It is well known that a degree-of-belief function P is coherent if and only if it satisfies the probability calculus. In this paper, we show that the notion of coherence can be extended to higher order probabilities such as P(P(h)=p)=q, and that a higher order degree-of-belief function P is coherent if and only if it satisfies the probability calculus plus the following axiom: P(h)=p iff P(P(h)=p)=1. Also, a number of lemmata which extend an incomplete (...) probability function to a complete one are established. (shrink)

Is it coherent to speak of the probability of a probability, and the probability of a probability of a probability, and so on? We show that it is, in the sense that a regress of higher-order probabilities can lead to convergent sequences that determine all these probabilities. By constructing an implementable model which is based on coin-making machines, we demonstrate the consistency of our regress.

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)

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...) have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

It is usually taken as given that consciousness involves superior or more elaborate forms of information processing. Contemporary models equate consciousness with global processing, system complexity, or depth or stability of computation. This is in stark contrast with the powerful philosophical intuition that being conscious is more than just having the ability to compute. I argue that it is also incompatible with current empirical findings. I present a model that is free from the strong assumption that consciousness predicts superior performance. (...) The model is based on Bayesian decision theory, of which signal detection theory is a special case. It reflects the fact that the capacity for perceptual decisions is fundamentally limited by the presence and amount of noise in the system. To optimize performance, one therefore needs to set decision criteria that are based on the behaviour, i.e. the probability distributions, of the internal signals. One important realization is that the knowledge of how our internal signals behave statistically has to be learned over time. Essentially, we are doing statistics on our own brain. This ‘higherorder’ learning, however, may err, and this impairs our ability to set and maintain optimal criteria for perceptual decisions, which I argue is central to perception consciousness. I outline three possibilities of how conscious perception might be affected by failures of ‘higher-order’ representation. These all imply that one can have a dissociation between consciousness and performance. This model readily explains blindsight and hallucinations in formal terms, and is beginning to receive direct empirical support. I end by discussing some philosophical implications of the model. (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.

Second or higher order probabilities have commonly been viewed with scepticism by those working within the realm of probability and decision theory. The aim of the present note is to show how the notion of second order probabilities can add to our understanding of judgmental and decision processes and how the traditional framework of Bayesian decision theory can be extended in a fruitful way by taking such entities into account. Section one consists of a brief account (...) of arguments put forth against higher order probabilities as well as of counterarguments. In order to provide an example of the applicability of second order probabilities a decision theory encompassing such probabilities will be presented in section two. In section three I will try to emphasize the value of second order probabilities for a deeper and more complete understanding of the notion of risk. (shrink)

Cognitive Science, Volume 46, Issue 4, April 2022.

Theories of what it is for a mental state to be conscious must answer two questions. We must say how we're conscious of our conscious mental states. And we must explain why we seem to be conscious of them in a way that's immediate. Thomas Natsoulas distinguishes three strategies for explaining what it is for mental states to be conscious. I show that the differences among those strategies are due to the divergent answers they give to the foregoing questions. Natsoulas (...) finds most promising the strategy that amounts to the higher-order-thought hypothesis that I've defended elsewhere. But he raises a difficulty for it, which he thinks probably can be met only by modifying that strategy. I argue that this is unnecessary. The difficulty is a special case of a general question, the answer to which is independent of any issues about consciousness. So it's no part of a theory of consciousness to address the problem, much less solve it. Moreover, the difficulty seems to have intuitive force only given the picture that underlies the other two explanatory strategies, which both Natsoulas and I reject. (shrink)

For nearly a decade, David Rosenthal has proposed that a mental state M of a creature C is conscious just in case C has a suitable higher-order thought directed toward M. While this theory has had its share of criticism in recent years, I believe that the real difficulties have been ignored. In this essay, I show that the presence of a higher order is insufficient for conscious experience, even if we suppose that the thought satisfies (...) the constraints that Rosenthal lists . The only way Rosenthal's view could possibly yield sufficient conditions is by requiring that the higher-order thought be suitably causally related to its object. Yet, as I also show, the only causal constraint strong enough to do the job is not only ill-motivated but probably false. (shrink)

A knowledge-based decision theory faces what has been called the prodigality problem : given that many propositions are assigned probability 1, agents will be inclined to risk everything when betting on propositions which are known. In order to undo probability 1 assignments in high risk situations, the paper develops a theory which systematically connects higher level goods with higher-order knowledge.

