We study the modal logic M L r of the countable random frame, which is contained in and `approximates' the modal logic of almost sure frame validity, i.e. the logic of those modal principles which are valid with asymptotic probability 1 in a randomly chosen finite frame. We give a sound and complete axiomatization of M L r and show that it is not finitely axiomatizable. Then we describe the finite frames of that logic and (...) show that it has the finite frame property and its satisfiability problem is in EXPTIME. All these results easily extend to temporal and other multi-modal logics. Finally, we show that there are modal formulas which are almost surely valid in the finite, yet fail in the countable random frame, and hence do not follow from the extension axioms. Therefore the analog of Fagin's transfer theorem for almost sure validity in first-order logic fails for modal logic. (shrink)

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning (...) can be reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery. (shrink)

DNA evidence is one of the most significant modern advances in the search for truth since the cross examination, but its format as a random-match-probability makes it difficult for people to assign an appropriate probative value (Koehler, 2001). While Frequentist theories propose that the presentation of the match as a frequency rather than a probability facilitates more accurate assessment (e.g., Slovic et al., 2000), Exemplar-Cueing Theory predicts that the subjective weight assigned may be affected by the frequency or probability (...) format, and how easily examples of the event, i.e., ‘exemplars’, are generated from linguistic cues that frame the match in light of further evidence (Koehler & Macchi, 2004). This paper presents two juror research studies to examine the difficulties that jurors have in assigning appropriate probative value to DNA evidence when contradictory evidence is presented. Study 1 showed that refuting evidence significantly reduced guilt judgments when exemplars were linguistically cued, even when the probability match and the refuting evidence had the same objective probative value. Moreover, qualitative reason for judgment responses revealed that interpreting refuting evidence was found to be complex and not necessarily reductive; refutation was found indicative of innocence or guilt depending on whether exemplars have been cued or not. Study 2 showed that the introduction of judges’ directions to linguistically cue exemplars, did not increase the impact of refuting evidence beyond its objective probative value, but less guilty verdicts were returned when jurors were instructed to consider all possible explanations of the evidence. The results are discussed in light of contradictory frequentist and exemplar-cueing theoretical positions, and their real-world consequences. (shrink)

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...) out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

The essay is framed by conflict between Christianity and Darwinian science over the history of the world and the nature of human personhood. Evolutionary science narrates a long prehuman geological and biological history filled with vast amounts, kinds, and distributions of apparently random brutal and pointless suffering. It also strongly suggests that the first modern humans were morally primitive. This science seems to discredit Christianity's common meta-narrative of the Fall, understood as a story of Paradise Lost. The author contends (...) that this Augustinian story and its character of Adam as endowed with superhuman gifts, and yet as so fragile as to fall, as claimed, is implausible, at any rate, even apart from science. He proposes that Christians consider adopting a Supralapsarian metaphysics of divine purpose supported by the intuitions of Irenaeus, who depicted the first human beings as comparable to innocent, but morally undeveloped children. In this approach the existence of evils is part of the divine plan to "defeat" them in and through the Incarnation, Atonement, and Resurrection of Christ. Putting an "Irenaean Adam" in place of the "Augustinian" counterpart may not remove conflict with science completely, but at least reduces it, and leads to a Christian narrative that is more plausible, in the light of science. (shrink)

This essay is framed by conflict between Christianity and Darwinian science over the history of the world and the nature of original human personhood. Evolutionary science narrates a long prehuman geological and biological history filled with vast amounts, kinds, and distributions of apparently random brutal and pointless suffering. It has also unveiled an original human person with animal psychosomatic heredity. This narrative seems to discredit Christianity's metanarrative of the Fall—Paradise Lost and Paradise Regained. The author contends that the Augustinian (...) story and its character of Adam are implausible, anyway, for reasons of theology and apologetics. He proposes that Christians adopt instead a Supralapsarian metaphysics of original human personhood and existence that grows from the intuitions of Irenaeus. The outcome will be improved Christian theology, more persuasive theodicy, and, above all, peace with Darwinian science. (shrink)

