Formal Epistemology, Misc

Just started a new book. The aim is to establish a science of knowledge in the same way that we have a science of physics or a science of materials. This might appear as an overly ambitious, possibly arrogant, objective, but bear with me. On the day I am beginning to write it–June 7th, 2020–, I think I am in possession of a few things that will help me to achieve this objective. Again, bear with me. My aim is well (...) reflected in the title I chose (just now) for this book: Knowledge & Logic: Towards a science of knowledge. Its most important feature is that I shall take logic to be to knowledge science as calculus is to physics or to materials science. I do not intend to reclaim knowledge from the bosom of philosophy, in which, known as epistemology its erudite discussion has hardly progressed since Plato first defined it as true belief with logos. With only a few adjustments, it will actually provide me with the right, science-bound start. More recently, knowledge has been reclaimed by the field of BA, a reclaim that has opened the box of Pandora: Among the evils, and perhaps at the head of the list, is an overly lay, essentially naive, notion of knowledge. But the very idea that one can have something like “knowledge (management) software” puts us on the right track. (shrink)

Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in our finitary (...) tool, which is our complete language. (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)

All of inquiry is a mental process from the known to the unknown within the realm of possibility. This process uses the three faculties of perception, conception, and abstraction, all fueled by information. These faculties have corollaries in Science and Philosophy of Religion. It is the thesis of this book that if these faculties are intelligible and reliability in Science, there is no reason to reject them when used in other fields of inquiry.

This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and s (...) that define a Galois connection on the power set PW of W. These maps can be used to define two distinct boundary operators bd and BD on W. The main theorem of the paper states that higher-order vagueness with respect to bd collapses to second-order vagueness. This does not hold for BD, the iterations of which behave in quite an erratic way. In contrast, the operator bd defines a variety of tolerance principles that do not fall prey to the sorites paradox and, moreover, do not always satisfy the principles of positive and negative introspection. (shrink)

This paper decomposes the Liar Paradox into its semantic atoms using Meaning Postulates (1952) provided by Rudolf Carnap. Formalizing truth values of propositions as Boolean properties of these propositions is a key new insight. This new insight divides the translation of a declarative sentence into its equivalent mathematical proposition into three separate steps. When each of these steps are separately examined the logical error of the Liar Paradox is unequivocally shown.

هل يمكن إذن أن أكون أنا لست أنا بانطباعات الزمان على جسدي وفكري؟ أليس لي جوهرٌ ثابتٌ تتبدل عليه الأعراض من حين إلى آخر، ومن ثم لا أفقد هويتي الحقيقية؟ لقد وُلدت منذ سنوات خلت، وتعلمت وعلمت أنني هو أنا، ويعلم المحيطون بي أنني هو أنا، بل يستطيع العلم المعاصر أن يُثبت أن لي تركيبًا جينيًا وراثيًا يميزني عن غيري، وأن لي بصمات أصابع وبصمة صوت لا تتطابق مع بصمات غيري، وسيحاسبني ربي يوم العرض عليه بوصفي شخصًا واحدًا هو أنا؛ (...) والشجرة التي تظلل باب منزلي هي ذات الشجرة التي أراها منذ سنوات، حقًا لقد تغيرت أعراضها، لكن جوهرها بالضرورة ثابت؛ وكوكب الزهرة المضيء مساءً وصباحًا هو ذات الكوكب الذي أراه كل يوم، قد تعتريه تغييرات عرضية، لكن جوهره قطعًا ثابت. ألسنا جميعًا نشترك في معرفة أن هذه الأشياء هي هي مهما تغيرت أعراضها؟. (shrink)

