How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain (...) or an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are sigma-algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we compare our results with existing results on binary judgment aggregation and Arrovian preference aggregation. This paper is the first of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

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

How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...) this idea by introducing a 'premise-based' approach to probabilistic opinion pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the 'premises'. This paper is the second of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’ account of probabilistic (...) knowledge or her semantics for epistemic modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower probabilities, lower previsions, sets of probabilities, sets of desirable gambles, and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We show that an important subclass of Mossean believers avoid Dutch bookability iff they have consistent probabilistic beliefs. (shrink)

A key challenge for probabilistic causal models is to distinguish non-causal probabilistic dependencies from true causal relations. To accomplish this task, causal models are usually required to satisfy several constraints. Two prominent constraints are the causal Markov condition and the faithfulness condition. However, other constraints are also needed. One of these additional constraints is the causal sufficiency condition, which states that models must not omit any direct common causes of the variables they contain. In this paper, I argue (...) that the causal sufficiency condition is problematic: (1) it is incompatible with the requirement that the variables in a model must not stand in non-causal necessary dependence relations, such as mathematical or conceptual relations, or relations described in terms of supervenience or grounding, (2) it presupposes more causal knowledge as primitive than is actually needed to create adequate causal models, and (3) if models are only required to be causally sufficient, they cannot deal with cases where variables are probabilistically related by accident, such as Sober’s example of the relationship between bread prices in England and the sea level in Venice. I show that these problems can be avoided if causal models are required to be monotonic in the following sense: the causal relations occurring in a model M would not disappear if further variables were added to M. I give a definition of this monotonicity condition and conclude that causal models should be required to be monotonic rather than causally sufficient. (shrink)

We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one (...) we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1] have called S-independence. We show that neither is more general than the other. (shrink)

In this paper, I challenge the traditional narrative that William James’s arguments against determinism were primarily motivated by his personal struggles with depression. I argue that James presents an alternative argument against determinism that is motivated by his commitment to sound scientific practice. James argues that determinism illegitimately extrapolates from observations of past events to predictions about future events without acknowledging the distinct metaphysical difference between them. This occupation with futurity suggests that James’s true target is better understood as logical (...) determinism rather than causal determinism. This has consequences for James’s proposed alternative, which I call his probabilistic underdeterminism, a conception of the universe that is built on chance, choice, and a local teleology. All of this forms part of a broader criticism of the scientific practices of his day based on their widespread failure to acknowledge the distorting effects of observation on that which is observed. (shrink)

A fundamental problem in understanding the nature of time is explaining its directionality. This 1990 PhD thesis re-examines the concepts of time flow, the physical directionality of time, and the semantics of tensed language. Several novel results are argued for that contradict the orthodox anti-realist views still dominant in the subject. Specifically, the concept of "metaphysical time flow" is supported as a valid scientific concept, and argued to be intrinsic to the directionality of objective probabilities in quantum mechanics; the common (...) claims that quantum probability theory is time reversible is shown to be based on an analytic error, stemming from a false choice for the criterion for reversibility of probabilistic theories (recognized by Satosi Watanabe in the 1950s but ignored in all philosophical discussions); and a consistent semantics for tensed language (adapted from the tree model of Storrs McCall) is constructed, showing that the common rejection of "time flow" as having no meaningful semantics is false. These debates are still ongoing in almost exactly the same state they were pre-1990, and there is appears to be no visible progress in the subject. Critical points made against errors in the orthodox account (which has been sustained for 70 years by the anti-realist philosophy of time, typified by the "Pittsburg School" of Grunbaum-Earman-Norton-Roberts), are still not recognized in the philosophy of time or physics. Some key technical proofs in this thesis have been published in physics proper. See p.ii-iii for full original abstract. (This pdf is uploaded from the Massey University archive.). (shrink)

The Comprehensive Human Decision-Making Equation presents a robust model for understanding Holistic Free Will (HFW), conceptualizing decision-making as an autonomous, non-deterministic process within a complex network of influences. This model addresses the Infinite Regress issue by portraying free will as an emergent property of interacting layers, including internal beliefs, external contexts, emotional responses, cognitive biases, and habitual tendencies. Departing from traditional linear models, the equation adopts a systemic framework where each choice reflects a cumulative utility, integrating multiple components such (...) as personal, ethical, social, and temporal utilities. This holistic approach emphasizes the probabilistic nature of free will, challenging deterministic interpretations and highlighting the ethical and relational dimensions of autonomy. By situating free will within a structured yet adaptive process, the model supports the notion that true autonomy is ethically aligned, relational, and embedded in a flexible reality, thereby promoting communal and ethical development. (shrink)

The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only (...) mathematical equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation. (shrink)

to appear in Lambert, E. and J. Schwenkler (eds.) Transformative Experience (OUP) -/- L. A. Paul (2014, 2015) argues that the possibility of epistemically transformative experiences poses serious and novel problems for the orthodox theory of rational choice, namely, expected utility theory — I call her argument the Utility Ignorance Objection. In a pair of earlier papers, I responded to Paul’s challenge (Pettigrew 2015, 2016), and a number of other philosophers have responded in similar ways (Dougherty, et al. 2015, (...) Harman 2015) — I call our argument the Fine-Graining Response. Paul has her own reply to this response, which we might call the Authenticity Reply. But Sarah Moss has recently offered an alternative reply to the Fine-Graining Response on Paul’s behalf (Moss 2017) — we’ll call it the No Knowledge Reply. This appeals to the knowledge norm of action, together with Moss’ novel and intriguing account of probabilistic knowledge. In this paper, I consider Moss’ reply and argue that it fails. I argue first that it fails as a reply made on Paul’s behalf, since it forces us to abandon many of the features of Paul’s challenge that make it distinctive and with which Paul herself is particularly concerned. Then I argue that it fails as a reply independent of its fidelity to Paul’s intentions. (shrink)

In this paper I offer an alternative - the ‘dispositional account’ - to the standard account of imprecise probabilism. Whereas for the imprecise probabilist, an agent’s credal state is modelled by a set of credence functions, on the dispositional account an agent’s credal state is modelled by a set of sets of credence functions. On the face of it, the dispositional account looks less elegant than the standard account – so why should we be interested? I argue that the dispositional (...) account is actually simpler, because the dispositional choice behaviour that fixes an agent’s credal state is faithfully depicted in the model of that agent’s credal state. I explore some of the implications of the account, including a surprising implication for the debate over dilation. (shrink)

Epistemic decision theory (EDT) employs the mathematical tools of rational choice theory to justify epistemic norms, including probabilism, conditionalization, and the Principal Principle, among others. Practitioners of EDT endorse two theses: (1) epistemic value is distinct from subjective preference, and (2) belief and epistemic value can be numerically quantified. We argue the first thesis, which we call epistemic puritanism, undermines the second.