This paper evaluates the claim that it is possible to use nature’s variation in conjunction with retention and selection on the one hand, and the absence of ultimate groundedness of hypotheses generated by the human mind as it knows on the other hand, to discard the ascription of ultimate certainty to the rationality of human conjectures in the cognitive realm. This leads to an evaluation of the further assumption that successful hypotheses with specific applications, in other words heuristics, seem to (...) have a firm footing because they were useful in another context. I argue that usefulness evaluated through adaptation misconstrues the search for truth, and that it is possible to generate talk of randomness by neglecting aspects of a system’s insertion into a larger situation. The framing of the problem in terms of the elimination of unfit hypotheses is found to be unsatisfying. It is suggested that theories exist in a dimension where they can be kept alive rather than dying as phenotypes do. The proposal that the subconscious could suggest random variations is found to be a category mistake. A final appeal to phenomenology shows that this proposal is orphan in the history of epistemology, not in virtue of its being a remarkable find, but rather because it is ill-conceived. (shrink)

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ (...) ⍯φ iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine – (...) Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate operators (ISaTCO) (...) derived directly from c without any assumptions. This paper does not change any of the accurate QED calculations of hydrogen’s energy levels, given the simplistic model of the proton used in these calculations [1]. The Proton Radius Puzzle [2, 3] may indicate that new physics is necessary beyond the Standard Model (SM), and this paper describes the bizarre, and very different, situation when the electron and muon are located “inside” the spatially extended proton with their Centers of Charge (CoCs) orbiting the proton at the speed of light in S energy states. The electron/muon center of charge (CoC) is a structureless point that vibrates rapidly in its inseparable, non-random vacuum whose geometry and time structure are defined by the electron/muon ISaTCO discrete geometry. The electron/muon self mass becomes finite in a natural way due to the ISaTCOs cutting off high virtual photon energies in the photon propagator. The Dirac-Maxwell-Wilson (DMW) Equations are derived from the ISaTCO for the EM fields of an electron/muon, and the electron/muon “look” like point particles in far field scattering experiments in the same way the electric field from a sphere with evenly distributed charge “e” “looks” like a point with the same charge in the far field (Gauss Law). The electron’s/muon’s three fluctuating CoC internal spatial coordinate operators have eight possible eigenvalues [4, 5, 6] that fall on a spherical shell centered on the electron’s CoM with radius in the rest frame. The electron/muon internal time operator is discrete, describes the rapid virtual electron/positron pair production and annihilation. The ISaTCO together create a current that produce spin and magnetic moment operators, and the electron and muon no longer have “intrinsic” properties since the ISaTCO kinematics define spin and magnetic moment properties. (shrink)

This study assessed quality assurance practices and students’ performance evaluation in universities of South-South Nigeria using an SEM approach. Three null hypotheses guided the study. Based on factorial research design, and using a stratified random sampling technique, a sample of 878 academic staff were drawn from a sampling frame of 15 universities in South-South Nigeria. Quality Assurance Practices Students’ Performance Evaluation Scale (QAPSPES) with split-half reliability estimates ranging from .86–.92, was used as the instruments for data collection. Multiple (...) regression and Confirmatory Factor Analyses (CFA) were used for the analysis of data, model building, and testing of the hypotheses at .05 alpha level. Findings showed a significant composite and relative influence (F=48.19, P<.05) of school management, staff, and students’ quality assurance practices on students’ performance evaluation. The results also indicated that there were positive and significant covariances between the four variables of this study, with the CFI, RMSEA, TLI, and SRMR values indicating a good model fit. It was recommended, based on the findings of this study that, each school should organize quality assurance orientation campaigns for new students and set up quality assurance committees at the school, faculty and departmental levels for optimal performance in schools. (shrink)

