Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show (...) that there is no strictly proper scoring rule for imprecise probabilities. -/- The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. We argue instead that another Joycean assumption — called strict immodesty— should be rejected, and we prove a representation theorem that characterizes all “mildly” immodest measures of inaccuracy. (shrink)

This paper is about a tension between two theses. The first is Value of Evidence: roughly, the thesis that it is always rational for an agent to gather and use cost‐free evidence for making decisions. The second is Rationality of Imprecision: the thesis that an agent can be rationally required to adopt doxastic states that are imprecise, i.e., not representable by a single credence function. While others have noticed this tension, I offer a new diagnosis of it. I show (...) that it arises when an agent with an imprecise doxastic state engages in an unreflective inquiry, an inquiry where they revise their beliefs using an updating rule that doesn't satisfy a weak reflection principle. In such an unreflective inquiry, certain synchronic norms of instrumental rationality can make it instrumentally irrational for an agent to gather and use cost‐free evidence. I then go on to propose a diachronic norm of instrumental rationality that preserves Value of Evidence in unreflective inquiries. This, I suggest, may help us reconcile this thesis with Rationality of Imprecision. (shrink)

How should we make decisions when we do not know the relevant physical probabilities? In these ambiguous situations, we cannot use our knowledge to determine expected utilities or payoffs. The traditional Bayesian answer is that we should create a probability distribution using some mix of subjective intuition and objective constraints. Imprecise Bayesians argue that this approach is inadequate for modelling ambiguity. Instead, they represent doxastic states using credal sets. Generally, insofar as we are more uncertain about the physical probability (...) of an event, there is more divergence in the credal set. Hence, their approach can represent these ambiguities via the extent of the divergence. Imprecise Bayesianism has mostly been advocated for its epistemological features. In this article, we examine its properties for decision-making. We develop a model for comparing standard and Imprecise Bayesianism by testing their performances in a classic decision problem. We find that the representational tools of Imprecise Bayesianism also cause it to underperform in our tests. This issue has been overlooked, because previous research on Imprecise Bayesianism has not utilised agent-based modelling to provide information about its performance in the short-run. Overall, we reveal the Ambiguity Dilemma for Imprecise Bayesianism: To what extent should one value representational power or decision-making performance? (shrink)

This article considers the extent to which Bayesian networks with imprecise probabilities, which are used in statistics and computer science for predictive purposes, can be used to represent causal structure. It is argued that the adequacy conditions for causal representation in the precise context—the Causal Markov Condition and Minimality—do not readily translate into the imprecise context. Crucial to this argument is the fact that the independence relation between random variables can be understood in several different ways when the (...) joint probability distribution over those variables is imprecise, none of which provides a compelling basis for the causal interpretation of imprecise Bayes nets. I conclude that there are serious limits to the use of imprecise Bayesian networks to represent causal structure. (shrink)

Many have claimed that epistemic rationality sometimes requires us to have imprecise credal states (i.e. credal states representable only by sets of credence functions) rather than precise ones (i.e. credal states representable by single credence functions). Some writers have recently argued that this claim conflicts with accuracy-centered epistemology, i.e., the project of justifying epistemic norms by appealing solely to the overall accuracy of the doxastic states they recommend. But these arguments are far from decisive. In this essay, we prove (...) some new results, which show that there is little hope for reconciling the rationality of credal imprecision with accuracy-centered epistemology. (shrink)

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

The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...) Winkler Risk Analysis, 19, 187–203, [7]; Dietrich and List [14]; Herzberg Theory and Decision, 1–19, [28]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi, 3–11, [39]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus. (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 basic Bayesian model of credence states, where each individual’s belief state is represented by a single probability measure, has been criticized as psychologically implausible, unable to represent the intuitive distinction between precise and imprecise probabilities, and normatively unjustifiable due to a need to adopt arbitrary, unmotivated priors. These arguments are often used to motivate a model on which imprecise credal states are represented by sets of probability measures. I connect this debate with recent work in Bayesian cognitive (...) science, where probabilistic models are typically provided with explicit hierarchical structure. Hierarchical Bayesian models are immune to many classic arguments against single-measure models. They represent grades of imprecision in probability assignments automatically, have strong psychological motivation, and can be normatively justified even when certain arbitrary decisions are required. In addition, hierarchical models show much more plausible learning behavior than flat representations in terms of sets of measures, which—on standard assumptions about update—rule out simple cases of learning from a starting point of total ignorance. (shrink)

