The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities (...) of conditionals violate standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

Leibniz’s account of probability has come into better focus over the past decades. However, less attention has been paid to a certain domain of application of that account, that is, the application of it to the moral or ethical domain—the sphere of action, choice and practice. This is significant, as Leibniz had some things to say about applying probability theory to the moral domain, and thought the matter quite relevant. Leibniz’s work in this area is conducted at a (...) high level of abstraction. It establishes a proof of concept, rather than concrete guidelines for how to apply calculations to specific cases. Still, this highly abstract material does allow us to begin to construct a framework for thinking about Leibniz’s approach to the ethical side of probability. (shrink)

When probability discounting (or probability weighting), one multiplies the value of an outcome by one's subjective probability that the outcome will obtain in decision-making. The broader import of defending probability discounting is to help justify cost-benefit analyses in contexts such as climate change. This chapter defends probability discounting under risk both negatively, from arguments by Simon Caney (2008, 2009), and with a new positive argument. First, in responding to Caney, I argue that small costs and (...) benefits need to be evaluated, and that viewing practices at the social level is too coarse-grained. Second, I argue for probability discounting using a distinction between causal responsibility and moral responsibility. Moral responsibility can be cashed out in terms of blameworthiness and praiseworthiness, while causal responsibility obtains in full for any effect which is part of a causal chain linked to one's act. With this distinction in hand, unlike causal responsibility, moral responsibility can be seen as coming in degrees. My argument is, given that we can limit our deliberation and consideration to that which we are morally responsible for and that our moral responsibility for outcomes is limited by our subjective probabilities, our subjective probabilities can ground probability discounting. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities (...) are not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by explaining (...) in simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability, combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the Guide to Numerical Results to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled The Mathematics of Games of Chance presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game s section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one, but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal.". (shrink)

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data (...) will run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data. (shrink)

Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely (...) thought to undercut this motivation: they present a world-ordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard’s semantics yields an adequate logic only if models are restricted to Noetherian pre-orders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data. (shrink)

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that (...) probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent’s prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent’s prior beliefs. Quantum certainty is therefore always some agent’s certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system. (shrink)

In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.

This paper is about teaching probability to students of philosophy who don’t aim to do primarily formal work in their research. These students are unlikely to seek out classes about probability or formal epistemology for various reasons, for example because they don’t realize that this knowledge would be useful for them or because they are intimidated by the material. However, most areas of philosophy now contain debates that incorporate probability, and basic knowledge of it is essential even (...) for philosophers whose work isn’t primarily formal. In this paper, I explain how to teach probability to students who are not already enthusiastic about formal philosophy, taking into account the common phenomena of math anxiety and the lack of reading skills for formal texts. I address course design, lesson design, and assignment design. Most of my recommendations also apply to teaching formal methods other than probability theory. (shrink)

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability (...) of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic. (shrink)

Peter Baumann uses the Monty Hall game to demonstrate that probabilities cannot be meaningfully applied to individual games. Baumann draws from this first conclusion a second: in a single game, it is not necessarily rational to switch from the door that I have initially chosen to the door that Monty Hall did not open. After challenging Baumann's particular arguments for these conclusions, I argue that there is a deeper problem with his position: it rests on the false assumption that (...) what justifies the switching strategy is its leading me to win a greater percentage of the time. In fact, what justifies the switching strategy is not any statistical result over the long run but rather the "causal structure" intrinsic to each individual game itself. Finally, I argue that an argument by Hilary Putnam will not help to save Baumann's second conclusion above. (shrink)

This paper is a discussion note on Isaacs et al. (2022), who have claimed to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of their proposal. In particular, I show that if their proposal is applied to a bounded 3-dimensional space, then they have to reject at least one of the following: (i) If A is at most as probable as B and B is at most (...) as probable as C, then A is at most as probable as C. (ii) Let A ∩ C = B ∩ C = ∅. A is at most as probable as B iff (A ∪ C) is at most as probable as (B ∪ C). But rejecting either statement seems unattractive. (shrink)

This chapter explores a philosophical hypothesis about the nature of (some) probabilities encountered in social sciences. It should be of interest to those with philosophical concerns about the foundations of probability, and to social scientists and philosophers of science who are somewhat puzzled by the nature of probability in social domains. As will become clear below, the chapter is not intended as a contribution to an empirical methodology such as a particular way of applying statistics.

One of our most sophisticated accounts of objective chance in quantum mechanics involves the Deutsch-Wallace theorem, which uses state-space symmetries to justify agents’ use of the Born rule when the quantum state is known. But Wallace argues that this theorem requires an Everettian approach to measurement. I find that this argument is unsound. I demonstrate a counter-example by applying the Deutsch-Wallace theorem to the de Broglie-Bohm pilot-wave theory.