Most epistemologists maintain that we are rationally required to believe what our evidence supports. Generally speaking, any factor that makes it more probable that a given state of affairs obtains (or does not obtain) is evidence (for that state of affairs). In line with this view, many metaethicists believe that we are rationally required to believe what’s morally right and wrong based on what our moral evidence (e.g. our moral intuitions, along with descriptive information about the world) supports. However, sometimes (...) we get information about our evidence, such as a theory that explains that all moral intuitions are ultimately caused by evolutionary forces. Such genealogical claims like this take form as a puzzle about how to rationally respond to higher-order evidence in moral epistemology. How should we change our moral views in response to genealogical claims about the evolutionary origin of our moral beliefs or about widespread moral disagreement? This introductory chapter first explains the issue about how to change our moral views based on an easily accessible example. Then it shows how recent debates about the puzzle of higher-order evidence bears on recent debates in moral epistemology, notably the debates about evolutionary debunking arguments in metaethics, the epistemic significance of moral peer disagreement, moral testimony, and collective moral knowledge before it introduces the chapters of this book. (shrink)

We present a propositional and a first-order logic for reasoning about higher-order upper and lower probabilities. We provide sound and complete axiomatizations for the logics and we prove decidability in the propositional case. Furthermore, we show that the introduced logics generalize some existing probability logics.

Suppose you hold the following opinions in the philosophy of logic. First-order predicate logic is expressively inadequate to regiment concepts of mathematic and natural language; logicism is plausible and attractive; set theory as an adjunct to logic is unnatural and ontologically extravagant; humanly usable languages are finite in lexicon and syntax; it is worth striving for a Tarskian semantics for mathematics; there are no Platonic abstract objects. Then you are probably already in cognitive distress. One way to decease your (...) unhappiness, short for embracing Platonism, is to accept higher-order logic and look, as did Arthur Prior, for a plausible way to neutralize the ontological commitment to abstract entities that this acceptance appears to entail. (shrink)

Some philosophers have claimed that it is meaningless or paradoxical to consider the probability of a probability. Others have however argued that second-order probabilities do not pose any particular problem. We side with the latter group. On condition that the relevant distinctions are taken into account, second-order probabilities can be shown to be perfectly consistent. May the same be said of an infinite hierarchy of higher-order probabilities? Is it consistent to speak of a (...) class='Hi'>probability of a probability, and of a probability of a probability of a probability, and so on, {\em ad infinitum}? We argue that it is, for it can be shown that there exists an infinite system of probabilities that has a model. In particular, we define a regress of higher-order probabilities that leads to a convergent series which determines an infinite-order probability value. We demonstrate the consistency of the regress by constructing a model based on coin-making machines. (shrink)

Problems are raised with the global workspace hypothesis of consciousness, for example about exactly how global the workspace needs to be for consciousness to suddenly be present. Problems are also raised with Carruthers’s (2019) version that excludes conceptual (categorical or discrete) representations, and in which phenomenal consciousness can be reduced to physical processes, with instead a different levels of explanation approach to the relation between the brain and the mind advocated. A different theory of phenomenal consciousness is described, in which (...) there is a particular computational system involved in which Higher Order Syntactic Thoughts are used to perform credit assignment on first order thoughts of multiple step plans to correct them by manipulating symbols in a syntactic type of working memory. This provides a good evolutionary reason for the evolution of this kind of computational module, with which, it is proposed, phenomenal consciousness is associated. Some advantages of this HOST approach to phenomenal consciousness are then described with reference not only to the global workspace approach, but also to Higher Order Thought (HOT) theories. It is hypothesized that the HOST system which requires the ability to manipulate first order symbols in working memory might utilize parts of the prefrontal cortex implicated in working memory, and especially the left inferior frontal gyrus, which is involved in language and probably syntactical processing. Overall, the approach advocated is to identify the computations that are linked to consciousness, and to analyze the neural bases of those computations. (shrink)