Orthodox Bayesian decision theory requires an agent’s beliefs representable by a real-valued function, ideally a probability function. Many theorists have argued this is too restrictive; it can be perfectly reasonable to have indeterminate degrees of belief. So doxastic states are ideally representable by a set of probability functions. One consequence of this is that the expected value of a gamble will be imprecise. This paper looks at the attempts to extend Bayesian decision theory to deal with such cases, and (...) concludes that all proposals advanced thus far have been incoherent. A more modest, but coherent, alternative is proposed. Keywords: Imprecise probabilities, Arrow’s theorem. (shrink)

How good are we at understanding what others communicate? It often seems to us, at least, that we understand quite well what others convey when speaking in a familiar language. However, a growing body of evidence from the psychology of language suggests that in various communicative settings comprehenders routinely form linguistic representations that are underdetermined, “sketchy”, “shallow” or imprecise, often without noticing it. The paper discusses some important consequences of this evidence. Following recent discussions in this strand of research, (...) I outline how the evidence is currently best interpreted as supporting a view on which operating at a certain level of imprecision and underdetermination is a functional feature of the system responsible for comprehension of linguistic utterances in humans. That this kind of imprecision and underdetermination is part and parcel of linguistic interactions, makes the exact success rate of comprehension particularly hard to estimate. This poses a unique and interesting challenge for assessing the quality of linguistic comprehension. Understanding what a speaker intended to convey with a linguistic utterance may be less transparent than it appears to us. I will discuss the extent to which this evidence may lead to pessimism about how good we are at comprehending what others communicate. However, as I will argue in the last part of the paper, in various cases language users can be sensitive to some types of imprecision and underdetermination in comprehension and make up for it by means of various forms of post hoc deliberation. I will describe some such clarificatory contexts and end by charting a map of important issues that require further investigation. (shrink)

The Approximate Number System (ANS) is a system that allows us to distinguish between collections based on the number of items, though only if the ratio between numbers is high enough. One of the questions that has been raised is what the representations involved in this system represent. I point to two important constraints for any account: (a) it doesn’t involve numbers, and (b) it can account for the approximate nature of the ANS. Furthermore, I argue that representations of pure (...) magnitude with vehicles that have an imprecision in the value of the unit of measurement (further clarified through a formal model from measurement theory) fit both these requirements. (shrink)

This paper looks at a central issue with embodiment theories in cognition: the role, if any, they provide for mental representation. Thelen and Smith hold that the concept of representations is either vacuous or misapplied in such systems. Others maintain a place for representations , but are imprecise about their nature and role. It is difficult to understand what those could be if representations are understood in the same sense as that used by computationalists: fixed or long-lasting neural structures (...) that represent the sensory stimuli that caused them , or whose “meaning” is fixed innately or in early development for particular functions . The paper proposes a distinctions between, on the one hand, neural patterns, traces of sensory activation that while not in themselves representations are available for representational activity, and on the other the act of representing, which is what gives representational content to neural patterns. (shrink)

Most areas of the cognitive and social sciences assume that knowledge representations are constructed and used during communication and that much of its content is social. Those of us who build computer models of comprehension and conversation are forced to be explicit about the nature of these knowledge representations and affiliated processes. There are some conditions when knowledge is not sufficiently social, and other conditions when knowledge is overly grounded in social mechanisms. The argument is advanced that constraints, coherence, and (...) precision are very much at the heart of an explanation of the nature and amount of social knowledge. Asocial content reigns supreme when the referential world knowledge is highly constrained, coherently structured, and precisely specified. The social context of knowledge construction becomes progressively more influential to the extent to that world knowledge is vague, open-ended, imprecise, underspecified, and fragmentary. (shrink)

Perhaps the time has come to re-examine the basic notions of cognitive science. Together with previous challenges against associationism, the target article should be viewed as a call to arms to re-evaluate the empirical basis for contemporary conceptualizations of human learning and the notion of a concept that has become too imprecise for describing the elements of cognition.