The research aims to identify the impact of the strategic orientations (Vision, Mission, goals) on crisis management agency, international relief in Gaza, the researchers used the descriptive and analytical approach and a survey for collection data, amounted to community size (881), and the study sample (268), and the sample was a stratified random. SPSS program used for entry, processing and analysis of data. The most important findings of the study: The results showed that the organization develop a clearly written (...) vision, mission and strategic goals and the organization's strategic objectives are consistent with the vision and mission of the organization. The results also showed that the organization develop a clear stage objectives framed with time bass which can be achieved on the ground. The employees in the organization's behavior comes within a disciplined set of principles and values that underpin the organization. Also the concept of the organization vision and mission are familiar for the employees. In general the views of the research sample agreed that there is a presence of strategic orientations (vision, message, goals). A direct positive correlation between the presence of strategic orientations (vision, mission and goals) and crisis management (before, during and after the crisis) in the international relief agency in Gaza. The research also concluded a series of recommendations, Researchers consistently recommend the continuous existence of strategic orientation and continue to develop the vision, mission and objectives in a clearly written method. In addition to that, the organization must develop in advance plans to deal with crises, taking into account past experience in this field through a specialized team, hold continuous meetings and discussions and workshops with the emergency team who has previous experience in dealing with crises. (shrink)

To improve the riding performance and levitation stability of a high‐speed magnetic levitation (maglev) train, a control strategy based on mixed H 2/H4 with regional pole placement and model‐reference controllers are proposed. First, the nonlinear maglev train model is established, then the proposed system is designed to observe the movement of a suspension frame and a control strategy based on mixed H 2/H4 with regional pole placement and model‐reference control method are proposed. Test and analysis of the proposed system (...) has been done using MATLAB toolbox for train levitation height, velocity and current consume. Comparative simulation results show that the mixed H 2/H4 with regional pole placement control strategy has a better performance under the condition of step and random train levitation height. (shrink)

This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory -- in particular, Savage's theory of subjective expected utility and personal probability. I show that Savage's reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealised assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational (...) value of sophisticated mathematical structures employed in applied sciences like decision theory. In the last part, I introduce countable additivity into Savage's theory and explore some technical properties in relation to other axioms of the system. (shrink)

I criticise a paper by Peter Forrest in which he argues that a principle of unrestricted countable fusion has paradoxical consequences. I argue that the paradoxical consequences that he exhibits may be due to his Whiteheadean assumptions about the nature of spacetime rather than to the principle of unrestricted countable fusion.

Early work on the frequency theory of probability made extensive use of the notion of randomness, conceived of as a property possessed by disorderly collections of outcomes. Growing out of this work, a rich mathematical literature on algorithmic randomness and Kolmogorov complexity developed through the twentieth century, but largely lost contact with the philosophical literature on physical probability. The present chapter begins with a clarification of the notions of randomness and probability, conceiving of the former as a property of a (...) sequence of outcomes, and the latter as a property of the process generating those outcomes. A discussion follows of the nature and limits of the relationship between the two notions, with largely negative verdicts on the prospects for any reduction of one to the other, although the existence of an apparently random sequence of outcomes is good evidence for the involvement of a genuinely chancy process. (shrink)

In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as \({XH + \mathbb{P}(X|H)H^c}\) ; in particular (the indicator of) a conditional event E|H is looked at as EH + P(E|H)H c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give (...) a meaning to the sum X|H + Y|K and we can define the iterated c.r.q. (X|H)|K. We analyze the conjunction of two conditional events, introduced by the authors in a recent work, in the setting of coherence. We show that the conjoined conditional is a conditional random quantity, which may be a conditional event when there are logical dependencies. Moreover, we introduce the negation of the conjunction and by applying De Morgan’s Law we obtain the disjoined conditional. Finally, we give the lower and upper bounds for the conjunction and disjunction of two conditional events, by showing that the usual probabilistic properties continue to hold. (shrink)

Passive frame theory attempts to illuminate what consciousness is, in mechanistic and functional terms; it does not address the “implementation” level of analysis (how neurons instantiate conscious states), an enigma for various disciplines. However, in response to the commentaries, we discuss how our framework provides clues regarding this enigma. In the framework, consciousness is passive albeit essential. Without consciousness, there would not be adaptive skeletomotor action.

