Philosophy of Probability, Misc

Recent developments in pure mathematics and in mathematical logic have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets and the logic of quotient sets, equivalence relations, or partitions. The analogue to an element of a subset is the notion of a distinction of a partition, and that leads to a whole stream of dualities or analogies--including the development of new logical foundations for information theory parallel to Boole's development of (...) logical finite probability theory. After outlining these dual concepts in mathematical terms, we turn to a more metaphysical speculation about two dual notions of reality, a fully definite notion using Boolean logic and appropriate for classical physics, and the other objectively indefinite notion using partition logic which turns out to be appropriate for quantum mechanics. The existence-information duality is used to intuitively illustrate these two dual notions of reality. The elucidation of the objectively indefinite notion of reality leads to the "killer application" of the existence-information duality, namely the interpretation of quantum mechanics. (shrink)

Gives two pared-down versions of the argument from design, which may prove more persuasive as to a Creator, discusses briefly the mathematics underpinning disbelief and nonbelief and its misuse and some proper uses, moves to why the full argument is needed anyway, viz., to demonstrate Providence, offers a theory as to how miracles (open and hidden) occur, viz. the replacement of any particular mathematics underlying a natural law (save logic) by its most appropriate nonstandard variant. -/- Note: This is an (...) extended abstract; there are no present plans to complete it. (shrink)

This chapter starts with a simple conventional presentation of time reversal in physics, and then returns to analyse it, rejects the conventional analysis, and establishes correct principles in their place.

The conventional claims and concepts of 5* - 8* are a hang-over from the classical theory of thermodynamics – i.e. thermodynamics based on a fully deterministic micro-theory, developed in the time of Boltzmann, Loschmidt and Gibbs in the late C19th. The classical theory has well-known ‘reversibility paradoxes’ when applied to the universe as a whole. But the introduction of intrinsic probabilities in quantum mechanics, and its consequent time asymmetry, fundamentally changes the picture.

Recently I proposed “quantum language” (or,“the linguistic Copenhagen interpretation of quantum mechanics”), which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes=Kant epistemology. Namely, quantum language is the scientific final goal of dualistic idealism. It has a great power to describe classical systems as well as quantum systems. In this research report, quantum language is seen as a fundamental theory of statistics and reveals the true nature of statistics.

Four intuitions are recurrent and influential in theories about conditionals: the Ramsey’s test, the Adams’ Thesis, the Equation, and the robustness requirement. For simplicity’s sake, I call these intuitions ‘the big four’. My aim is to show that: (1) the big four are interdependent; (2) they express our inferential dispositions to employ a conditional on a modus ponens; (3) the disposition to employ conditionals on a modus ponens doesn’t have the epistemic significance that is usually attributed to it, since the (...) acceptability or truth conditions of a conditional is not necessarily associated with its employability on a modus ponens. (shrink)

Abstract: Four main forms of Doomsday Argument (DA) exist—Gott’s DA, Carter’s DA, Grace’s DA and Universal DA. All four forms use different probabilistic logic to predict that the end of the human civilization will happen unexpectedly soon based on our early location in human history. There are hundreds of publications about the validity of the Doomsday argument. Most of the attempts to disprove the Doomsday Argument have some weak points. As a result, we are uncertain about the validity of DA (...) proofs and rebuttals. In this article, a meta-DA is introduced, which uses the idea of logical uncertainty over the DA’s validity estimated based on a virtual prediction market of the opinions of different scientists. The result is around 0.4 for the validity of some form of DA, and even smaller for “Strong DA”, which predicts the end of the world in the near term. We discuss many examples of the validity of the DA in real life as an instrument to prove it “experimentally”. We also show that DA becomes strongest if it is based on the idea of the “natural reference class” of observers, that is, the observers who know about the DA (i.e. a Self-Referenced DA). Such a DA predicts that there is a high probability of a global catastrophe with human extinction in the 21st century, which aligns with what we already know based on analysis of different technological risks. (shrink)