In the recent philosophical literature on inquiry, epistemologists point out that their subject has often begun at the point at which you already have your evidence and then focussed on identifying the beliefs for which that evidence provides justification. But we are not mere passive recipients of evidence. While some comes to us unbidden, we often actively collect it. This has long been recognised, but typically epistemologists have taken the norms that govern inquiry to be practical, not epistemic. The recent (...) literature challenges this assumption and uncovers a rich range of questions about the epistemic normativity of inquiry. In this paper, I approach these questions from the formal side of epistemology. Developing out of the philosophy of science, as it did, this branch of epistemology has long discussed inquiry. And, building on the insights of Janina Hosiasson (1931), David Blackwell (1951), and I. J. Good (1967), it has produced a reasonably well-developed framework in which to understand norms of inquiry, both epistemic and practical. In the first half of the paper, I will present the pragmatic versions of this framework due to Hosiasson, Blackwell, and Good, and the epistemic version due to Graham Oddie (1997); in the second half of the paper, I put this framework to work, turning to some of the questions from the recent debate about inquiry and asking how the framework can help us answer them. Questions include: When should we initiate an inquiry, when should we continue it, when should we conclude it, and when should we reopen it? How do epistemic norms of inquiry relate to epistemic norms of belief or credence, and can they conflict, as Jane Friedman (2020) contends? How should we resolve the apparent puzzle raised by Friedman's example of counting the windows in the Chrysler Building? How should we direct our attention, as Georgi Gardiner (2022) asks? How should we choose and reason after receiving evidence we'd rather not have received? And how should we understand the epistemic error that occurs when someone is resistant to evidence in the way Mona Simion (2023) describes? (shrink)

That the state-of-affairs of cognitive science is not good is brought into figural salience in "What happened to cognitive science?" (Núñez et al., 2019). We extend their objective description of 'what's wrong' to a prescription of 'how to correct'. Cognitive science, in its quest to elucidate 'how we know', embraces a long list of subjects, while ignoring Mathematics (Fig. 1a, Núñez et al., 2019). Mathematics is known for making the unknown to be known (cf. solving for unknowns). This acknowledgement naturally (...) raises the question: does mathematical knowing inform knowing in general? Here we show that drawing parallels to mathematical knowing can facilitate the advancement of cognitive science (Lawvere, 1994). (shrink)

In this article, I present a new argument for God’s existence, which I term the argument from non-bruteness. The argument is premised on the idea that the fundamental structure of reality cannot be a brute fact and must have an ultimate reason. By focusing on the concept of self-evidence, I first examine the relationship between possible worlds and what I refer to as cognitive perspectives. I then argue that an ultimate explanation for reality's fundamental structure necessitates an absolute perspective—one that (...) fully grasps this explanation— thereby affirming the existence of God as the absolute subject who possesses it. I summarize the core ideas of the argument, provide a formal exposition, and address potential objections. (shrink)

The much-debated Reflection principle states that a coherent agent’s cre- dences must match their estimates for their future credences. Defenders claim that there are Dutch-book arguments in its favor, putting it on the same normative footing as probabilistic coherence. Critics claim that those arguments rely on the implicit, implausible assumption that the agent is introspective: that they are certain what their own credences are. In this paper, we clarify this debate by surveying several different concep- tions of the book scenario. (...) We show that the crucial disagreement hinges on whether agents who are not introspective are known to reliably act on their credences: if they are, then coherent Reflection failures are (at best) ephemeral; if they aren’t, then Reflection failures can be robust— and perhaps rational and coherent. We argue that the crucial question for future debates is which notion of coherence makes sense for such unreliable agents, and sketch a few avenues to explore. (shrink)

A common view among nontheists combines the de jure objection that theism is epistemically unacceptable with agnosticism about the de facto objection that theism is false. Following Plantinga, we can call this a “proper” de jure objection—a de jure objection that does not depend on any de facto objection. In his Warranted Christian Belief, Plantinga has produced a general argument against all proper de jure objections. Here I first show that this argument is logically fallacious (it makes subtle probabilistic fallacies (...) disguised by scope ambiguities), and proceed to lay the groundwork for the construction of actual proper de jure objections. (shrink)

Which premisses should we use to start our inquiries? Which transitions during inquiry should we take next? When should we switch lines of inquiry? In this paper, I address these open questions about inquiry, formulating novel norms for such decisions during deductive reasoning. I use the first-order predicate calculus, in combination with Carnap’s state description framework, to state such norms. Using that framework, I first demonstrate some properties of sets of sentences used in deduction. I then state some norms for (...) decisions made during deductive reasoning, establishing initial benchmarks for efficient deduction by ideal reasoners. When deciding which transition to make next, reasoners should choose the most informative transition, the one that maximally reduces uncertainty in the sense of ruling out the largest number of state descriptions relevant to their inquiry. Finally, inspired by optimal foraging theory, I show that, under certain assumptions of ignorance, reasoners should change premiss sets when their information intake drops below the global average information intake across premiss sets. (shrink)

Bayesian epistemology’s most fundamental diachronic constraint is the norm of Conditionalization. This entry begins by describing the structure of Conditionalization and its generalization, Jeffrey Conditionalization. It goes on to discuss rational constraints on Conditionalization and justifications for Conditionalization. It concludes by considering how Conditionalization handles cases involving memory loss, old evidence, and context-sensitivity.