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

In several papers, John Norton has argued that Bayesianism cannot handle ignorance adequately due to its inability to distinguish between neutral and disconfirming evidence. He argued that this inability sows confusion in, e.g., anthropic reasoning in cosmology or the Doomsday argument, by allowing one to draw unwarranted conclusions from a lack of knowledge. Norton has suggested criteria for a candidate for representation of neutral support. Imprecise credences (families of credal probability functions) constitute a Bayesian-friendly framework that allows us to (...) avoid inadequate neutral priors and better handle ignorance. The imprecise model generally agrees with Norton's representation of ignorance but requires that his criterion of self-duality be reformulated or abandoned. (shrink)

There has been considerable puzzlement over how to respond to higher-order evidence. The existing dilemmas can be defused by adopting a ‘two-dimensional’ representation of doxastic attitudes which incorporates not only substantive uncertainty about which first-order state of affairs obtains but also the degree of conviction with which we hold the attitude. This makes it possible that in cases of higher-order evidence the evidence sometimes impacts primarily on our conviction, rather than our substantive uncertainty. I argue that such a two-dimensional representation (...) is naturally developed by making use of imprecise probabilities. (shrink)

The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they constitute a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of these arguments cannot be dissolved within the framework of orthodox Bayesianism. I show that adopting an imprecise framework of probabilistic reasoning allows for a more adequate representation (...) of ignorance in Bayesian reasoning and explains away these puzzles. (shrink)

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology. -/- The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the (...) cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such arguments are an inadequate representation of indifference, and lead to unfounded predictions. It has been argued that this inability to represent ignorance is a fundamental flaw of any inductive framework using additive measures. In the first paper, I examine how imprecise probabilities fare as an inductive framework and avoid such unwarranted inferences. In the second paper, I detail how this framework allows us to successfully avoid the conclusions of Doomsday arguments in a way no Bayesian approach that represents credal states by single credence functions could. -/- There are in the cosmology literature several kinds of arguments referring to self- locating uncertainty. In the multiverse framework, different "pocket-universes" may have different fundamental physical parameters. We don’t know if we are typical observers and if we can safely assume that the physical laws we draw from our observations hold elsewhere. The third paper examines the validity of the appeal to the "Sleeping Beauty problem" and assesses the nature and role of typicality assumptions often endorsed to handle such questions. -/- A more general issue for the use of probabilities in cosmology concerns the inadequacy of Bayesian and statistical model selection criteria in the absence of well-motivated measures for different cosmological models. The criteria for model selection commonly used tend to focus on optimizing the number of free parameters, but they can select physically implausible models. The fourth paper examines the possibility for Bayesian model selection to circumvent the lack of well-motivated priors. (shrink)

Emerging evidence is now challenging the view that patients diagnosed with schizophrenia experience a selective deficit in their sense of agency. Additional disturbances seem to exist in their sense of body ownership. However, the factors underlying this disturbance in body ownership remain elusive. Knowledge of these factors, and increased understanding of how body ownership is related to other abnormalities seen in schizophrenia, could ultimately advance development of new treatments. Research on body ownership in schizophrenia has mainly been investigated with the (...) rubber hand illusion (RHI). Schizophrenia patients show higher susceptibility to the RHI, which may be explained by a stronger reliance on multisensory information over weaker stored body representations. This review shows that a coherent sense of body ownership arises from the integration of both bottom-up sensory processes and higher order, top-down bodily- and perceptual representations. Multisensory integration, temporal binding, anticipation, intention and efferent signals all partly modulate the complex experience of body ownership. Specifically, we propose that patients with schizophrenia have weaker stored body representations, and rely to a greater extent on external stimuli, such as visual information, due to imprecise or highly variable internal predictions on the consequences of action. Moreover, the reduced sense of agency in schizophrenia may additionally contribute to the disturbed sense of body ownership, as evidence from healthy participants suggests that agency and body ownership are interrelated. Vice versa, a reduced sense of body ownership may also contribute to a reduced sense of agency. Future studies should explicitly target the precise relation between the two in schizophrenia. (shrink)

The contents of representations in non-human animals, human core cognition, and perception cannot precisely be characterized by sentences of a natural language. However, this fact does not stop us from giving imprecise characterizations of these contents through natural language. In this paper, I develop an account of the precision of content characterizations by appealing to possible-world semantics combined with set and measurement theory.

We propose a model of uncertain belief. This models coherent beliefs by a filter, ????, on the set of probabilities. That is, it is given by a collection of sets of probabilities which are closed under supersets and finite intersections. This can naturally capture your probabilistic judgements. When you think that it is more likely to be sunny than rainy, we have{????|????(????????????????????)>????(????????????????????)}∈????. When you think that a gamble ???? is desirable, we have {????|Exp????[????]>0}∈????. It naturally extends the model of credal (...) sets; and we will show it captures all the expressive power of the desirable gambles model. It also captures the expressive power of sets of desirable gamble sets (with a mixing axiom, but no Archimadean axiom). (shrink)

Epistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population is (...) “completely ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting? (shrink)