The goal of this essay is to explore "the highly contested nature of [decision-making through adopting] a historically comparative and interdisciplinary approach." Internalist history of game theory treats decision theory as a science of making choices to maximize expected gain. Game theory is applied to nuclear deterrence and military strategy, building markets and designing institutions, analyzing collective action, developing jurisprudence, and addressing crime and punishment. This essay draws on recent historiography of Cold War decision-making to draw into focus the constructive (...) aspects of decision theory to argue that the perceived need to avoid worst-case scenarios has instead contributed to a world in which the worst outcome is probabilistically assured to occur over the long duree timeframe. (shrink)

Recent experiments allowed concluding that Bell-type inequalities are indeed violated thus it is important to understand what it means and how can we explain the existence of strong correlations between outcomes of distant measurements. Do we have to announce that: Einstein was wrong, Nature is nonlocal and nonlocal correlations are produced due to the quantum magic and emerge, somehow, from outside space-time? Fortunately such conclusions are unfounded because if supplementary parameters describing measuring instruments are correctly incorporated in a theoretical model (...) then Bell-type inequalities may not be proven .We construct a simple probabilistic model explaining these correlations in a locally causal way. In our model measurement outcomes are neither predetermined nor produced in irreducibly random way. We explain in detail why, contrary to the general belief; an introduction of setting dependent parameters does not restrict experimenters’ freedom of choice. Since the violation of Bell-type inequalities does not allow concluding that Nature is nonlocal and that quantum theory is complete thus the Bohr-Einstein quantum debate may not be closed. The continuation of this debate is not only important for a better understanding of Nature but also for various practical applications of quantum phenomena. (shrink)

This chapter of the Handbook of Utility Theory aims at covering the connections between utility theory and social ethics. The chapter first discusses the philosophical interpretations of utility functions, then explains how social choice theory uses them to represent interpersonal comparisons of welfare in either utilitarian or non-utilitarian representations of social preferences. The chapter also contains an extensive account of John Harsanyi's formal reconstruction of utilitarianism and its developments in the later literature, especially when society faces uncertainty rather than (...) probabilistic risk. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there (...) are two sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

What can rational deliberation indicate about belief? Belief clearly influences deliberation. The principle that rational belief is stake-invariant rules out at least one way that deliberation might influence belief. The principle is widely, if implicitly, held in work on the epistemology of categorical belief, and it is built into the model of choice-guiding degrees of belief that comes to us from Ramsey and de Finetti. Criticisms of subjective probabilism include challenges to the assumption of additive values (the package principle) (...) employed by defenses of probabilism. But the value-interaction phenomena often cited in such challenges are excluded by stake-invariance. A comparison with treatments of categorical belief suggests that the appeal to stake-invariance is not ad hoc. Whether or not to model belief as stake-invariant is a question not settled here. (shrink)

The aim of this paper is to argue for a revised and precisified version of the infamous Verifiability Criterion for the meaningfulness of declarative sentences. The argument is based on independently plausible premises concerning probabilistic confirmation and meaning as context-change potential, it is shown to be logically valid, and its ramifications for potential applications of the criterion are being discussed. Although the paper is not historical but systematic, the criterion thus vindicated will resemble the original one(s) in some important (...) ways. At the same time, it will also be more modest insofar as meaningfulness will turn out to be relativized linguistically and probabilistically, and different choices of the linguistic and probabilistic parameters may lead to different verdicts on meaningfulness. (shrink)

Suppositions can be introduced in either the indicative or subjunctive mood. The introduction of either type of supposition initiates judgments that may be either qualitative, binary judgments about whether a given proposition is acceptable or quantitative, numerical ones about how acceptable it is. As such, accounts of qualitative/quantitative judgment under indicative/subjunctive supposition have been developed in the literature. We explore these four different types of theories by systematically explicating the relationships canonical representatives of each. Our representative qualitative accounts of indicative (...) and subjunctive supposition are based on the belief change operations provided by AGM revision and KM update respectively; our representative quantitative ones are offered by conditionalization and imaging. This choice is motivated by the familiar approach of understanding supposition as `provisional belief revision' wherein one temporarily treats the supposition as true and forms judgments by making appropriate changes to their other opinions. To compare the numerical judgments recommended by the quantitative theories with the binary ones recommended by the qualitative accounts, we rely on a suitably adapted version of the Lockean thesis. Ultimately, we establish a number of new results that we interpret as vindicating the often-repeated claim that conditionalization is a probabilistic version of revision, while imaging is a probabilistic version of update. (shrink)

LLMs have dramatically improved in capabilities in recent years. This raises the question of whether LLMs could become genuine agents with beliefs and desires. This paper demonstrates an in principle limit to LLM agency, based on their architecture. LLMs are next word predictors: given a string of text, they calculate the probability that various words can come next. LLMs produce outputs that reflect these probabilities. I show that next word predictors are exploitable. If LLMs are prompted to make probabilistic (...) predictions about the world, these predictions are guaranteed to be incoherent, and so Dutch bookable. If LLMs are prompted to make choices over actions, their preferences are guaranteed to be intransitive, and so money pumpable. In short, the problem is that selecting an action based on its potential value is structurally different then selecting the description of an action that is most likely given a prompt: probability cannot be forced into the shape of expected value. The in principle exploitability of LLMs raises doubts about how agential they can become. This exploitability also offers an opportunity for humanity to safely control such AI systems. (shrink)