Abstract. In this article is presented a model of the change of the probability of the global catastrophic risks in the world with exponentially evolving technologies. Increasingly cheaper technologies become accessible to a larger number of agents. Also, the technologies become more capable to cause a global catastrophe. Examples of such dangerous technologies are artificial viruses constructed by the means of synthetic biology, non-aligned AI and, to less extent, nanotech and nuclear proliferation. The model shows at least double exponential growth (...) of the probability of the global catastrophe which means that the accumulated probability of the catastrophe will grow from negligible to overwhelming at the period of a few doubling times of the technological capabilities. For biotech and AI, such doubling time roughly corresponds to the doubling period of Moore’s law and its analogues in other technologies and is around 2 years. Thus the global catastrophe in the exponential technologies world will most likely happen during a “dangerous decade”. Such a dangerous decade could start as early as in the 2020s. We also found that the double exponential growth in the model makes the model less sensitive to its initial conditions, like the number of dangerous agents or initial probabilities constants. The model also shows that smaller catastrophes could happen earlier than larger ones, and such a smaller catastrophe may be able to stop the technological growth before larger ones become possible, thus global risks will be self-limiting. However, if the growth of the number of dangerous agents will be very quick, the multiple smaller catastrophes could happen simultaneously and will be equal to a global catastrophe. (shrink)

In the following we will investigate whether von Mises’ frequency interpretation of probability can be modified to make it philosophically acceptable. We will reject certain elements of von Mises’ theory, but retain others. In the interpretation we propose we do not use von Mises’ often criticized ‘infinite collectives’ but we retain two essential claims of his interpretation, stating that probability can only be defined for events that can be repeated in similar conditions, and that exhibit frequency stabilization. The central idea (...) of the present article is that the mentioned ‘conditions’ should be well-defined and ‘partitioned’. More precisely, we will divide probabilistic systems into object, initializing, and probing subsystem, and show that such partitioning allows to solve problems. Moreover we will argue that a key idea of the Copenhagen interpretation of quantum mechanics (the determinant role of the observing system) can be seen as deriving from an analytic definition of probability as frequency. Thus a secondary aim of the article is to illustrate the virtues of analytic definition of concepts, consisting of making explicit what is implicit. (shrink)

We show that the physical meaning of the wave function can be derived based on the established parts of quantum mechanics. It turns out that the wave function represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space.

This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not continuous but (...) discontinuous and random. This result suggests a new interpretation of the wave function, according to which the wave function is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wave function disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the random discontinuous motion of particles may provide an appropriate random source to collapse the wave function. (shrink)

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and (...) relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)

I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...) if one has substantive information about the world when one does not. I sketch the outlines of a solution in part I, showing how it differs from others, with full details to follow in subsequent parts. The solution is pragmatic in sentiment (though differs in specifics to arguments from, for example, William James); the conceptions we use to guide our actions are and should be at least partly determined by preferences. This is cashed out in a reformulation of decision theory motivated by a non-reductive formulation of hypotheses and logic. A distinction emerges between initial assumptions--that can be non-dogmatic--and effective assumptions that can simultaneously be substantive. An explanation is provided for the plausibility arguments used to explain assigned probabilities in BCT. -/- In subsequent parts, logic is constructed from principles independent of language and mind. In particular, propositions are defined to not have form. Probabilities are logical and uniquely determined by assumptions. The problems considered fatal to logical probabilities--Goodman's `grue' problem and the uniqueness of priors problem are dissolved due to the particular formulation of logic used. Other problems such as the zero-prior problem are also solved. -/- A universal theory of (non-linguistic) meaning is developed. Problems with counterfactual conditionals are solved by developing concepts of abstractions and corresponding pictures that make up hypotheses. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. -/- Theoretical virtues for hypotheses emerge from the theory. Explanatory force is explicated. The significance of effective assumptions is partly determined by combinatoric factors relating to the structure of hypotheses. I conjecture that this is the origin of simplicity. (shrink)

Real human agents, even when they are rational by everyday standards, sometimes assign different credences to objectively equivalent statements, such as “George Orwell is a writer” and “Eric Arthur Blair is a writer”, or credences less than 1 to necessarily true statements, such as not-yet-proven theorems of arithmetic. Anna Mahtani calls this the phenomenon of “opacity” (a form of hyperintensionality). Opaque credences seem probabilistically incoherent, which goes against a key modelling assumption of probability theory. I sketch a modelling strategy for (...) capturing opaque credence assignments without abandoning probabilistic coherence. I draw on ideas from judgment-aggregation theory, where we face similar challenges of defining the “objects of judgment”. (shrink)

Rational agents seem more confident in any possible event than in an impossible event. But if rational credences are real-valued, then there are some possible events that are assigned 0 credence nonetheless. How do we differentiate these events from impossible events then when we order events? de Finetti (1975), Hájek (2012) and Easwaran (2014) suggest that when ordering events, conditional credences and subset relations are as relevant as unconditional credences. I present a counterexample to all their proposals in this paper. (...) While their proposals order possible and impossible events correctly, they deliver the wrong verdict for disjoint possible events assigned equal positive credence. (shrink)

The Ontology of Knowledge (OK) does not claim to expose the truth of reality but only to propose a coherent model of representation according to which: -Reality is not subject to form or time. -The Knowing Subject is a wave of meaning running through the immobile reality.

