Philosophy of Probability, Misc

Normative judgments involve two gradable features. First, the judgments themselves can come in degrees; second, the strength of reasons represented in the judgments can come in degrees. Michael Smith has argued that non-cognitivism cannot accommodate both of these gradable dimensions. The degrees of a non-cognitive state can stand in for degrees of judgment, or degrees of reason strength represented in judgment, but not both. I argue that (a) there are brands of noncognitivism that can surmount Smith’s challenge, and (b) any (...) brand of non-cognitivism that has even a chance of solving the Frege–Geach Problem and some related problems involving probabilistic consistency can also thereby solve Smith’s problem. Because only versions of non-cognitivism that can solve the Frege–Geach Problem are otherwise plausible, all otherwise plausible versions of noncognitivism can meet Smith’s challenge. (shrink)

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)

Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form ‘p, but it might be that not p’ appears to be a contradiction, 'might not p' does not entail 'not p', which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. Some theories predict that (...) 'p and might not p', a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not allow substitution of logical equivalents; these theories underpredict the infelicity of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that intuitively fail, like distributivity and disjunctive syllogism, but also rules like non-contradiction, excluded middle, De Morgan’s laws, and disjunction introduction, which intuitively remain valid for epistemic modals. In this paper, we aim for a middle ground, developing a semantics and logic for epistemic modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We start with an algebraic semantics, based on ortholattices instead of Boolean algebras, and then propose a more concrete possibility semantics, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. Then we show how to extend our semantics to explain parallel phenomena involving probabilities and conditionals. The goal throughout is to retain what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary. (shrink)

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.

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.

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)

Ex ante predicted outcomes should be interpreted as counterfactuals (potential histories), with errors as the spread between outcomes. But error rates have error rates. We reapply measurements of uncertainty about the estimation errors of the estimation errors of an estimation treated as branching counterfactuals. Such recursions of epistemic uncertainty have markedly different distributial properties from conventional sampling error, and lead to fatter tails in the projections than in past realizations. Counterfactuals of error rates always lead to fat tails, regardless of (...) the probability distribution used. A mere .01% branching error rate about the STD (itself an error rate), and .01% branching error rate about that error rate, etc. (recursing all the way) results in explosive (and infinite) moments higher than 1. Missing any degree of regress leads to the underestimation of small probabilities and concave payoffs (a standard example of which is Fukushima). The paper states the conditions under which higher order rates of uncertainty (expressed in spreads of counterfactuals) alters the shapes the of final distribution and shows which a priori beliefs about conterfactuals are needed to accept the reliability of conventional probabilistic methods (thin tails or mildly fat tails). (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)

I argue for a connection between two debates in the philosophy of probability. On the one hand, there is disagreement about conditional probability. Is it to be defined in terms of unconditional probability, or should we instead take conditional probability as the primitive notion? On the other hand, there is disagreement about how additive probability is. Is it merely finitely additive, or is it additionally countably additive? My thesis is that, if conditional probability is primitive, then it is not countably (...) additive. (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)

It is tempting to think that a process of choosing a point at random from the surface of a sphere can be probabilistically symmetric, in the sense that any two regions of the sphere which differ by a rotation are equally likely to include the chosen point. Isaacs, Hájek, and Hawthorne (2022) argue from such symmetry principles and the mathematical paradoxes of measure to the existence of imprecise chances and the rationality of imprecise credences. Williamson (2007) has argued from a (...) related symmetry principle to the failure of probabilistic regularity. We contend that these arguments fail, because they rely on auxiliary assumptions about probability which are inconsistent with symmetry to begin with. We argue, moreover, that symmetry should be rejected in light of this inconsistency, and because it has implausible decision- theoretic implications. -/- The weaker principle of probabilistic invariance says that the probabilistic comparison of any two regions is unchanged by rotations of the sphere. This principle supports a more compelling argument for imprecise probability. We show, however, that invariance is incompatible with mundane judgments about what is probable. Ultimately, we find reason to be suspicious of the application of principles like symmetry and invariance to nonmeasurable regions. (shrink)