A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers are in a position of self-locating uncertainty during the period between the branches of the wave function splitting via decoherence and the observer registering the outcome of the measurement. In this period it is tempting to regard each branch as equiprobable, but (...) we argue that the temptation should be resisted. Applying lessons from this analysis, we demonstrate (using methods similar to those of Zurek's envariance-based derivation) that the Born rule is the uniquely rational way of apportioning credence in Everettian quantum mechanics. In doing so, we rely on a single key principle: changes purely to the environment do not affect the probabilities one ought to assign to measurement outcomes in a local subsystem. We arrive at a method for assigning probabilities in cases that involve both classical and quantum self-locating uncertainty. This method provides unique answers to quantum Sleeping Beauty problems, as well as a well-defined procedure for calculating probabilities in quantum cosmological multiverses with multiple similar observers. (shrink)

This study applies Arne Naess’ ecosophy as a tool for possible progressive research material concerning the National Greening Program (NGP) of the Department of Environment and Natural Resources (DENR). This study aims to conduct a phenomenological analysis of tree farming advantages, driven by a philosophical approach and practical strategy integrated through the principle of deep ecology. The philosophy of deep ecology presupposes ethics and the interrelatedness of human beings to nature that generally can be experienced anywhere. This study aims to (...) assess the core motives, plans, objectives, strategic implications, initiatives, provisions, and the probable outcome of the said government program. To realize this, this research enunciates a possible parallel study between Naess's deep ecology and the DENR's goal. Since this study is concerned with the current situation of human beings, it delves into the context of the phenomenological research approach. It provides different perspectives on the other government officials who were once the program's authors and implementers. As this research goes on, the findings have various outlooks on applying deep ecology to facilitate the government's NGP. The crucial part of making this program absolute must be the participation of every individual in such advocacy as a sole environmental bailiff. However, the challenge never ceases to interrupt the goodwill of human beings. On the other hand, man's passion never fails to contribute to sustainable ecological preservation, biodiversity, reparation, and community commitment. (shrink)

Whereas many philosophers accept the validity of 'probability' and confine themselves to interpreting it, this paper challenges its conceptual coherence by critically examining its use in the empirical world. While measure theory provides a rigorous mathematical framework for manipulating probability functions, we argue that applying precise probability measures to empirically uncertain outcomes introduces a fundamental contradiction. Probability measures claim to quantify uncertainty while simultaneously implying a degree of understanding about events that we do not fully possess. (...) This inconsistency undermines the idea that probability offers objective or reliable insights into reality. Moreover, we argue that it is impossible to assign a correct probability in the empirical world—neither deduction nor induction provides a justifiable basis for doing so. Therefore, despite probability appearing to work as a practical tool for managing uncertainty, its theoretical foundation collapses under scrutiny in empirical applications. (shrink)

Unlike other classical arguments for the existence of God, Pascal’s Wager provides a pragmatic rationale for theistic belief. Its most popular version says that it is rationally mandatory to choose a way of life that seeks to cultivate belief in God because this is the option of maximum expected utility. Despite its initial attractiveness, this long-standing argument has been subject to various criticisms by many philosophers. What is less discussed, however, is the rationality of this choice in situations where the (...) decision-makers are confronted with greater uncertainty. In this paper, I examine the imprecise version of Pascal’s Wager: those scenarios where an agent’s credence that God exists is imprecise or vague rather than precise. After introducing some technical background on imprecise probabilities, I apply five different principles for decision-making to two cases of state uncertainty. In the final part of the paper, I argue that it is not rationally permitted to include zero as the lower probability of God’s existence. Although the conditions for what makes an act uniquely optimal vary significantly across those principles, I also show how the option of wagering for God can defeat any mixed strategy under two distinct interpretations of salvation. (shrink)

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite (...) and uniform. In this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces. (shrink)

The concept of causation is essential for understanding relationships among various phenomena, yet its fundamental nature and the criteria for establishing it continue to be debated. This paper presents a new theory of causation through a quasi-axiomatic approach. The core of this framework is Probability Distribution Determinism (PDD), which updates traditional determinism by representing states of affairs as probability distributions, with the if-then function serving as its foundational definition. Based on PDD, by merely using appropriate naming strategies, it (...) is possible to derive systems in which the structural characteristics of relationships among things closely resemble those in the real world, such as having various forms of nested hierarchies. Additionally, there are two related yet distinctly different contexts about relationships in PDD: one emphasizes the potential influence of conditions on outcomes in the general sense, while the other focuses on attributing responsibility for the state changes in specific scenarios. The formula for determining the relationship in the general sense is established as S(Y |S1(X), Ψ) ̸≡ S(Y |S2(X), Ψ). Subsequently, within the PDD framework, the paper clarifies the legitimate use of a series of concepts related to causation in those two contexts, thus encompassing the entire detailed connotation of the concept of causation. The comparison with other theories of causation and the analysis of case applications demonstrate that the new theory applies not only to situations where other theories are competent but also to situations where they are not. This suggests that, although certain aspects within the new framework may require further analysis, it provides a highly promising direction for a deeper understanding of causation. (shrink)