This paper investigates the logic of reasons. Its aim is to provide an analysis of the sentences of the form ‘p is a reason for q’ that yields a coherent account of their logical properties. The idea that we will develop is that ‘p is a reason for q’ is acceptable just in case a suitably defined relation of incompatibility obtains between p and ¬q. As we will suggest, a theory of reasons based on this idea can solve three challenging (...) puzzles that concern, respectively, contraposing reasons, conflicting reasons, and supererogatory reasons, and opens a new perspective on some classical issues concerning non-deductive inferences. (shrink)

In this work, we focus on the philosophical aspects and technical challenges that underlie the axiomatization of the non-Kolmogorovian probability framework, in connection with the problem of quantum contextuality. This fundamental feature of quantum theory has received a lot of attention recently, given that it might be connected to the speed-up of quantum computers—a phenomenon that is not fully understood. Although this problem has been extensively studied in the physics community, there are still many philosophical questions that should be properly (...) formulated. We analyzed different problems from a conceptual standpoint using the non-Kolmogorovian probability approach as a technical tool. (shrink)

A number of authors, including me, have argued that the output of our most complex climate models, that is, of global climate models and Earth system models, should be assessed possibilistically. Worries about the viability of doing so have also been expressed. I examine the assessment of the output of relatively simple climate models in the context of discovery and point out that this assessment is of epistemic possibilities. At the same time, I show that the concept of epistemic possibility (...) used in the relevant studies does not fit available analyses of this concept. Moreover, I provide an alternative analysis that does fit the studies and broad climate modelling practices as well as meshes with my existing view that climate model assessment should typically be of real possibilities. On my analysis, to assert that a proposition is epistemically possible is to assert that it is not known to be false and is consistent with at least approximate knowledge of the basic way things are. I, finally, consider some of the implications of my discussion for available possibilistic views of climate model assessment and for worries about such views. I conclude that my view helps to address worries about such assessment and permits using the full range of climate models in it. (shrink)

No es pensando como creamos mundos. Es comprendiendo el mundo como aprendemos a pensar. Cosmovisión es un término que debe significar un conjunto de fundamentos a partir de los cuales emerge una comprensión sistémica del Universo, sus componentes como la vida, el mundo en que vivimos, la naturaleza, el fenómeno humano y sus relaciones. Es, por tanto, un campo de la filosofía analítica alimentado por las ciencias, cuyo objetivo es ese conocimiento agregado y epistemológicamente sostenible sobre todo lo que somos (...) y contenemos, que nos rodea y con lo que nos relacionamos de alguna manera. Es algo tan antiguo como el pensamiento humano y, además de utilizar elementos de la cosmología científica, engloba todo lo que en filosofía y ciencia se refiere al universo y la vida. Una cosmovisión no es un conjunto de ideas, hipótesis y suposiciones, sino un sistema basado en la observación, el análisis, la evidencia y la demostración. Ninguna cosmovisión pretende definir, establecer, proponer, sino solo comprender, analizar e interpretar. Cada uno de nosotros construimos y transportamos nuestra cosmovisión a lo largo de nuestra vida, sin establecer formas, como trasfondo de nuestro pensamiento y comportamiento. Lingüísticamente, el término “cosmovisión” se deriva del alemán, equivalente al concepto de “Weltanschauung” utilizado por varios filósofos. Sin embargo, esta relación lingüística no es aplicable porque va en contra de lo que proponemos como cosmovisión. Esta palabra alemana hace referencia a una visión prelógica o protoexperimental de la realidad, con un contexto intuitivo y alejado de un conocimiento crítico que aún no existía en el momento de su formulación. Sin duda, las cosmovisiones, no tiene sentido en que las entendamos, cobijen y utilicen estos elementos proto-experimentales o prelógicos que incluyen la historia, el inconsciente colectivo y todos los arquetipos que portamos. Sin embargo, en el concepto que aquí aplicamos, la cosmovisión va mucho más allá de este contenido, primero al someterlo constantemente al pensamiento crítico actual y, finalmente, al hacer de la experiencia analítica (y no del pensamiento o la intuición en sí) su verdadero universo. António Lopes expone la amplitud de este contenido: -/- “Las cosmovisiones no son el producto del pensamiento. No nacen del simple deseo de saber. La aprehensión de la realidad es un momento importante en su configuración, sin embargo, es uno solo. Proviene de la conducta vital, de la experiencia de vida, de la estructura de nuestra totalidad psíquica. El apoyo de la vida a la conciencia en el conocimiento de la realidad, en la apreciación de la vida y en la realidad volitiva, es el trabajo lento y arduo que ha hecho la humanidad en el desarrollo de los conceptos de vida. (W. Dilthey, 1992 [1911]: 120)” . En este trabajo buscamos esbozar una cosmovisión a partir de las realidades que ofrece la ciencia en la actualidad. No nos proponemos, en ningún momento, hacer ciencia; o teorizar la filosofía, pero siempre buscaremos ser apoyados por ellos o, al menos, protegidos por ellos de las distorsiones cognitivas que solemos llevar. -/- . (shrink)