Suppose there are no in-principle restrictions on the contents of arbitrarily intelligent agents’ goals. According to “instrumental convergence” arguments, potentially scary things follow. I do two things in this paper. First, focusing on the influential version of the instrumental convergence argument due to Nick Bostrom, I explain why such arguments require an account of “promotion,” i.e., an account of what it is to “promote” a goal. Then, I consider whether extant accounts of promotion in the literature -- in particular, probabilistic (...) and fit-based views of promotion -- can be used to support dangerous instrumental convergence. I argue that neither account of promotion can do the work. The opposite is true: accepting either account of promotion undermines support for instrumental convergence arguments’ existentially worrying conclusions. The conclusion is that we needn’t be scared -- at least not because of arguments concerning instrumental convergence. (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.

Globalisation destabilises indigenous cultures from mining in rainforests to the erasure of indigenous identities due to the impact of globalising information technology (IT). Extinguishing these cultures means deleting strategies needed for the survival of humankind. Within its short time of existence, IT has already achieved the creation of virtual environments with virtual agents equipped with artificial intelligence (AI). As a leverage point for reconciling indigenous and globalised views the Simulation Hypothesis is proposed, which postulates that our world has been programmed (...) from a metalevel. This concept assumes a programmer, which is consistent with religion in general, including the rather complex Christian concept of salvation. The perspective of the universe being a complex programme is compatible with indigenous worldviews of the universe being created by the Creator, and thus, with spirituality. It is suggested that IT users should respect indigenous peoples, especially since they pay a very high price for something they hardly enjoy themselves. (shrink)

This paper is an amended version of a talk Saul Kripke gave at the Eastern Division meeting of the APA in 1992 (an extended abstract was previously published as Kripke, 1992). It contains philosophical reflections and technical results concerning “Carnapian” quantified modal logic, that is, modal logic with quantification over individual concepts. The paper contains the fullest statement by the author available of (un)axiomatizability results he obtained in the 1970s. (The Editors.).

Real human agents, even when they are rational by everyday standards, sometimes assign different credences to objectively equivalent statements, such as ‘Orwell is a writer’ and ‘E.A. 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’. 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 judgement-aggregation theory, where we face similar challenges of defining the ‘objects of judgement’. (shrink)

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)

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)

Pluralistische Wissenschaftstheorie ist kein etabliertes Format. Herkömmliche Darstellungen nehmen meist die Perspektive einer einzelnen Ausprägung von Wissenschaft ein, verbunden mit impliziten Wertungen und unbefragten Präferenzen. So belasten Kämpfe um Deutungshoheit notorisch die kooperative Forschung. Werner Kogge entfaltet demgegenüber einen neuen Ansatz: Er zeichnet nach, wie sich aus mehreren historischen Quellen verschiedene Typen wissenschaftlicher Forschung ausprägten, und wie diese Typen heute praktiziert werden. So entsteht ein Bild unterschiedlicher, aber gleichberechtigter Formen wissenschaftlicher Forschungspraxis, ohne hierarchische Staffelung oder eine evolutionäre Entwicklungslinie. Mit dieser (...) Pluralität kommt auch eine neue Form von Interdisziplinarität in den Blick: strukturell, modular und praxisbezogen. (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)