Abstract: The Pull Bayesian Significance Test (FBST) for precise hy- potheses is applied to a Multivariate Normal Structure (MNS) model. In the FBST we compute the evidence against the precise hypothesis. This evi- dence is the probability of the Highest Relative Surprise Set (HRSS) tangent to the sub-manifold (of the parameter space) that defines the null hypothesis. The MNS model we present appears when testing equivalence conditions for genetic expression measurements, using micro-array technology.

To obtain effective fusion results of multi source evidences with different importance, an evidence fusion method with importance discounting factors based on neutrosopic probability analysis in DSmT framework is proposed. First, the reasonable evidence sources are selected out based on the statistical analysis of the pignistic probability functions of single focal elements. Secondly, the neutrosophic probability analysis is conducted based on the similarities of the pignistic probability functions from the prior evidence knowledge of the reasonable evidence (...) sources. Thirdly, the importance discounting factors of the reasonable evidence sources are obtained based on the neutrosophic probability analysis and the reliability discounting factors of the real-time evidences are calculated based on probabilistic-based distances. Fourthly, the real-time evidences are discounted by the importance discounting factors and then the evidences with the mass assignments of neutrosophic empty sets are discounted by the reliability discounting factors. Finally, DSmT+PCR5 of importance discounted evidences is applied. Experimental examples show that the decision results based on the proposed fusion method are different from the results based on the existed fusion methods. Simulation experiments of recognition fusion are performed and the superiority of proposed method is testified well by the simulation results. (shrink)

We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case).

Amongst invertebrates, molluscs show great variability in their nervous system ranging from primitive arrangement in Chitons to the complex mass of fused ganglia forming the ‘brain’ of cephalopods. Most of the effector organs used for pharmacological or physiological experiments. The neurosecretory cells (NSCs) with their combination of neuronal and glandular capabilities are perfectly suited to translate a neuronal input into the hormonal output best suited to long-term process. In this capacity, the NSCs may produce hormones, which act directly upon the (...) peripheral target or it may exert its effect indirectly by influencing the activity of other non-neural, endocrine organs. Neurosecretory cells have been detected in the cerebral, pedal and visceral ganglia of Lamellidens corrianus. The distribution and biology of freshwater bivalve like Lamellidens corrianus is influenced by local ecological factors (like temperature, pH, inorganic salts, type of soil etc.), water flow system and presence of micro-organisms, teleost fishes and seasonal variations in these parameters. Nitrogenous excretory changes which include ammonia in these molluscs is also influenced by these local ecological factors in which temperature is plays very crucial role. It is well known fact that the high stress conditions during drought or severe winter conditions have been conquered by several lineage of gastropods and sand bivalves and their ability to enter the resistant or dormant stages (low food) protein catabolism increased. Present investigation deals with the oxygen consumption and ammonia excretion ratio of these freshwater pelecypode Lamellidens corrianus. Study on Lemellidens corrianus directed in understanding the different behavioral and physiological aspects after cerebral ganglia removal and injection of their extracts revealed significant changes during summer (April-May). (shrink)

This eighth book of the author on gambling math presents in accessible terms the cold mathematics behind the sparkling slot machines, either physical or virtual. It contains all the mathematical facts grounding the configuration, functionality, outcome, and profits of the slot games. Therefore, it is not a so-called how-to-win book, but a complete, rigorous mathematical guide for the slot player and also for game producers, being unique in this respect. As it is primarily addressed to the slot player, its goal (...) is to present practical applications of the mathematical models of slot games, in order to provide numerical results that a player can use as criteria for gaming decisions or just as information for any slot game and any predicted winning event. These results are focused on probability and expected value, these being the most important parameters for decisional criteria in slots. The book is packed with plenty of figures, tables, and formulas. The content is organized so that readers can skip the theoretical parts and go picking the practical results (numerical, in tables of values where possible, or ready-to-compute formulas) for the desired situation. The practical results are gathered in the last chapter, titled "Practical Applications and Numerical Results," the largest part of the book, for the most popular categories of slot machines, namely with 3, 5, 9, and 16 reels. Any other category of slot games is covered in the theoretical part of the book, where the general formulas apply not only to existing slot games, but also to possible future slot games of any design and configuration. The author does not just throw the slot mathematics to the audience and run away, but offers an ultimate practical contribution with the chapter "How to estimate the number of stops and the symbol distribution on a reel", a surprise for both players and producers, where one can see that mathematics provides players with some statistical methods as well as methods based on physical measurements for retrieving these missing data. Having these data along with the mathematical results of this book, anyone can generate the PAR sheet of any slot machine. In the last decade, mathematics has been taken more and more seriously into account in gaming, as being the essence that governs the games of chance and the only rigorous tool providing information on optimal play, where possible. For the popular game of slots, mathematics already fulfilled its duty by providing all the data that it can provide and that cannot be found on the display of the slot machines - it is all here in this book. (shrink)