It seems like we care about at least two features of our credence function: gradational-accuracy and verisimilitude. Accuracy-first epistemology requires that we care about one feature of our credence function: gradational-accuracy. So if you want to be a verisimilitude-valuing accuracy-firster, you must be able to think of the value of verisimilitude as somehow built into the value of gradational-accuracy. Can this be done? In a recent article, Oddie has argued that it cannot, at least if we want the accuracy measure (...) to be proper. I argue that it can. 1Introduction2Some Nuts and Bolts3First Attempts4Oddie’s Constraint5The Good5.1Proximity over the disagreement metric 5.2Proximity over the magnitude metric 6The Bad and the Ugly 7Some More Good: The Role of Evenness of Distribution 8Some More Bad: Which Propositions to Privilege? 9Concluding Thoughts: Accuracy and Practical Value. (shrink)

Being a researcher is challenging, especially in the beginning. Early Career Researchers (ECRs) need achievements to secure and expand their careers. In today’s academic landscape, researchers are under many pressures: data collection costs, the expectation of novelty, analytical skill requirements, lengthy publishing process, and the overall competitiveness of the career. Innovative thinking and the ability to turn good ideas into good papers are the keys to success.

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. I (...) suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even the proponent of the Expected Utility Objection should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument. (shrink)

يعتبر موضوع القراءة الحرة من المواضيع الهامة التي لم تلق من الاهتمام ما تستحقه، فهي طريق المعرفة، وهي المفتاح الحضاري الذي فتح لأمتنا منذ فجر التاريخ الإسلامي أبواب العلم والمعرفة والإبداع والشهود الحضاري، لذلك تحتل مفردات (القراءة والكتاب والعلم) موقعا متميزا في المنظومة الفكرية. فالمجتمع الذي لا يقرأ هو مجتمع مصاب بالأمية الثقافية، ويصنع لنفسه معيقات التقدم. ومن الصعب – إن لم يكن من المستحيل – التواصل مع العلوم والمعارف بمختلف ميادينها ومجالاتها ومستوياتها وأشكالها وتجلياتها خارج القراءة. فالقراءة إذن عملية (...) إنسانية مرتبطة بوجود الفرد القارئ واستمراره. من خلال الأهمية القصوى للقراءة كقدرة وممارسة وتفاعل، يتجلى لنا صدق الرسالة الإسلامية عندما انطلقت من القراءة، ومن الحث عليها لنشر العلم والمعرفة والهداية الربانية، فقد كانت أول كلمة أنزلها الله سبحانه وتعالى في القرآن الكريم (اِقْـرَأْ)، وفي هذا تنويه من الله عز وجل بشأن القراءة والكتابة، والعلم والتعلم في حياة الفرد والمجتمع. وظلت القراءة، وستظل عماد العلم والمعرفة، والوسيلة الأساسية لكسب المعارف والمعلومات، والاتصال المباشر بالمواد القرائية المختلفة دون وسيط، أو جهاز يحكم وقتها، وأسلوب ممارستها، فأينما كان الإنسان فإنه يستطيع القراءة، طالما وفرت له، أو وفر لنفسه ما يقرأ. وعلى الرغم من تطور وسائل الاتصال الحديثة، ونمو تكنولوجيا المعلومات التي يسرت نقل الثقافة والمعرفة، واختزانها واسترجاعها، فإن القراءة لم تفقد مكانتها المتميزة، ولم تتراجع عن دورها في التعليم والتثقيف، بل إن هذه المكانة زادت أهميتها، وهذا الدور زاد تأكدا. ورغم أهمية القراءة الحرة ودورها في التعلم الذاتي إلا أن فعـل القراءة أصبح غائبا اليوم عن أمتنا، وتـرى ذلك واضحا جليا في بعد الطلبة والتلاميذ والشباب عامة و نفورهم من الكتب والمكتبـات، حـتى أصبحت هذه الظاهرة سمة واضحة علـى جيـل بأكمله. فما هي يا ترى أسباب العزوف عن القراءة؟ وكيف السبيل إلى إعادة الاعتبار لفعل القراءة وصنع مجتمع قارئ؟ . (shrink)

