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.

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)

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)

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)

This study analyzes the ideals of responsibility and accountability, asking such questions as when it is legitimate to blame top officials of an organization for mistakes made by personnel below them in the bureaucratic hierarchy; when things go wrong in a large and complex organization like the Canadian Forces, who is responsible and accountable; and whether a plea of ignorance is a good excuse. The study also analyzes the doctrine of ministerial responsibility in both the British and Canadian parliamentary (...) traditions, asking whether it is realistic to expect that a government minister should be held responsible for everything that goes wrong in his/her department. Finally, traditional military values are examined, considering the kinds of attitudes and values expected from Canada's armed forces and the differences between the military and civilian sectors. (shrink)

The Argonautica is the dramatic story of Jason's quest for the Golden Fleece and his relations with the dangerous Colchian princess, Medea. The only extant Greek epic poem to bridge the gap between Homer and late antiquity, it is a major product of the brilliant world of the Ptolemaic court at Alexandria, written by Apollonius of Rhodes in the 3rd century BC. Apollonius explores many of the fundamental aspects of life in a highly original way: love, deceit, heroism, human (...) class='Hi'>ignorance of the diven, the limits of science. This volume offers the first scholarly translation into English prose for many years, combining readability with accuracy and an attention to detail that will appeal to readers both with and without Greek. `Based on a deep understanding of the text, this translation, with informative notes and an excellent introduction, will bring Apollonius to the audience he deserves....' ABOUT THE SERIES: For over 100 years Oxford World's Classics has made available the widest range of literature from around the globe. Each affordable volume reflects Oxford's commitment to scholarship, providing the most accurate text plus a wealth of other valuable features, including expert introductions by leading authorities, helpful notes to clarify the text, up-to-date bibliographies for further study, and much more. (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)

This paper challenges the first Gettier counterexample to the tripartite account of knowledge. Noting that 'the man who will get the job' is a description and invoking Donnellan's distinction between their 'referential' and 'attributive' uses, I argue that Smith does not actually believe that the man who will get the job has ten coins in his pocket. Smith's ignorance about who will get the job shows that the belief cannot be understood referentially, his ignorance of the coins in (...) his pocket shows that it cannot be understood attributively. An explanation for why Smith appeared to have justified true belief is given by distinguishing between 'belief' and 'belief in truth'. Smith believes the sentence 'the man who will get the job has ten coins in his pocket' to be true (he mistakenly believes that Jones will get the job, of whom he knows that he has ten coins in his pocket) (hence his 'belief'), the sentence is true (hence 'truth'), and he has sufficient reason to assent to it (hence his 'justification'). But he does not believe the proposition expressed. Hence he does not know it either. (shrink)

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)

Marine ecosystems are under increasing pressure from human activity, yet successful management relies on knowledge. The evidence-based policy (EBP) approach has been promoted on the grounds that it provides greater transparency and consistency by relying on ‘high quality’ information. However, EBP also creates epistemic responsibilities. Decision-making where limited or no empirical evidence exists, such as is often the case in marine systems, creates epistemic obligations for new information acquisition. We argue that philosophical approaches can inform the science-policy interface. Using marine (...) biosecurity examples, we specifically examine the epistemic challenges in the acquisition and acceptance of evidence to inform policy, discussing epistemic due care and biases in consideration of evidence. (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)

Agnotology is the study of how ignorance arises via circulation of misinformation calculated to mislead. Legates et al. had questioned the applicability of agnotology to politically-charged debates. In their reply, Bedford and Cook, seeking to apply agnotology to climate science, asserted that fossil-fuel interests had promoted doubt about a climate consensus. Their definition of climate ‘misinformation’ was contingent upon the post-modernist assumptions that scientific truth is discernible by measuring a consensus among experts, and that a near unanimous consensus exists. (...) However, inspection of a claim by Cook et al. of 97.1 % consensus, heavily relied upon by Bedford and Cook, shows just 0.3 % endorsement of the standard definition of consensus: that most warming since 1950 is anthropogenic. Agnotology, then, is a two-edged sword since either side in a debate may claim that general ignorance arises from misinformation allegedly circulated by the other. Significant questions about anthropogenic influences on climate remain. Therefore, Legates et al. appropriately asserted that partisan presentations of controversies stifle debate and have no place in education. (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)

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}.