The author uses a series of examples to illustrate two versions of a new, nonprobabilist principle of epistemic rationality, the special and general versions of the metacognitive, expected relative frequency principle. These are used to explain the rationality of revisions to an agent’s degrees of confidence in propositions based on evidence of the reliability or unreliability of the cognitive processes responsible for them—especially reductions in confidence assignments to propositions antecedently regarded as certain—including certainty-reductions to instances of the law of excluded (...) middle or the law of noncontradiction in logic or certainty-reductions to the certainties of probabilist epistemology. The author proposes special and general versions of the MERF principle and uses them to explain the examples, including the reasoning that would lead to thoroughgoing fallibilism—that is, to a state of being certain of nothing. The author responds to the main defenses of probabilism: Dutch Book arguments, Joyce’s potential accuracy defense, and the potential calibration defenses of Shimony and van Fraassen by showing that, even though they do not satisfy the probability axioms, degrees of belief that satisfy the MERF principle minimize expected inaccuracy in Joyce’s sense; they can be externally calibrated in Shimony and van Fraassen’s sense; and they can serve as a basis for rational betting, unlike probabilist degrees of belief, which, in many cases, human beings have no rational way of ascertaining. The author also uses the MERF principle to subsume the various epistemic akrasia principles in the literature. Finally, the author responds to Titelbaum’s argument that epistemic akrasia principles require that we be certain of some epistemological beliefs, if we are rational. (shrink)

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

‘Probability dynamics’ (PD) is a second-order probabilistic theory in which probability distribution d X = (P(X 1), . . . , P(X m )) on partition U m X of sample space Ω is weighted by ‘credence’ (c) ranging from −∞ to +∞. c is the relative degree of certainty of d X in ‘α-evidence’ α X =[c; d X ] on U m X . It is shown that higher-order probabilities cannot provide a theory (...) of PD. PD applies to both subjectivist and frequentist theories. ‘Straight PD’ (SPD) produces associative and commutative mergers of evidence, in which evidences of positive credence are mutually reinforcing. ‘Offsetting PD’ (OPD) sets off conflicting evidences against each other. Subjectivist PD is a quantified second-order logic of action. Frequentist PD relates to descriptions of physical states of affairs. Acceptance of evidence α 1 X = [c 1; d 1 X ] at t 1 updates α 0 X = [c 0; d 0 X ] at t 0 into SPD-merger or OPD-merger . Given ‘co-evidence’ at t 0 < t 1, ‘indirect’ PD accepts evidence at t 1 and produces support for update α 10 X = [c10;d 10 X α 0 X such that in SPD and in OPD. For binary X and Y, with α 0 X = [c 0; P 0(X)] at t 0 (short-hand for ) and the accepted evidence, the support is ; ; where ρ0(X, Y) is the correlation coefficient of X and Y, and update α 10 X of α 0 X is with ‘accord’ λ = 1 in SPD and in OPD. As , tends toward update P 1(Y) of P 0(Y), but P 10(X) does not converge toward ‘ ’ of ‘probability kinematics’. Therefore PD is not compatible with probability kinematics. A process of ‘normalization’ interprets ‘β-evidence’ [[c 1; q 1]& . . . &[c m ; q m ]; U m X ]] with [c j ; q j ] on and m ≥ 3, as an α-evidence on {X 1, . . . , X m }. It is shown that SPD- and OPD-updates can be derived from updated cumulative functions. Time-biased updates are discussed. A PD-based theory of confirmation (PDCT) is presented. (shrink)