The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. After indicating the ways in which these accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability of a process. This proposal arguably captures the intuitive desiderata for the concept of randomness; at least it should suggest (...) that the commonly accepted accounts cannot be the whole story and more philosophical attention needs to be paid. 1. Randomness in science1.1Random systems1.2Random behaviour1.3Random sampling1.4Caprice, arbitrariness and noise2. Concepts of randomness2.1Von Mises/church/martin-löf randomness2.2KCS-randomness3. Randomness is unpredictability: preliminaries3.1Process and product randomness3.2Randomness is indeterminism?4. Predictability4.1Epistemic constraints on prediction4.2Computational constraints on prediction4.3Pragmatic constraints on prediction4.4Prediction defined5. Unpredictability6. Randomness is unpredictability6.1Clarification of the definition of randomness6.2Randomness and probability6.3Subjectivity and context sensitivity of randomness7. Evaluating the analysis[R]andomness … is going to be a concept which is relative to our body of knowledge, which will somehow reflect what we know and what we don't know. Henry E. Kyburg, Jr ([1974], p. 217)Phenomena that we cannot predict must be judged random. Patrick Suppes ([1984], p. 32). (shrink)

We consider two ways one might use algorithmic randomness to characterize a probabilistic law. The first is a generative chance* law. Such laws involve a nonstandard notion of chance. The second is a probabilistic* constraining law. Such laws impose relative frequency and randomness constraints that every physically possible world must satisfy. While each notion has virtues, we argue that the latter has advantages over the former. It supports a unified governing account of non-Humean laws and provides independently motivated solutions to (...) issues in the Humean best-system account. On both notions, we have a much tighter connection between probabilistic laws and their corresponding sets of possible worlds. Certain histories permitted by traditional probabilistic laws are ruled out as physically impossible. As a result, such laws avoid one variety of empirical underdetermination, but the approach reveals other varieties of underdetermination that are typically overlooked. (shrink)

This research note challenges the idea that Random Somatic Mutations are entirely random, highlighting their non-equiprobable nature and their influence on evolution, involution, or indeterminacy. It recalls the Neutrosophic Theory of Evolution, extending Darwin’s theory, and emphasizes the importance of distinguishing between different senses of ‘random mutation’ in evolutionary theory.

I address Sinnott-Armstrong's argument that evidence of framing effects in moral psychology shows that moral intuitions are unreliable and therefore not noninferentially justified. I begin by discussing what it is to be epistemically unreliable and clarify how framing effects render moral intuitions unreliable. This analysis calls for a modification of Sinnott-Armstrong's argument if it is to remain valid. In particular, he must claim that framing is sufficiently likely to determine the content of moral intuitions. I then re-examine the evidence which (...) is supposed to support this claim. In doing so, I provide a novel suggestion for how to analyze the reliability of intuitions in empirical studies. Analysis of the evidence suggests that moral intuitions subject to framing effects are in fact much more reliable than perhaps was thought, and that Sinnott-Armstrong has not succeeded in showing that noninferential justification has been defeated. (shrink)

In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC_2) with the full second-order semantics. Main results: (i) :~Con(ZFC2_); (ii) let k be an inaccessible cardinal, V is an standard model of ZFC (ZFC_2) and H_k is a set of all sets having hereditary size less then k; then : ~Con(ZFC + E(V)(V = Hk)):.

In 1947 Donald Cary Williams claimed in The Ground of Induction to have solved the Humean problem of induction, by means of an adaptation of reasoning first advanced by Bernoulli in 1713. Later on David Stove defended and improved upon Williams’ argument in The Rational- ity of Induction (1986). We call this proposed solution of induction the ‘Williams-Stove sampling thesis’. There has been no lack of objections raised to the sampling thesis, and it has not been widely accepted. In our (...) opinion, though, none of these objections has the slightest force, and, moreover, the sampling thesis is undoubtedly true. What we will argue in this paper is that one particular objection that has been raised on numerous occasions is misguided. This concerns the randomness of the sample on which the inductive extrapolation is based. (shrink)