Fisher criticised the Neyman-Pearson approach to hypothesis testing by arguing that it relies on the assumption of “repeated sampling from the same population.” The present article considers the responses to this criticism provided by Pearson and Neyman. Pearson interpreted alpha levels in relation to imaginary replications of the original test. This interpretation is appropriate when test users are sure that their replications will be equivalent to one another. However, by definition, scientific researchers do not possess sufficient knowledge about the relevant (...) and irrelevant aspects of their tests and populations to be sure that their replications will be equivalent to one another. Pearson also interpreted the alpha level as a personal rule that guides researchers’ behavior during hypothesis testing. However, this interpretation fails to acknowledge that the same researcher may use different alpha levels in different testing situations. Addressing this problem, Neyman proposed that the average alpha level adopted by a particular researcher can be viewed as an indicator of that researcher’s typical Type I error rate. Researchers’ average alpha levels may be informative from a metascientific perspective. However, they are not useful from a scientific perspective. Scientists are more concerned with the error rates of specific tests of specific hypotheses, rather than the error rates of their colleagues. It is concluded that neither Neyman nor Pearson adequately rebutted Fisher’s “repeated sampling” criticism. Fisher’s significance testing approach is briefly considered as an alternative to the Neyman-Pearson approach. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...) reasoning with idealized models in science. (shrink)

Catastrophic risk raises questions that are not only of practical importance, but also of great philosophical interest, such as how to define catastrophe and what distinguishes catastrophic outcomes from non-catastrophic ones. Catastrophic risk also raises questions about how to rationally respond to such risks. How to rationally respond arguably partly depends on the severity of the uncertainty, for instance, whether quantitative probabilistic information is available, or whether only comparative likelihood information is available, or neither type of information. Finally, catastrophic risk (...) raises important ethical questions about what to do when catastrophe avoidance conflicts with equity promotion. (shrink)

Bài mới xuất bản vào ngày 19-5-2020 với tác giả liên lạc là NCS Nguyễn Minh Hoàng, cán bộ nghiên cứu của Trung tâm ISR, trình bày tiếp cận thống kê Bayesian cho việc nghiên cứu dữ liệu khoa học xã hội. Đây là kết quả của định hướng Nhóm nghiên cứu SDAG được nêu rõ ngay từ ngày 18-5-2019.

What is required for an action to promote the satisfaction of a desire? We reject extant answers and propose an alternative. Our account differs from competing answers in two ways: first, it is contrastive, in that actions promote the satisfaction of desires only as contrasted with other possible actions. Second, it employs a notion of expected fit between desire and world, defined as the weighted sum of the fit between the desire and the world in all possible outcomes, where each (...) weight is given by the probability of the agent’s obtaining the relevant outcome. According to our proposal, then, an action promotes a desire when the expected fit for the desire given that the agent performs the action is greater than the expected fit of the desire given that the agent performs the contrasting action. We highlight this account’s attractive features and explain how it improves on its competitors. (shrink)

We present a puzzle about knowledge, probability and conditionals. We show that in certain cases some basic and plausible principles governing our reasoning come into conflict. In particular, we show that there is a simple argument that a person may be in a position to know a conditional the consequent of which has a low probability conditional on its antecedent, contra Adams’ Thesis. We suggest that the puzzle motivates a very strong restriction on the inference of a conditional from a (...) disjunction. (shrink)