Ground Representationism is the position that for each phenomenal feature there is a representational feature that accounts for it. Against this thesis, Ned Block (The Puzzle of Phenomenal Precision, 2015) has provided an intricate argument that rests on the notion of “phenomenal precision”: the phenomenal precision of a percept may change at a different rate from its representational counterpart. If so, there is then no representational feature that accounts for a specific change of this phenomenal feature. Therefore, Ground Representationism cannot (...) be generally true. -/- Although the notion of phenomenal precision is intuitive, it is admittedly in need of clarification. Here I reconstruct Block’s argument by suggesting a way of estimating phenomenal precision that is based on the assumption that parts of perceptual wholes can share phenomenal features independently of their place in the whole. Understood like this, the overall argument shows what it is supposed to show. -/- A more thorough look at the notion of phenomenal precision suggests tension with Block’s other work: in order to be non-trivial, we have to accept that some of our phenomenality is not concrete, but only generic. Such “solely generic phenomenology”, however, is a position mainly held by opponents to Block’s Access- vs. Phenomenal Consciousness-distinction. Interpreting phenomenal imprecision as constituted by introspective imprecision does not suffice as a way out. It seems that phenomenal precision is either trivial, self-contradictory, or incompatible with Block’s position elsewhere. So some additional elucidation on this crucial notion is needed. (shrink)

Résumé L’imaginaire est une catégorie plastique qui renvoie à des conceptions préscientifiques, aux fictions politiques et juridiques, aux croyances religieuses, aux stéréotypes ou préjugés, sans se confondre avec tous ces objets. Notion imprécise et fourre-tout, l’imaginaire serait inutile pour saisir avec rigueur les objets du monde : il relèverait du subjectif et de l’insaisissable. Pourtant, l’imaginaire a bien un contenu, des structures et dévoile une visée de la conscience. En se fondant sur les écrits de Castoriadis, et notamment la distinction (...) imaginaire instituant et imaginaire institué, on propose d’utiliser cette notion comme un outil méthodologique d’analyse du droit. L’imaginaire n’est d’ailleurs pas étranger à la théorie du droit, principalement américaine, et notamment au sein de l’Université de Yale. Elle recoupe les préoccupations du courant des Cultural Legal studies, où l’on retrouve des auteurs tels que Paul Kahn, David Nelken, Austin Sarat et Jonathan Simon, etc. Le droit constituant une représentation du réel, l’usage de l’imaginaire doit chercher à saisir les significations profondes des normes juridiques, leur de manière de structurer notre pensée et les luttes qu’elles engendrent pour imposer des vérités toujours renégociables. (shrink)

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for (...) number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind of number being represented. In response, we propose that the ANS represents not only natural numbers, but also non-natural rational numbers. It does not represent irrational numbers, however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research. (shrink)

This piece is a comment on Quilty-Dunn, Jake, Nicolas Porot, and Eric Mandelbaum. 2023. “The Best Game in Town: The Reemergence of the Language-of-Thought Hypothesis across the Cognitive Sciences.” Behavioral and Brain Sciences 46: e261. -/- The target article signal boosts important ongoing work across the cognitive sciences. However, its theoretical claims, generative value, and purported contributions are – where not simply restatements of arguments extensively explored elsewhere – imprecise, noncommittal, and underdeveloped to a degree that makes them difficult (...) to evaluate. The article's apparent force results from engaging with straw rather than steel opponents. (shrink)

The theory of lower previsions is designed around the principles of coherence and sure-loss avoidance, thus steers clear of all the updating anomalies highlighted in Gong and Meng's "Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss, and Simpson's Paradox" except dilation. In fact, the traditional problem with the theory of imprecise probability is that coherent inference is too complicated rather than unsettling. Progress has been made simplifying coherent inference by demoting sets of probabilities from fundamental building blocks to secondary (...) representations that are derived or discarded as needed. (shrink)

Differences in mutation rates, transmission chain-length, phenotypic manifestations, or the relative complexity of the mental representations in which they are embedded do not distinguish between “core” (intramodular) and “developing” (intermodular) memes, as Atran suggests. Dividing memes into types seems premature when our knowledge of mental representation is as imprecise as the unit of biological inheritance was in Darwin's time.