Horizontal gene transfer (HGT) has been a paramount mechanism of interest in recent literature addressing the origins of biological evolution. However, research on lightning-triggered electroporation represents the innovative and still insufficiently grasped approach to HGT (Kotnik, 2013). On the other hand, prebiotic synthesis is a fundamental process for chemical evolution. Recently, the effects of volcanic lightning on nitrogen fixation and phosphate reduction have also been considered (NavarroGonzález and Segura, 2004). This paper aims to present a top-down approach to the question (...) of the origin of life on early Earth. By considering the conditions necessary for the emergence of biological and chemical evolution, emphasizing electrostatic discharges, we will attempt to link previous theoretical and experimental research. Furthermore, we will present a recent endeavor at applying the Drake equation to calculating the probability of volcanic lightning impact on the prebiotic synthesis and derive a similar use in estimating the contribution of lightning to HGT (Weaver, 2013). We will also display that choosing a type of probability appropriate for the context of life sciences is not necessarily a quantitative issue. Finally, we will show that significant conceptual constraints, like determining the relevant factors and sources of uncertainty when considering the origin of life on early Earth, are fundamentally philosophical issues. We hope that the results of our research – deriving Drake’s equation in the domain of chemical evolution and considering Bayesian and counterfactual types as potentially more suitable candidates for calculating probabilities in the evolutionary framework – will contribute to developing new discussions in life sciences. (shrink)

What is the boundary between the animate and inanimate world? It is obvious that the animate world is under rules of inanimate world. Is the converse true? This paper is aimed at imposing the well-known Darwin's theory of evolution to inanimate world of atomic realm where bizarre behavior of electron challenges our everyday perception of inanimate world. This paper, suggests a weird, peculiar and highly elegant speculation of existing, leads suspicious about validity of the law of conservation of mass, provides (...) conceptual foundation for many odd explanations of quantum mechanics such wave-particle duality of elementary particles, the inherent randomness and probabilistic nature of world as quantum mechanics states, the Louis de Broglie proposition of wave-like behavior of moving particles, Schrödinger's wave function description of probability of finding electron at any location around the nucleus and even the roots of causality. It defines existence as follows: "All the elementary particles emerge spontaneously and randomly in space where the possibility of conforming the physical laws is higher and after appearing if they not conform the laws of physics, they vanish." It proposes, the emerging from nothing, as a natural process and in other word there is an inherent urge to existence not only for animate world but also for inanimate world. Assuming the correctness of the proposed speculation, leads to dramatic development of human perception of existing, reality and interaction with world. (shrink)

Abstract: Proponents of the this-universe objection to fine-tuning arguments for a multiverse claim that while the multiverse hypothesis raises the probability that some universe is fine-tuned for life, it fails to raise the probability that this one is. Because that is so, they further argue, those who take the fine-tuning of this universe as evidence for the multiverse hypothesis are guilty of a probabilistic fallacy. I argue that a proper evaluation of the this-universe objection requires the development of (...) a general, formal framework for reasoning probabilistically with evidence statements expressed using indexical terms (such as the statement This universe is fine-tuned). I proceed to develop such a framework and then to apply it to the this-universe objection. While my primary aim is to defend the this-universe objection from recent rebuttals, a secondary aim is to exhibit the utility of the framework itself, which has the potential for wider application. (shrink)