In a fair finite lottery with n tickets, the probability assigned to each ticket winning is 1/n and no other answer. That is, 1/n is unique. Now, consider a fair lottery over the natural numbers. What probability is assigned to each ticket winning in this lottery? Well, this probability value must be smaller than 1/n for all natural numbers n. If probabilities are real-valued, then there is only one answer: 0, as 0 is the only real and non-negative value that (...) is smaller than 1/n for all natural numbers n. However, this answer seems counter-intuitive, as it violates Regularity: for all possible events A that are assigned a probability, A is assigned a positive probability. It is possible for ticket i to win in the second lottery. So, the set {i} should be assigned a positive probability and not 0. Consequently, in order to satisfy Regularity, probabilities must be allowed to take on `non-real' values, e.g. a positive infinitesimal x that is smaller than 1/n for all natural numbers n. So, what regular probability is assigned to {i} in the second lottery? This probability value must be positive but smaller than 1/n for all natural numbers n. Given the definition of x, x is a correct answer. But x isn't unique, because every other positive infinitesimal is a correct answer as well and there are uncountably many positive infinitesimals. After all, every positive infinitesimal is strictly between 0 and 1/n for all natural numbers n. Nothing about a fair lottery over the natural numbers uniquely determines x as the correct answer and nothing about the lottery rules out other positive infinitesimals as a correct answer as well. What probability to assign to {i} is underdetermined. -/- In this thesis, I explore this difference between fair finite lotteries and fair infinite lotteries. The constraints governing the former uniquely determine the probabilities assigned to events in those lotteries, but this isn't true for the latter lotteries, when Regularity is a constraint on probabilities. Now, although there are uncountably many correct probability values that can be assigned to {i} in the second lottery, there are some applications of probability theory, for which at least one correct probability value must be chosen in order to accomplish that application, e.g. calculation of expected utilities. In this thesis, I spell out sufficient conditions for when a choice like that is problematic. These conditions apply to precise probabilities, imprecise probabilities, and qualitative probabilities. So, I will consider Benci et al. (2018)'s and Pruss (2021)'s suggestion of allowing probabilities to be imprecise, as well as resorting to qualitative probabilities, to overcome the choice problem. I will argue that both don't solve the problem. Furthermore, there's a hitherto unnoticed difficulty in deriving imprecise probabilities by supervaluating over precise `non-real' probability values. To avoid this difficulty, precise probability values should be real-valued. Thus, Regularity cannot be a constraint on probabilities. But as it turns out, dropping Regularity as a constraint and requiring precise probabilities to be real-valued solve the choice problem. (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.

While it is natural to assume that contradiction between alleged witness testimonies to some event disconfirms the event, this generalization is subject to important qualifications. I consider a series of increasingly complex probabilistic cases that help us to understand the effect of contradictions more precisely. Due to the possibility of honest error on a difficult detail even on the part of highly reliable witnesses, agreement on such a detail can confirm H much more than contradiction disconfirms H. It is also (...) possible to model scenarios where we strongly suspect ahead of time that one source has copied another. In these cases, contradiction on a detail due to witness error can even confirm H by disconfirming collusion or copying. Finally, still more complex scenarios show that indirect confirmation, as opposed to exact agreement, provides the “best of both worlds,” simultaneously disconfirming suspected copying while permitting the statements of both sources to be true. (shrink)

The Borel-Kolmogorov paradox is often presented as an obscure problem that certain mathematical accounts of conditional probability must face. In this article, we point out that the paradox arises in the physical sciences, for physical probability or chance. By carefully formulating the paradox in this setting, we show that it is a puzzle for everyone, regardless of one’s preferred probability formalism. We propose a treatment that is inspired by the approach that scientists took when confronted with these cases.

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)

One of the most widely discussed philosophical issues is the problem of future contingents. Basically, the challenge is to create an adequate semantic theory of future-tensed sentences. Twardowski (1900) suggests that future contingent statements should be analyzed using the concept of probability. The aim of this paper is to show that (1) such an analysis is not appropriate and (2) that Twardowski’s main theses imply the Thin Red Line Theory. I discuss three potential arguments against my proposal and sketch the (...) connection with Schaffer’s Parallelism Thesis (2012). (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)