Humor is unlike other forms of communication because its content is not meant literally. Like acts of play, humor is not intended to be taken at face value. As a consequence, the assumptions and rules that govern normal conversation do not apply. Humor therefore depends upon both the speaker and the audience fully understanding that what was communicated should be treated in this unique way. The play frame refers to this shared understanding about the nature of the communication. Analyzing (...) whether a communication falls within the play frame may help us better understand not only whether the communication can be deemed non-serious or serious, but also whether it can be treated uniquely as merely the speaker’s attempt at play or as a typical instance of literal speech for which the speaker can be deemed ethically responsible. (shrink)

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and (...) complete for the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$ (the relevant logic $\mathsf {R}^+$, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question. (shrink)

Are there any truly ontologically random events? This paper argues that randomness is an unavoidably epistemic concept and therefore ascription of ontological randomness to any particular event or series of events can never be justified.

Alexander Rosenberg (1994) claims that the omniscient viewpoint of the evolutionary process would have no need for the concept of random drift. However, his argument fails to take into account all of the processes which are considered to be instances of random drift. A consideration of these processes shows that random drift is not eliminable even given a position of omniscience. Furthermore, Rosenberg must take these processes into account in order to support his claims that evolution is (...) deterministic and that evolutionary biology is an instrumental science. (shrink)

Sortition, i.e. random appointment for public duty, has been employed by societies throughout the years as a firewall designated to prevent illegitimate interference between parties in a legal case and agents of the legal system. In judicial systems of modern western countries, random procedures are mainly employed to select the jury, the court and/or the judge in charge of judging a legal case. Therefore, these random procedures play an important role in the course of a case, and (...) should comply with some principles, such as transparency and complete auditability. Nevertheless, these principles are neglected by random procedures in some judicial systems, which are performed in secrecy and are not auditable by the involved parties. The assignment of cases in the Brazilian Supreme Court is an example of such a procedure, for it is performed using procedures unknown to the parties involved in the judicial cases. This article presents a review of how sortition has been historically employed by societies and discusses how Mathematical Statistics may be applied to random procedures of the judicial system, as it has been applied for almost a century on clinical trials, for example. A statistical model for assessing randomness in case assignment is proposed and applied to the Brazilian Supreme Court. As final remarks, guidelines for the development of good randomization procedures are outlined. (shrink)

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

A framing effect occurs when an agent's choices are not invariant under changes in the way a decision problem is presented, e.g. changes in the way options are described (violation of description invariance) or preferences are elicited (violation of procedure invariance). Here we identify those rationality violations that underlie framing effects. We attribute to the agent a sequential decision process in which a “target” proposition and several “background” propositions are considered. We suggest that the agent exhibits a framing effect if (...) and only if two conditions are met. First, different presentations of the decision problem lead the agent to consider the propositions in a different order (the empirical condition). Second, different such “decision paths” lead to different decisions on the target proposition (the logical condition). The second condition holds when the agent's initial dispositions on the propositions are “implicitly inconsistent,” which may be caused by violations of “deductive closure.” Our account is consistent with some observations made by psychologists and provides a unified framework for explaining violations of description and procedure invariance. (shrink)

A puzzle of an unmarked clock, used by Timothy Williamson to question the KK principle, was separately adapted by David Christensen and Adam Elga to critique a principle of Rational Reflection. Both authors, we argue, flout the received relationship between ideal agency and the classical distinction between systematic and random error, namely that ideal agents are subject only to the latter. As a result, these criticisms miss their mark.