We advocate and develop a states-based semantics for both nominal and adjectival confidence reports, as in "Ann is confident/has confidence that it's raining", and their comparatives "Ann is more confident/has more confidence that it's raining than that it's snowing". Other examples of adjectives that can report confidence include "sure" and "certain". Our account adapts Wellwood's account of adjectival comparatives in which the adjectives denote properties of states, and measure functions are introduced compositionally. We further explore the prospects of applying these (...) tools to the semantics of probability operators. We emphasize three desirable and novel features of our semantics: (i) probability claims only exploit qualitative resources unless there is explicit compositional pressure for quantitative resources; (ii) the semantics applies to both probabilistic adjectives (e.g., "likely") and probabilistic nouns (e.g., "probability"); (iii) the semantics can be combined with an account of belief reports that allows thinkers to have incoherent probabilistic beliefs (e.g. thinking that A & B is more likely than A) even while validating the relevant purely probabilistic claims (e.g. validating the claim that A & B is never more likely than A). Finally, we explore the interaction between confidence-reporting discourse (e.g., "I am confident that...") and belief-reports about probabilistic discourse (e.g.,"I think it's likely that.."). (shrink)

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination defines (...) a dutch book, but we only have a partial converse. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

This paper aims to scrutinize how the notion of risk should be understood and applied to possibly catastrophic cases. I begin with clarifying the standard usage of the notion of risk, particularly emphasizing the conceptual relation between risk and probability. Then, I investigate how to make decisions in the case of seemingly catastrophic disasters by contrasting the precautionary principle with the preventive (prevention) principle. Finally, I examine what kind of causal thinking tends to be actually adopted when we (...) make decisions on emergent cases. My arguments are mainly based on Japan's 2011 massive earthquake and nuclear power station accident. Masaki Ichinose. (shrink)

We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically notof the Cartesian product form). We apply these representationsto (1)streams of commodity baskets through time, (2)uncertain social (...) prospects, (3)uncertain individual prospects. Concerning(1), we propose a finite horizon variant of Koopmans’s (1960) axiomatization of infinite discounted utility sums. The main results concern(2). We push the classic comparison between the exanteand expostsocial welfare criteria one step further by avoiding any expected utility assumptions, and as a consequence obtain what appears to be the strongest existing form of Harsanyi’s (1955) Aggregation Theorem. Concerning(3), we derive a subjective probability for Anscombe and Aumann’s (1963) finite case by merely assuming that there are two epistemically independent sources of uncertainty. (shrink)

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

In most academic and non-academic circles throughout history, the world and its operation have been viewed in terms of cause and effect. The principles of causation have been applied, fruitfully, across the sciences, law, medicine, and in everyday life, despite the lack of any agreed-upon framework for understanding what causation ultimately amounts to. In this engaging and accessible introduction to the topic, Douglas Kutach explains and analyses the most prominent theories and examples in the philosophy of causation. The book (...) is organized so as to respect the various cross-cutting and interdisciplinary concerns about causation, such as the reducibility of causation, its application to scientific modeling, its connection to influence and laws of nature, and its role in causal explanation. Kutach begins by presenting the four recurring distinctions in the literature on causation, proceeding through an exploration of various accounts of causation including determination, difference making and probability-raising. He concludes by carefully considering their application to the mind-body problem. _Causation_ provides a straightforward and compact survey of contemporary approaches to causation and serves as a friendly and clear guide for anyone interested in exploring the complex jungle of ideas that surround this fundamental philosophical topic. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The (...) probability bounds imposed by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence (XAI), a fast-growing research area that is so far lacking in firm theoretical foundations. Building on work in logic, probability, and causality, we establish the central role of necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We provide a sound and complete algorithm for computing (...) explanatory factors with respect to a given context, and demonstrate its flexibility and competitive performance against state of the art alternatives on various tasks. (shrink)