The indirect argument (IA) for incompatibilism is based on the principle that an action to which there is no alternative is unfree, which we shall call ‘PA’. According to PA, to freely perform an action A, it must not be the case that one has ‘no choice’ but to perform A. The libertarian and hard determinist advocates of PA must deny that free will would exist in a deterministic world, since no agent in such a world would perform an (...) action to which there were alternatives: an action there being the necessary consequence of preceding events and the laws of nature, it would not be possible for a person to perform actions besides those he actually performs. Determinism is seen here as “indirectly” ruling out free will by making the satisfaction of a necessary condition of free agency impossible, the former requiring, according to the leading proponent of libertarianism, Robert Kane, the performance of free actions. To have a free will, on his view, is to have committed “self-forming” actions, that is, to have done things to which there were alternatives the doing of which led to the development of the desires, preferences, and beliefs that make up one’s character. -/- The range of phenomena obeying probabilistic laws has yet to be ascertained. Under certain assumptions, both STR and GTR entail an indeterministic mechanics. But, contrary what is often claimed, quanta do not behave indeterministicly: the wave function/probabilistic laws being necessary only insofar as we wish to macroscopicly describe their behavior. It is far less clear, however, that the macro-events involved in human decision making and behavior, such as the releasing of neurotransmitters and the contracting of muscles, occur indeterministically. The ontological status of these events-whether or not they are the necessary effects of prior occurrences-is, of course, what matters in the free will debate. For present purposes, however, this question will be put aside. Instead, I will concentrate on buttressing the existing case against PA, aiming to show that even if deterministic laws hold at the level of macro-phenomena, free will remains a possibility. That is to say, I shall defend the thesis that so-called “Frankfurt cases” demonstrate that alternatives are not required to perform an action that is free in the sense of being something for which its agent is responsible. -/- My defense will be carried out in three stages. First, I must respond to those who maintain that a Frankfurt case is not a counterexample to PA because it is not an example of someone acting without alternatives. Here, I confront the question of how “robust” an alternative must bein order to provide an agent with a way of avoiding praise or blame for the action that she actually commits. Secondly, I must show that an agent may be praiseworthy or blameworthy despite lacking alternatives at the time at which she acts, i.e., an appropriate object of one of a Strawsonian “reactive attitude” sans what I shall call “local” alternatives. At this point, I must attend to David Widerker’s recent critique of the use of Frankfurt cases as counterexamples to PA. Finally, I set for myself what I take to be the most difficult task of a compatibilist: demonstrating that not even an “historical” alternative-the possibility of having chosen a different path in life than the one that one has actually taken-is needed to have a free will. In this connection, it will be incumbent upon me to explain why it would be fair to hold someone accountable for behavior issuing from a self she did not create, dispositions originating from natural conditions she did not establish. That is to say, in denying that a free will entails the ability to transcend oneself, I shall be faced with what Kane calls the “ultimacy” problem: how to explain away the incompatibilist’s intuition that it is senseless to adopt a reactive attitude towards someone incapable of self-transcendence, even if such a reaction is itself unavoidable. By showing that the desire for self-transcendence is itself irrational, I intend to solve this problem. I will, thus, be left defending a version of compatibilism according to which a free will is to be understood as a healthy faculty-the will-being exercised in an environment conducive to self-realization, which is its purpose. (shrink)

This epistemic project examines an understudied existential risk emerging in the deepfake era: the fortunately up to this time (but not indefinitely so) reversible peril of humanity’s epistemic self-sabotage through an overestimation of algorithms linked to quantitative aspects and a paired underestimation of the own epistemic potential whose manifestations are in principle expressible via scientifically analyzable but currently often neglected qualitative facets. This scenario is metaphorically referred to as "π-Doom scenario". Instead of carefully crafting opaque hypotheses and formulating probabilistic (...) predictions of timelines that could easily evade scrutiny and/or could even themselves be initially generated by algorithms, scientifically and responsibly counteracting π-Doom requires new better riskier explanatory theories of intelligence, creativity and consciousness. A brief non-comprehensive literature review suggests that quite a few scientific instantiations (all of which have not yet been provisionally refuted) of that transformative requirement are already available at present. In short, π-Doom – the voluntarily or unintentionally effectuated cognitive resignation engendering an irrational algorithmically-motored process of running around in (epistemic) circles that could endanger the immediate future of a vulnerable civilization like present-day humanity – is wholly contingent on a choice of focus. (shrink)

As a moral foundation for vegetarianism and other consumer choices, act consequentialism can be appealing. When we justify our consumer and dietary choices this way, however, we face the problem that our individual actions rarely actually precipitate more just agricultural and economic practices. This threshold or individual impotence problem engaged by consequentialist vegetarians and their critics extends to morally motivated consumer decision-making more generally, anywhere a lag persists between individual moral actions taken and systemic moral progress made. Regan and others (...) press just this point against Singer's utilitarian basis for vegetarianism; recently Chartier criticizes act-consequentialist vegetarianism by identifying many factors weakening the connection between individual meat purchases and changes in animal production. While such factors are relevant to act-consequentialist moral reasoning, I argue, they need not defeat the act-consequentialist case for vegetarianism and consumer ethics. This is shown by offering a probabilistic account of the threshold issue and discussing the positive and negative role-modelling effects of our morally motivated dietary and consumer choices. (shrink)

This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold both types of belief simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List (2018, 2021). The nature, relevance, and implications of the tension are explained and assessed.

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new theorems. (...) Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

Epistemologists often appeal to the idea that a normative theory must provide useful, usable, guidance to argue for one normative epistemology over another. I argue that this is a mistake. Guidance considerations have no role to play in theory choice in epistemology. I show how this has implications for debates about the possibility and scope of epistemic dilemmas, the legitimacy of idealisation in Bayesian epistemology, uniqueness versus permissivism, sharp versus mushy credences, and internalism versus externalism.

