Conventionalism about mathematics claims that mathematical truths are true by linguistic convention. This is often spelled out by appealing to facts concerning rules of inference and formal systems, but this leads to a problem: since the incompleteness theorems we’ve known that syntactic notions can be expressed using arithmetical sentences. There is serious prima facie tension here: how can mathematics be a matter of convention and syntax a matter of fact given the arithmetization of syntax? This challenge has been pressed in (...) the literature by Hilary Putnam and Peter Koellner. In this paper I sketch a conventionalist theory of mathematics, show that this conventionalist theory can meet the challenge just raised , and clarify the type of mathematical pluralism endorsed by the conventionalist by introducing the notion of a semantic counterpart. The paper’s aim is an improved understanding of conventionalism, pluralism, and the relationship between them. (shrink)

Why are natural theories pre-well-ordered by consistency strength? In previous work, an approach to this question was proposed. This approach was inspired by Martin's Conjecture, one of the most prominent conjectures in recursion theory. Fixing a reasonable subsystem $T$ of arithmetic, the goal was to classify the recursive functions that are monotone with respect to the Lindenbaum algebra of $T$. According to an optimistic conjecture, roughly, every such function must be equivalent to an iterate $\mathsf{Con}_T^\alpha$ of the consistency (...) operator ``in the limit'' within the ultrafilter of sentences that are true in the standard model. In previous work the author established the first case of this optimistic conjecture; roughly, every recursive monotone function is either as weak as the identity operator in the limit or as strong as $\mathsf{Con}_T$ in the limit. Yet in this note we prove that this optimistic conjecture fails already at the next step; there are recursive monotone functions that are neither as weak as $\mathsf{Con}_T$ in the limit nor as strong as $\mathsf{Con}_T^2$ in the limit. In fact, for every $\alpha$, we produce a function that is cofinally equivalent to $\mathsf{Con}^\alpha_T$ yet cofinally equivalent to $\mathsf{Con}_T$. (shrink)

Consideration of a paradox originally discovered by John Buridan provides a springboard for a general solution to paradoxes within the Liar family. The solution rests on a philosophical defence of truth-value-gaps and is consistent (non-dialetheist), avoids ‘revenge’ problems, imports no ad hoc assumptions, is not applicable to only a proper subset of the semantic paradoxes and implies no restriction of the expressive capacities of language.

The best developed formulation of closed system quantum theory that handles multiple-time statements, is the consistent (or decoherent) histories approach. The most important weaknesses of the approach is that it gives rise to many different consistent sets, and it has been argued that a complete interpretation should be accompanied with a natural mechanism leading to a (possibly) unique preferred consistent set. The existence of multiple consistent sets becomes more problematic because it allows the existence of contrary inferences [1]. We analyse (...) the conceptual difficulties that arise from the existence of multiple consistent sets and provide a suggestion for a natural set selection criterion. This criterion does not lead to a unique physical consistent set, however it evades the existence of consistent sets with contrary inferences. The criterion is based on the concept of preclusion and the requirement that probability one propositions and their inferences should be non-contextual. The allowed consistent sets turn-out to be compatible with coevents which are the ontology of an alternative, histories based, formulation [2–4]. (shrink)

People sometimes explain behavior by appealing to an essentialist concept of the self, often referred to as the true self. Existing studies suggest that people tend to believe that the true self is morally virtuous; that is deep inside, every person is motivated to behave in morally good ways. Is this belief particular to individuals with optimistic beliefs or people from Western cultures, or does it reflect a widely held cognitive bias in how people understand the self? To address this (...) question, we tested the good true self theory against two potential boundary conditions that are known to elicit different beliefs about the self as a whole. Study 1 tested whether individual differences in misanthropy—the tendency to view humans negatively—predict beliefs about the good true self in an American sample. The results indicate a consistent belief in a good true self, even among individuals who have an explicitly pessimistic view of others. Study 2 compared true self-attributions across cultural groups, by comparing samples from an independent country and a diverse set of interdependent countries. Results indicated that the direction and magnitude of the effect are comparable across all groups we tested. The belief in a good true self appears robust across groups varying in cultural orientation or misanthropy, suggesting a consistent psychological tendency to view the true self as morally good. (shrink)