Abstract In this paper I consider an easier-to-read and improved to a certain extent version of the causal chance-based analysis of counterfactuals that I proposed and argued for in my A Theory of Counterfactuals. Sections 2, 3 and 4 form Part I: In it, I survey the analysis of the core counterfactuals (in which, very roughly, the antecedent is compatible with history prior to it). In section 2 I go through the three main aspects of this analysis, which are the (...) following. First, it is a causal analysis, in that it requires that intermediate events to which the antecedent event is not a cause be preserved in the main truth-condition schema. Second, it highlights the central notion to the semantics of counterfactuals on the account presented here -- the notion of the counterfactual probability of a given counterfactual, which is the probability of the consequent given the following: the antecedent, the prior history, and the preserved intermediate events. Third, it considers the truth conditions for counterfactuals of this sort as consisting in this counterfactual probability being higher than a threshold. In section 3, I re-formulate the analysis of preservational counterfactuals in terms of the notion of being a cause, which ends up being quite compact. In section 4 I illustrate this analysis by showing how it handles two examples that have been considered puzzling – Morgenbesser's counterfactual and Edgington's counterfactual. Sections 5 and on constitute Part II: Its main initial thrust is provided in section 5, where I present the main lines of the extension of the theory from the core counterfactuals (analyzed in part I) to counterfactuals (roughly) whose antecedents are not compatible with their prior history. In this part II, I elaborate on counterfactuals that don't belong to the core, and more specifically on so-called reconstructional counterfactuals (as opposed to the preservational counterfactuals, which constitute the core counterfactual-type). The heart of the analysis is formulated in terms of processes leading to the antecedent (event/state), and more specifically in terms of processes likely to have led to the antecedent, a notion which is analyzed entirely in terms of chance. It covers so-called reconstructional counterfactuals as opposed to the core, so-called preservational counterfactuals, which are analyzed in sections 2 and 3 of part I. The counterfactual probability of such reconstructional counterfactuals is determined via the probability of possible processes leading to the antecedent weighed, primarily and roughly, by the conditional probability of the antecedent given such process: The counterfactual probability is thus, very roughly, a weighted sum for all processes most likely to have led to the antecedent, diverging at a fixed time. In section 6 I explain and elaborate further on the main points in section 5. In section 7 I illustrate the reconstructional analysis. I specify counterfactuals which are so-called process-pointers, since their consequent specifies stages in processes likely to have led to their antecedent. I argue that so-called backtracking counterfactuals are process-pointers counterfactuals, which fit into the reconstructional analysis, and do not call for a separate reading. I then illustrate cases where a speaker unwittingly employs a certain counterfactual while charitably construable as intending to assert (or ‘having in mind’) another. Here I also cover the issue of how to construe what one can take as back-tracking counterfactuals, or counterfactuals of the reconstructional sort, and more specifically, which divergence point they should be taken as alluding to (prior to which the history is held fixed). Some such cases also give rise to what one can take as a dual reading of a counterfactual between preservational and reconstructional readings. Such cases may yield an ambiguity, where in many cases one construal is dominant. In section 8 I illustrate the analysis by applying it to the famous Bizet-Verdi counterfactuals. This detailed analysis of counterfactuals (designed for the indeterministic case) has three main distinctive elements: its being chance-based, its causal aspect, and the use it makes of processes most likely to have led to the antecedent-event. This analysis is couched in a very different conceptual base from, and is an alternative account to, analyses in terms of the standard notion of closeness or distance of possible worlds, which is the main feature of the Stalnaker-Lewis-type analyses of counterfactuals. This notion of closeness or distance plays no role whatsoever in the analysis presented here. (This notion of closeness has been left open by Stalnaker, and to significant extent also by Lewis's second account.) . (shrink)

In a recent paper in this journal, Carter and Peterson raise two distinctly epistemological puzzles that arise for anyone aspiring to defend the precautionary principle. The first puzzle trades on an application of epistemic contextualism to the precautionary principle; the second puzzle concerns the compatibility of the precautionary principle with the de minimis rule. In this note, I argue that neither puzzle should worry defenders of the precautionary principle. The first puzzle can be shown to be an instance of the (...) familiar but conceptually harmless challenge of adjudicating between relevant interests to reach assessments of threats when applying the precautionary principle. The second puzzle can be shown to rely on a subtle but crucial misrepresentation of the relevant probabilities at play when applying the precautionary principle. (shrink)

Gambling addiction is special type of addiction not only through the object of the addiction, the psychobiological constitution of the individual, and the pattern of the development of a pathological behaviour and condition, but also through the methods available for preventing and fighting against it and their effectiveness. This latter specificity has not been clearly established and thus has not been exploited much in problem-gambling research; but specificity should be reflected in warning messages and counselling content.

Carl Hempel (1965) argued that probabilistic hypotheses are limited in what they can explain. He contended that a hypothesis cannot explain why E is true if the hypothesis says that E has a probability less than 0.5. Wesley Salmon (1971, 1984, 1990, 1998) and Richard Jeffrey (1969) argued to the contrary, contending that P can explain why E is true even when P says that E’s probability is very low. This debate concerned noncontrastive explananda. Here, a view of (...) contrastive causal explanation is described and defended. It provides a new limit on what probabilistic hypotheses can explain; the limitation is that P cannot explain why E is true rather than A if P assign E a probability that is less than or equal to the probability that P assigns to A. The view entails that a true deterministic theory and a true probabilistic theory that apply to the same explanandum partition are such that the deterministic theory explains all the true contrastive propositions constructable from that partition, whereas the probabilistic theory often fails to do so. (shrink)