It is important to have an adequate model of uncertainty, since decisions must be made before the uncertainty can be resolved. For instance, flood defenses must be designed before we know the future distribution of flood events. It is standardly assumed that probability theory offers the best model of uncertain information. I think there are reasons to be sceptical of this claim. I criticise some arguments for the claim that probability theory is the only adequate model of uncertainty. In particular (...) I critique Dutch book arguments, representation theorems, and accuracy based arguments. Then I put forward my preferred model: imprecise probabilities. These are sets of probability measures. I offer several motivations for this model of uncertain belief, and suggest a number of interpretations of the framework. I also defend the model against some criticisms, including the so-called problem of dilation. I apply this framework to decision problems in the abstract. I discuss some decision rules from the literature including Levi’s E-admissibility and the more permissive rule favoured by Walley, among others. I then point towards some applications to climate decisions. My conclusions are largely negative: decision making under such severe uncertainty is inevitably difficult. I finish with a case study of scientific uncertainty. Climate modellers attempt to offer probabilistic forecasts of future climate change. There is reason to be sceptical that the model probabilities offered really do reflect the chances of future climate change, at least at regional scales and long lead times. Indeed, scientific uncertainty is multi-dimensional, and difficult to quantify. I argue that probability theory is not an adequate representation of the kinds of severe uncertainty that arise in some areas in science. I claim that this requires that we look for a better framework for modelling uncertainty. (shrink)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the (...) evidence calls for. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

Computation and information processing are among the most fundamental notions in cognitive science. They are also among the most imprecisely discussed. Many cognitive scientists take it for granted that cognition involves computation, information processing, or both – although others disagree vehemently. Yet different cognitive scientists use ‘computation’ and ‘information processing’ to mean different things, sometimes without realizing that they do. In addition, computation and information processing are surrounded by several myths; first and foremost, that they are the same thing. In (...) this paper, we address this unsatisfactory state of affairs by presenting a general and theory-neutral account of computation and information processing. We also apply our framework by analyzing the relations between computation and information processing on one hand and classicism and connectionism on the other. We defend the relevance to cognitive science of both computation, in a generic sense that we fully articulate for the first time, and information processing, in three important senses of the term. Our account advances some foundational debates in cognitive science by untangling some of their conceptual knots in a theory-neutral way. By leveling the playing field, we pave the way for the future resolution of the debates’ empirical aspects. (shrink)

In this paper, we prove that Neutrosophic Statistics is more general than Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities and has more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond (...) to the arguments by Woodall et al. [1]. We show that not all indeterminacies (uncertainties) may be represented by intervals. Also, in some cases, we should better use hesitant sets (that have less indeterminacy) instead of intervals. We redirect the authors to the Plithogenic Probability and Plithogenic Statistics which are the most general forms of MultiVariate Probability and Multivariate Statistics respectively (including, of course, the Imprecise Probability and Interval Statistics as subclasses). (shrink)

Sometimes, art theory addresses the same type of image from discursive disparity. This is the case of the portrait, whose imprecise definition complicates its conceptual and formal definition within the limits of the Western culture. Although this text does not intend to resolve doubts about one of the most significant questions in art—even the question of art, if portraits are born with it—it does attempt to show the difficulties in reaching an agreement on the conventions that define it, from (...) its antecedents in Antiquity and its establishment in modern times, up to the advent of its contemporary crisis that some authors attribute to the saturation suffered by the image in mass society, and others, to the new artistic paradigm that is imposed from Impressionism onwards. (shrink)

