An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the (...) context of probabilistic epistemology, however, _does_ challenge prominent subjectivist responses to the problem of the priors. (shrink)

Con el objeto de dar cuenta de la dinámica del derecho, Alchourrón y Bulygin distinguen los conceptos de sistema jurídico y de orden jurídico. El primero hace referencia a un conjunto de enunciados que contiene todas sus consecuencias deductivas, entre las cuales hay normas cuyo contenido son actos coactivos. Se trata de una entidad estática. El orden jurídico, por su parte, es concebido como una secuencia de sistemas jurídicos enlazados por algún criterio de legalidad o validez, y conserva su identidad (...) a través de los cambios producidos por la sanción o derogación de normas. Es mi propósito presentar argumentos tendientes a sostener que la noción de orden jurídico no es adecuada para los fines que se propone y, además, su postulación, con el sentido que le atribuyen los autores, resulta innecesaria. Aiming to account for the dynamic nature of law, the Argentinian philosophers Carlos Alchourrón and Eugenio Bulygin discriminate the concepts of legal system and legal order. The first makes reference to a set of statements that includes all their deductive consequences, among which there are norms that prescribe coercive acts. It is a static entity. legal order, on the other hand, is conceived as a sequence of legal systems connected by some criterion of legal validity and keeps its identity through the changes produced by the passing or abrogation of laws. The aim of this paper is to present arguments leading to support that the notion of legal order is inadequate for its declared purpose and, furthermore, its conception, with the meaning the authors assign to it, is unnecessary. (shrink)

Our purpose in this paper is to contribute to a practice-based characterization of scientific inference. We want to explore whether Brandom’s pragmatist–inferentialist framework can suitably accommodate several types of ampliative inference common in scientific reasoning and explanation (probabilistic reasoning, abduction and idealisation). First, we argue that Brandom’s view of induction in terms of merely permissive inferences is inadequate; in order to overcome the shortcoming of Brandom’s proposal, we put forward an alternative conception of inductive, probabilistic reasoning by appeal to the (...) notion of degrees of commitment. Moreover, we examine the sorts of inferential commitments operative in other types of ampliative inferences, such as abduction or reasoning involving idealizations and assumptions. We suggest that agents engaging in these forms of reasoning often undertake restricted inferential commitments, whose scope and reach are more limited that in the case of the commitments associated with full beliefs. (shrink)

I argue that Epistemic Disjunctivism doesn’t sustain a successful anti-sceptical strategy. I contend, in particular, that the treatment of scepticism that Duncan Pritchard puts forward on behalf of Epistemic Disjunctivism is unsatisfactory.

Knowledge is closed under implication, according to standard theories. Orthodoxy can allow, though, that apparent counterexamples to closure exist, much as Kripkeans recognize the existence of illusions of possibility which they seek to explain away. Should not everyone, orthodox or not, want to make sense of “intimations of openness”? This paper compares two styles of explanation: evidence that boosts P’s probability need not boost that of its consequence Q; evidence bearing on P’s subject matter may not bear on the subject (...) matter of Q. (shrink)

Timothy Williamson argues against the tactic of criticizing confidence in a theory by identifying a logical consequence of the theory whose probability is not raised by the evidence. He dubs it “the consequence fallacy”. In this paper, we will show that Williamson’s formulation of the tactic in question is ambiguous. On one reading of Williamson’s formulation, the tactic is indeed a fallacy, but it is not a commonly used tactic; on another reading, it is a commonly used tactic (or at (...) least more often used than the former tactic), but it is not a fallacy. (shrink)

We compare Jan ?ukasiewicz's and Karl Popper's views on induction. The English translation of the two ?ukasiewicz's papers is included in the Appendix.