According to the Theory of the Second Best, in non-ideal circumstances, approximating ideals might be suboptimal (with respect to a specific interpretation of what “approximating an ideal” means). In this paper, I argue that the formal model underlying the Theory can apply to problems in epistemology. Two applications are discussed: First, in some circumstances, second-best problems arise in Bayesian settings. Second, the division of epistemic labour can be subject to second-best problems. These results matter. They allow us to evaluate the (...) claim, made by many philosophers, that second-best problems have import in epistemology (and the specific conditions under which the Theory finds applications). They also allow us to see that talk of “approximating an ideal” is ambiguous, and to clarify the conditions in which approximating an epistemic ideal might be beneficial. (shrink)

At its core this book is concerned with logic and computation with respect to the mathematical characterization of sentient biophysical structure and its behavior. -/- Three related theories are presented: The first of these provides an explanation of how sentient individuals come to be in the world. The second describes how these individuals operate. And the third proposes a method for reasoning about the behavior of individuals in groups. -/- These theories are based upon a new explanation of experience in (...) nature, the construction of senses, and motile behavior. This new approach is developed from first principles to enable a rigorous and systematic explanation of the variety of associated intelligent behaviors. -/- Alongside this development is a further account that focuses upon the nature of our work. It discusses the existential aspects of scientific inquiry, its epistemology and logic. It seeks to clarify the nature of the mathematical characterization and computation of natural behaviors, dealing with questions in the foundations of logic. It explores methodological issues related to reduction and the refinement of ideas from intuition to formal logical structure. -/- In support of this inquiry we work toward the development of a calculus for biophysical construction and its dynamics. If successful this mechanics mathematically characterizes sensory and motile behavior. -/- Upon this foundation we propose a model of apprehension and explore how its products are processed by the organism. Finally, we develop a probabilistic theory that enables us to reason about inaccessible factors in group behavior. -/- The mechanics we propose suggests the design and physical realization of a new model of computation; one in which structure and the concurrency of action are a first-order consideration. -/- We identify opportunities for experimental verification of the theory and we suggest a proof of our results in practice by the identification of this mechanism, allowing the construction of machines that experience. (shrink)

Recently, Dardashti, Hartmann, Thébault, and Winsberg (2019) proposed a Bayesian model for establishing Hawking radiation by analogical inference. In this paper we investigate whether their model would work as a general model for analogical inference. We study how it performs when varying the believed degree of similarity between the source and the target system. We show that there are circumstances in which the degree of confirmation for the hypothesis about the target system obtained by collecting evidence from the source system (...) goes down when increasing the believed degree of similarity between the two systems. We then develop an alternative model in which the direction of the variation of the degree of confirmation always coincides with the direction of the believed degree of similarity. Finally, we argue that the two models capture different types of analogical inference. (shrink)

Epistemology is the study of knowledge. This entry covers epistemology in two parts: one historical, one contemporary. The former provides a brief theological history of epistemology. The latter outlines three categories of contemporary epistemology: traditional epistemology, social epistemology, and formal epistemology, along with corresponding theological questions that arise in each.

