

This paper presents a new solution to the well-known exchange paradox, or what is sometimes referred to as the two-envelope paradox. Many recent commentators have analyzed the paradox in terms of the agent’s biased concern for the contents of his own arbitrarily chosen envelope, claiming that such bias violates the manifest symmetry of the situation. Such analyses, however, fail to make clear exactly how the symmetry of the situation is violated by the agent’s hypothetical conclusion that he ought (...) to switch envelopes on the assumption that his own envelope contains some specific amount of money. In this paper, I offer an explanation of this fact based on the idea that the agent’s deliberations are not only constrained by the epistemic symmetry reflected in the agent’s uniform ignorance as to the contents of the two envelopes, but also by a deeper methodological symmetry that manifests itself in the intuition that the two envelopes constitute equally legitimate sources of potential information. I interpret this intuition as implying that the agent’s final decision should reflect a point of rational equilibrium arrived at through an iterated process of counterfactual self-reflection, whereby the agent takes account of what he would have thought had he instead chosen the other envelope. I provide a formal model of this method of counterfactual self-reflection and show, in particular, that it cannot issue in the paradoxical conclusion that the agent ought to switch regardless of how much money is in his envelope. In this way, by correcting for the bias in the agent’s reasoning, the paradox is resolved. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Feeling IgnorantA Phenomenology of Ignorance1Emily McRaeWhat does it feel like to be confused? What does it feel like to ignore something? These questions, although not prioritized in Western epistemologies, nevertheless matter in our lives. We often use our feelings as feedback on our epistemic states. Feeling ignorant is a reason to think we are ignorant and can motivate us to do something about it. Such feelings are fallible, of (...) course—we can feel like we know something we do not in fact know—but they provide rough, practical guidance to tracking our own epistemic states and motivations. In fact, feelings of ignorance may be central to the activity of learning. It is doubtful that we could learn effectively without them.But the affective profile and phenomenology of ignorance are rarely theorized in Western accounts, in large part, I suspect, because of the pervasive dichotomy of "thinking and feeling" that historically has dominated Western philosophical approaches to the mind. This dichotomy encourages us to sort phenomena according to their boundaries, and, if we must choose, ignorance seems to be more of an epistemic event than an affective one. Luckily, though, we do not have to choose. Buddhist psychological taxonomies, as I will show, are drawn along different lines. This positions Buddhist moral psychology to be a productive framework to investigate ignorance, since it allows us to attend to its epistemic, affective, and somatic contours.This paper focuses on the affective component of ignorance: what ignorance feels like, when and why these feelings arise (and when and why [End Page 26] they do not), and what feeling ignorant, particularly in moral contexts, can do for us. Drawing on the fourth-century Indian Buddhist philosopher Vasubandhu, I examine the phenomenology of ignorance and argue that how ignorance feels depends on our epistemic access to our ignorance (whether and to what extent we know that we are ignorant) and the object of ignorance (what our ignorance is about). I argue that ignorance has a complex affective profile: it can feel a lot of different ways, ranging from unpleasant fogginess to clueless confidence. This complex affective profile makes ignorance difficult to spot, especially in ourselves, and marks a difference between ignorance and other problematic mental states, such as hatred or resentment, that have a more straightforward phenomenology. Understanding the connection between the object of ignorance, the epistemology of ignorance, and its affective phenomenology allows us to take on the project, essential in the Buddhist philosophical traditions, of locating and addressing our ignorance. Without careful attention to these three components, it is possible, and likely, to simply ignore our ignorance. I conclude with the suggestion that the ability to attend to our ignorance requires the cultivation of equanimity.This investigation into the affective side of ignorance requires the introduction of a core Buddhist philosophical and psychological category: the dysfunctional states (kleśa; nyon mongs). This is not only because the category of kleśa is a productive framework for understanding the phenomenology and epistemology of ignorance, as I will argue in the next section, but also because traditional Western categories of reason and emotion, or thinking and feeling, are not up to the task of investigating the affective aspects of ignorance. This dichotomy makes a division exactly at the place where my inquiry in this paper begins, for ignorance—as an affective, epistemic, and somatic experience—straddles the divide between thinking and feeling. The category of kleśa includes ignorance, along with other states that Western taxonomies would classify as emotions, such as hatred or envy. This allows for an investigation into features that ignorance may share with emotions without the commitment to the cumbersome claim that ignorance is (or is not) an emotion in the Western sense.The KleśasThe kleśas are dysfunctional states that cause wrong actions and suffering. They are typically divided into primary and secondary kleśas, where the primary kleśas are the root dysfunctional states and the secondary kleśas arise from the primary ones. Different texts and traditions include different kleśas as primary and secondary, but all agree that ignorance, desire, and hatred are among the primary kleśas... (shrink)