The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The (...) relevant mathematical structure is Hilbert arithmetic in a wide sense, in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem. (shrink)

Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics and behavioural sciences teach us that random variables ‘measuring’ the same content (the answer to the same Yes or No question) may vary, if ‘measured’ jointly with other random variables. Alice’s and Bob’s raw data confirm Einsteinian non-signaling, but setting dependent experimental protocols are used to create samples (...) of coupled pairs of distant ±1 outcomes and to estimate correlations.Marginal expectations, estimated using these final samples, depend on distant settings. Therefore,a system of random variables ‘measured’ in Bell tests is inconsistently connected and it should be analyzed using a Contextuality- by-Default approach, what is done for the first time in this paper.The violation of Bell inequalities and inconsistent connectedness may be explained using a contextual locally causal probabilistic model in which setting dependent variables describing measuring instruments are correctly incorporated. We prove that this model does not restrict experimenters` freedom of choice which is a prerequisite of science. Contextuality seems to be the rule and not an exception; thus, it should be carefully tested. (shrink)

The article is devoted to the analysis of the evident scientific method of Galen, which establishes the necessity of correct diagnosis of diseases, determination of true symptoms and causes of diseases, which results in the choice of the exact method of treatment. The article focuses on how Galen seeks to achieve reliable knowledge based on an undeniable logical necessity. Logical reliability is contrasted with “dialectical”, that is, probabilistic judgments, often leading to the opposite of what was originally asserted (...) in them. Probabilistic judgments were characteristic of the Stoic philosophical school, with which Galen hotly argues, asserting his understanding of truth. Truth, in his opinion, is achieved through facts based on true premises. The criterion of truth for Galen is the study of the device of a living organism, and the logical conclusions depend on the accuracy of knowledge of human anatomy. Thus, the nature of the proof judgments of Galen depends on their practical content and not on the formal and logical structure offered by the Stoics when studying the functions of the human body, which ultimately leads to incorrect methods of treatment. (shrink)