Recent work in epistemology defends the unorthodox theses that belief is (1) an evidentially weak, and (2) question-sensitive attitude, and (3) that forming beliefs is sometimes a matter of guessing. What motivates these theses are examples of rationally permissible belief-ascriptions that exhibit these traits. The main aim of this paper is to outline a semantic account of categorical and conditional belief-ascriptions that captures the motivating data. We then survey some consequences of the proposed semantics, particularly with respect to the question (...) of whether closure under rules of inference is rationally required for weak, question-sensitive belief. (shrink)

Unspecific evidence calls for imprecise credence. My aim is to vindicate this thought. First, I will pin down what it is that makes one's imprecise credences more or less epistemically valuable. Then I will use this account of epistemic value to delineate a class of reasonable epistemic scoring rules for imprecise credences. Finally, I will show that if we plump for one of these scoring rules as our measure of epistemic value or utility, then a popular family of decision rules (...) recommends imprecise credences. In particular, a range of Hurwicz criteria, which generalise the Maximin decision rule, recommend imprecise credences. If correct, the moral is this: an agent who adopts precise credences, rather than imprecise ones, in the face of unspecific and incomplete evidence, goes wrong by gambling with the epistemic utility of her doxastic state in too risky a fashion. Precise credences represent an overly risky epistemic bet, according to the Hurwicz criteria. (shrink)

The twin pillars of Levi’s epistemology are his infallibilism and his corrigibilism. According to infallibilism, any agent is committed to being absolutely certain about anything she fully believes. From her own perspective, there is no serious possibility that any proposition she believes is false. She takes her own beliefs to be infallible, in this sense. But this need not make her dogmatic, on Levi’s view. According to his corrigibilism, an agent might come to have good reason to change her beliefs (...) and respond accordingly. She might also recognise this possibility ex ante, despite being absolutely certain that her current beliefs are true. This brief review explores whether Levi’s infallibilism can be made to sit comfortably both with his account of rational belief change, and his account of epistemic value (or with any reasonable account of epistemic value for that matter). I argue that it cannot. (shrink)

This contribution discusses the notion of an ideal language and its implications for the development of knowledge organization theory. We explore the notion of an ideal language from both a historical and a formal perspective and seek to clarify the key concepts involved. An overview of some of the momentous attempts to produce an ideal language is combined with an elucidation of the consequences the idea had in modern thought. We reveal the possibilities that the idea opened up and go (...) into some detail to explain the theoretical boundaries it ran into. (shrink)

Our main aims in this paper is to discuss and criticise the core thesis of a position that has become known as phenomenal conservatism. According to this thesis, its seeming to one that p provides enough justification for a belief in p to be prima facie justified (a thesis we label Standard Phenomenal Conservatism). This thesis captures the special kind of epistemic import that seemings are claimed to have. To get clearer on this thesis, we embed it, first, in a (...) probabilistic framework in which updating on new evidence happens by Bayesian conditionalization, and second, a framework in which updating happens by Jeffrey conditionalization. We spell out problems for both views, and then generalize some of these to non-probabilistic frameworks. The main theme of our discussion is that the epistemic import of a seeming (or experience) should depend on its content in a plethora of ways that phenomenal conservatism is insensitive to. (shrink)

I argue that normative formal epistemology (NFE) is best understood as modelling, in the sense that this is the reconstruction of its methodology on which NFE is doing best. I focus on Bayesianism and show that it has the characteristics of modelling. But modelling is a scientific enterprise, while NFE is normative. I thus develop an account of normative models on which they are idealised representations put to normative purposes. Normative assumptions, such as the transitivity of comparative credence, are characterised (...) as modelling idealisations motivated normatively. I then survey the landscape of methodological options: what might formal epistemologists be up to? I argue the choice is essentially binary: modelling or theorising. If NFE is theorising it is doing very poorly: generating false claims with no clear methodology for separating out what is to be taken seriously. Modelling, by contrast, is a successful methodology precisely suited to the management of useful falsehoods. Regarding NFE as modelling is not costless, however. First, our normative inferences are less direct and are muddied by the presence of descriptive idealisations. Second, our models are purpose-specific and limited in their scope. I close with suggestions for how to adapt our practice. (shrink)