Ce travail pose la question des critères de la „progression biologique“ , d'après les documents fossiles, dans le monde des organismes, c'est-à-dire de ce perfectionnement qui ne s'arrête pas à l'intérieur du cadre d'un phylum donné, comme le „perfectionnement de l'adaptation“, mais qui conduit, au-de-là de phylums de rang différent, à des types supérieurs, par exemple, des Poissons pas les Amphibies et les Reptiles jusqu'aux Mammifères ou aux Oiseaux. Deux groupes de critères y sont recensés en détail, leur contenu est (...) exposé, et on les examine pour voir s'ils caractérisent sans ambiguïté la „progression biologique“. Le premier groupe comprend les critères de „différenciation croissante“ et „d'intégration harmonique”. Ils sont fondés sur la différenciation morphophysiologique ou plus exactement sur la „totalité” des organismes, c'est-à-dire leur multiplicité dans l'unité. Le second groupe de critères, à savoir „indépendance croissante du milieu” et „autonomie individuelle croissante”, part des relations de l'organisme au milieu et aux autres formes vivantes et souligne la „subsistence” des individus, c'est-à-dire leur plus ou moins grande indépendence ou leur stabilité interne. Comme „totalité” et „subsistence” sont les éléments décisifs d'une définition biologique de l'individu, on peut dire que la „progression biologique“ d'un organisme est d'autant plus élevée que sa totalité et subsistence et par là son être individuel sont plus accusés.Tous les critères mentionnés ne sont pas uniformes. Les motifs de leur imprécision sont divers. Tout d'abord, il n'y a pas encore de définition unique et complète de l'individu biologique, de sorte qu'on ne peut circonscrire d'une manière univoque ce qui confère à un organisme une individualité plus forte ou moins forte. Ensuite les lignées au-delà desquelles s'accomplissent des perfectionnements, et dont l'une reste intérieur au phylum , tandis que l'autre le transcende , sont entrelacées si intimement et d'une façon si particulière qu'elles ne se laissent pas séparer franchement et décrire rigoureusement selon leurs signes distinctifs. Tout représentant d'un phylum, peu importe son palier, est en effet nécessairement inséré dans un milieu et en quelque façon spécialisé. Il n'existe pas des types à caractères phylétiques purs, qui ne montrent dans aucune direction un „perfectionnement de l'adaptation”, mais seulement des marques caractéristiques de la „progression biologique”. Enfin nous ne connaissons pas les restes fossiles que le développement ou la formation des grands phylums du règne animal, à savoir du rameau des Vertébrés et des divers groupes des Invertébrés, mais non pas le plus intéressant et le plus important, leur „progression biologique” jusqu'au degré d'organisation qu'ils présentent déjà à l'époque du Silurien ou plutôt du Cambrien. C'est cela seulement qui permettrait une vue plus profonde sur la nature de la „progression biologique”.Die Arbeit stellt die Frage nach den Kriterien des fossil belegten Biologischen Aufstiegs” der Organismenwelt, d.h. derjenigen Vervollkommnung, die sich nicht innerhalb des Rahmens eines gegebenen Bauplans hält, wie die „Anpassungsvervollkommnung”, sondern über verschiedenrangige Baupläne hinweg zu höheren Typen führt, z.B. von den Fischen über die Amphibien und Reptilien zu den Säugern bzw. Vögeln. Ausführlich werden zwei Gruppen von Kriterien besprochen, ihr Inhalt dargelegt und ihre Eindeutigkeit zur Charakterisierung des „Biologischen Aufstiegs” untersucht. Die erste Gruppe umfasst die Kriterien der „zunehmenden Differenzierung” und „harmonischeren Integration”. Diese legen die morphologisch-physiologische Differenzierung oder genauer die „Ganzheit” der Organismen zugrunde, d.h. ihre Vielheit in der Einheit. Die zweite Kriteriengruppe, nämlich „zunehmende Umweltunabhängigkeit” und „zunehmende individuelle Autonomie”, geht von den Beziehungen des Organismus zur Umwelt und zu andern Lebensformen aus und betont die „Subsistenz” der Individuen, d.h. ihr grösseres oder geringeres Losgelöstsein oder ihre Selbständigkeit. Da nun „Ganzheit” und „Subsistenz” die entscheidenden Elemente einer biologischen Definition des Individuums sind, lässt sich sagen, dass der „Biologische Aufstieg” eines Organismus um so höher ist, je stärker seine Ganzheit und Subsistenz und damit sein Individuumsein ist.Eindeutigkeit kommt allen genannten Kriterien nicht zu. Die Gründe für ihre Unschärfe sind verschiedener Art. Zunächst gibt es noch keine eindeutige und vollständige Definition des biologischen Individuums, so dass sich nicht eindeutig umreissen lässt, was einem Organismus eine stärkere oder weniger starke Individualität verleiht. Dann sind die Linien, über die sich Vervollkommnungen vollziehen und von denen die eine innerhalb des Bauplans bleibt , die andere aber über ihn hinausführt so innig und in so eigenartiger Weise miteinander verflochten, dass sie sich nicht sauber scheiden und in ihren charakteristischen Merkmalen genau beschreiben lassen. Jeder Vertreter eines Bauplans, ganz gleich von welcher Ranghöhe, ist nämlich notwendig in eine Umwelt eingepasst und irgendwie spezialisiert. Es gibt keine Typen mit reinen Bauplanmerkmalen, die nach keiner Richtung hin eine „Anpassungsvervollkommnung”, sondern nur Merkmale des „Biologischen Aufstiegs” aufweisen. Schliesslich kennen wir fossil nur die Entfaltung oder Ausgestaltung der Grossbaupläne des Tierreichs, nämlich des Wirbeltierstammes und der verschiedenen Gruppen der Wirbellosen, nicht aber das Interessanteste und Wichtigste, nämlich ihren „Biologischen Aufstieg” zu der organisatorischen Höhe, mit der sie sich im Silur bzw. im Kabrium bereits vorstellen. Das erst würde einen tieferen Einblick in das Wesen des „Biologischen Aufstiegs” vermitteln.This article deals with the question of the criteria for the “biological ascent” of the organic world, resting on fossil evidence. That is, of that improvement which is not only restricted to the framework of a given “general structure” as is the “improvement of adaptation”, but which also leads beyond general structures of differentiated levels to a higher type,e.g. from the fishes through the amphibians and reptiles to the mammals or birds. Two groups of criteria are discussed at length, their content exposed and their univocity for the characterisation of this “biological ascent” is examined. The first group includes the criteria of “increasing differentiation” and “more harmonious integration”. The basis for these is the morphological-physiological differentiation, or more exactly, the “totality” of the organisms,i.e., their variety-in-unity. The second group of criteria, “increasing independence of environment” and “increasing individual autonomy”, is derived from the relationships of the organism to its environment and to other living forms, and stresses the “subsistence” of individuals,i.e., their greater or lesser degree of independence or self-sufficiency. Now since “totality” and “subsistence” are the decisive elements in a biological definition of the individual, it may be said that the “biological ascent” of an organism is higher, the more perfect its totality and subsistence and therefore its individuality is.The criteria mentioned are not univocal. The reasons for this lack of clarity are varied. First of all, there is no univocal and complete definition of the biological individual, so that it cannot be exactly stated just what gives an organism a more or less perfect individuality. Then the lines, along which improvements are made, and according to which the one remains within the general structure and the other goes beyond the general structure , are so intimately and singularly bound together, that they cannot be cleanly distinguished, and their characteristic notes exactly described. For each representative of a general structure, regardless of its level, is necessarily fitted into an environment and somehow or other specialised. There are no types with only notes of the general structure which show in no direction an “improvment of adaption”, but only the signs of “biological ascent”. Finally, we only have fossil evidence for the development or deployment of the “great general structures” of the animal world, namely that of the vertebrates and of the different groups of invertebrates, not for the most interesting and most important, that is, their “biological ascent” to the level of organisation with which they are found in the Silurian or Cambrian periods. Only that would give us a deeper insight into the essence of “biological ascent”. (shrink)