The aim of this study is to justify the belief that there are biological normative mechanisms that fulfill non-trivial causal roles in the explanations (as formulated by researchers) of actions and behaviors present in specific systems. One example of such mechanisms is the predictive mechanisms described and explained by predictive processing (hereinafter PP), which (1) guide actions and (2) shape causal transitions between states that have specific content and fulfillment conditions (e.g. mental states). Therefore, I am guided by a specific (...) theoretical goal associated with the need to indicate those conditions that should be met by the non-trivial theory of normative mechanisms and the specific models proposed by PP supporters. In this work, I use classical philosophical methods, such as conceptual analysis and critical reflection. I also analyze selected studies in the field of cognitive science, cognitive psychology, neurology, information theory and biology in terms of the methodology, argumentation and language used, in accordance with their theoretical importance for the issues discussed in this study. In this sense, the research presented here is interdisciplinary. My research framework is informed by the mechanistic model of explanation, which defines the necessary and sufficient conditions for explaining a given phenomenon. The research methods I chose are therefore related to the problems that I intend to solve. In the introductory chapter, “The concept of predictive processing”, I discuss the nature of PP as well as its main assumptions and theses. I also highlight the key concepts and distinctions for this research framework. Many authors argue that PP is a contemporary version of Kantianism and is exposed to objections similar to those made against the approach of Immanuel Kant. I discuss this thesis and show that it is only in a very general sense that the PP framework is neo-Kantian. Here we are not dealing with transcendental deduction nor with the application of transcendental arguments. I argue that PP is based on reverse engineering and abduction inferences. In the second part of this chapter, I respond to the objection formulated by Dan Zahavi, who directly accuses this research framework of anti-realistic consequences. I demonstrate that the position of internalism, present in the so-called conservative PP, does not imply anti-realism, and that, due to the explanatory role played in it by structural representations directed at real patterns, it is justified to claim that PP is realistic. In this way, I show that PP is a non-trivial research framework, having its subject, specific methods and its own epistemic status. Finally, I discuss positions classified as the socalled radical PP. In the chapter “Predictive processing as a Bayesian explanatory model” I justify the thesis according to which PP offers Bayesian modeling. Many researchers claim that the brain is an implemented statistical probabilistic network that is an approximation of the Bayesian 7 rule. In practice, this means that all cognitive processes are to apply Bayes' rule and can be described in terms of probability distributions. Such a solution arouses objections among many researchers and is the subject of wide criticism. The purpose of this chapter is to justify the thesis that Bayesian PP is a non-trivial research framework. For this purpose, I argue that it explains certain phenomena not only at the computational level described by David Marr, but also at the level of algorithms and implementation. Later in this chapter I demonstrate that PP is normative modeling. Proponents of the use of Bayesian models in psychology or decision theory argue that they are normative because they allow the formulation of formal rules of action that show what needs to be done to make a given action optimal. Critics of this approach emphasize that such thinking about the normativity of Bayesian modeling is unjustified and that science should shift from prescriptive to descriptive positions. In a polemic with Shira Elqayam and Jonathan Evans (2011), I show that the division they propose into prescriptivism and Bayesian descriptivism is apparent, because, as I argue, there are two forms of prescriptivism, i.e. the weak and the strong. I argue that the weak version is epistemic and can lead to anti-realism, while the strong version is ontic and allows one to justify realism in relation to Bayesian models. I argue that a weak version of prescriptivism is valid for PP. It allows us to adopt anti-realism in relation to PP. In practice, this means that you can explain phenomena using Bayes' rule. This does not, however, imply that they are Bayesian in nature. However, the full justification of realism in relation to the Bayesian PP presupposes the adoption of strong prescriptivism. This position assumes that phenomena are explained by Bayesian rule because they are Bayesian as such. If they are Bayesian in nature, then they should be explained using Bayesian modeling. This thesis will be substantiated in the chapters “Normative functions and mechanisms in the context of predictive processing” and “Normative mechanisms and actions in predictive processing”. In the chapter “The Free Energy Principle in predictive processing”, I discuss the Free Energy Principle (hereinafter FEP) formulated by Karl Friston and some of its implications. According to this principle, all biological systems (defined in terms of Markov blankets) minimize the free energy of their internal states in order to maintain homeostasis. Some researchers believe that PP is a special case of applying this principle to cognition, and that predictive mechanisms are homeostatic mechanisms that minimize free energy. The discussion of FEP is important due to the fact that some authors consider it to be important for explanatory purposes and normative. If this is the case, then FEP turns out to be crucial in explaining normative predictive mechanisms and, in general, any normative biological mechanisms. To define the explanatory possibilities of this principle, I refer to the discussion of its supporters on the issue they define as the problem of continuity and discontinuity between life and mind. A critical analysis of this discussion and the additional arguments I have formulated have allowed me to revise the explanatory ambitions of FEP. I also reject the belief that this principle is necessary to explain the nature of predictive mechanisms. I argue that the principle formulated and defended by Friston is an important research heuristic for PP analysis. 8 In the chapter “Normative functions and mechanisms in predictive processing”, I start my analyzes by formulating an answer to the question about the normative nature of homeostatic mechanisms. I demonstrate that predictive mechanisms are not homeostatic. I defend the view that a full explanation of normative mechanisms presupposes an explanation of normative functions. I discuss the most important proposals for understanding the normativity of a function, both from a systemic and teleosemantic perspective. I conclude that the non-trivial concept of a function must meet two requirements which I define as explanatory and normative. I show that none of the theories I have invoked satisfactorily meets both of these requirements. Instead, I propose a model of normativity based on Bickhard's account, but supplemented by a mechanistic perspective. I argue that a function is normative when: (1) it allows one to explain the dysfunction of a given mechanism; (2) it contributes to the maintenance of the organism's stability by shaping and limiting possible relations, processes and behaviors of a given system; and when (3) (according to the representational and predictive functions) it enables explaining the attribution of logical values of certain representations / predictions. In such an approach, a mechanism is normative when it performs certain normative functions and when it is constitutive for a specific action or behavior, despite the fact that for some reason it cannot realize it either currently or in the long-term. Such an understanding of the normativity of mechanisms presupposes the acceptance of the epistemic hypothesis. I argue that this hypothesis is not cognitively satisfactory, and therefore the ontic hypothesis should be justified, which is directly related to adopting the position of ontic prescriptivism. For this reason, referring to the mechanistic theory of scientific explanations, I formulate an ontical interpretation of the concept of a normative mechanism. According to this approach, a mechanism or a function is normative when they perform such and such causal roles in explaining certain actions and behaviors. With regard to the normative properties of predictive mechanisms and functions, this means that they are the causes of specific actions an organism carries out in the environment. In this way, I justify the necessity of accepting the ontic hypothesis and rejecting the epistemic hypothesis. The fifth chapter, “Normative mechanisms and actions in predictive processing”, is devoted to the dark room problem and the related exploration-exploitation trade-off. A dark room is the state that an agent could be in if it minimized the sum of all potential prediction errors. I demonstrate that, in accordance with the basic assumption of PP about the need for continuous and long-term minimization of prediction errors, such a state should be desirable for the agent. Is it really so? Many authors believe it is not. I argue that the test of the value of PP is the possibility of a non-trivial solution of this problem, which can be reduced to the choice between active and uncertainty-increasing exploration and safe and easily predictable exploitation. I show that the solution proposed by PP supporters present in the literature does not enable a fully satisfactory explanation of this dilemma. Then I defend the position according to which the full explanation of the normative mechanisms, and, subsequently, the solution to the dilemma of exploration and exploitation, involves reference to the existence of constraints present in the environment. The constraints 9 include elements of the environment that make a given mechanism not only causal but also normative. They are therefore key to explaining the predictive mechanisms. They do not only play the role of the context in which the mechanism is implemented, but, above all, are its constitutive component. I argue that the full explanation of the role of constraints in normative predictive mechanisms presupposes the integration of individual models of specific cognitive phenomena, because only the mechanistic integration of PP with other models allows for a non-trivial explanation of the nature of normative predictive mechanisms that would have a strong explanatory value. The explanatory monism present in many approaches to PP makes it impossible to solve the problem of the dark room. Later in this chapter, I argue that the Bayesian PP is normative not because it enables the formulation of such and such rules of action, but because the predictive mechanisms themselves are normative. They are normative because they condition the choice of such and such actions by agents. In this way, I justify the hypothesis that normative mechanisms make it possible to explain the phenomenon of agent motivation, which is crucial for solving the dark room problem. In the last part of the chapter, I formulate the hypothesis of distributed normativity, which assumes that the normative nature of certain mechanisms, functions or objects is determined by the relations into which these mechanisms, functions or objects enter. This means that what is normative (in the primary sense) is the relational structure that constitutes the normativity of specific items included in it. I suggest that this hypothesis opens up many areas of research and makes it possible to rethink many problems. In the “Conclusion”, I summarize the results of my research and indicate further research perspectives. (shrink)

If the goal of statistical analysis is to form justified credences based on data, then an account of the foundations of statistics should explain what makes credences justified. I present a new account called statistical reliabilism (SR), on which credences resulting from a statistical analysis are justified (relative to alternatives) when they are in a sense closest, on average, to the corresponding objective probabilities. This places (SR) in the same vein as recent work on the reliabilist justification of credences generally (...) [Dunn, 2015, Tang, 2016, Pettigrew, 2018], but it has the advantage of being action-guiding in that knowledge of objective probabilities is not required to identify the best-justified available credences. The price is that justification is relativized to a specific class of candidate objective probabilities, and to a particular choice of reliability measure. On the other hand, I show that (SR) has welcome implications for frequentist-Bayesian reconciliation, including a clarification of the use of priors; complemen- tarity between probabilist and fallibilist [Gelman and Shalizi, 2013, Mayo, 2018] approaches towards statistical foundations; and the justification of credences outside of formal statistical settings. Regarding the latter, I demonstrate how the insights of statistics may be used to amend other reliabilist accounts so as to render them action-guiding. I close by discussing new possible research directions for epistemologists and statisticians (and other applied users of probability) raised by the (SR) framework. (shrink)