The problem of induction belongs to the most controversial issues in philosophy of science. If induction is understood widely, it covers every fallible inference, that is, such that its conclusion is not logically entailed by its premises. This paper analyses so-called reductive induction, that is, reasoning in which premises follow from the conclusion, but the reverse relation does not hold. Two issues are taken into account, namely the definition of reductive inference and its justification. The analysis proposed in the paper (...) employs metalogical tools. The author agrees with the view that a quantitative account of degree of confirmation for universal theories via logical probability is problematic. However, prospect for a qualitative approach look as more promising. Using the construction of maximally consistent sets allows to distinguish good and worthless induction as well as shows how to understand induction in a semantic way. A closer analysis of deductivism in the theory of justification shows that it is a hidden inductivism. (shrink)

We define a semantics for conditionals in terms of stochastic graphs which gives a straightforward and simple method of evaluating the probabilities of conditionals. It seems to be a good and useful method in the cases already discussed in the literature, and it can easily be extended to cover more complex situations. In particular, it allows us to describe several possible interpretations of the conditional and to formalize some intuitively valid but formally incorrect considerations concerning the probabilities of conditionals under (...) these two interpretations. It also yields a powerful method of handling more complex issues. The stochastic graph semantics provides a satisfactory answer to Lewis’s arguments against the PC = CP principle, and defends important intuitions which connect the notion of probability of a conditional with the notion of conditional probability. It also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues. (shrink)

We live in a world in which scientific expertise and its epistemic authority become more important. On the other hand, the financial interests in research, which could potentially corrupt science, are increasing. Due to these two tendencies, a concern for the integrity of scientific research becomes increasingly vital. This concern is, however, hollow if we do not have a clear account of research integrity. Therefore, it is important that we explicate this concept. Following Rudolf Carnap’s characterization of the task of (...) explication, this means that we should develop a concept that is similar to our common sense notion of research integrity, exact, fruitful, and as simple as possible. Since existing concepts do not meet these four requirements, we develop a new concept in this article. We describe a concept of epistemic integrity that is based on the property of deceptiveness, and argue that this concept does meet Carnap’s four requirements of explication. To illustrate and support our claims we use several examples from scientific practice, mainly from biomedical research. (shrink)

Selectionist evolutionary theory has often been faulted for not making novel predictions that are surprising, risky, and correct. I argue that it in fact exhibits the theoretical virtue of predictive capacity in addition to two other virtues: explanatory unification and model fitting. Two case studies show the predictive capacity of selectionist evolutionary theory: parallel evolutionary change in E. coli, and the origin of eukaryotic cells through endosymbiosis.

That one person's modus ponens is another's modus tollens is the bane of philosophy because it strips many philosophical arguments of their persuasive force. The problem is that philosophical arguments become mere pantomemes: arguments that are reasonable to resist simply by denying the conclusion. Appeals to proof, intuition, evidence, and truth fail to alleviate the problem. Two broad strategies, however, do help in certain circumstances: an appeal to normal informal standards of what is reasonable (nisowir) and argument by interpretation. The (...) method of explication features prominently in both strategies, and the paper extends this method to apply to nisowir, introducing the concept of canonical explication. The paper illustrates the two strategies with examples of arguments from formal epistemology and suggests that an appeal to nisowir might help to defend against philosophical scepticism by shifting the burden of proof to the sceptic. (shrink)

It is argued that a subject's evidence consists of all and only the propositions that the subject knows.

As is well known, the Humean account of causal inference gives a central location to inference habits. Some of these habits one can discipline. Thus, one can so discipline oneself as to reason in accordance with the “rules by which to judge of causes and effects”, that is, one can discipline oneself to think scientifically, rather than, say, in accordance with the rules of prejudice, or of superstition. All such judgments, even those of science, are, however, upon the Humean account (...) fallible. Some, or rather very many, have raised the issue about how any such causal judgment or inference is justified. That is, how can such inference habits be justified, shown to be reasonable. Hume meets this challenge by arguing that there are some habits all men do and must have. Because we must have them we ought to have them. They are, therefore, justified. (shrink)

Schurz (2019, ch. 4) argues that probabilistic accounts of induction fail. In particular, he criticises probabilistic accounts of induction that appeal to direct inference principles, including subjective Bayesian approaches (e.g., Howson 2000) and objective Bayesian approaches (see, e.g., Williamson 2017). In this paper, I argue that Schurz’ preferred direct inference principle, namely Reichenbach’s Principle of the Narrowest Reference Class, faces formidable problems in a standard probabilistic setting. Furthermore, the main alternative direct inference principle, Lewis’ Principal Principle, is also hard to (...) reconcile with standard probabilism. So, I argue, standard probabilistic approaches cannot appeal to direct inference to explicate the logic of induction. However, I go on to defend a non-standard objective Bayesian account of induction: I argue that this approach can both accommodate direct inference and provide a viable account of the logic of induction. I then defend this account against Schurz’ criticisms. (shrink)