ArgumentIt seems theoretically convenient to construe knowledge practices in financial markets and organizations as “applied economics.” Alternatively or additionally, one might argue that practitioners draw on economic knowledge in order to systematically orient their actions towards profit-maximization; models, then, are understood as devices that make calculative rationality possible. However, empirical studies do not entirely confirm these theoretical positions: Practitioners’ actual calculations are often not “framed” by models; organizations and institutions influence the choice and adoption of models; and different professional groups (...) in financial markets have diverging attitudes towards model calculations. In order to account for this diversity, this article proposes the concept ofcultures of economic and financial expertise; the concept focuses on the patterns of knowledge practices and knowledge-related self-definitions of groups within financial organizations and markets; it also facilitates an analysis of the relations between and, more specifically, the hierarchies among different practices and identities. The article then goes on to explore the process of foreign exchange forecasting in a particular bank. The description immediately reveals that two groups are involved in this process: economists and analysts. These groups maintain quite different practices and self-descriptions in relation to models: While the economists in the bank use the models as organizational resources for consistent forecasting procedures and observe data with the help of simple model structures, analysts approach model forecasts from the perspective of critics: They see limits in the variable-centered, as opposed to a “thematic” approach and they disregard a model's imposed temporality. Nevertheless, analysts use model forecasts as anchors for developing their own “paths” and stories about possible future expectation changes in the markets. The specific division of labor between economists and analysts, and specifically the dominant role of analysts in the forecasting process, fit into a larger picture: The rise of institutional investors in the foreign exchange markets and their demand for genuine market knowledge for speculative investment projects has contributed to the rise and dominance of analysts’ culture. (shrink)

This paper attempts to address the question what logical strength theories of truth have by considering such questions as: If you take a theory T and add a theory of truth to it, how strong is the resulting theory, as compared to T? Once the question has been properly formulated, the answer turns out to be about as elegant as one could want: Adding a theory of truth to a finitely axiomatized theory T is more or less equivalent to a (...) kind of abstract consistency statement. A large part of the interest of the paper lies in the way syntactic theories are 'disentangled' from object theories. (shrink)

Many contemporary ethicists use case-based reasoning to reach consistent beliefs about ethical matters. The idea is that particular cases elicit moral intuitions, which provide defeasible reasons to believe in their content. However, most proponents of case-based moral reasoning are not very explicit about how they resolve inconsistencies and how they abstract principles from judgments about particular cases. The aim of this article is to outline a methodology—called Consistency Reasoning Casuistry—for case-based reasoning in ethics. This methodology draws on Richmond Campbell (...) and Victor Kumar’s naturalistic model for the resolution of inconsistencies between the content of intuitions about particular cases. I argue that reasons similar to those that motivate their model also support a more abstract form of moral reasoning that goes beyond mere resolutions of inconsistencies between case judgments and demands the formulation of more abstract moral norms. Consistency Reasoning Casuistry, it is argued, is a good candidate for a methodology for case-based moral reasoning that is in harmony with paradigms of contemporary moral psychology and that can accommodate the methodology implicit in the work of many contemporary ethicists. (shrink)

It is a commonplace in the analytic geometry of physical space-time that an extended straight line segment, having positive length, is treated as “consisting of” unextended points, each of which has zero length. Analogously, time intervals of positive duration are resolved into instants, each of which has zero duration.

Kurt Gödel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Gödel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Göttingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty. His 1940 book, better known by its short title, The Consistency (...) of the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Gödel set forth his proof for this problem. In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk. He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond. (shrink)

ABSTRACT If acting morally can be viewed as acting consistently with a moral principle or rule, then being a person with moral integrity can be viewed as consistently applying moral principles or rules across different types of situations. We advance a view of moral integrity that incorporates three distinct, but interrelated, types of moral consistency: cognitive, emotional and motivational moral consistency. Our approach is based on Self-Determination Theory, a motivational theory that can explain when a moral rule becomes (...) the primary motive for behavior. We argue that moral integrity is achieved when a person acts on the basis of an internal moral system of principles, emotions and motives and provide an account of the way that it develops during a person’s interaction with the environment. (shrink)