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.

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)

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)

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)

The two-point correlation functions of classical electromagnetic zero-point radiation fields are evaluated in four-vector notation. The manifestly Lorentz-covariant expressions are then shown to be invariant under scale transformations and under the conformal transformations of Bateman and Cunningham. As a preliminary to the electromagnetic work, analogous results are obtained for a scalar Gaussian random classical field with a Lorentz-invariant spectrum.

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)

Earman (2018) has recently argued that the Principal Principle, a principle of rationality connecting objective chance and credence, is a theorem of quantum probability theory. This paper critiques Earman's argument, while also offering a positive proposal for how to understand the status of the Principal Principle in quantum probability theory.

In The Virtues of Ignorance the author demonstrates that classical theories of virtue are flawed and developes a consequentialist theory of virtue. ;Virtues are excellences of character. They are traits which are considered to be valuable in some way. A person who is virtuous is one who has a tendency to act well. Classical philosophers, such as Plato and Aristotle, believed that virtues, as human excellences, could not involve ignorance in any way. On their view, the virtuous agent, (...) when acting well, knows what she is doing under the description which makes the action conform to virtue. For example, the generous person must know that she is, in fact, helping others in need. Yet, there is a class of virtues, the "virtues of ignorance," which essentially involve ignorance. For example, modesty requires that the agent underestimate self worth. In the first portion of the dissertation, this class of virtues is discussed, and problems raised for the traditional theories of virtue. ;In the latter portion of the dissertation, the author outlines a consequentialist theory of virtue. It is argued that the only hope of developing a unified theory of virtue is along consequentialist lines, because attempts at identifying the psychological state which is necessary for virtue have failed. On a consequentialist theory, a virtue is defined in terms of its consequences. Thus, the moral quality of the character trait is determined by how much good it brings about . The virtues of ignorance can easily be accommodated in such a theory because these traits do bring about good, even if the agent possessing the trait acts out of ignorance. (shrink)

Leading scholars explore how different forms of ignorance are produced and sustained, and the role they play in knowledge practices.

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)

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)

Thoroughly researched contributions from conferences at Harvard and Paris on coping with ignorance in late medieval and early modern administrative practices, science, literature and the arts, are tightly connected by a new theoretical framework on how to historicize ignorance.

While mechanics was developed under the idea of reciprocal action (interactions), electromagnetism, as we know it today, takes a form more akin to unilateral action. Interactions call for spatial relations, unilateral action calls for space, just one reference centre. In contrast, interactions are matters of relations that require at least two centres. The development of the relational electromagnetism encouraged by Gauss appears to stop around 1870 for reasons that are not completely clear but are certainly not solely scientific. By the (...) same time, Maxwell recognised the equivalence in formulae of his electromagnetism and the one advocated by Gauss and called for an explanation of why such theories so differently conceived have such a large part in common. In this work we reconstruct and update the relational electromagnetism up to the contributions of Lorentz guided by the non-arbitrariness principle (NAP) that requests arbitrary choices to be accompanied by groups of symmetries. We show that a-priori there must be two more symmetries in electromagnetism, one related to the breaking (in the description) of the relation source/detector and one relating all the perceptions of the same source by detectors moving with different (constant) relative velocities. We show that the idea of electromagnetic waves put forward in concept by Lorenz (1861-1863) before Maxwell (1865) and in formulae (1867) just after Maxwell, together with the ``least action principle'' proposed by Lorentz are enough to derive Maxwell's equations, the continuity equation and the Lorentz' force, and that there is a dual formulation in terms of fields of the receiver (as opposed to fields of the source). While Galilean transformations are associated with removing the arbitrariness implied in the election of a reference space, they will not explicitly appear in a formulation based upon a relational space although we occasionally mention their usefulness. In contrast, Lorentz' transformations will emerge in this formulation involving the relations between the perceived fields of different receivers. Moreover, the role of the full Poincaré-Lorentz group as a group of transformations of the perceived actions is elucidated. In summary, we answer Maxwell's philosophical question showing how the same theory in formulae can be abduced using different inferred entities. Each form of abduction implies as well an interpretation and a facilitation of the theoretical construction. This work relies heavily on logical concepts as abduction put forward by C. Peirce, needed for the construction of theories. (shrink)