Review of "Exploring Randomness" (200) and "The Unknowable" (1999) by Gregory Chaitin.

n this text, we revisit part of the analysis of anti-entropy in Bailly and Longo (2009} and develop further theoretical reflections. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in ontogenesis and in evolution. This approach, in particular, focuses on the role of global entropy production and provides a tool for a mathematical understanding of some fundamental observations by Gould on the increasing phenotypic complexity along evolution. Lastly, (...) we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong link with randomness. (shrink)

Suppose that a patient is receiving treatment options from her doctor. In one case, the doctor says, “the surgery has a 90% survival rate.” Now, suppose the doctor instead said, “the procedure has a 10% mortality rate.” Predictably, the patient is more likely to consent on the first description and more likely to dissent on the second. This is an example of a framing effect. A framing effect occurs when “the description of [logically-equivalent] options in terms of gains (positive (...) class='Hi'>frame) rather than losses (negative frame) elicits systematically different choices.” Framing effects are ubiquitous, but they are particularly troublesome in medicine. Many worry that there is tension between valuing informed consent and using framing effects in clinical settings. In this paper, I answer this question: if an individual is subject to a framing effect when she gives her consent, does this undermine the validity of her consent? I argue that framing effects do not undermine consent in general. (shrink)

Academic discussions of the count/mass distinction in Chinese feature three general problems, upon which this essay critically reflects: 1) Most studies focus either on modern or on classical Chinese thus representing parallel discussions that never intersect; 2) studies on count/mass grammar are often detached from reflections on count/mass semantics, which results in serious theoretical and terminological flaws; 3) approaches to Chinese often crucially depend on observations of English grammar and semantics, as, e.g., many/much vs. few/little patterns, the use of plural (...) inflections, etc., which is seldom justified. The article investigates the relevant discourse on the count/mass issue in classical and modern Chinese and concludes with exploring two distinct areas related to countability: the semantics of singular in contexts in which objects are introduced as referential-indefinite and the semantics of number and countability as revealed in diangu. (shrink)

On absolute random and restricted random .

There is an emerging view according to which countability is not an integral part of the lexical meaning of singular count nouns, but is ‘added on’ or ‘made available’, whether syntactically, semantically or both. This view has been pursued by Borer and Rothstein among others in order to deal with classifier languages such as Chinese as well as challenges to standard views of the mass-count distinction such as object mass nouns such as furniture. I will discuss a range of data, (...) partly from German, that such a grammar-based view of countability receives support when applied to verbs with respect to the event argument position. Verbs themselves fail to specify events as countable in English and related languages; instead countability is made available only by the use of the event classifier time or else particular lexical items, such as frequency expressions, German beides ‘both’, or the nominalizing light noun -thing. The paper will not adopt or elaborate a particular version of the grammar-based view of countability, but rather critically discuss existing versions and present two semantic options of elaborating the view. (shrink)

I argue that the scope of rational framing effects may be broader than Bermúdez assumes. Even in many “canonical experiments,” the explanation of the judgment reversals or shifts may refer to reasons, including moral ones. Referring to the Asian disease paradigm (ADP), I describe how non-consequentialist reasons related to fairness and the distinction between doing and allowing may help explain and justify the typical pattern of choices in the cases like ADP.

Explaining the behaviour of ecosystems is one of the key challenges for the biological sciences. Since 2000, new-mechanicism has been the main model to account for the nature of scientific explanation in biology. The universality of the new-mechanist view in biology has been however put into question due to the existence of explanations that account for some biological phenomena in terms of their mathematical properties (mathematical explanations). Supporters of mathematical explanation have argued that the explanation of the behaviour of ecosystems (...) is usually provided in terms of their mathematical properties, and not in mechanistic terms. They have intensively studied the explanation of the properties of ecosystems that behave following the rules of a non-random network. However, no attention has been devoted to the study of the nature of the explanation in those that form a random network. In this paper, we cover that gap by analysing the explanation of the stability behaviour of the microbiome recently elaborated by Coyte and colleagues, to determine whether it fits with the model of explanation suggested by the new-mechanist or by the defenders of mathematical explanation. Our analysis of this case study supports three theses: (1) that the explanation is not given solely in terms of mechanisms, as the new-mechanists understand the concept; (2) that the mathematical properties that describe the system play an essential explanatory role, but they do not exhaust the explanation; (3) that a non-previously identified appeal to the type of interactions that the entities in the network can exhibit, as well as their abundance, is also necessary for Coyte and colleagues’ account to be fully explanatory. From the combination of these three theses we argue for the necessity of an integrative pluralist view of the nature of behaviour explanation when this is given by appealing to the existence of a random network. (shrink)