Accuracy-first epistemology says that the rational update rule is the rule that maximizes expected accuracy. Externalism says, roughly, that we do not always know what our total evidence is. It’s been argued in recent years that the externalist faces a dilemma: Either deny that Bayesian Conditionalization is the rational update rule, thereby rejecting traditional Bayesian epistemology, or else deny that the rational update rule is the rule that maximizes expected accuracy, thereby rejecting the accuracy-first program. Call this the Bayesian Dilemma. (...) Here is roughly how the argument goes. Schoenfield (2017) has shown that following Metaconditionalization maximizes expected accuracy. But if externalism is true, Metaconditionalization is not Bayesian Conditionalization. Therefore, the externalist must choose between the rule that maximizes expected accuracy (Metaconditionalization) and Bayesian Conditionalization. I am not convinced by this argument; once we make the premises fully explicit, we see that it relies on assumptions that the externalist has every reason to reject. Still, I think that the Bayesian Dilemma is a genuine dilemma. I give a new argument—I call it the continuity argument—that doesn’t make any assumptions the externalist rejects. Roughly, I show that if you're sufficiently confident that you will correctly identify your evidence, then you'll expect adopting a rule that I call Accurate Metaconditionalization to be more accurate than adopting Bayesian Conditionalization. (shrink)

In formal modelling, it is essential that models be supplied with an interpretative story: there must be a clear and coherent account of how the formal model relates to the phenomena it is supposed to model. The traditional representation of degrees of belief as mathematical probabilities comes with a clear and simple interpretative story. This paper argues that the model of degrees of belief as imprecise probabilities (sets of probabilities) lacks a workable interpretation. The standard interpretative story given in the (...) literature is shown to lead to unacceptable results -- and, it is argued, there is no way for imprecise probabilists to restrict, replace or finesse this story so as either to avoid or to be able to live with the consequences. Thus the imprecise probabilist lacks a viable account of how a set of probability functions models a belief state: a story about which properties of the model correspond to facts about the thing modelled and how exactly we are to extract information about an agent's belief state from a set of probabilities. (shrink)

The precautionary principle is invoked in a number of important personal and policy decision contexts. Peterson shows that certain ways of making the principle precise are inconsistent with other criteria of decision-making. Some object that the results do not apply to cases of deep uncertainty or value incommensurability which are alleged to be in the principle’s wheelhouse. First, I show that Peterson’s impossibility results can be generalized considerably to cover cases of both deep uncertainty and incommensurability. Second, I contrast an (...) alternative way of giving voice to the precautionary impulse. (shrink)

Is the pool of fair predictive algorithms fair? It depends, naturally, on both the criteria of fairness and on how we pool. We catalog the relevant facts for some of the most prominent statistical criteria of algorithmic fairness and the dominant approaches to pooling forecasts: linear, geometric, and multiplicative. Only linear pooling, a format at the heart of ensemble methods, preserves any of the central criteria we consider. Drawing on work in the social sciences and social epistemology on the theoretical (...) foundations of the wisdom of crowds, we explain how our observations present an exception to the general trend of finding tradeoffs between the accuracy and fairness of forecasts. (shrink)

The Value of Evidence thesis (VE) tells us to gather evidence before deciding in any decision problem, if the evidence is free. This appar- ently plausible principle faces two problems. First, it fails on evidence externalism or nonclassical decision theories. Second, it’s not general enough: it tells us to prefer gaining free evidence to gaining no evi- dence, but it doesn’t tell us to prefer gaining more informative evidence to gaining less informative evidence when both are free. This paper defends (...) an alternative value-of-evidence principle that solves the above two problems. We call it ‘the Comparative Value of Evidence for the Resolute (CVER).’ CVER not only generalizes VE to the comparative case but is also compatible with evidence externalism and nonclassical decision theories. Our argument, if successful, broadens the scope of the value-of-evidence principle and shows that it’s more robust than previously imagined. (shrink)

Reflective equilibrium ("RE", for short) is a method of justification which works roughly as follows: We start with our pre-theoretical judgements (about, e.g. moral issues) and try to explain them by a systematic theory. This leads to a process in which judgements and principles are mutually adjusted to each other until a state of equilibrium is reached. For more than half a century, RE has been very popular, as well as controversial, among philosophers of many persuasions. Given how frequently the (...) method is mentioned, embraced and attacked, it is surprising that only very few attempts have been made at analysing and developing RE in detail. This topical collection brings together papers that develop RE on a conceptual level, analyse it using formal methods or investigate applications of RE. (shrink)