Bayesian probability is normally defined over a fixed language or eventspace. But in practice language is susceptible to change, and thequestion naturally arises as to how Bayesian degrees of belief shouldchange as language changes. I argue here that this question poses aserious challenge to Bayesianism. The Bayesian may be able to meet thischallenge however, and I outline a practical method for changing degreesof belief over changes in finite propositional languages.

Timothy Williamson has a marvelously precise account of epistemic justification in terms of knowledge and probability. I argue that the account runs aground on certain cases involving the probability values 0 and 1.

Peirce's study of Kant, and later of Hegel, and Dewey's (1930) retention of much of Hegel's social philosophy are recognised idealist sources of pragmatism. Here I argue that the transition from idealism to pragmatic realism was already achieved by Hegel. Hegel's ‘Objective Logic’ corresponds in part to Kant's ‘Transcendental Logic’ (WdL,GW21:47.1-3). Hegel faults Kant for relegating concepts of reflection to an Appendix to his Transcendental Logic (WdL,GW12:19.34-38), and for treating reason as ‘only dialectical’ and as ‘merely regulative’ (WdL,GW12:23.12,.16-17). I present (...) three important yet neglected features of Kant'sCritique of Pure Reasonwhich are key enthymemes undergirding Hegel's critical reconstruction of Kant's Critical philosophy (§2). I then summarise some features of the philosophical context within which Hegel begins to re-assess and reconstruct Kant's Transcendental Logic (§3), and review several key steps in this direction Hegel undertook in the 1807Phenomenology(§4). (A related paper extends these results to Hegel'sLogicandEncyclopaedia.) These points show that Hegel's reanalysis of Kant's Critical philosophy is the first and still one of the most sophisticated and adequate pragmatic — specifically pragmatic realist — accounts of thea priori. (shrink)

Recent years have seen a surge in online collaboration between experts and amateurs on scientific research. In this article, we analyse the epistemological implications of these crowdsourced projects, with a focus on Zooniverse, the world’s largest citizen science web portal. We use quantitative methods to evaluate the platform’s success in producing large volumes of observation statements and high impact scientific discoveries relative to more conventional means of data processing. Through empirical evidence, Bayesian reasoning, and conceptual analysis, we show how information (...) and communication technologies enhance the reliability, scalability, and connectivity of crowdsourced e-research, giving online citizen science projects powerful epistemic advantages over more traditional modes of scientific investigation. These results highlight the essential role played by technologically mediated social interaction in contemporary knowledge production. We conclude by calling for an explicitly sociotechnical turn in the philosophy of science that combines insights from statistics and logic to analyse the latest developments in scientific research. (shrink)

The paper presents a comprehensive solution to the new riddle of induction. Gruesome induction is blocked because “grue” is not independent of our sampling and observation methods. Before presenting my theory, I critically survey previous versions of what I call the “independence strategy”, tracing the strategy to three different papers from the 1970s by (respectively) Wilkerson, Moreland, and Jackson. Next I critically examine recent approaches by Okasha, Godfrey-Smith, Schramm, and Freitag. All of these approaches have their virtues, but none of (...) them rules out every problem case. Nor do any of them alone explain exactly what goes wrong in all types of gruesome reasoning. My account aims to do both. Learning lessons from my criticisms of previous theories, I argue that there are several crucial types of independence. All of them are needed to rule out every problem case. I close by suggesting that the independence solution can also be adopted by proponents of other approaches—Bayesians, fans of natural kinds, and pragmatists. (shrink)

Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods with values of objective chances or relative frequencies. The best known version of a direct inference principle is David Lewis’s Principal Principle. Certain kinds of statements undermine direct inferences. Lewis calls such statements inadmissible. We show that on any Bayesian account of direct inference several kinds of intuitively innocent statements turn out to be inadmissible. This may pose a significant challenge to Bayesian accounts of direct inference. We suggest some ways in which (...) these challenges may be addressed. (shrink)