Although there are several monistic and dualistic approaches to the mind-body problem on the basis of classical or quantum mechanics, thus far no consensus exists about a solution. Recently, the Elementary Process Theory (EPT) has been developed: this corresponds with a fundamentally new disciplinary matrix for the study of physical reality. The purpose of the present research was to investigate the mind-body problem within this newly developed disciplinary matrix. The main finding is that the idea of a duality of body (...) and mind has to be rejected as an incomplete representation of reality: in the universe of the EPT, man hás to be a trinity of body, spirit and soul, where ‘body’, ‘spirit’ and ‘soul’ are names for distinct physical things. The mind is then a mere idea that arises from (self-)experience, but without onto-logical connotation. In addition a mechanism for mental causation, which implies a principle of choice, is rigorously formulated. The main conclusion is that a fundamentally new physicalist approach to the mind-body problem, according to which man has a free will, has been formulated strictly within the language of the EPT. Further physical research is then required to describe how the interaction between body, spirit and soul is to be understood in terms of fundamental interactions. In addition, further philosophical-theological research has to establish whether the presently discussed trinity and the trinities of body, spirit and soul mentioned in the Bible and the Vedic texts are one and the same thing. -/- Edit: a revised version of this preprint has been published as a book chapter. (shrink)

-/- The Integration of Angelito Malicse’s Universal Formula with Quantum Computer Design, AGI Algorithmic Design, and Education -/- In the pursuit of developing intelligent systems, the realms of quantum computing, artificial general intelligence (AGI), and educational frameworks face the significant challenge of balancing complex feedback mechanisms, ethical decision-making, and system stability. The universal formula developed by Angelito Malicse provides a pioneering approach to understanding free will, human behavior, and decision-making. His three laws, deeply rooted in the concept of natural balance, (...) offer valuable insights into addressing problems related to technological systems, such as quantum computers and AGI. This essay explores how Malicse’s universal formula can be integrated into quantum computer design, AGI algorithmic development, and educational models, emphasizing the importance of feedback loops, balance, and ethical decision-making as critical components in these fields. -/- The Universal Formula: An Overview -/- Angelito Malicse’s universal formula consists of three key laws: -/- 1. The Law of Karma (Cause and Effect): This law posits that every action leads to a consequence. It emphasizes that systems—whether natural or man-made—must function without defects to ensure they operate effectively and safely. Any imbalance or disruption in the system causes dysfunction, whether the system is biological, mechanical, or computational. -/- 2. The Homeostasis Principle: This principle asserts that systems—be they biological, technological, or social—must maintain equilibrium to function correctly. When an imbalance occurs, the system seeks to restore balance. This is a critical process in all functional systems, from the human body to technological networks. -/- 3. The Ethical Decision-Making Law: This law underscores the importance of ethical decision-making within systems. It suggests that choices must promote balance and avoid disrupting the natural harmony of the system. If decisions violate this balance, they result in negative consequences, reflecting the idea that imbalance leads to dysfunction in both societal and technological systems. -/- These principles, while addressing human behavior and societal functioning, also have profound implications for the development of quantum computing and AGI, areas that are critical to future advancements in technology. -/- Quantum Computing and the Universal Formula -/- Quantum computing represents a revolutionary leap in computational power, utilizing quantum mechanics principles—such as superposition, entanglement, and interference—to solve problems in parallel. Quantum systems, however, are highly sensitive to errors and disturbances, which could affect their ability to function reliably. Thus, understanding and applying the universal formula to quantum computer design is essential. -/- Quantum Causal Inference and the Law of Karma -/- Quantum computing is built on probabilistic models where each quantum state evolves based on prior interactions, an approach that mirrors the concept of cause and effect. Quantum systems follow causal inference, meaning that each quantum operation is influenced by the previous one. This aligns directly with the Law of Karma—every operation in a quantum computer has consequences, which can either lead to a stable state or introduce error. If the system is defective or disrupted, it results in instability, just as a defective system in nature or society fails to function correctly. -/- Quantum algorithms, such as those used in quantum machine learning, rely heavily on cause-effect relationships to guide the computation. The delicate balance between quantum states and operations mirrors the need for balance in natural systems: if a quantum system is not free from errors, its performance will degrade, reflecting Malicse’s principle that systems must be free of defects to operate properly. -/- Quantum Neural Networks (QNNs) and Feedback Mechanisms -/- Quantum Neural Networks (QNNs) aim to replicate the neural network structure of the human brain using quantum bits (qubits) and quantum gates. These networks utilize feedback loops, where the system continuously adapts and updates based on prior outputs, enhancing its learning process. This closely aligns with Malicse’s feedback loop principle, which emphasizes the importance of continuous adjustment based on environmental feedback. -/- QNNs utilize quantum feedback to optimize learning. However, just like biological systems, they require feedback that operates in balance, ensuring that each decision made by the system aligns with previous learnings and the larger goal of the system. For a quantum system to achieve reliable performance, the feedback mechanism must be balanced and precise, aligning with Malicse’s view that all systems—whether biological or technological—must act to restore balance when disrupted. -/- Homeostasis in Quantum Systems -/- The ability of quantum systems to maintain homeostasis—to return to a balanced state after a disturbance—is another vital aspect of quantum computing. Quantum error correction algorithms play a central role in ensuring that quantum states do not deviate significantly from their intended positions due to noise or errors. These mechanisms allow quantum systems to maintain internal equilibrium despite external interference, mirroring the concept of homeostasis in biological systems. -/- Malicse’s Homeostasis Principle is directly applicable here: just as biological systems restore balance to ensure survival, quantum systems require constant error-correction and recalibration to maintain balance. This principle ensures that quantum computations are accurate and that imbalances (such as errors or instabilities) are corrected swiftly, maintaining the overall stability of the quantum system. -/- AGI and the Universal Formula -/- The field of AGI seeks to develop machines capable of generalizing knowledge and solving complex problems across multiple domains. As AGI systems evolve, the challenge lies in ensuring they adhere to ethical principles and maintain balance within their decision-making processes. The universal formula offers guidance on how AGI can be structured to make decisions that reflect the principles of natural balance. -/- Feedback Mechanisms and Ethical Decision-Making -/- One of the core challenges of AGI is ensuring that it can make decisions ethically, even when faced with complex, ambiguous situations. AGI systems learn from feedback, adapting their decisions based on both the data they receive and the ethics embedded within their algorithms. The feedback loop in AGI is similar to that of human decision-making—data inputs (environmental feedback) are processed, and decisions are refined to optimize outcomes. -/- Malicse’s Ethical Decision-Making Law can be applied to AGI systems to ensure that their actions promote balance and avoid harm. For example, an AGI system designed for healthcare must balance patient needs with resource availability, ensuring that decisions benefit society while maintaining fairness and equity. If the AGI violates this balance—say, by favoring one group over another—it could result in negative consequences, such as social inequality or resource misallocation. -/- Homeostasis in AGI Systems -/- Much like quantum systems, AGI must strive for homeostasis to maintain long-term operational stability. AGI should be able to detect imbalances in its decision-making process and correct them accordingly. For instance, an AGI operating in a financial system must adjust its strategies based on market feedback, ensuring that it consistently contributes to the stability of the market, without causing disruptive cycles. -/- Integrating Malicse’s Homeostasis Principle in AGI ensures that these systems are capable of continuous adaptation, balancing inputs and outputs in a way that prevents harmful outcomes. In decision-making, this means the AGI will always strive for balance, ensuring that no decision undermines the overall health of the system, whether it’s societal, economic, or environmental. -/- The Role of Education in Promoting Natural Balance -/- Educational systems are fundamental to shaping the leaders and innovators of the future. By incorporating the principles of natural balance, ethical decision-making, and feedback-based learning, we can produce individuals capable of understanding the complexities of quantum systems and AGI. -/- Malicse’s universal formula should be integrated into the educational curriculum at all levels, fostering a generation of thinkers who can balance cause and effect, understand feedback loops, and navigate the ethical challenges of technology. Through this holistic education, students will be better equipped to understand and contribute to the design of future technologies, ensuring that they maintain harmony with natural systems and societal needs. -/- Conclusion -/- Angelito Malicse’s universal formula offers a profound framework for understanding the fundamental principles of decision-making, both in human and computational systems. By integrating these principles into the design of quantum computers and AGI systems, we can create technologies that adhere to the natural laws of balance and ethics, preventing harmful outcomes and ensuring stable, sustainable progress. -/- In the realms of quantum computing and AGI, the application of the Law of Karma, Homeostasis, and Ethical Decision-Making will ensure that these advanced systems work in harmony with their environments, just as natural systems do. Further, by embedding these principles into educational curricula, we can train future generations to harness the power of these technologies in a way that benefits society, promotes fairness, and sustains the natural balance of the universe. -/- By applying Malicse’s universal formula across these domains, we can foster a future where technology and humanity work together in a sustainable, ethical, and balanced way. -/- . (shrink)