When does it make sense to act randomly? A persuasive argument from Bayesian decision theory legitimizes randomization essentially only in tie-breaking situations. Rational behaviour in humans, non-human animals, and artificial agents, however, often seems indeterminate, even random. Moreover, rationales for randomized acts have been offered in a number of disciplines, including game theory, experimental design, and machine learning. A common way of accommodating some of these observations is by appeal to a decision-maker’s bounded computational resources. Making this suggestion both (...) precise and compelling is surprisingly difficult. Toward this end, I propose two fundamental rationales for randomization, drawing upon diverse ideas and results from the wider theory of computation. The first unifies common intuitions in favour of randomization from the aforementioned disciplines. The second introduces a deep connection between randomization and memory: access to a randomizing device is provably helpful for an agent burdened with a finite memory. Aside from fit with ordinary intuitions about rational action, the two rationales also make sense of empirical observations in the biological world. Indeed, random behaviour emerges more or less where it should, according to the proposal. (shrink)

This essay concerns Heidegger’s assertion that the biography of the poet is unimportant when interpreting great works of poetry. I approach the question in three ways. First, I consider its merits as a principle of literary interpretation and contrast Heidegger’s view with those of other Trakl interpreters. This allows me to clarify his view as a unique variety of non-formalistic interpretation and raise some potential worries about his approach. Second, I consider Heidegger’s view in the context of his broader philosophical (...) project. Viewed this way, Heidegger’s decision to neglect the poet’s biography seems quite reasonable and consistent with his inquiry into the being of language. Finally, I consider Heidegger’s suggestion that Trakl is a kind of mad genius. I recast this paradigmatic figure in terms of what I call the ‘wretched prophet’ and consider some ways in which its appeal sheds light on the crisis of modernity and the aestheticization of politics. (shrink)

Context sensitivity is one of the distinctive marks of human intelligence. Understanding the flexible way in which humans think and act in a potentially infinite number of circumstances, even though they’re only finite and limited beings, is a central challenge for the philosophy of mind and cognitive science, particularly in the case of those using representational theories. In this work, the frame problem, that is, the challenge of explaining how human cognition efficiently acknowledges what is relevant from what is (...) not in each context, has been adopted as a guide. By using it, we’ve been able to describe a fundamental tension between context sensitivity and the mental representations used in cognition theories. The first chapter discusses the nature of the frame problem,as well as the reasons for its persistence. In the second and third chapters, the problem is used as a measure tool in order to inquiry a few representational approaches and check how well suited they are to deal with context dependencies. The problems found are then correlated with the frame problem. Throughout the discussion, we try to show that 1) none of the evaluated approaches is capable of dealing with context sensitivity in a proper manner, but 2) that’s not a reason to think that the frame problem constitutes an argument against representational approaches in general, and 3) that it constitutes a fundamental conceptual tool in contemporary research -/- A sensibilidade ao contexto é uma das marcas distintivas da inteligência humana. Compreender o modo flexível como o ser humano pensa e age em função de um número potencialmente infinito de circunstâncias, ainda que munido de recursos finitos e limitados, é um desafio central para a filosofia da mente e para a ciência cognitiva, em particular aos que fazem uso de teorias representacionalistas. Nesse trabalho, adotou-se como fio condutor o modo como isso se manifesta no "frame problem": a dificuldade em explicar como a cognição humana reconhece, de maneira eficiente, o que é ou não relevante em cada contexto. A partir dele, buscou-se caracterizar uma tensão fundamental entre a sensibilidade ao contexto e o uso de representações mentais em teorias da cognição. O primeiro capítulo discute a natureza do frame problem, bem como as razões de sua resiliência. No segundo e terceiro capítulos, faz-se uso do problema como métrica para investigar o quão adequado é o tratamento das dependências contextuais no âmbito de várias abordagens representacionais. No decorrer da discussão, realiza-se um esforço argumentativo para mostrar que 1) nenhuma das estratégias abordadas é capaz tratar adequadamente da sensibilidade ao contexto, mas que 2) apesar disso, o frame problem não constitui argumento fatal para teorias representacionalistas em geral, e que 3) ele constitui uma ferramenta conceitual fundamental para pesquisas contemporâneas. (shrink)