Representationalists who hold that phenomenal character can be explained in terms of representational content currently cannot explain counter-examples that involve indeterminate perceptual content, such as in the case of objects seen blurrily by someone with poor eyesight, or objects seen vaguely in misty conditions. But this problem can be resolved via provision of a more sophisticated double content (DC) view, according to which the representational content of perception is structured in two nested levels. I start by outlining the DC view (...) via consideration of four closely related cases of perceptual imprecision. Then, after a demonstration that the DC view can also explain imprecise photographic content, inadequacies in the more standard single content (SC) view are demonstrated. The results are then generalized so as to apply to the content of any kinds of non-conventional representation. The paper continues with evidence that a DC account provides a moderate rather than extreme realist account of perception, and it concludes with an initial analysis of the failure of nomic covariance accounts of information in indeterminacy cases. (shrink)

The central claim of computationalism is generally taken to be that the brain is a computer, and that any computer implementing the appropriate program would ipso facto have a mind. In this paper I argue for the following propositions: (1) The central claim of computationalism is not about computers, a concept too imprecise for a scientific claim of this sort, but is about physical calculi (instantiated discrete formal systems). (2) In matters of formality, interpretability, and so forth, analog computation (...) and digital computation are not essentially different, and so arguments such as Searle''s hold or not as well for one as for the other. (3) Whether or not a biological system (such as the brain) is computational is a scientific matter of fact. (4) A substantive scientific question for cognitive science is whether cognition is better modeled by discrete representations or by continuous representations. (5) Cognitive science and AI need a theoretical construct that is the continuous analog of a calculus. The discussion of these propositions will illuminate several terminology traps, in which it''s all too easy to become ensnared. (shrink)

Formal epistemologists often claim that our credences should be representable by a probability function. Complete probabilistic coherence, however, is only possible for ideal agents, raising the question of how this requirement relates to our everyday judgments concerning rationality. One possible answer is that being rational is a contextual matter, that the standards for rationality change along with the situation. Just like who counts as tall changes depending on whether we are considering toddlers or basketball players, perhaps what counts as rational (...) shifts according to whether we are considering ideal agents or creatures more like ourselves. Even though a number of formal epistemologists have endorsed this type of solution, I will argue that there is no way to spell out this contextual account that can make sense of our everyday judgments about rationality. Those who defend probabilistic coherence requirements will need an alternative account of the relationship between real and ideal rationality. (shrink)