We propose a model of unawareness that remains close to the paradigm of Aumann’s model for knowledge [R. J. Aumann, International Journal of Game Theory 28 (1999) 263-300]: just as Aumann uses a correspondence on a state space to define an agent’s knowledge operator on events, we use a correspondence on a state space to define an agent’s awareness operator on events. This is made possible by three ideas. First, like the model of [A. Heifetz, M. Meier, and B. Schipper, (...) Journal of Economic Theory 130 (2006) 78-94], ours is based on a space of partial specifications of the world, partially ordered by a relation of further specification or refinement, and the idea that agents may be aware of some coarser-grained specifications while unaware of some finer-grained specifications; however, our model is based on a different implementation of this idea, related to forcing in set theory. Second, we depart from a tradition in the literature, initiated by [S. Modica and A. Rustichini, Theory and Decision 37 (1994) 107- 124] and adopted by Heifetz et al. and [J. Li, Journal of Economic Theory 144 (2009) 977-993], of taking awareness to be definable in terms of knowledge. Third, we show that the negative conclusion of a well- known impossibility theorem concerning unawareness in [Dekel, Lipman, and Rustichini, Econometrica 66 (1998) 159-173] can be escaped by a slight weakening of a key axiom. Together these points demonstrate that a correspondence on a partial-state space is sufficient to model unawareness of events. Indeed, we prove a representation theorem showing that any abstract Boolean algebra equipped with awareness, knowledge, and belief operators satisfying some plausible axioms is representable as the algebra of events arising from a partial-state space with awareness, knowledge, and belief correspondences. (shrink)

In a recent paper, Stefan Wintein criticizes my responses to the objections he raised to my modal-epistemic argument (MEA) for the existence of God. In this paper, I continue our debate and respond to Wintein’s criticisms of my previous responses. I argue that Wintein’s criticisms are unsuccessful. As a result, the MEA still stands.

This paper aims to flesh out the celebrated notion of reflective equilibrium within a probabilistic framework for epistemic rationality. On the account developed here, an agent's attitudes are in reflective equilibrium when there is a certain sort of harmony between the agent's credences, on the one hand, and what the agent accepts, on the other hand. Somewhat more precisely, reflective equilibrium is taken to consist in the agent accepting, or being prepared to accept, all and only claims that follow from (...) a maximally comprehensive theory that is more probable than any other such theory. Drawing on previous work, the paper shows that when an agent is in reflective equilibrium in this sense, the set of claims they accept or are prepared to accept is bound to be logically consistent and closed under logical implication. The paper also argues that this account can explain various features of philosophical argumentation in which the notion of reflective equilibrium features centrally, such as the emphasis on evaluating philosophical theories holistically rather than in a piecemeal fashion. (shrink)

Some theories of rational belief assume that beliefs should be closed under conjunction. I motivate the rejection of the conjunction closure, and point out that the consequences of this rejection are not as severe as it is usually thought. An often raised objection is that without the conjunction closure people are unable to reason. I outline an approach in which we can – in usual cases – reason using conjunctions without accepting the closure in its whole generality. This solution is (...) based on the notion of confidence levels, which can be defined using probabilities. Moreover, on this approach, reasoning has a scalable computational complexity adaptable to cognitive abilities of both rationally bounded and perfectly rational agents. I perform a simulation to assess its error rate, and compare it to reasoning with conjunction closure. (shrink)

Ever since antiquity, attempts have been made at defining knowledge through belief augmented by additional properties such as truth and justification. These characterizations have been challenged by Gettier counterexamples and their variants. A modern proposal, what is known as defeasibility theory, characterizes knowledge through stability under revision of beliefs on the basis of true or arbitrary information. A formal investigation of such a proposal calls for the methods of dynamic epistemic logic: well developed semantic approaches to dynamic epistemic logic have (...) been given through the plausibility models, but a corresponding proof theory is still in its infancy. We shall recast plausibility models in terms of more general neighbourhood models and develop on their basis complete proof systems. An inferential treatment of epistemic and doxastic notions such as safe belief will give a new way to study their relationships; among these, the characterization of knowledge as belief stable under arbitrary revision will be grounded through formal labelled sequent calculus derivations. (shrink)