Engaging with the specific ways current media technologies interact with, or directly access the human body, we suggest developing a ‘symmetrical’ theory of touch. Critically referring to Bruno Latour’s invocation of ‘symmetrical anthropology’, we reconsider tactile agency as ‘technological agency’, arguing that the concept of touch – traditionally viewed as an exclusively human ability – should be extended to non-human actors and analysed in view of the cultural logic of capitalism. Its systematic focus, then, is on the productive intersections and (...) contact zones between biology and technology: from phenomena of non-human touch in industrial production to the material touching taking place in the instrumental grasp on the living in the 19th-century physiological laboratories and the invisible operations of tracing, tracking and sensing taking place in the technological milieus of today’s environments. In highlighting the tactile dimension of digital modernity and its economic genealogies, this article aims to advance a combined concept of human and non-human touch which provides a crucial angle for reconsidering bodies and technologies in the age of ubiquitous computing. (shrink)

This essay aims to clarify the value of developing systematic studies of ignorance as a component of any robust theory of knowledge. The author employs feminist efforts to recover and create knowledge of women's bodies in the contemporary women's health movement as a case study for cataloging different types of ignorance and shedding light on the nature of their production. She also helps us understand the ways resistance movements can be a helpful site for understanding how to identify, (...) critique, and transform ignorance. (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)

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)

Ignorance is a neglected issue in philosophy. This is surprising for, contrary to what one might expect, it is not clear what ignorance is. Some philosophers say or assume that it is a lack of knowledge, whereas others claim or presuppose that it is an absence of true belief. What is one ignorant of when one is ignorant? What kinds of ignorance are there? This neglect is also remarkable because ignorance plays a crucial role in all (...) sorts of controversial societal issues. Ignorance is often thought to be a moral and legal excuse; it is a core concept in medical ethics and debates about privacy, and it features in religious traditions and debates about belief in God. This book does not only study an epistemic phenomenon that is interesting in itself, but also provides important tools that can be fruitfully used in debates within and beyond philosophy. (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)

Feminist decolonial scholars have called for disengaging from the current system built on a hierarchical logic of race and gender central to modern, colonial thinking. They have looked to worlds outside the modern system to lead us out of current unjust practices harming both humans and the environment. Although policymaking may be seen as the stronghold of the current political agenda and of the structures that have led to the climate crisis, we argue that climate policies too, are also crucial (...) for rethinking and transforming societies. Our examination of climate adaptation policies in Sweden and the literature from Europe shows how policy documents ignore and unknow the oppressive intersections of gender and power despite the knowledge that exists on these issues in the public domain. Drawing on the tools of agnotology, we examine how this is achieved by strategies of ‘denial, dismissal, diversion and displacement.’ Building on feminist post and decolonial scholarship, we make explicit the gendered and racial hierarchies and dichotomies underpinning these policy documents. At the same time, we bring attention to the nuances in the policy documents we study and look for the openings that might be used to bring about transformation by making these hierarchies explicit and calling them into question. We argue that a transformation is possible through a feminist post and decolonial intervention, even in policymaking otherwise ignorant of culture, values and the colonial histories that have produced contemporary society. (shrink)

Rik Peels has forcefully argued that, contrary to what is widely held, ignorance is not equivalent to the lack or absence of knowledge. In doing so, he has argued against the Standard View of Ignorance according to which they are equivalent, and argued for what he calls “the New View” according to which ignorance is equivalent (merely) to the lack or absence of true belief. In this paper, I defend the Standard View against Peels’s latest case for (...) the New View. (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)