This paper discusses the discrete symmetries of off-shell electromagnetism, the Stueckelberg–Schrodinger relativistic quantum theory and its associated 5D local gauge theory. Seeking a dynamical description of particle/antiparticle interactions, Stueckelberg developed a covariant mechanics with a monotonically increasing Poincaré-invariant parameter. In Stueckelberg’s framework, worldlines are traced out through the parameterized evolution of spacetime events, which may advance or retreat with respect to the laboratory clock, depending on the sign of the energy, so that negative energy trajectories appear as antiparticles when the (...) observer describes the evolution using the laboratory clock. The associated gauge theory describes local interactions between events (correlated by the invariant parameter) mediated by five off-shell gauge fields. These gauge fields are shown to transform tensorially under under space and time reflections—unlike the standard Maxwell fields—and the interacting quantum theory therefore remains manifestly Lorentz covariant. Charge conjugation symmetry in the quantum theory is achieved by simultaneous reflection of the sense of evolution and the fifth scalar field. Applying this procedure to the classical gauge theory leads to a purely classical manifestation of charge conjugation, placing the CPT symmetries on the same footing in the classical and quantum domains. In the resulting picture, interactions do not distinguish between particle and antiparticle trajectories—charge conjugation merely describes the interpretation of observed negative energy trajectories according to the laboratory clock. (shrink)

It is proposed that symmetry of stone tools may derive from perceptual similarity rather than from cognitively more complex awareness of symmetry. Although encodement of shapes necessarily involves symmetry (as evidenced by the confusability of enantiomorphs), it does not imply awareness of symmetry. Responses of relatively simple organisms, such as bees, support the notion that the processes involved are likely to be perceptual.

How and why does the moon cause the tides? How and why does God answer prayers? For many, the answer to the former question is unknown; the answer to the latter question is a mystery. Across three studies testing a largely Christian sample within the United States (N= 2524), we investigate attitudes toward ignorance and inquiry as a window onto scientific versus religious belief. In Experiment 1, we find that science and religion are associated with different forms of (...) class='Hi'>ignorance: scientific ignorance is typically expressed as a personal unknown (“it's unknown to me”), whereas religious ignorance is expressed as a universal mystery (“it's a mystery”), with scientific unknowns additionally regarded as more viable and valuable targets for inquiry. In Experiment 2, we show that these forms of ignorance are differentially associated with epistemic goals and norms: expressing ignorance in the form of “unknown” (vs. “mystery”) more strongly signals epistemic values and achievements. Experiments 2 and 3 additionally show that ignorance is perceived to be a greater threat to science and scientific belief than to religion and religious belief. Together, these studies shed light on the psychological roles of scientific and religious belief in human cognition. (shrink)

Michael J. Zimmerman explores whether and how our ignorance about ourselves and our circumstances affects what our moral obligations and moral rights are. He rejects objective and subjective views of the nature of moral obligation, and presents a new case for a 'prospective' view.

In this paper, we continue the study of the Killing symmetries of an N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the finite structure of the space–time rotations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space M_4, for which we derive the explicit general form of the (...) finite rotations and boosts in different parametric bases. (shrink)

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the translations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\widetilde M_4 $$ \end{document}.

In this paper we argue that there is a kind of moral disagreement that survives the Rawlsian veil of ignorance. While a veil of ignorance eliminates sources of disagreement stemming from self-interest, it does not do anything to eliminate deeper sources of disagreement. These disagreements not only persist, but transform their structure once behind the veil of ignorance. We consider formal frameworks for exploring these differences in structure between interested and disinterested disagreement, and argue that consensus models (...) offer us a solution concept for disagreements behind the veil of ignorance. (shrink)

According to structural realism, in mature science there is structural continuity along theoretical change. A major counterexample to this thesis is the transition from the Eightfold Way to the Standard Model in particle physics. Nevertheless, the notion of structure is significantly important in comprehending the theoretical picture of particle physics, where particles change and undergo transmutations, while the only thing which remains unchanged is the basic structure, i.e. the symmetry group which controls the transmutations. This kind of view agrees (...) with the paradigmatic case where the structure is an internal symmetry and the instantiations are the elementary particles. The metaphysical view which reflects this situation is a version of ontic structuralism. (shrink)

I discuss the question of when knowledge of higher order ignorance is possible and show in particular that, under quite plausible assumptions, knowledge of second order ignorance is impossible.