There is a current debate about the extent to which Academic Freedom should be permitted in our universities. On the one hand, we have traditionalists who maintain that Academic Freedom should be unrestricted: people who have the appropriate qualifications and accomplishments should be allowed to develop theories about how the world is, or ought to be, as they see fit. On the other hand, we have post-traditional philosophers who argue against this degree of Academic Freedom. I consider a conservative version (...) of post-traditional philosophy that permits restrictions on Academic Freedom only if the following conditions are met, Condition 1: The dissemination of the results of a given research project R must cause significant harm to some people, especially to people from oppressed groups. Condition 2: Condition 1 must possess strong empirical support, and which accepts the following assumptions: (1) there is a world of objective facts that is, in principle, discoverable, (2) rational means are the means of discovering it and, (3) rational means requires strong empirical support. I define strong empirical support for an hypothesis h on evidence e in probabilistic terms, as a ratio of posterior to prior probabilities substantially exceeding 1. I now argue in favour of a research policy that accepts unrestricted Academic Freedom. My argument is that there is a formal and general quandary that arises within the standard theory of probability when we apply this account of empirical support to a set of possible causal hypotheses framed in such a way that the “reverse probabilities”, pr(e/h) are 1. I consider various possible ways to escape this quandary, none of which are without difficulties, concluding that a research policy allowing for unrestricted Academic Freedom is probably the best that we can hope for. (shrink)

Complex constraints like conditionals ('If A, then B') and probabilistic constraints ('The probability that A is p') pose problems for Bayesian theories of learning. Since these propositions do not express constraints on outcomes, agents cannot simply conditionalize on the new information. Furthermore, a natural extension of conditionalization, relative information minimization, leads to many counterintuitive predictions, evidenced by the sundowners problem and the Judy Benjamin problem. Building on the notion of a `paradigm shift' and empirical research in psychology and economics, (...) I argue that the model of hypothesis testing can explain how people learn complex, theory-laden propositions like conditionals and probability constraints. Theories are formalized as probability distributions over a set of possible outcomes and theory change is triggered by a constraint which is incompatible with the initial theory. This leads agents to consult a higher order probability function, or a 'prior over priors,' to choose the most likely alternative theory which satisfies the constraint. The hypothesis testing model is applied to three examples: learning a simple probabilistic constraint involving coin bias, the sundowners problem for conditional learning, and the Judy Benjamin problem for learning conditional probability constraints. (shrink)

The study aimed to identify the knowledge management processes and their role in achieving competitive advantage at Al-Quds Open University. The study was based on the descriptive analytical method, and the study population consists of academic and administrative staff in each of the branches of Al-Quds Open University in (Tulkarm, Nablus and Jenin). The researchers selected a sample of the study population by the intentional non-probability method, the size of (70) employees. A questionnaire was prepared and supervised by a (...) number of specialists in order to obtain the results of the study. The study concluded that there is a positive direct relationship, that is, the higher the degree of application of knowledge management processes, the greater the degree of competitive advantage. Knowledge Technology came first with a score of 80.02% on all items. Competitive advantage came second with 81.74%. In the third place came "knowledge generation" where the total score on all paragraphs in this area (78.24%). In the fourth place, "knowledge transfer" (77.21%). "Developing and storing knowledge" came in fifth place (77.13%). "Acquisition of knowledge" came in sixth place (76.45%). Knowledge Organization ranked seventh (74.26%). The study recommended that the university should enable the employees to benefit from the experiences and expertise available to help generate knowledge. The University encourages the creation of knowledge through the system of incentives and open the way for creators to apply their creations and spread and invest in excellence and creativity. The university should design work performance levels based on the integration of knowledge and organize it according to policies that support freedom of research. The need for Palestinian universities to adopt a knowledge management approach. The need to adopt a system of incentives that rewards cognitive efforts, and give workers enough freedom to enable them to apply their knowledge. (shrink)

In this paper, a critical discussion is made of the role of entailments in the so-called New Paradigm of psychology of reasoning based on Bayesian models of rationality (Elqayam & Over, 2013). It is argued that assessments of probabilistic coherence cannot stand on their own, but that they need to be integrated with empirical studies of intuitive entailment judgments. This need is motivated not just by the requirements of probability theory itself, but also by a need to enhance the (...) interdisciplinary integration of the psychology of reasoning with formal semantics in linguistics. The constructive goal of the paper is to introduce a new experimental paradigm, called the Dialogical Entailment task, to supplement current trends in the psychology of reasoning towards investigating knowledge-rich, social reasoning under uncertainty (Oaksford and Chater, 2019). As a case study, this experimental paradigm is applied to reasoning with conditionals and negation operators (e.g. CEM, wide and narrow negation). As part of the investigation, participants’ entailment judgments are evaluated against their probability evaluations to assess participants’ cross-task consistency over two experimental sessions. (shrink)