Epistemic transparency tells us that, if an agent S knows a given proposition p , then S knows that she knows that p . This idea is usually encoded in the so-called KK principle of epistemic logic. The paper develops an argument in favor of a moderate version of KK , which I dub quasi-transparency , as a normative rather than a descriptive principle. In the second Section I put forward the suggestion that epistemic transparency is not a demand of (...) ideal rationality, but of ideal epistemic responsibility, and hence that ideally responsible agents verify transparency principles of some sort; I also contend that their satisfaction should not be tied to an internalist epistemology. The central argument in favor of transparency is then addressed in Sections 3 to 8, through the development of a formal system. I show that, in a well-behaved formal setting, a moderate version of transparency is imposed upon us as a result of a number of independent decisions on the structure of higher-order probabilities, as long as we request that our probability and knowledge attributions cohere with each other. Thus I give a rationale to build a model for a hierarchy of languages with different levels of knowledge and probability operators; we obtain an analogous to KK for successive knowledge operators without actually demanding transitivity. The formal argument reinforces the philosophical intuition that epistemic transparency is an important desideratum we should not be too ready to dismiss. (shrink)

The technique of minimizing information (infomin) has been commonly employed as a general method for both choosing and updating a subjective probability function. We argue that, in a wide class of cases, the use of infomin methods fails to cohere with our standard conception of rational degrees of belief. We introduce the notion of a deceptive updating method and argue that non-deceptiveness is a necessary condition for rational coherence. Infomin has been criticized on the grounds that there are no (...) higher order probabilities that ‘support’ it, but the appeal to higher order probabilities is a substantial assumption that some might reject. Our elementary arguments from deceptiveness do not rely on this assumption. While deceptiveness implies lack of higher order support, the converse does not, in general, hold, which indicates that deceptiveness is a more objectionable property. We offer a new proof of the claim that infomin updating of any strictly-positive prior with respect to conditional-probability constraints is deceptive. In the case of expected-value constraints, infomin updating of the uniform prior is deceptive for some random variables but not for others. We establish both a necessary condition and a sufficient condition (which extends the scope of the phenomenon beyond cases previously considered) for deceptiveness in this setting. Along the way, we clarify the relation which obtains between the strong notion of higher order support, in which the higher order probability is defined over the full space of first order probabilities, and the apparently weaker notion, in which it is defined over some smaller parameter space. We show that under certain natural assumptions, the two are equivalent. Finally, we offer an interpretation of Jaynes, according to which his own appeal to infomin methods avoids the incoherencies discussed in this paper. (shrink)

Attributing the stability‐based theory to Hume explains his equation of degree of belief with degree of evidence in his treatment of philosophical probability. In his discussion of the fourth kind of unphilosophical probability, Hume uncovers contradictions that arise from accidental or rash generalizations; his response, that stability can be restored by appeal to higher‐order generalizations or general rules, facilitates his analysis of causation. Hume's first three kinds of unphilosophical probability involve variation in degrees of confidence (...) that parallels variation in moral judgments due to the operation of sympathy. Such variation and fluctuation in sentiment and degree of confidence feel like contradictions in that they give rise to uneasiness or discomfort that we seek to relieve. Hume thus identifies psychological pressures that motivate corrections to variable judgments about probability and virtue and vice, resulting in more stable judgments that have normative standing. (shrink)

Most legal evidence scholars agree that proof of guilt beyond a reasonable doubt requires the belief that the defendant probably committed the alleged acts. However, they also agree that this is not a sufficient condition, as this belief may be unreasonable. I focus on two popular proposals for additional conditions: (i) that the degree of belief should be robust and (ii) that it should be reasonable given the available evidence (should be an evidential probability). Both criteria face difficulties regarding (...) their meaning and utility. I propose an interpretation which overcomes these difficulties and which combines the two conditions into a single criterion on which both conditions are about the possibility of overlooked, exculpatory information. Proof of guilt beyond a reasonable doubt requires that we are sufficiently certain that we did not miss such information for the sake of achieving accurate beliefs and a just error distribution. How certain we can be that we did not miss anything relevant depends on our higher-order evidence. One important type of higher-order evidence is whether the hypotheses under consideration are sufficiently detailed. This point leads to a novel way of combining the Bayesian and explanation-based accounts of rational legal proof. (shrink)