In this paper, we introduce the concept of N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. This is the first of a series of papers devoted to the investigation of the Killing symmetries of generalized Minkowski spaces. In particular, we discuss here the infinitesimal-algebraic structure of the space-time rotations in such spaces. It is shown that the maximal Killing group of these spaces is the direct product (...) of a generalized Lorentz group and a generalized translation group. We derive the explicit form of the generators of the generalized Lorentz group in the self-representation and their related, generalized Lorentz algebra. The results obtained are specialized to the case of a 4-dimensional, “deformed” Minkowski space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\widetilde M}$$ \end{document}4, i.e., a pseudoeuclidean space with metric coefficients depending on energy. (shrink)

In this paper, we propose a new theory of rationality defeat. We propose that defeaters are "indicators of ignorance", evidence that we’re not in a position to know some target proposition. When the evidence that we’re not in a position to know is sufficiently strong and the probability that we can know is too low, it is not rational to believe. We think that this account retains all the virtues of the more familiar approaches that characterise defeat in terms (...) of its connection to reasons to believe or to confirmation but provides a better approach to higher-order defeat. We also think that a strength of this proposal is that it can be embedded into a larger normative framework. On our account the no-defeater condition is redundant. We can extract our theory of defeat from our theory of what makes it rational to believe—it is rational to believe when it is sufficiently probable that our belief would be knowledge. Thus, our view can provide a monistic account of defeat, one that gives a unifying explanation of the toxicity of different defeaters that is grounded in a framework that either recognises knowledge as the norm of belief or identifies knowledge as the fundamental epistemic good that full belief can realise. (shrink)

The veil of ignorance argument was used by John C. Harsanyi to defend Utilitarianism and by John Rawls to defend the absolute priority of the worst off. In a recent paper, Lara Buchak revives the veil of ignorance argument, and uses it to defend an intermediate position between Harsanyi's and Rawls' that she calls Relative Prioritarianism. None of these authors explore the implications of allowing that agent's behind the veil are averse to ambiguity. Allowing for aversion to ambiguity---which (...) is both the most commonly observed and a seemingly reasonable attitude to ambiguity---however supports a version of Egalitarianism, whose logical form is quite different from the theories defended by the aforementioned authors. Moreover, it turns out that the veil of ignorance argument neither supports standard Utilitarianism nor Prioritarianism unless we assume that rational people are insensitive to ambiguity. (shrink)

Critics of the Implicit Association Test —a measure of the strength of a person’s automatic, memory-based association between two concepts, such as “black” and “threatening” or “white” and “caring”—have at least three main objections. Their symmetry argument is that the IAT should but does not give equally valid results for black-on-white and white-on-black racism. Their cultural-awareness argument is that the IAT illegitimately presupposes that use of racial stereotypes presupposes no stereotype acceptance, only stereotype awareness. Their completeness argument is that (...) at best the IAT measures only questionable or implicit, not explicit, bias because IAT ignores the fact that subjects’ conscious desires to avoid bias often enable them to check their biased behavior. Examining each of these anti-IAT stances, the paper summarizes the IAT and then argues for 6 main claims. Clarifying concepts like racism is important for progress in social science. IAT critics’ SA presupposes an ahistorical/acultural concept of racism. IAT critics’ AA presupposes a linguistically-insensitive concept of racism, one presupposing that the language we use provides no behavioral evidence for racism. IAT critics’ CA presupposes a concept of racism subject to conscious, deliberate control. IAT proponents endorse a more plausible concept of racism, one that is contextual, linguistically sensitive, and often not susceptible to conscious control. Although the IAT debate is unsettled, IAT critics’ use of a questionable concept of racism gives grounds for doubting their claims. (shrink)

A long line of epistemologists including Sosa (2021), Feldman (2002), and Chisholm (1977) have argued that, at least for a certain class of questions that we take up, we should (or should aim to) close inquiry iff by closing inquiry we would meet a unique epistemic standard. I argue that no epistemic norm of this general form is true: there is not a single epistemic standard that demarcates the boundary between inquiries we are forbidden and obligated to close. In short, (...) such norms are false because they are insensitive to the potentially ambitious epistemic goals that agents may permissibly bring to bear on an inquiry. Focusing particularly on knowledge-oriented versions of the norm, I argue that ignorance has a positive role to play in epistemic life by licensing prolonged inquiry into questions that we especially care about. (shrink)

The work of René Girard invites us to re-imagine a ‘religious–secular’ interactivity within social space in a way released from the violent dualisms of the ‘sacred/profane.’ Earlier Dietrich Bonhoeffer considered the same task and suggested directions for a positive theology of church-state relations, even as the inherited forms of these institutions were collapsing about him. This paper explores the Girardian scenario for church and state becoming rivalrous ‘doubles’– whether it be secular utopic projects doubling religious narratives of redemption, or churches (...) doubling the state as parallel yet purer societies – and suggests resources from Bonhoeffer by which a non-rivalrous church-state relationality - both mutually-constituting and mutually-limiting - may be configured. (shrink)