After a brief survey of the different meanings of consistency, the study is restricted to consistency understood as non-contradiction of sets of sentences. The philosophical reasons for this requirement are discussed, both in relation to the problem of sense and the problem of truth. The issue of mathematical truth is then addressed, and the different conceptions of it are put in relation with consistency. The formal treatment of consistency and truth in mathematical logic is then considered, (...) with particular attention paid to the relation between syntactic and semantic properties of sets and calculi. After the crisis of mathematical intuition and the dominance of the formalistic view, it seemed that consistency could totally replace the requirement of truth in mathematics, also in the sense that the existence of "objects" of axiomatic systems could be granted by their consistency. A rejection of this claim is presented, whose central point is a detailed analysis of the theorem that any consistent set S of sentences of first order logic has a model. A critical scrutiny shows that this model is very peculiar, being offered by the elements of the same language that is being interpreted, and the satisfiability conditions for any sentence being constituted by the mere fact of belonging to S. Though not being insignificant from a metatheoretical point of view, this theorem fails to endow consistency with an "ontological creativity", that is, with the capability of providing a model ontologically distinct from the language itself. A final discussion regarding the different "ontological regions" and the referential nature of truth clarifies the different aspects of the whole issue discussed. (shrink)

We determine the consistency strength of determinacy for projective games of length ω^2. Our main theorem is that $\Pi _{n + 1}^1$-determinacy for games of length ω^2 implies the existence of a model of set theory with ω + n Woodin cardinals. In a first step, we show that this hypothesis implies that there is a countable set of reals A such that M_n(A), the canonical inner model for n Woodin cardinals constructed over A, satisfies $A = R$ and (...) the Axiom of Determinacy. Then we argue how to obtain a model with ω + n Woodin cardinal from this. We also show how the proof can be adapted to investigate the consistency strength of determinacy for games of length ω^2 with payoff in $R^R\Pi _1^1$ or with σ-projective payoff. (shrink)

There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by Deutsch, which were developed from a consistency condition that assumes that mixed quantum states uniquely describe the physical state of a system. We criticize this choice of consistency condition from an epistemic perspective, i.e., a perspective in which the quantum state represents (...) a state of knowledge about a system. We demonstrate that directly applying Deutsch’s condition when mixed states are treated as representing an observer’s knowledge of a system can conceal time travel paradoxes from the observer, rather than resolving them. To shed further light on the appropriate dynamics for quantum systems traversing CTCs, we make use of a toy epistemic theory with a strictly classical ontology due to Spekkens and show that, in contrast to the results of Deutsch, many of the traditional paradoxical effects of time travel are present. (shrink)

What should individuals do when their firmly held moral beliefs are prima facie inconsistent with their religious beliefs? In this article weoutline several ways of posing such consistency challenges and offer a detailed taxonomy of the various responses available to someone facing a consistency challenge of this sort. Throughout the paper, our concerns are primarily pedagogical: how best to pose consistency challenges in the classroom, how to stimulate discussion of the various responses to them, and how to (...) relate such consistency challenges to larger issues, such as whether scripture is, in general, a reliable guide to truth. (shrink)

This study examined whether holding a status-consistent or status-inconsistent position affected the work satisfaction of college-educated, white-collar employees. The status-consistent group contained 128 women and 118 men. The status-inconsistent group was composed of 89 women and 102 men. Our results indicated that workers in occupations in which the majority of workers are the same gender had significantly higher levels of work satisfaction than those in status-inconsistent occupations. However, subsequent analyses revealed that men and women employed in occupations in which the (...) majority of workers are men had higher levels of work satisfaction than those employed in women-dominated occupations. These findings held when controlling for other work-satisfaction factors, such as individual earnings, hours worked per week, and length of time employed. We suggest that the effect of status consistency on work satisfaction is mediated by the cultural value attached to the occupations men dominate. (shrink)