Despite extensive research and a multitude of computer systems, there is no viable computerized system that is even remotely capable of approaching the skill of an expert human physician. Minor obstacles in the design of a practical system include imprecise medical terminology, the use of nonindependent clinical parameters, incorrect or inaccurate information supplied to the computer, and static representation of a patient's medical history. Major problems that go beyond computer manipulation of data include the requirement for a massive data (...) base, representation of medical knowledge in general rather than specific terms, and physician fallibility in the design of a computer system. CiteULike Connotea Del.icio.us What's this? (shrink)

Hierarchical models are commonly used for modelling uncertainty. They arise whenever there is a `correct' or `ideal' uncertainty model but the modeller is uncertain about what it is. Hierarchical models which involve probability distributions are widely used in Bayesian inference. Alternative models which involve possibility distributions have been proposed by several authors, but these models do not have a clear operational meaning. This paper describes a new hierarchical model which is mathematically equivalent to some of the earlier, possibilistic models and (...) also has a simple behavioural interpretation, in terms of betting rates concerning whether or not a decision maker will agree to buy or sell a risky investment for a specified price. We give a representation theorem which shows that any consistent model of this kind can be interpreted as a model for uncertainty about the behaviour of a Bayesian decision maker. We describe how the model can be used to generate buying and selling prices and to make decisions. (shrink)

RésuméFerdinand de Saussure postule une science générale des signes qu’il ap-pelle sémiologie. La langue n’en serait qu’un cas particulier caractériée par l’arbitrariété totale de ses unités. Cette caractéristique reviendrait aussi à l’écriture qui n’est cependant pas un systéme sémiologique primaire, mais un système secondaire dont la fonction est de représenter un système pri-maire. Il existe en outre des systèmes tertiaires comme, par example, l’alphabet Morse, l’écriture Braille, les systèmes de chiffrage, etc. Les modes de manifestation peuvent être soit acoustique soit (...) visuel. Tandis que la langue et l’écriture sont totalement arbitraires, les autres systèmes sémiologiques peuvent être motivés jusqu’à un certain de-gré. À côté des sémiologies utilitaires il existe aussi des sémiologies esthé-tiques comme, par example, les légendes. La sémiologie elle-même n’est qu’un cas particulier de la sémiotique qui tient aussi compte des signes naturels. Les frontières entre langue, sémiologie et et sémiotique sont souvent flottantes et imprécises. (shrink)

In this paper we show that Neutrosophic Statistics is an extension of Interval Statistics, since it deals with all kinds of indeterminacy (with respect to data, inferential procedures, probability distributions, graphical representations, etc.), allows for indeterminacy reduction, and uses neutrosophic probability which is more general than imprecise and classical probabilities, and has more detailed corresponding probability density functions. Whereas Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments of Woodall et (...) al [1]. We show that not all indeterminacies (uncertainties) can be represented by intervals. Moreover, in some applications, we should use hesitant sets (which have less indeterminacy) instead of intervals. We redirect the authors to Plitogenic Probability and Plitogenic Statistics which are the most general forms of Multivariate Probability and Multivariate Statistics respectively (including, of course, Imprecise Probability and Interval Statistics as subclasses). (shrink)

This dissertation aims to determine the optimal level of granularity for the variables used in probabilistic causal models. These causal models are useful for generating explanations in a number of scientific contexts. In Chapter 1, I argue that there is rarely a unique level of granularity at which a given phenomenon can be causally explained, thereby rejecting various causal exclusion arguments. In Chapter 2, I consider several recent proposals for measuring the explanatory power of causal explanations, and show that these (...) measures fail to track the comparative depth of explanations given at different levels of granularity. In Chapter 3, I offer a pragmatic account of how to partition the measure space of a causal variable so as to optimally explain its effect. My account uses the decision-theoretic notion of value of information, and indexes the relative depth of an explanation to a particular agent faced with a particular decision problem. Chapter 4 applies this same decisiontheoretic framework to answer the epistemic question of how to discover constitutive relationships in nature. In Chapter 5, I describe the formal details of the relationship between random variables that are meant to be coarse-grained and fine-grained representations of the same type of phenomenon. I use this formal framework to rebut a popular argument for the view that special science probabilities can be objective chances. Chapter 6 discusses challenges related to the causal interpretation of Bayes nets that use imprecise rather than precise probabilities. (shrink)