Richard Swinburne, in his The Existence of God (2004), presents a cosmological argument in defence of theism (Swinburne 1991: 119, 135). God, Swinburne argues, is more likely to bring about an ordered universe than other states (ibid.: 144, 299). To defend this view, Swinburne presents the following arguments: (1) That this ordered universe is a priori improbable (2004: 49, 150, 1991: 304 et seq.), given the stringent requirements for life (cf. also Leslie 2000: 12), and the Second Law of Thermodynamics (...) (Giancoli 1990: 396); (2) That it seems as if this ordered universe can be explained by theism; (3) A theistic explanation for the universe is more probable because it is a simple explanation. To this end, Swinburne makes use of Bayes’ Theorem. Symbolically, this claim can be represented as (e) for the evidence of the existence of a complex universe, and (h) for a hypothesis. Swinburne’s argument is that theism has a higher prior probability, P(htheism) > P(hmaterialism), since theism is simpler than materialism. He concludes that P(e|htheism) > P(e|hmaterialism). In this paper I will address only this argument (3) above, and defend the view that it is false: theism is not simpler than materialism, nor it is more probably true. I conclude that theism is less probable than materialism, expressed by P(htheism) < P(hmaterialism) : 2/N(2n+1) < 1/n, where N is the number of possible universes and n the number of entities in existence. (shrink)

This paper begins with a problem stemming from Hume regarding credences about credences. Suppose one has a credence of .95 in p, and suppose one assesses the credence to be such. But suppose one’s second-order credence in this assessment is less than 1. Then, by a standard conditionalization rule, one’s credence in p becomes less than .95. Moreover, such “erosion” can iterate by considering one’s, third-, fourth-, fifth-order credences, etc. (In light of this, some have rejected higher- (...) class='Hi'>order credences; however, it is argued that Lewis’ “Principal Principle” forbids this.) The paper then offers a partial solution by describing circumstances under which a person has reason to assign credence 1 to a first-order credence. The solution takes the form of a “transparency” view of self-knowledge from Parent (2017, chapter 8). Briefly, it is argued that when one “reflex-like” utters a sentence “The probability of p is n”, then as a matter of psychological law, the utterance is an expression of one’s own judgment. The Principal Principle then necessitates that one’s credence in p is n, assuming one is being rational. Thus, upon perceiving such an utterance, one can thereby have a reason to assign a second-order credence of 1. (shrink)

Internal sets and the Boolean algebras of the collection of the internal sets are of central importance in non-standard analysis. Boolean algebras are the algebraization of propositional logic while the logic applied in non-standard analysis (in non-standard stochastics) is the first order or the higher order logic (type theory). We present here a first order logic algebraization for the collection of internal sets rather than the Boolean one. Further, we define an unusual probability on this (...) algebraization. (shrink)

Bayesianism is the position that scientific reasoning is probabilistic and that probabilities are adequately interpreted as an agent's actual subjective degrees of belief, measured by her betting behaviour. Confirmation is one important aspect of scientific reasoning. The thesis of this paper is the following: if scientific reasoning is at all probabilistic, the subjective interpretation has to be given up in order to get right confirmation—and thus scientific reasoning in general. The Bayesian approach to scientific reasoning Bayesian confirmation theory The (...) example The less reliable the source of information, the higher the degree of Bayesian confirmation Measure sensitivity A more general version of the problem of old evidence Conditioning on the entailment relation The counterfactual strategy Generalizing the counterfactual strategy The desired result, and a necessary and sufficient condition for it Actual degrees of belief The common knock-down feature, or ‘anything goes’ The problem of prior probabilities. (shrink)

An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson’s bound for the nonlocal correlations. Considering multiple-slit experiments—not only the traditional configuration with two slits, but also configurations with three and more slits—Sorkin detected that third-order (and higher-order) interference is not possible in quantum mechanics. The EPR experiments show that quantum mechanics involves nonlocal correlations which are demonstrated in a violation of the Bell (...) or CHSH inequality, but are still limited by a bound discovered by Tsirelson. It now turns out that Tsirelson’s bound holds in a broad class of probabilistic theories provided that they rule out third-order interference. A major characteristic of this class is the existence of a reasonable calculus of conditional probability or, phrased more physically, of a reasonable model for the quantum measurement process. (shrink)