Autism has been defined as a disorder of social cognition, interaction and communication where ritualistic, repetitive behaviors are commonly observed. But how should we understand the behavioral and cognitive differences that have been the main focus of so much autism research? Can high-level cognitive processes and behaviors be identified as the core issues people with autism face, or do these characteristics perhaps often rather reflect individual attempts to cope with underlying physiological issues? Much research presented in this volume will point (...) to the latter possibility, i.e. that people on the autism spectrum cope with issues at much lower physiological levels pertaining not only to Central Nervous Systems (CNS) function, but also to peripheral and autonomic systems (PNS, ANS) (Torres, Brincker, et al. 2013). The question that we pursue in this chapter is what might be fruitful ways of gaining objective measures of the large-scale systemic and heterogeneous effects of early atypical neurodevelopment; how to track their evolution over time and how to identify critical changes along the continuum of human development and aging. We suggest that the study of movement variability—very broadly conceived as including all minute fluctuations in bodily rhythms and their rates of change over time (coined micro-movements (Figure 1A-B) (Torres, Brincker, et al. 2013))—offers a uniquely valuable and entirely objectively quantifiable lens to better assess, understand and track not only autism but cognitive development and degeneration in general. This chapter presents the rationale firstly behind this focus on micro-movements and secondly behind the choice of specific kinds of data collection and statistical metrics as tools of analysis (Figure 1C). In brief the proposal is that the micro-movements (defined in Part I – Chapter 1), obtained using various time scales applied to different physiological data-types (Figure 1), contain information about layered influences and temporal adaptations, transformations and integrations across anatomically semi-independent subsystems that crosstalk and interact. Further, the notion of sensorimotor re-afference is used to highlight the fact that these layered micro-motions are sensed and that this sensory feedback plays a crucial role in the generation and control of movements in the first place. In other words, the measurements of various motoric and rhythmic variations provide an access point not only to the “motor systems”, but also access to much broader central and peripheral sensorimotor and regulatory systems. Lastly, we posit that this new lens can also be used to capture influences from systems of multiple entry points or collaborative control and regulation, such as those that emerge during dyadic social interactions. (shrink)

B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.

Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of (...) pooling functions (most of them classic, but one new) and argue that linear pooling can be justified procedurally, but not epistemically, while the other two pooling methods can be justified epistemically. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. We conclude by mentioning a number of other pooling methods. (shrink)

There is a widespread view that in order to be rational we must mostly know what we believe. In the probabilistic tradition this is defended by arguments that a person who failed to have this knowledge would be vulnerable to sure loss, or probabilistically incoherent. I argue that even gross failure to know one's own beliefs need not expose one to sure loss, and does not if we follow a generalization of the standard bridge principle between first-order and second-order beliefs. (...) This makes it possible for a subject to use probabilistic decision theory to manage in a rational way cases of potential failure of this self-knowledge, as we find in implicit bias. Through such cases I argue that it is possible for uncertainty about what our beliefs are to be not only rationally permissible but advantageous. (shrink)

We offer a new argument for the claim that there can be non-degenerate objective chance (“true randomness”) in a deterministic world. Using a formal model of the relationship between different levels of description of a system, we show how objective chance at a higher level can coexist with its absence at a lower level. Unlike previous arguments for the level-specificity of chance, our argument shows, in a precise sense, that higher-level chance does not collapse into epistemic probability, despite higher-level properties (...) supervening on lower-level ones. We show that the distinction between objective chance and epistemic probability can be drawn, and operationalized, at every level of description. There is, therefore, not a single distinction between objective and epistemic probability, but a family of such distinctions. (shrink)

On absolute random and restricted random .

Humean promotionalists about reasons think that whether there is a reason for an agent to ϕ depends on whether her ϕ-ing promotes the satisfaction of at least one of her desires. Several authors have recently defended probabilistic accounts of promotion, according to which an agent’s ϕ-ing promotes the satisfaction of one of her desires just in case her ϕ-ing makes the satisfaction of that desire more probable relative to some baseline. In this paper I do three things. First, I formalize (...) an argument, due to Jeff Behrends and Joshua DiPaolo, to the effect that Mark Schroeder’s and Stephen Finlay’s probabilistic accounts of promotion cannot be correct. Next, I extend this argument to a recent alternative offered by D. Justin Coates and show how Coates’ attempt to avoid the argument by introducing a distinction between ‘intrinsic’ and ‘extrinsic’ probability doesn’t help. Finally, I suggest an alternative way of understanding promotion in terms of increase in degree of fit between the causal upshot of an action and the content of a desire. I show how this view, disjunctively paired with probabilism about promotion, solves the problems with previous accounts. (shrink)

MỘT SỐ QUÁ TRÌNH NGẪU NHIÊN CÓ BƯỚC NHẢY -/- Hoàng Thị Phương Thảo -/- Luận án Tiến sỹ -/- TRƯỜNG ĐẠI HỌC KHOA HỌC TỰ NHIÊN ĐẠI HỌC QUỐC GIA HÀ NỘI -/- Hà Nội - 2015 .