NOTE TO THE READER - December, 2021 ●●●●● -/- After a long period of time devoted to research in other areas, the author returned to the subject of this paper in a book-length study, CRITIQUE OF IMPURE REASON: Horizons of Possibility and Meaning. In this book (Chapter 11, “The Metalogic of Meaning”), the position developed in the 1982 paper, "Referential Consistency as a Criterion of Meaning", has been substantively revised and several important corrections made. It is recommended that readers (...) read the revised and corrected version that appears in the book, CRITIQUE OF IMPURE REASON. ●●●●● -/- The book is available in a printed edition, ISBN 978-0-578-88646-6, from online booksellers such as Barnes & Noble, Amazon, and through independent bookstores. The book is also available as a freely downloadable _corrected second edition_ eBook, DOI: 10.5281/zenodo.5458352, through PhilSci, PhilPapers, HAL, and other online archives. ●●●●● -/- In addition to the above-mentioned book, readers may find "A Primer on Bartlett's CRITIQUE OF IMPURE REASON" to be useful as a guide to the nearly 900-page CRITIQUE. The primer is available as a free download through PhilPapers. ●●●●● -/- "Referential Consistency as a Criterion of Meaning" describes a logically compelling criterion of meaning — that is, a necessary condition of meaning, one which is non-arbitrary and compelling. One cannot _not_ accept the proposed criterion without self-referential inconsistency. This “metalogical” variety of self-referential inconsistency is new, opening a third category beyond semantical and pragmatical forms of self-referential inconsistency. ●●●●● -/- It is argued that such a criterion of meaning can serve as an instrument of internal criticism for any theoretical framework that permits reference to a class of objects. The paper combines the concern of the logical empiricists to formulate a rigorous meaning criterion, with the analytical interest in identifying and eliminating self-defeating statements through an analysis of the referential structure of theories. ●●●●● -/- The paper is followed by a list of other publications by the author that further develop and extend the ideas presented here. (shrink)

There has been longstanding interest in the consistency of decisions made by research ethics committees in the UK, but most of the evidence has come from single studies submitted to multiple committees. A systematic comparison was carried out of the decisions made on 18 purposively selected applications, each of which was reviewed independently by three different RECs in a single strategic health authority. Decisions on 11 applications were consistent, but disparities were found among RECs on decisions on seven applications. (...) An analysis of the agreement between decisions of RECs yielded an overall measure of agreement of κ = 0.286 , indicating a level of agreement that, although probably better than chance, may be described as “slight”. The small sample size limits the robustness of these findings. Further research on reasons for inconsistencies in decision making between RECs, and on the importance of such inconsistencies for a range of arguments, is needed. (shrink)

It is a well known empirical observation that natural axiomatic theories are pre-well-ordered by consistency strength. For any natural theory $T$, the next strongest natural theory is $T+\mathsf{Con}_T$. We formulate and prove a statement to the effect that the consistency operator is the weakest natural way to uniformly extend axiomatic theories.

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be (...) logically consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations. (shrink)

Relativism is one of the most tenacious theories about truth, with a pedigree as old as philosophy itself. Nearly as ancient is the chief criticism of relativism, namely the charge that the theory is self-refuting. This paper develops a logic of relativism that (1) illuminates the classic self-refutation charge and shows how to escape it; (2) makes rigorous the ideas of truth as relative and truth as absolute, and shows the relations between them; (3) develops an intensional logic for relativism; (...) (4) provides a framework in which relativists can consistently promote ethical, mathematical, scientific, religious, and political truths (among others) as being relative; (5) argues that the notion of incommensurability is far less troubling than is commonly thought; and (6) argues that the concept of a perspective as needed by the theory is not prey to Davidson's well-known critique of conceptual schemes. The paper will not defend relativism as the correct theory of truth, nor will it provide a fully satisfying theory about the nature of a perspective. The logic of relativism is primarily meant to provide a formal framework in which relativists can consistently develop their theories. This alone is a considerable step forward, since the debate about relativism often founders upon the rock of self-refutation. It is argued that while 'everything is relative' is inconsistent, 'everything true is relatively true' is not. The latter is all a relativist really needs. (shrink)

It is generally unquestioned that human subjects research review boards should assess the ethical acceptability of protocols. It says so right on the tin, after all: they are explicitly called research ethics committees in the UK. But it is precisely those sorts of unchallenged assumptions that should, from time to time, be assessed and critiqued, in case they are in fact unfounded. John Stuart Mill's objection to suppressers of dissent is instructive here: “If the opinion is right, they are deprived (...) of the opportunity of exchanging error for truth: if wrong, they lose, what is almost as great a benefit, the clearer perception and livelier impression of truth, produced by its collision with error”.1 Andrew Moore and Andrew Donnelly's compelling article, “The job of ‘ethics committees’”, is just this sort of challenge to conventional wisdom, a rejection of the notion that review boards should be considering ethical matters at all.2 If true, we should be substantially reforming our research ethics policies. And if false, rebuttals would help strengthen and ground the otherwise unquestioned assumption of the role of ethics committees. As it happens, I will argue that their critiques fall into the second category. While mistaken, they present a valuable opportunity to clarify the role of ethics committees and their relationship to relevant codes. In particular, I will defend a hybrid account where codes have strict primacy, but leave significant room for review boards …. (shrink)