Lloyd analyzes every proposed evolutionary explanation of female orgasm and argues that all but one suffers from serious evidential errors. Lloyd attributes these errors to two main biases: androcentrism and adaptationism. This paper begins by arguing that the explanation Lloyd favors—the by-product account—is guilty of the androcentrism which supposedly implicates the other explanations of female orgasm with numerous evidential discrepancies. This suggests that there is another error afflicting orgasm research in addition to the biases Lloyd identities. I attempt to diagnose (...) and characterize this additional error. In short, I think the error is using an imprecise definition of the trait in question. Further, Lloyd takes her analysis to support Longino’s contextual empiricist model of scientific objectivity. I consider what implications this analysis has for contextual empiricism. Finally, I argue that theorizing about female orgasm should be done from a conceptual engineering approach. (shrink)

This paper argues for two conclusions: (1) evaluating the success of engineered concepts necessarily involves empirical work; and (2) the Carnapian Explication criterion precision ought to be a methodological standard in conceptual engineering. These two conclusions provide a new analysis of the race and gender debate between Sally Haslanger and Jennifer Saul. Specifically, the argument identifies the resources Haslanger needs to respond to Saul’s main objections. Lastly, I contrast the methodology advocated here with the so-called “method of cases” and draw (...) out some general implications for how we should think about concepts. (shrink)

This paper argues for two conclusions: (1) evaluating the success of engineered concepts necessarily involves empirical work; and (2) the Carnapian Explication criterion precision ought to be a methodological standard in conceptual engineering. These two conclusions provide a new analysis of the race and gender debate between Sally Haslanger and Jennifer Saul. Specifically, the argument identifies the resources Haslanger needs to respond to Saul’s main objections. Lastly, I contrast the methodology advocated here with the so-called “method of cases” and draw (...) out some general implications for how we should think about concepts. (shrink)

A frequentist confidence interval can be constructed by inverting a hypothesis test, such that the interval contains only parameter values that would not have been rejected by the test. We show how a similar definition can be employed to construct a Bayesian support interval. Consistent with Carnap’s theory of corroboration, the support interval contains only parameter values that receive at least some minimum amount of support from the data. The support interval is not subject to Lindley’s paradox and provides an (...) evidence-based perspective on inference that differs from the belief-based perspective that forms the basis of the standard Bayesian credible interval. (shrink)

Many papers have been devoted to the semantic turn Carnap took in the late 1930s after Tarski had explained to him his method for defining truth and his work on the establishment of scientific semantics. Commentators have often argued that the major turn in Carnap’s approach to languages had already been taken in the Logical Syntax of Language, but they have usually assumed that Carnap was happy to subsequently follow Tarski and adopt Tarskian semantics. In this paper, it is argued (...) that this assumption needs to be qualified and that Carnap was actually far from following Tarski when he decided to complement his syntactic method with a semantic one. Carnap and Tarski had different goals, divergent programs, and dissenting views on truth and semantics. After exploring several possible methods for the explication of logical concepts such as L-truth and L-implication, Carnap opted for definitions based on concepts he had found in Wittgenstein’s Tractatus and Waismann’s work on a logical interpretation of probability. Carnap’s reasons for taking a semantic turn are to be understood in the context of his principle of tolerance. He first hoped he could use Tarski’s technique to recover in the semantic setting the completeness result he had tried to establish in the Logical Syntax. His eventual adoption of non-Tarskian semantics can be accounted for by his program of a logical analysis of science—including empirical science—and his ambition to elaborate a unified logical framework for deductive, inductive, and modal logic, and for explicating analyticity. (shrink)

The project of integrated HPS has occupied philosophers of science in one form or another since at least the 1960s. Yet, despite this substantial interest in bringing together philosophical and historical reflections on the nature of science, history of science and formal philosophy of science remain as divided as ever. In this paper, I will argue that the continuing separation between historical and formal philosophy of science is ill-founded. I will argue for this in both abstract and concrete terms. At (...) the abstract level, I reconstruct two possible arguments for the incompatibility of historical and formal philosophy of science and argue that they are both wanting. At the concrete level, I discuss how historical and formal philosophy of science have been brought together in practice, namely: in the form of a largely forgotten research tradition that I will refer to here as the study of formalized macro-units. After a brief exposition, I argue that this research tradition has been unduly overlooked by historically minded philosophers of science. Bringing together these observations, I argue that the divide between historical and formal philosophy of science is not grounded in any substantive arguments, but can be primarily attributed to disciplinary happenstance. (shrink)