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)

This paper attempts to delineate the interaction between trust, emotion, and ethical decision making. The authors first propose that trust can either incite an individual toward ethical decisions or drag him or her away from ethical decisions, depending on different situations. The authors then postulate that the feeling of guilt is central in understanding how trust affects the ethical decision making process. Several propositions based on these assumptions are introduced and implications for practice discussed.

The canonical Bayesian solution to the ravens paradox faces a problem: it entails that black non-ravens disconfirm the hypothesis that all ravens are black. I provide a new solution that avoids this problem. On my solution, black ravens confirm that all ravens are black, while non-black non-ravens and black non-ravens are neutral. My approach is grounded in certain relations of epistemic dependence, which, in turn, are grounded in the fact that the kind raven is more natural than the kind black. (...) The solution applies to any generalization “All F’s are G” in which F is more natural than G. (shrink)

Abstract The Preface Paradox, first introduced by David Makinson (1961), presents a plausible scenario where an agent is evidentially certain of each of a set of propositions without being evidentially certain of the conjunction of the set of propositions. Given reasonable assumptions about the nature of evidential certainty, this appears to be a straightforward contradiction. We solve the paradox by appeal to stake size sensitivity, which is the claim that evidential probability is sensitive to stake size. The argument is that (...) because the informational content in the conjunction is greater than the sum of the informational content of the conjuncts, the stake size in the conjunction is higher than the sum of the stake sizes in the conjuncts. We present a theory of evidential probability that identifies knowledge with value and allows for coherent stake sensitive beliefs. An agent’s beliefs are represented two dimensionally as a bid – ask spread, which gives a bid price and an ask price for bets at each stake size. The bid ask spread gets wider when there is less valuable evidence relative to the stake size, and narrower when there is more valuable evidence according to a simple formula. The bid-ask spread can represent the uncertainty in the first order probabilistic judgement. According to the theory it can be coherent to be evidentially certain at low stakes, but less than certain at high stakes, and therefore there is no contradiction in the Preface. The theory not only solves the paradox, but also gives a good model of decisions under risk that overcomes many of the problems associated with classic expected utility theory. (shrink)

N. Cartwright’s results on invariance under intervention and causality (2003) are reconsidered. Procedural approach to causality elicited in this paper and contrasted with Cartwright’s apparently philosophical one unravels certain ramifications of her results. The procedural approach seems to license only a constrained notion of intervention and in consequence the “correctness to invariance” part of Cartwright’s first theorem fails for a class of cases. The converse “invariance to correctness” part of the theorem relies heavily on modeling assumptions which prove to be (...) difficult to validate in practice and are often buttressed by independently acquired evidence. (shrink)

A number of Bayesians claim that, if one has no evidence relevant to a proposition P, then one's credence in P should be spread over the interval [0, 1]. Against this, I argue: first, that it is inconsistent with plausible claims about comparative levels of confidence; second, that it precludes inductive learning in certain cases. Two motivations for the view are considered and rejected. A discussion of alternatives leads to the conjecture that there is an in-principle limitation on formal representations (...) of belief: they cannot be both fully accurate and maximally specific. (shrink)

Twenty extremal principles of the natural sciences are reformulated to the general ontological scheme. The hypothesis is substantiated that the unique role of the principle of least action is based on its probabilistic interpretation. It is shown how most of the variational principles can be reduced to the principle of maximal probability, which is based on a realistic interpretation of Feynman’s path integral method.