In this paper, we present a new semantic challenge to the moral error theory. Its first component calls upon moral error theorists to deliver a deontic semantics that is consistent with the error-theoretic denial of moral truths by returning the truth-value false to all moral deontic sentences. We call this the ‘consistency challenge’ to the moral error theory. Its second component demands that error theorists explain in which way moral deontic assertions can be seen to differ in meaning despite (...) necessarily sharing the same intension. We call this the ‘triviality challenge’ to the moral error theory. Error theorists can either meet the consistency challenge or the triviality challenge, we argue, but are hard pressed to meet both. (shrink)

G. Priest's anti-consistency argument (Priest 1979, 1984, 1987) and J. R. Lucas's anti-mechanist argument (Lucas 1961, 1968, 1970, 1984) both appeal to Gödel incompleteness. By way of refuting them, this paper defends the thesis of quartet compatibility, viz., that the logic of the mind can simultaneously be Gödel incomplete, consistent, mechanical, and recursion complete (capable of all means of recursion). A representational approach is pursued, which owes its origin to works by, among others, J. Myhill (1964), P. Benacerraf (1967), (...) J. Webb (1980, 1983) and M. Arbib (1987). It is shown that the fallacy shared by the two arguments under discussion lies in misidentifying two systems, the one for which the Gödel sentence is constructable and to be proved, and the other in which the Gödel sentence in question is indeed provable. It follows that the logic of the mind can surpass its own Gödelian limitation not by being inconsistent or non-mechanistic, but by being capable of representing stronger systems in itself; and so can a proper machine. The concepts of representational provability, representational maximality, formal system capacity, etc., are discussed. (shrink)

We formalize the notion of Herbrand Consistency in an appropriate way for bounded arithmetics, and show the existence of a finite fragment of IΔ0 whose Herbrand Consistency is not provable in IΔ0. We also show the existence of an IΔ0-derivable Π1-sentence such that IΔ0 cannot prove its Herbrand Consistency.

In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and 1 1-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and (...) T prove the existence of infinitely many non-logical objects (T deriving,moreover, the nonexistence of the value-range concept). Some implications concerning the interpretation of Frege's proof of referentiality and the possibility of classifying any of these subsystems as logicist are discussed. Finally, I explore the relation of T toCantor's theorem which is somewhat surprising. (shrink)

In their insightful article, ‘The Disvalue of Death in the Global Burden of Disease’, Solberg et al argue that there is a potential incoherence in the way disability-adjusted life years are calculated. Morbidity is measured in years lived with disability in a way quite unlike the way mortality is measured in years of life lost. This potentially renders them incommensurable, like apples and oranges, and makes their aggregate—DALYs—conceptually unsound. The authors say that it is ‘vital’ to address this problem, that (...) ‘[n]eglecting [it] is not an option’, and that ‘one cannot add YLLs and YLDs together in [their] current form’.1 Though one might object to their argument in various ways, let us assume the authors are correct that there is a potential inconsistency here. I want to ask why we should be troubled by that. Now, this question may scarcely seem worth asking. Consistency and coherence are regarded as non-negotiable in so many domains that of course we should demand them in a measure such as the DALY. And this desire for coherence is clearly shared by both the architects of the DALY and their critics.2 3 I think, though, that things are more complicated. In 2012, I wrote an article discussing the epidemiological perspective from which DALYs should be calculated.4 Simplifying greatly, here is the problem: both YLDs and YLLs can be calculated either from prevalence data or from incidence data. The most natural way to calculate YLDs bases them on prevalences, because when we think about morbidity our initial thought is of people who are suffering. The most natural way to calculate YLLs bases them on an incidence measure, because when …. (shrink)

The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules.

A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories for propositional modal logic (...) to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making. (shrink)

In this article, I examine two of the standard objections to forms of value hedonism. The first is the common claim, most famously made by Bradley and Moore, that Mill's qualitative hedonism is inconsistent. The second is the apparent problem for quantitative hedonism in dealing with malicious pleasures. I argue that qualitative hedonism is consistent, even if it is implausible on other grounds. I then go on to show how our intuitions about malicious pleasure might be misleading.