Evidentialists say that a necessary condition of sound epistemic reasoning is that our beliefs reflect only our evidence. This thesis arguably conflicts with standard Bayesianism, due to the importance of prior probabilities in the latter. Some evidentialists have responded by modelling belief-states using imprecise probabilities (Joyce 2005). However, Roger White (2010) and Aron Vallinder (2018) argue that this Imprecise Bayesianism is incompatible with evidentialism due to “inertia”, where Imprecise Bayesian agents become stuck in a state of ambivalence towards hypotheses. Additionally, (...) escapes from inertia apparently only create further conflicts with evidentialism. This dilemma gives a reason for evidentialist imprecise probabilists to look for alternatives without inertia. I shall argue that Henry E. Kyburg’s approach offers an evidentialist-friendly imprecise probability theory without inertia, and that its relevant anti-inertia features are independently justified. I also connect the traditional epistemological debates concerning the “ethics of belief” more systematically with formal epistemology than has been hitherto done. (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)

Current approaches used in educational research and practice to evaluate the quality of written arguments often rely on structural analysis. In such assessments, credit is awarded for the presence of structural elements of an argument, such as claims, evidence, and rebuttals. In this article, we discuss limitations of such approaches, including the absence of criteria for evaluating the quality of the argument elements. We then present an alternative framework, based on the Rational Force Model (RFM), which originated from the work (...) of a Nordic philosopher Næss. Using an example of an argumentative essay, we demonstrate the potential of the RFM to improve argument analysis by focusing on the acceptability and relevance of argument elements, two criteria widely considered to be fundamental markers of argument strength. We outline possibilities and challenges with using the RFM in educational contexts and conclude by proposing directions for future research. (shrink)

Epistemic rationality is typically taken to be immodest at least in this sense: a rational epistemic state should always take itself to be doing at least as well, epistemically and by its own light, than any alternative epistemic state. If epistemic states are probability functions and their alternatives are other probability functions defined over the same collection of proposition, we can capture the relevant sense of immodesty by claiming that epistemic utility functions are (strictly) proper. In this paper I examine (...) what happens if we allow for the alternatives to an epistemic state to include probability functions with different domains. I first prove an impossibility result: on minimal assumptions, I show that there is no way of vindicating strong immodesty principles to the effect that any probability function should take itself to be doing at least as well than any alternative probability function, regardless of its domain. I then consider alternative, weaker generalizations of the traditional immodesty principle and prove some characterization results for some classes of epistemic utility functions satisfying each of the relevant principles. (shrink)

We argue that there is a tension between two monistic claims that are the core of recent work in epistemic consequentialism. The first is a form of monism about epistemic value, commonly known as veritism: accuracy is the sole final objective to be promoted in the epistemic domain. The other is a form of monism about a class of epistemic scoring rules: that is, strictly proper scoring rules are the only legitimate measures of inaccuracy. These two monisms, we argue, are (...) in tension with each other. If only accuracy has final epistemic value, then there are legitimate alternatives to strictly proper scoring rules. Our argument relies on the way scoring rules are used in contexts where accuracy is rewarded, such as education. (shrink)

On at least one of its uses, ‘higher-order evidence’ refers to evidence about what opinions are rationalized by your evidence. This chapter surveys the foundational epistemological questions raised by such evidence, the methods that have proven useful for answering them, and the potential consequences and applications of such answers.

Enjoying great popularity in decision theory, epistemology, and philosophy of science, Bayesianism as understood here is fundamentally concerned with epistemically ideal rationality. It assumes a tight connection between evidential probability and ideally rational credence, and usually interprets evidential probability in terms of such credence. Timothy Williamson challenges Bayesianism by arguing that evidential probabilities cannot be adequately interpreted as the credences of an ideal agent. From this and his assumption that evidential probabilities cannot be interpreted as the actual credences of human (...) agents either, he concludes that no interpretation of evidential probabilities in terms of credence is adequate. I argue to the contrary. My overarching aim is to show on behalf of Bayesians how one can still interpret evidential probabilities in terms of ideally rational credence and how one can maintain a tight connection between evidential probabilities and ideally rational credence even if the former cannot be interpreted in terms of the latter. By achieving this aim I illuminate the limits and prospects of Bayesianism. (shrink)