This book examines the dominant discourses in higher education. From the moment academics enter higher education, they are met with binaries such as teaching vs. research, quantitative vs. qualitative research, and constructivists vs. positivists. When embarking upon a teaching career in a university there are further binaries that immediately present themselves, with deep vs. surface learning probably being the most pervasive. Kinchin and Gravett contend that this presents a distorted view and contributes to the disconnect between the aims (...) and observable practice of higher education. Rather than celebrating difference, dominant discourses tend to seek similarities in an attempt to simplify and manage the environment, in what the authors perceive as a less than scholarly mode. In order to break down the barriers between 'structuralist' or 'traditional' academics and those who are more familiar with poststructuralist, critical perspectives, the authors explore the overlaps between these perspectives to offer a richer and more inclusive interrogation of the dominant discourses that pervade higher education. Offering methodological approaches to explore these perspectives, the authors bring together academics working in different parts of the university and examine the concept of a 'rich cartography', exploring how this can offer meaning within higher education research and practice. (shrink)

In this paper we discuss the ``admissibility troubles'' for Bayesian accounts of direct inference proposed in, which concern the existence of surprising, unintuitive defeaters even for mundane cases of direct inference. We first show that one could reasonably suspect that the source of these troubles was informal talk about higher-order probabilities: for cardinality-related reasons, classical probability spaces abound in defeaters for direct inference. We proceed to discuss the issues in the context of the rigorous framework of (...) class='Hi'>Higher Probability Spaces. However, we show that the issues persist; we prove a few facts which pertain both to classical probability spaces and to HOPs, in our opinion capturing the essence of the problem. In effect we strengthen the message from the admissibility troubles: they arise not only for approaches using classical probability spaces---which are thus necessarily informal about metaprobabilistic phenomena like agents having credences in propositions about chances---but also for at least one respectable framework specifically tailored for rigorous discussion of higher-order probabilities. (shrink)

Although the correlation between Entrepreneurial Orientation and concrete actions to set up a business or the Probability of Starting a Business has been widely studied, the psychological factors that can affect this relationship have not yet been sufficiently addressed in the field of entrepreneurship. One of them is curiosity. Both at theoretical and empirical level, a distinction are usually made between two types of curiosity. I-type curiosity is associated with the anticipated pleasure of discovering something new, and D-type curiosity (...) is associated with reducing uncertainty and eliminating unwanted states of ignorance. Consequently, this paper aims to analyze the moderating role that the types of curiosity play in the relationship between EO and PSB, considering their interaction with sociodemographic variables. The sample of this cross-sectional study consisted of 1,761 participants. The EO scale and a curiosity scale were applied. In addition, participants were asked, based on their perception, how likely they were to start their own business within the next 5 years. A simple moderation analysis was considered to test the moderating role of both types of curiosity in the relationship between EO and PSB. Next, a double moderation analysis was carried out in order to identify, which sociodemographic variables moderate the moderating effect of curiosity. The results show that only the D-type component moderates the relationship between EO and PSB: The higher the D-type curiosity, the stronger the association between EO and PSB. In terms of sociodemographic variables, neither culture nor gender showed a moderating effect on the moderation exerted by D-type curiosity. While, age did moderate the moderating effect of D-type curiosity on the relationship between EO and PSB. Results are discussed in terms of spirituality and the resolution of problems associated with the entrepreneurial process, considering cognitive and psychological factors, particularly with an emphasis on explaining why only D-type curiosity shows a moderating effect. Finally, the limitations of the study and potential future lines of research are pointed out. (shrink)