The scientific study of living organisms is permeated by machine and design metaphors. Genes are thought of as the ‘‘blueprint’’ of an organism, organisms are ‘‘reverse engineered’’ to discover their functionality, and living cells are compared to biochemical factories, complete with assembly lines, transport systems, messenger circuits, etc. Although the notion of design is indispensable to think about adaptations, and engineering analogies have considerable heuristic value (e.g., optimality assumptions), we argue they are limited in several important respects. In particular, the (...) analogy with human-made machines falters when we move down to the level of molecular biology and genetics. Living organisms are far more messy and less transparent than human-made machines. Notoriously, evolution is an opportunistic tinkerer, blindly stumbling on ‘‘designs’’ that no sensible engineer would come up with. Despite impressive technological innovation, the prospect of artificially designing new life forms from scratch has proven more difficult than the superficial analogy with ‘‘programming’’ the right ‘‘software’’ would suggest. The idea of applying straightforward engineering approaches to living systems and their genomes— isolating functional components, designing new parts from scratch, recombining and assembling them into novel life forms—pushes the analogy with human artifacts beyond its limits. In the absence of a one-to-one correspondence between genotype and phenotype, there is no straightforward way to implement novel biological functions and design new life forms. Both the developmental complexity of gene expression and the multifarious interactions of genes and environments are serious obstacles for ‘‘engineering’’ a particular phenotype. The problem of reverse-engineering a desired phenotype to its genetic ‘‘instructions’’ is probably intractable for any but the most simple phenotypes. Recent developments in the field of bio-engineering and synthetic biology reflect these limitations. Instead of genetically engineering a desired trait from scratch, as the machine/engineering metaphor promises, researchers are making greater strides by co-opting natural selection to ‘‘search’’ for a suitable genotype, or by borrowing and recombining genetic material from extant life forms. (shrink)

Neuro-ethics is probablу fastest growing part of applied ethics. The main thesis is that certain natural processes in brain and nerves produce certain moral, and immoral, behaviors. All these processes can be explained causally, and (if this is so) neuro-ethics might be the final result of neuroscience. There are some metaphysical and ethical pitfalls to be considered, however, like the (incorrect) conflation of causal explanation and rational justification in defining values, not only non-moral values but moral values as well. (...) Certainly, the knowledge of how neurological processes function could help to enhance the quality of human life, not only in coping with defects but also in improving the so-called "normal life." This implies that neuroethics is instrumental, dealing with values which are instrumental as well. However, neuroethics, it seems, aspires to go further than that: to explain how goals come into existence and what their articulation should look like. All of this should be causally explained, or at least explainable; and the main focus of the paper is an analysis of this aspiration. The analysis refers to some important distinctions like the distinction between causes and reasons, explanation and justification, or the one between means and ends. At the end of the paper there is a section about applications, where some of the benefits and risks are summarily indicated, with a conclusion that neuroethics surely might help in advancing the overall quality of human life, individual and social. (shrink)

Since the release of OpenAI's ChatGPT, the world has entered a race to develop more capable and powerful AI, including artificial general intelligence (AGI). The development is constrained by the dependency of AI on the model, quality, and quantity of training data, making the AI training process highly costly in terms of resources and environmental consequences. Thus, improving the effectiveness and efficiency of the AI training process is essential, especially when the Earth is approaching the climate tipping points and planetary (...) boundaries. It is evident that AI can function better when trained to mimic certain human mental processes. Based on insights from quantum mechanics and the informational entropy-based notion of value, we suggest AI developers can enhance the AI training processes' effectiveness and efficiency by creating and implementing parameter systems that are capable of effectively assigning probabilities to informational quanta. Such systems can help reduce entropy within the system, which lowers the energy required for data storage and processing while decreasing the likelihood of information loss during training. Successfully applying the concept of information entropy-based value in AI development will be crucial for advancing generative AI and achieving AGI in a sustainable manner. (shrink)

Based on Kolchinsky and Wolpert’s work on the semantics of autonomous agents, I propose an application of Mathematical Logic and Probability to model cognitive processes. In this work, I will follow Bateson’s insights on the hierarchy of learning in complex organisms and formalize his idea of applying Russell’s Type Theory. Following Weaver’s three levels for the communication problem, I link the Kolchinsky–Wolpert model to Bateson’s insights, and I reach a semantic and conceptual hierarchy in living systems as an explicative (...) model of some adaptive constraints. Due to the generality of Kolchinsky and Wolpert’s hypotheses, I highlight some fundamental gaps between the results in current Artificial Intelligence and the semantic structures in human beings. In light of the consequences of my model, I conclude the paper by proposing a general definition of knowledge in probabilistic terms, overturning de Finetti’s Subjectivist Definition of Probability. (shrink)