Conceptual analysis has been typically recognized as a traditional methodology within analytic philosophy, but many philosophers have heavily criticized it. In contrast, the methodology of Carnapian explication has been undergoing a revival as a methodological alternative due to its revisionary aim. I will make explicit the shared structural properties and goals of Carnapian explication and the kind of conceptual analysis advanced by the advocates of the Canberra Plan. Also, I will argue that although their goal to make philosophy more scientific (...) is desirable, they cannot achieve their goal of clearly distinguishing philosophy from science. Moreover, since traditional conceptual analysis is an element of both revisionary methodologies, it is also unable to mark a clear distinction between them. The comparison throws some light on the relationship between traditional conceptual analysis and the two revisionary methodologies, their implicit theoretical commitments and deficiencies. (shrink)

According to a widespread but implicit thesis in Bayesian confirmation theory, two confirmation measures are considered equivalent if they are ordinally equivalent—call this the “ordinal equivalence thesis”. I argue that adopting OET has significant costs. First, adopting OET renders one incapable of determining whether a piece of evidence substantially favors one hypothesis over another. Second, OET must be rejected if merely ordinal conclusions are to be drawn from the expected value of a confirmation measure. Furthermore, several arguments and applications of (...) confirmation measures given in the literature already rely on a rejection of OET. I also contrast OET with stronger equivalence theses and show that they do not have the same costs as OET. On the other hand, adopting a thesis stronger than OET has costs of its own, since a rejection of OET ostensibly implies that people’s epistemic states have a very fine-grained quantitative structure. However, I suggest that the normative upshot of the paper in fact has a conditional form, and that other Bayesian norms can also fruitfully be construed as having a similar conditional form. (shrink)

According to a widespread but implicit thesis in Bayesian confirmation theory, two confirmation measures are considered equivalent if they are ordinally equivalent—call this the “ordinal equivalence thesis” (OET). I argue that adopting OET has significant costs. First, adopting OET renders one incapable of determining whether a piece of evidence substantially favors one hypothesis over another. Second, OET must be rejected if merely ordinal conclusions are to be drawn from the expected value of a confirmation measure. Furthermore, several arguments and applications (...) of confirmation measures given in the literature already rely on a rejection of OET. I also contrast OET with stronger equivalence theses and show that they do not have the same costs as OET. On the other hand, adopting a thesis stronger than OET has costs of its own, since a rejection of OET ostensibly implies that people’s epistemic states have a very fine-grained quantitative structure. However, I suggest that the normative upshot of the paper in fact has a conditional form, and that other Bayesian norms can also fruitfully be construed as having a similar conditional form. (shrink)

Stanley Stevens draws a useful distinction among ordinal scales, interval scales, and ratio scales. Most recent discussions of confirmation measures have proceeded on the ordinal level of analysis. In this article, I give a more quantitative analysis. In particular, I show that the requirement that our desired confirmation measure be at least an interval measure naturally yields necessary conditions that jointly entail the log-likelihood measure. Thus, I conclude that the log-likelihood measure is the only good candidate interval measure.

Christopher Boorse’s Health care ethics: an introduction, Temple University Press, Philadelphia, pp 359–393, 1987; in Humber, Almeder, Totowa What is disease?, Humana Press, New York City, pp 1–134, 1997; J Med Philos, 39:683–724, 2014) Bio-Statistical Theory comprehends diseases in terms of departures from natural norms, which involve an objectively describable deviation from the proper physiological or psychological functioning of parts of the human organism. I argue that while recent revisions and additional considerations shield the BST from a number of issues (...) raised by critics, they give rise to significant new challenges. These are related to the attribution of epistemic authority, the possibility of multiple concepts in the authoritative literature, and the framing of BST as “philosophical explication.” The conclusion is that, in its current form, the BST is unable to provide a robust framework for a naturalist classification. (shrink)