The aim of this article is to establish that current thought about the point of a publicly funded university faces a dilemma. On the one hand, influential and attractive ‘macro’-level principles about how state resources ought to be accountably used entail that academic freedom should be utilised solely for the sake of social justice or some other concrete public good. Standard theories of public morality entail that an academic’s responsibility is entirely to be ‘responsive’ or ‘relevant’ to her social context (...) in the way she teaches and researches. On the other hand, ‘micro’-level self-conceptions of teachers and researchers include the idea that it can be proper to use academic freedom in order to discover and impart knowledge that is unlikely to foster social justice, however construed. Probably most academics accept the idea that ‘knowledge for its own sake’ can often merit pursuit and transmission. In this article, I use the most space to defend the second horn of the dilemma, the micro-level perspective, by indicating just how counterintuitive the macro one is. As a foil I critically discuss a recent report by the South African Council on Higher Education, which occasions awareness of the position that the right to academic freedom is exhausted by a duty to benefit society. However, I conclude by noting prima facie defences of the first horn, pointing out that dominant accounts of institutional ethics forbid scholars from seeking knowledge for its own sake, and hence indicating the need to resolve an antinomy about the proper final ends of a state university. (shrink)

A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order (...) probability to be developed. In particular, it is emphasized that it is sometimes uncertain which propositions are part of one's total evidence; some surprising implications of this fact are drawn out. (shrink)

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

Today professionals have to deal with more uncertainties in their field than before. We live in complex and rapidly changing environments. The British philosopher Ronald Barnett adds the term ‘supercomplexity’ to highlight the fact that ‘we can no longer be sure how even to describe the world that faces us’ (Barnett, 2004). Uncertainty is, nevertheless, not a highly appreciated notion. An obvious response to uncertainty is to reduce it—or even better, to wipe it away. The assumption of this approach is (...) that uncertainty has no advantages. This assumption is, however, not correct as several contemporary authors have argued. Rather than problematising uncertainty, I will investigate the pros and cons of embedding uncertainty in educational practice of professional higher education. In order to thoroughly explore the probabilities and challenges that uncertainty poses in education, I will dwell on the radical ideas on uncertainty of the German philosopher Friedrich Nietzsche. In The Birth of Tragedy (1872) he recognises two forces: the Apollinian, that is the pursuit of order and coherence, and the Dionysian, that is the human tendency to nullify all systematisation and idealisation. Uncertainty is part of the Dionysian. I will argue that when educators take Nietzsche's plea to make room for the Dionysian to heart, they can better prepare students for an uncertain world. If, and only if, students are encouraged to deploy both tendencies—the Apollinian and the Dionysian—they can become professionals who are able to stand their ground in an uncertain and changing (professional) world. (shrink)

A theory of probabilities of probabilities is articulated and defended. Hume's argument against higher probabiHties is critically evaluated. Conflicting probability assignments for a hypothetis or theory may result from the appHcation of different methods or perspectives, for example, those of consensual authority and individual ratiocination. When we have conflicting probabilities we may assign probabilities to the diverse probabilities initially obtained. These second level probabilities may also conflict as a result of applying diverse methods or perspectives, and the same (...) is true of higher order probabilities. However, when higher order probabilities are normalized to obtain weights that are used to average the probabilities of the next lower level, the averaging process will yield convergence towards a single first order probability condensing higher order information. An infinite averaging process can be finitely calculated to obtain a coherent assignment. Hence there is no vicious regress of probabilities. Memory beliefs illustrate the convergence of an infinite hierarchy. (shrink)

Some philosophers, most notably Hempel and Salmon, have tried to reduce explanation to probability by proposing analyses of explanation in probabilistic terms. Hempel claims, roughly, that a hypothesis H explains a datum D if and only if the conditional probability P is close to 1. It is well known that such an account fails in cases where H is irrelevant for D. Even though it is highly likely that Tom will not become pregnant, given that he regularly takes (...) his wife’s birth control pills, the latter does not explain the former. Neither does an idea work which is in the proximity of Salmon’s, namely, that H explains D if and only if P > P. Suppose Susan swallows a pound of arsenic in order to commit suicide. Shortly after, however, she dies because she is run over by a bus. The probability of dying, given that one ingests a pound of arsenic, is usually higher than the prior probability of dying. Nonetheless, it is not the arsenic but the collision with the bus which explains Susan’s death. The aforementioned objections are directed against …. (shrink)