(This is for the series Elements of Decision Theory published by Cambridge University Press and edited by Martin Peterson) -/- Our beliefs come in degrees. I believe some things more strongly than I believe others. I believe very strongly that global temperatures will continue to rise during the coming century; I believe slightly less strongly that the European Union will still exist in 2029; and I believe much less strongly that Cardiff is east of Edinburgh. My credence in something is (...) a measure of the strength of my belief in it; it represents my level of confidence in it. These are the states of mind we report when we say things like ‘I’m 20% confident I switch off the gas before I left' or ‘I’m 99.9% confident that it is raining outside'. -/- There are laws that govern these credences. For instance, I shouldn't be more confident that sea levels will rise by over 2 metres in the next 100 years than I am that they'll rise by over 1 metre, since the latter is true if the former is. This book is about a particular way we might try to establish these laws of credence: the Dutch Book arguments (For briefer overviews of these arguments, see Alan Hájek’s entry in the Oxford Handbook of Rational and Social Choice and Susan Vineberg’s entry in the Stanford Encyclopaedia.) -/- We begin, in Chapter 2, with the standard formulation of the various Dutch Book arguments that we'll consider: arguments for Probabilism, Countable Additivity, Regularity, and the Principal Principle. In Chapter 3, we subject this standard formulation to rigorous stress-testing, and make some small adjustments so that it can withstand various objections. What we are left with is still recognisably the orthodox Dutch Book argument. In Chapter 4, we set out the Dutch Strategy argument for Conditionalization. In Chapters 5 and 6, we consider two objections to Dutch Book arguments that cannot be addressed by making small adjustments. Instead, we must completely redesign those arguments, replacing them with ones that share a general approach but few specific details. In Chapter 7, we consider a further objection to which I do not have a response. In Chapter 8, we'll ask what happens to the Dutch Book arguments if we change certain features of the basic framework in which we've been working: first, we ask how Dutch Book arguments fare when we consider credences in self-locating propositions, such as It is Monday; second, we lift the assumption that the background logic is classical and explore Dutch Book arguments for non-classical logics; third, we lift the assumption that an agent's credal state can be represented by a single assignment of numerical values to the propositions she considers. In Chapter 9, we present the mathematical results that underpin these arguments. (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)

The problem of inferring probability comparisons between events from an initial set of comparisons arises in several contexts, ranging from decision theory to artificial intelligence to formal semantics. In this paper, we treat the problem as follows: beginning with a binary relation ≥ on events that does not preclude a probabilistic interpretation, in the sense that ≥ has extensions that are probabilistically representable, we characterize the extension ≥+ of ≥ that is exactly the intersection of all probabilistically representable extensions of (...) ≥. This extension ≥+ gives us all the additional comparisons that we are entitled to infer from ≥, based on the assumption that there is some probability measure of which ≥ gives us partial qualitative information. We pay special attention to the problem of extending an order on states to an order on events. In addition to the probabilistic interpretation, this problem has a more general interpretation involving measurement of any additive quantity: e.g., given comparisons between the weights of individual objects, what comparisons between the weights of groups of objects can we infer? (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)

This paper examines and evaluates a range of methodologies that have been proposed for making useful claims about the probability of phenomena that would contribute to existential risk. Section One provides a brief discussion of the nature of such claims, the contexts in which they tend to be made and the kinds of probability that they can contain. Section Two provides an overview of the methodologies that have been developed to arrive at these probabilities and assesses their advantages and disadvantages. (...) Section Three contains four suggestions to improve best practice in existential risk assessment. These suggestions centre on the types of probabilities used in risk assessment, the role of methodology rankings including the ranking of probabilistic information, the extended use of expert elicitation, and the use of confidence measures to better communicate uncertainty in probability assessments. Finally, Section Four provides an annotated literature review of catastrophic and existential risk probability claims as well as the methodologies that were used to produce each of them. (shrink)

The paper will compare two methods used in the design of diagnostic strategies. The first one is a method that precises predictive value of diagnostic tests. The second one is based on the use of Bayes’ theorem. The main aim of this article is to identify the epistemological assumptions underlying both of these methods. For the purpose of this objective, example projects of one and multi-stage diagnostic strategy developed using both methods will be considered.

Probability is a central concept in utilitarian moral theory, almost impossible to do without. I attempt to clarify the role of probability, so that we can be clear about what we are aiming for when we apply utilitarian theory to real cases. I point out the close relationship between utilitarianism and expected-utility theory, a normative standard for individual decision-making. I then argue that the distinction between “ambiguity” and risk is a matter of perception. We do not need this distinction in (...) the theory itself. In order to make this argument I rely on the personalist theory of probability, and I try to show that, within this theory, we do not need to give up completely on the idea that a “true probability” exists. Finally, I discuss several examples of applied utilitarianism, emphasizing the role of probability in each example: reasonable doubt, the precautionary principle in risk regulation, charity, climate change, and voting. (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)