Are probabilism and special relativity compatible? Dieks argues that they are. But the possible universe he specifies, designed to exemplify both probabilism and special relativity, either incorporates a universal “now”, or amounts to a many world universe, or fails to have any one definite overall Minkowskian-type space-time structure. Probabilism and special relativity appear to be incompatible after all. What is at issue is not whether “the flow of time” can be reconciled with special relativity, but rather whether explicitly probabilistic (...) versions of quantum theory should be rejected because of incompatibility with special relativity. (shrink)

In this paper I expound an argument which seems to establish that probabilism and special relativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole.

The aim of the paper is to develop general criteria of argumentative validity and adequacy for probabilistic arguments on the basis of the epistemological approach to argumentation. In this approach, as in most other approaches to argumentation, proabilistic arguments have been neglected somewhat. Nonetheless, criteria for several special types of probabilistic arguments have been developed, in particular by Richard Feldman and Christoph Lumer. In the first part (sects. 2-5) the epistemological basis of probabilistic arguments is discussed. With (...) regard to the philosophical interpretation of probabilities a new subjectivist, epistemic interpretation is proposed, which identifies probabilities with tendencies of evidence (sect. 2). After drawing the conclusions of this interpretation with respect to the syntactic features of the probability concept, e.g. one variable referring to the data base (sect. 3), the justification of basic probabilities (priors) by judgements of relative frequency (sect. 4) and the justification of derivative probabilities by means of the probability calculus are explained (sect. 5). The core of the paper is the definition of '(argumentatively) valid derivative probabilistic arguments', which provides exact conditions for epistemically good probabilistic arguments, together with conditions for the adequate use of such arguments for the aim of rationally convincing an addressee (sect. 6). Finally, some measures for improving the applicability of probabilistic reasoning are proposed (sect. 7). (shrink)

We investigate a basic probabilistic dynamic semantics for a fragment containing conditionals, probability operators, modals, and attitude verbs, with the aim of shedding light on the prospects for adding probabilistic structure to models of the conversational common ground.

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) (...) is high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

Actual causes - e.g. Suzy's being exposed to asbestos - often bring about their effects - e.g. Suzy's suffering mesothelioma - probabilistically. I use probabilistic causal models to tackle one of the thornier difficulties for traditional accounts of probabilistic actual causation: namely probabilistic preemption.