We extend a result by Gallow concerning the impossibility of following two epistemic masters, so that it covers a larger class of pooling methods. We also investigate a few ways of avoiding the issue, such as using non-convex pooling methods, employing the notion of imperfect trust or moving to higher-order probability spaces. Along the way we suggest a conceptual issue with the conditions used by Gallow: whenever two experts are considered, whether we can trust one of them (...) is decided by the features of the other! (shrink)

A theory of probabilities of probabilities is articulated and defended. Hume's argument against higher probabiHties is critically evaluated. Conflicting probability assignments for a hypothetis or theory may result from the appHcation of different methods or perspectives, for example, those of consensual authority and individual ratiocination. When we have conflicting probabilities we may assign probabilities to the diverse probabilities initially obtained. These second level probabilities may also conflict as a result of applying diverse methods or perspectives, and the same (...) is true of higher order probabilities. However, when higher order probabilities are normalized to obtain weights that are used to average the probabilities of the next lower level, the averaging process will yield convergence towards a single first order probability condensing higher order information. An infinite averaging process can be finitely calculated to obtain a coherent assignment. Hence there is no vicious regress of probabilities. Memory beliefs illustrate the convergence of an infinite hierarchy. (shrink)

Simulation evidence obtained within a Bayesian model of price-setting in a betting market, where anonymous gamblers queue to bet against a risk-neutral bookmaker, suggests that a gambler who wants to maximize future profits should trade on the advice of the analyst cum probability forecaster who records the best probability score, rather than the highest trading profits, during the preceding observation period. In general, probability scoring rules, specifically the log score and better known “Brier” (quadratic) score, are found (...) to have higher probability of ranking rival analysts in predetermined “correct” order than either (i) the more usual method of counting categorical forecast errors (misclassifications), or (ii) an economic measure of forecasting success, described here as the “Kelly score” and defined as the trading profits accumulated by making log optimal bets (i.e. Kelly betting) against the market maker based on the probability forecasts of the analyst being assessed. This runs counter to the conventional wisdom that financial forecasts are more aptly evaluated in terms of their financial consequences than by an abstract non-monetary measure of statistical accuracy such as the number of misclassifications or a probability score. (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)

Decision theory aims at a general account of rationality covering humans but to begin makes idealizations about decision problems and agents' resources and circumstances. It treats inerrant agents with unlimited cognitive power facing tractable decision problems. This book systematically rolls back idealizations and without loss of precision treats errant agents with limited cognitive abilities facing decision problems without a stable top option. It recommends choices that maximize utility using quantizations of beliefs and desires in cases where probabilities and utilities are (...) indeterminate and using higher-order utility analysis in cases of limited access to probabilities and utilities. For agents burdened with mistakes, it advocates reasonable attempts to correct unacceptable mistakes before deciding. In decision problems without a stable top option, a topic of game theory, it proposes maximizing self-conditional utility among self-supporting options. In games of strategy, the new principles lead to solutions that are Pareto optimal among equilibria composed of jointly self-supporting strategies. Offering an account of bounded rationality, the bookmakes large strides toward realism in decision theory. (shrink)

Higher‐order theories purport to account for the conscious character of such states in terms of higher‐order representations. This chapter focuses on three classes of higher‐order theory of phenomenal consciousness, including inner‐sense theory, actualist higher‐order thought theory, and dispositionalist higher‐order thought theory. All three of these higher‐order theories purport to offer reductive explanations of phenomenal consciousness. Inner‐sense theory has important positive virtues, but faces problems; whereas actualist higher‐order (...) thought theory avoids those problems, but at the cost of losing the positive virtues. Actualist higher‐order thought theory has the advantage that no special organs or mechanisms need to be postulated. Dispositionalist higher‐order thought theory claims to split the difference, providing an account that has all of the advantages of inner‐sense theory with none of the flaws. The success of dispositionalist higher‐order thought theory is premised upon the existence of dual analog contents. (shrink)