Despite the recent increase in interest in philosophy about ignorance, little attention has been paid to the question of what makes it possible for a being to become aware of their own ignorance. In this paper, I try to provide such an account by arguing that, for a being to become aware of their own ignorance, they must have the mental capacity to represent something as being unknown to them. For normal adult humans who have mastered a (...) language, mental representation of an unknown is enabled by forming linguistic expressions whose content is grasped, but whose referent is unknown. I provide a neo-Fregean, a neo-Russellian, and then a unified account of this. On that basis, I then argue further that the content of ignorance can always be captured by a question. I then distinguish between propositional ignorance and non-propositional ignorance and argue that propositional ignorance attributions can be of three types, that-ignorance, whether-ignorance, and fact-ignorance. I conclude by arguing that the acquisition of truths, even when it yields knowledge that is certain, does not always eliminate one’s ignorance and that there is a degree of ignorance in almost everything we claim to know. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given (...) time; an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

In this article I discuss how Jacques Rancière’s thought invites us to re-conceptualize the education–emancipation nexus. The primary goal of traditional approaches to emancipatory and anti-oppressive education has been to empower the oppressed so that the latter can (re)gain their voice and transform their situations. Building on Rancière’s ideas, I argue that the processes of empowering the oppressed imply that one has the power to empower the other, and thus start with an assumption of inequality. I conclude the article with (...) a call for a pedagogy of ignorance. Grounded in Rancière’s thought, this pedagogy is ignorant of any division and hierarchy of intelligence. (shrink)

Physicists routinely claim that the fundamental laws of physics are 'time symmetric' or 'time reversal invariant' or 'reversible'. In particular, it is claimed that the theory of quantum mechanics is time symmetric. But it is shown in this paper that the orthodox analysis suffers from a fatal conceptual error, because the logical criterion for judging the time symmetry of probabilistic theories has been incorrectly formulated. The correct criterion requires symmetry between future-directed laws and past-directed laws. This criterion is (...) formulated and proved in detail. The orthodox claim that quantum mechanics is reversible is re-evaluated. The property demonstrated in the orthodox analysis is shown to be quite distinct from time reversal invariance. The view of Satosi Watanabe that quantum mechanics is time asymmetric is verified, as well as his view that this feature does not merely show a de facto or 'contingent' asymmetry, as commonly supposed, but implies a genuine failure of time reversal invariance of the laws of quantum mechanics. The laws of quantum mechanics would be incompatible with a time-reversed version of our universe. (shrink)

It is argued that the two main accounts of ignorance in the contemporary literature—in the terms of the lack of knowledge and the lack of true belief—are lacking in key respects. A new way of thinking about ignorance is offered that can accommodate the motivations for both of the standard views, but which in the process also avoids the problems that afflict these proposals. In short, this new account of ignorance incorporates the idea that ignorance essentially (...) involves not just the absence of a certain epistemic good, but also an intellectual failing of inquiry. It is further contended that making sense of this normative dimension to ignorance requires one to situate one’s account of ignorance within a wider epistemic axiology. (shrink)

This article investigates the connections between the logics of being wrong, introduced in Steinsvold (2011, Notre Dame J. Form. Log., 52, 245–253), and factive ignorance, presented in Kubyshkina and Petrolo (2021, Synthese, 198, 5917–5928). The first part of the paper provides a sound and complete axiomatization of the logic of factive ignorance that corrects errors in Kubyshkina and Petrolo (2021, Synthese, 198, 5917–5928) and resolves questions about the expressivity of the language. In the second half, it is shown (...) that the relationship between the two logics suggests an alternative axiomatization for the logic of factive ignorance, the adequacy of which is easily proved via straightforward translations. (shrink)

In these challenging pages, Unger argues for the extreme skeptical view that, not only can nothing ever be known, but no one can ever have any reason at all for anything. A consequence of this is that we cannot ever have any emotions about anything: no one can ever be happy or sad about anything. Finally, in this reduction to absurdity of virtually all our supposed thought, he argues that no one can ever believe, or even say, that anything is (...) the case. (shrink)

Recent years have seen a surge in publications about the epistemology of ignorance. In this article, I examine the proliferation of the concept ignorance that has come with the increased interest in the topic. I identify three conceptions of ignorance in the current literature: (1) ignorance as lack of knowledge/true belief, (2) ignorance as actively upheld false outlooks and (3) ignorance as substantive epistemic practice. These different conceptions of ignorance are as of yet (...) unacknowledged but are bound to impede epistemology of ignorance and, therefore, need to be uncovered. After discussing three unsuccessful ways of dealing with these varying conceptions, I put forward an integrated conception of ignorance that is more adequate for serving as the foundation of epistemology of ignorance. Introducing an alternative conception of ignorance provides us with a foundation for both epistemological and more broadly philosophical work on ignorance. (shrink)