Recent work by Peijnenburg, Atkinson, and Herzberg suggests that infinitists who accept a probabilistic construal of justification can overcome significant challenges to their position by attending to mathematical treatments of infinite probabilistic regresses. In this essay, it is argued that care must be taken when assessing the significance of these formal results. Though valuable lessons can be drawn from these mathematical exercises (many of which are not disputed here), the essay argues that it is entirely unclear that the (...) form of infinitism that results meets a basic requirement: namely, providing an account of infinite chains of propositions qua reasons made available to agents. (shrink)

In mathematics, any form of probabilistic proof obtained through the application of a probabilistic method is not considered as a legitimate way of gaining mathematical knowledge. In a series of papers, Don Fallis has defended the thesis that there are no epistemic reasons justifying mathematicians’ rejection of probabilistic proofs. This paper identifies such an epistemic reason. More specifically, it is argued here that if one adopts a conception of mathematical knowledge in which an epistemic subject can know (...) a mathematical proposition based solely on a probabilistic proof, one is then forced to admit that such an epistemic subject can know several lottery propositions based solely on probabilistic evidence. Insofar as knowledge of lottery propositions on the basis of probabilistic evidence alone is denied by the vast majority of epistemologists, it is concluded that this constitutes an epistemic reason for rejecting probabilistic proofs as a means of acquiring mathematical knowledge. (shrink)

I put forward a micro realistic, probabilistic version of quantum theory, which specifies the precise nature of quantum entities thus solving the quantum wave/particle dilemma, and which both reproduces the empirical success of orthodox quantum theory, and yields predictions that differ from orthodox quantum theory for as yet unperformed experiments.

The explanatory role of natural selection is one of the long-term debates in evolutionary biology. Nevertheless, the consensus has been slippery because conceptual confusions and the absence of a unified, formal causal model that integrates different explanatory scopes of natural selection. In this study we attempt to examine two questions: (i) What can the theory of natural selection explain? and (ii) Is there a causal or explanatory model that integrates all natural selection explananda? For the first question, we argue that (...) five explananda have been assigned to the theory of natural selection and that four of them may be actually considered explananda of natural selection. For the second question, we claim that a probabilistic conception of causality and the statistical relevance concept of explanation are both good models for understanding the explanatory role of natural selection. We review the biological and philosophical disputes about the explanatory role of natural selection and formalize some explananda in probabilistic terms using classical results from population genetics. Most of these explananda have been discussed in philosophical terms but some of them have been mixed up and confused. We analyze and set the limits of these problems. (shrink)

The best and most popular argument for probabilism is the accuracy-dominance argument, which purports to show that alethic considerations alone support the view that an agent’s degrees of belief should always obey the axioms of probability. I argue that extant versions of the accuracy-dominance argument face a problem. In order for the mathematics of the argument to function as advertised, we must assume that every omniscient credence function is classically consistent; there can be no worlds in the set of dominance-relevant (...) worlds that obey some other logic. This restriction cannot be motivated on alethic grounds unless we’re also willing to accept that rationality requires belief in every metaphysical necessity, as the distinction between a priori logical necessities and a posteriori metaphysical ones is not an alethic distinction. To justify the restriction to classically consistent worlds, non-alethic motivation is required. And thus, if there is a version of the accuracy-dominance argument in support of probabilism, it isn’t one that is grounded in alethic considerations alone. (shrink)

We often have some reason to do actions insofar as they promote outcomes or states of affairs, such as the satisfaction of a desire. But what is it to promote an outcome? I defend a new version of 'probabilism about promotion'. According to Minimal Probabilistic Promotion, we promote some outcome when we make that outcome more likely than it would have been if we had done something (anything) else. This makes promotion easy and reasons cheap.

What makes a choice hard? I discuss and criticize three common answers and then make a proposal of my own. Paradigmatic hard choices are not hard because of our ignorance, the incommensurability of values, or the incomparability of the alternatives. They are hard because the alternatives are on a par; they are comparable, but one is not better than the other, and yet nor are they equally good. So understood, hard choices open up a new way of thinking about (...) what it is to be a rational agent. (shrink)

According to a standard assumption in epistemology, if one only partially believes that p , then one cannot thereby have knowledge that p. For example, if one only partially believes that that it is raining outside, one cannot know that it is raining outside; and if one only partially believes that it is likely that it will rain outside, one cannot know that it is likely that it will rain outside. Many epistemologists will agree that epistemic agents are capable of (...) partial beliefs in addition to full beliefs and that partial beliefs can be epistemically assessed along some dimensions. However, it has been generally assumed that such doxastic attitudes cannot possibly amount to knowledge. In Probabilistic Knowledge, Moss challenges this standard assumption and provides a formidable defense of the claim that probabilistic beliefs—a class of doxastic attitudes including credences and degrees of beliefs—can amount to knowledge too. Call this the probabilistic knowledge claim . Throughout the book, Moss goes to great lengths to show that probabilistic knowledge can be fruitfully applied to a variety of debates in epistemology and beyond. My goal in this essay is to explore a further application for probabilistic knowledge. I want to look at the role of probabilistic knowledge within a “knowledge-centered” psychology—a kind of psychology that assigns knowledge a central stage in explanations of intentional behavior. My suggestion is that Moss’s notion of probabilistic knowledge considerably helps further both a knowledge-centered psychology and a broadly intellectualist picture of action and know-how that naturally goes along with it. At the same time, though, it raises some interesting issues about the notion of explanation afforded by the resulting psychology. (shrink)

In this article, I introduce the term “cognitivism” as a name for the thesis that degrees of belief are equivalent to full beliefs about truth-valued propositions. The thesis (of cognitivism) that degrees of belief are equivalent to full beliefs is equivocal, inasmuch as different sorts of equivalence may be postulated between degrees of belief and full beliefs. The simplest sort of equivalence (and the sort of equivalence that I discuss here) identifies having a given degree of belief with having a (...) full belief with a specific content. This sort of view was proposed in [C. Howson and P. Urbach, Scientific reasoning: the Bayesian approach. Chicago: Open Court (1996)].In addition to embracing a form of cognitivism about degrees of belief, Howson and Urbach argued for a brand of probabilism. I call a view, such as Howson and Urbach’s, which combines probabilism with cognitivism about degrees of belief “cognitivist probabilism”. In order to address some problems with Howson and Urbach’s view, I propose a view that incorperates several of modifications of Howson and Urbach’s version of cognitivist probabilism. The view that I finally propose upholds cognitivism about degrees of belief, but deviates from the letter of probabilism, in allowing that a rational agent’s degrees of belief need not conform to the axioms of probability, in the case where the agent’s cognitive resources are limited. (shrink)

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, (...) and may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align. (shrink)