Par risques majeurs, on entend ceux qui s’attachent à des événements dont les conséquences défavorables, pour l’humanité ou pour l’environnement, sont d’une gravité exceptionnelle. On n’ajoutera ni que ces événements sont d’une intensité physique extrême, ni qu’ils surviennent rarement, car ce n’est pas toujours le cas. Seuls des risques majeurs de nature civile seront considérés dans cet ouvrage, et il s'agira, plus limitativement, de risques naturels, comme ceux d’inondation et de submersion marine, illustrés par la tempête Xynthia en 2010, de (...) risques technologiques industriels, comme celui d’une explosion d'usine, illustré par la catastrophe AZF en 2001, et de risques nucléaires, pour autant qu’ils mettent en jeu les dangers de la radioactivité, et qu’illustrent, hors de France, les catastrophes de Three Miles Island (1979), Tchernobyl (1986) et Fukushima (2011), -/- Conçu comme un rapport destiné au Conseil d'analyse économique (CAE) du Premier Ministre français, l'ouvrage comporte une introduction traitant du risque majeur pris en général (section 1). Dans sa partie principale, il aborde les trois risques majeurs qu'il a sélectionnés à travers les prismes successifs de la géographie et de la technologie (section 2), de l’histoire institutionnelle et juridique (section 3), enfin d’un bilan normatif accompagné de recommandations pour l'action publique (section 4). -/- Neuf compléments spécialisés, dus à d'autres auteurs, complètent l'ouvrage. Ils portent sur des aspects technologiques (F. Ménage; A. Quantin et D. Moucoulon; P. Saint-Raymond), juridiques (V. Sanseverino-Godfrin), économiques généraux (C. Grislain-Letrémy et B. Villeneuve; R. Lahidji; J. Percebois; A. Schmitt et S. Spaeter) et financiers (M. Pappalardo) et ils concernent principalement le risque nucléaire. -/- Dans cet ensemble de vaste format, on espère avoir su proposer, non seulement des évaluations et des préconisations destinées aux pouvoirs publics, comme il convenait au projet initial de rapport, mais aussi une synthèse qui soit utilisable par tous ceux - décideurs, scientifiques ou simples observateurs - que préoccupent les questions de risques majeurs. (shrink)

Abstract The opening section outlines probabilism in the 20th century philosophy and shortly discusses the major accomplishments of Polish probabilist thinkers. A concise characterization of Bayesianism as the major recent form of probabilism follows. It builds upon the core personalist version of Bayesianism towards more objectively oriented versions thereof. The problem of a priori probability is shortly discussed. A tentative characterization of Kazimierz Ajdukiewicz’s standpoint regarding the inductive inference is cast in Bayesian terms. His objections against it presented in Pragmatic (...) Logic are presented. His 1958 paper on justification of non-deductive inference, as amply demonstrated by K. Szaniawski and I. Niiniluoto, extends his earlier Baysian position from 1928 monograph. In the closing section Ajdukiewicz’s standpoint is presented as a characteristically pragmatist and empiricist version of Bayesianism, which remains an unexplored and stimulating position. (shrink)

Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences of (...) a rational agent should always be weighted averages of truth value assignments. In the special case where the truth values are classical, the weighted averages of truth value assignments are exactly the probability functions. But in the more general case, probabilistic axioms formulated in terms of classical logic are violated—but we will show that generalized versions of the axioms formulated in terms of non-classical logics are satisfied. (shrink)

This volume presents research that integrates decision making and creativity within the social contexts in which these processes occur. The volume is an essential addition to and expansion of recent approaches to decision making. Such approaches attempt to incorporate more of the psychological and socio-cultural context in which human decision making takes place. The authors come from different disciplines and also belong to a broad spectrum of research traditions. They present innovative chapters dealing with both theoretical and empirical aspects of (...) decision making in different personal and organizational contexts. All chapters are written from the perspective that human decision making is inherently social and more or less creative. The volume addresses fundamental questions about the nature of human decision making as it occurs in different social contexts. Thereby, it becomes essential reading for researchers in decision making and for advanced students in psychology, management science, informatics, and related disciplines. (shrink)

Research on human decision making is at the present time undergoing rapid changes. From previously being much focused on models and approaches with an origin in economy, much of the present day research finds its inspiration from disciplinary approaches concerned with incorporating more of the context that the decision making takes place in. This context includes psychological aspects of the decision maker and social-cultural aspects of the situation he or she acts in. All human decision making occurs in dynamically changing (...) contexts. One factor contributing to this is that human beings or groups in many situations act as entrepreneurs trying to improve the situation for themselves or their organization. Given that this is the case, it is of increasing interest for both researchers and practitioners interested in the social aspects of decision making to consider the relation between creativity and decision making. (shrink)