Intersectionality is a term that arose within the black feminist intellectual tradition for the purposes of identifying interlocking systems of oppression. As a descriptive term, it refers to the ways human identity is shaped by multiple social vectors and overlapping identity categories (such as sex, race, class) that may not be readily visible in single-axis formulations of identity, but which are taken to be integral to robustly capture the multifaceted nature of human experience. As a diagnostic term, it captures the (...) confluence of power and domination on the social construction of identity in order to remedy concrete harms that result from this convergence. It is not a prescriptive methodology or closed system of analysis, but rather an open-ended hermeneutic lens through which interconnected systems of oppression can come into focus in the fight for social justice. (shrink)

In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics and a set of logical constants (with specified arities). The first generator returns formulae of exactly the given depth, using all or some of the propositional letters. The second does the same but samples up-to the given depth. The third generator outputs formulae with exactly (...) the desired depth and all the atomics in the set. To make the generators uniform (i.e. to make them return every formula in their space with the same probability), we will prove various cardinality results about those spaces. (shrink)

Proper names are generally taken to be count nouns. This paper argues that this is mistaken and that at least in some languages, for example German, names divide into mass and count. Making use of Kayne's (2005, 2010) theory of light nouns, this paper argues that light nouns are part of (simple) names and that a mass-count distinction among light nouns explains the behavior of certain types of names in German as mass rather than count. The paper elaborates the role (...) of light nouns with new generalizations regarding their linguistic behavior in quantificational and pronominal NPs, their selection of relative pronouns in German, and a general difference in the support of plural anaphora between English and German. (shrink)

This article offers a conceptual framework for discussing the role of envy within processes of transitional justice. Transitional justice importantly includes the transformation of intergroup dynamics of interaction in the aftermath of societal conflicts and upheavals. Such transformation aims to realise “interactive” justice in transitional justice by reshaping belief and value systems, and by moulding emotional responses between the involved parties. A nuanced understanding of the emotions at play in intergroup antagonistic dynamics of interaction is thus essential to transitional justice. (...) Among the many emotions that we could address in such scenarios, we target envy. Envy, in its various forms, features prominently in many societal conflicts and upheavals, and has, therefore, the potential to undermine or, conversely, support just intergroup interactions. However, the ambivalent role of this emotion has been scantly analysed in the philosophical literature on transitional justice. We make a start on filling this lacuna by developing a conceptual framework which is necessary to appreciate how envy and its varieties are epistemically and practically relevant to realising interactive justice in transitional justice processes. (shrink)

What values, if any, would be undermined by determinism?[i] Traditionally this question has been tackled by asking whether determinism is compatible with free will or whether it is compatible with moral responsibility. Compatibilists say that determinism would not threaten free will or moral responsibility, and hence that people’s values should not be influenced by whether or not they believe in determinism. Incompatibilists say that determinism would undermine free will or moral responsibility, and hence that a belief in determinism should have (...) a considerable impact on one’s values, precluding many popular evaluative beliefs. (shrink)

This paper explores the nature of curiosity from an epistemological point of view. First it motivates this exploration by explaining why epistemologists do and should care about what curiosity is. Then it surveys the relevant literature and develops a particular approach.

_Framing effects_ concern the having of different attitudes towards logically or necessarily equivalent contents. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We model a typical kind of framing, grounded in (i) the structural distinction between beliefs activated in working memory and beliefs left inactive in long term memory, and (ii) the topic- or subject matter-sensitivity of belief: a feature of propositional attitudes which is attracting growing research attention. We introduce (...) a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class. (shrink)