Recently, natural language pragmatics started to make use of decision-, game-, and information theoretical tools to determine the usefulness of questions and assertions in a quantitative way. In the first part of this paper several of these notions are related with each other. It is shown that under particular natural assumptions the utility of questions and answers reduces to their informativity, and that the ordering relation induced by utility sometimes even reduces to the logical relation of entailment. The second part (...) of the paper shows how different proposals (using either protocols or likelihood functions) to measure the relevance/utility of non-partitional questions come down to the same thing. (shrink)

In debates about the nature of scientific explanation, one theme repeatedly arises: that explanation is about providing understanding. However, the concept of understanding has only recently been explored in any depth, and this paper attempts to introduce a useful concept of understanding to that literature and explore it. Understanding is a higher level cognition, the recognition of connections between various pieces of knowledge. This conception can be brought to bear on the conceptual issues that have thus far been unclear in (...) the literature. Though this notion of understanding is broad, explaining various concepts of explanation, it is robust enough to underwrite an objective and useful notion of explanation. (shrink)

I show how scoring rules, interpreted as measuring the inaccuracy of a set of degrees of belief, may be exploited to construct confirmation measures as used in Bayesian confirmation theory. I construct two confirmation measures from two particular standard scoring rules. One of these measures is genuinely new, the second is trivially ordinally equivalent to the difference measure. These two measures are tested against three well-known measures of confirmation in a simple but illuminating case that contains in a natural way (...) the problem of irrelevant conjunction. The genuinely new measure emerges, arguably, as the best. (shrink)

In this paper we discuss the new Tweety puzzle. The original Tweety puzzle was addressed by approaches in non-monotonic logic, which aim to adequately represent the Tweety case, namely that Tweety is a penguin and, thus, an exceptional bird, which cannot fly, although in general birds can fly. The new Tweety puzzle is intended as a challenge for probabilistic theories of epistemic states. In the first part of the paper we argue against monistic Bayesians, who assume that epistemic states can (...) at any given time be adequately described by a single subjective probability function. We show that monistic Bayesians cannot provide an adequate solution to the new Tweety puzzle, because this requires one to refer to a frequency-based probability function. We conclude that monistic Bayesianism cannot be a fully adequate theory of epistemic states. In the second part we describe an empirical study, which provides support for the thesis that monistic Bayesianism is also inadequate as a descriptive theory of cognitive states. In the final part of the paper we criticize Bayesian approaches in cognitive science, insofar as their monistic tendency cannot adequately address the new Tweety puzzle. We, further, argue against monistic Bayesianism in cognitive science by means of a case study. In this case study we show that Oaksford and Chater’s (2007, 2008) model of conditional inference—contrary to the authors’ theoretical position—has to refer also to a frequency-based probability function. (shrink)

This paper concerns the issue of whether the so-called left wing of the Vienna Circle (Carnap, Neurath, Frank) can be understood as having provided the blueprint for a bipartite metatheory with a formal-logical part (the “logic of science”) supporting and being supported by a naturalistic-empirical part (the “behavioristics of science”). A claim to this effect was recently met by a counterclaim that there was indeed an attempt made to broaden Carnap’s formalist conception of philosophy by the pragmatist Morris, but that (...) this initiative failed and that Carnap showed no interest in it. To defend the original claim this paper provides an analysis of Carnap and Morris on the subject matter of pragmatics in order to show that and how Carnap adopted Morris’s proposals in so far as they agreed with bipartite metatheory conception. (shrink)

This paper offers a refutation of J. C. Pinto de Oliveira's recent critique of revisionist Carnap scholarship as giving undue weight to two brief letters to Kuhn expressing his interest in the latter's work. First an argument is provided to show that Carnap and Kuhn are by no means divided by a radical mismatch of their conceptions of the rationality of science as supposedly evidenced by their stance towards the distinction of the contexts of discovery and justification. This is followed (...) by an argument to the effect that the fact that Carnap's own work concentrated on formal aspects of scientific theories does not licence the conclusion that he thought historical investigations and concerns irrelevant for what we nowadays would rightly call "philosophy of science". (shrink)

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)