A norm of local expert deference says that your credence in an arbitrary proposition A, given that the expert's probability for A is n, should be n. A norm of global expert deference says that your credence in A, given that the expert's entire probability function is E, should be E(A). Gaifman (1988) taught us that these two norms are not equivalent. Stalnaker (2019) conjectures that Gaifman's example is "a loophole". Here, I substantiate Stalnaker's suspicions by providing characterisation theorems which (...) tell us precisely when the norms give different advice. They tell us that, in a good sense, Gaifman's example is the only case where the two norms differ. I suggest that the lesson of the theorems is that Bayesian epistemologists need not concern themselves with the differences between these two kinds of norms. While they are not strictly speaking equivalent, they are equivalent for all philosophical purposes. (shrink)

”It is often assumed that knowledge claims must be justified. But what kind of justification is required for knowledge ? . . . ” (*) -/- presupposition: the kind of epistemic justification depends on the type of the knowledge claim and its respective knowledge claim tradeoff ’vague vs. precise’. -/- procedere: in two - almost purely logical - case studies I account for this tradeoff and question in each case what (if any) were its general outcome wrt justification -/- first (...) for basic measurement statements of the form ′′ϕ(x) = r ∈ IR ± δ′′ (wrt ”measurement accuracy realism” debate) -/- and secondly predication statements of the form ′′x is ( a case of )P′′ (wrt ”epistemic vagueness” debate). (shrink)

It is often claimed that credences are not reducible to ordinary beliefs about probabilities. Such a reduction appears to be decisively ruled out by certain sorts of triviality results–analogous to those often discussed in the literature on conditionals. I show why these results do not, in fact, rule out the view. They merely give us a constraint on what such a reduction could look like. In particular they show that there is no single proposition belief in which suffices for having (...) a particular credence, regardless of one’s evidence. But if we allow such propositions to vary with evidence–as we should–then the results do not rule out a reduction. So, at least on this count, credences might very well just be beliefs about probabilities. (shrink)

Abstract. Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological models of knowledge (...) and belief. On the other hand, there exists a special class of topological models (based on so called nodec spaces) for which traditional JTB-epistemology is valid. Further, it is shown that for each topological model of Stalnaker’s combined logic KB of knowledge and belief a canonical JTB-model (its JTB-doppelganger) can be constructed that shares many structural properties with the original model but is free of Gettier situations. The topological model and its JTB-doppelganger both share the same justified belief operator and have very similar knowledge operators. Seen from a somewhat different perspective, the JTB-account of epistemology amounts to a simplification of a more general epistemological account of knowledge and belief that assumes that these two concepts may differ in some cases. The JTB-account of knowledge and belief assumes that the epistemic agent’s cognitive powers are rather large. Thereby in the JTB-epistemology Gettier cases do not occur. Eventually, it is shown that for all topological models of Stalnaker’s KB-logic Gettier situations are topologically characterized as nowhere dense situations. This entails that Gettier situations are epistemologically invisible in the sense that they can neither be known nor believed with justification with respect to the knowledge operator and the belief operator of the models involved. (shrink)

Die kumulative Habilitation besteht aus einer philosophiegeschichtlichen Arbeit (G), drei vorwiegend theoretischen Arbeiten (T1–T3) und vier anwendungsorientierten Arbeiten (A1–A4).

This book, the first of its kind, puts forward a novel, unified cognitive account of skeptical doubt. Historically, most philosophers have tried to tackle this difficult topic by directly arguing that skeptical doubt is false. But N. Ángel Pinillos does something different. He begins by trying to uncover the hidden mental rule which, for better or worse, motivates our skeptical inclinations. He then gives an account of the broader cognitive purpose of having and applying this rule. Based on these ideas, (...) he shows how we can give a new response to the traditional problem of global skepticism. He also argues that philosophical skepticism is not just something that comes up during philosophical reflection, as David Hume, Charles Sanders Peirce and other philosophers have urged. Instead, it is of great practical significance. The rule which produces skepticism may itself be operative in certain pathologies such as obsessive-compulsive disorder, in creative endeavors, and in conspiratorial thinking. The rule can also explain some of our reluctance to trust statistical evidence, especially in legal settings. More broadly, this volume aims to breathe new life into a classic problem in philosophy by tackling it from a new perspective and exploring new areas of application. The book will be of interest to philosophers, psychologists and anyone interested in the human capacity to doubt and to question our beliefs. (shrink)