In addition to beliefs, people have attitudes of confidence called credences. Combinations of credences, like combinations of beliefs, can be inconsistent. It is common to use tools from probability theory to understand the normative relationships between a person’s credences. More precisely, it is common to think that something is a consistency norm on a person’s credal state if and only if it is a simple transformation of a truth of probability. Though it is common to challenge the right-to-left direction (...) of this biconditional, I argue in this paper that the left-to-right direction is false for standard versions of probability theory. That is, I make the case that there are consistency constraints on credal states that are not simple transformations of truths of standard versions of probability theory. I do so by drawing on a newly discovered type of credal attitude, a quantificational credence, and by showing how the consistency norms on this attitude can’t be represented as simple transformations of truths of standard versions of probability theory. I conclude by showing that a probability theory that could avoid the result would have to be strikingly different from the standard versions—so different that I suspect many would hesitate to call it a theory of probability at all. (shrink)

This paper focuses on tacit versus explicit uses of plural performance metrics as a primary methodological characteristic. This characteristic usefully distinguishes two schools of normative analysis and their approaches to normative interpretations of bounded rationality. Both schools of thought make normative claims about bounded rationality by comparing the performance of decision procedures using more than one performance metric. The consistency school makes tacit reference to performance metrics outside its primary axiomatic framework, but lexicographically promotes internal axiomatic consistency as (...) the primary, and in most cases sufficient, normative outcome with which to undertake welfare comparisons. The consistency school's axiomatization program, in both neoclassical and behavioral forms, pre-commits to welfare interpretations that follow a hierarchy of rationalities based on the stringency of restrictions that different axiomatizations impose on choice data. In contrast, the ecological rational.. (shrink)

We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the universe is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of (...) quantum states which are superpositions of expanding and contracting universes suggests that a “quantum bounce” is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a “quantum bounce” is thus not possible in these models. (shrink)

It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.

I argue that Graham Priest's story 'Sylvan's Box' has an attractive consistent reading. Priest's hope that this story can be used as an example of a non-trivial 'essentially inconsistent' story is thus threatened. I then make some observations about the role 'Sylvan's Box' might play in a theory of unreliable narrators.

Over time, research programs focusing on the processes that underlie dissonance and regret diverged to the point that the present literature only occasionally draws explicit connections between regret and consistency seeking processes. One of our aims in this chapter is to reestablish the connection between regret and consistency within the context of a theory that examines two independent factors that critically interact to enhance or diminish regret. The first of these is opportunity, which includes both perceptions of past (...) opportunities to make alternative choices and future opportunities to take corrective actions, and the second is mitigation, which is the ability to justify one's actions or otherwise engage regulatory processes that allow for the diminishment of regret. We examine both opportunity and mitigation separately before describing how the two may interact to elicit differential experiences of regret. (shrink)

This paper presents proof that Buss's S22 can prove the consistency of a fragment of Cook and Urquhart's PV from which induction has been removed but substitution has been retained. This result improves Beckmann's result, which proves the consistency of such a system without substitution in bounded arithmetic S12. Our proof relies on the notion of "computation" of the terms of PV. In our work, we first prove that, in the system under consideration, if an equation is proved (...) and either its left- or right-hand side is computed, then there is a corresponding computation for its right- or left-hand side, respectively. By carefully computing the bound of the size of the computation, the proof of this theorem inside a bounded arithmetic is obtained, from which the consistency of the system is readily proven. This result apparently implies the separation of bounded arithmetic because Buss and Ignjatović stated that it is not possible to prove the consistency of a fragment of PV without induction but with substitution in Buss's S12. However, their proof actually shows that it is not possible to prove the consistency of the system, which is obtained by the addition of propositional logic and other axioms to a system such as ours. On the other hand, the system that we have considered is strictly equational, which is a property on which our proof relies. (shrink)

John Doris has recently argued that since we do not possess character traits as traditionally conceived, virtue ethics is rooted in a false empirical presupposition. Gopal Sreenivasan has claimed, in a paper in Mind, that Doris has not provided suitable evidence for his empirical claim. But the experiment Sreenivasan focuses on is not one that Doris employs, and neither is it relevantly similar in structure. The confusion arises because both authors use the phrase ‘cross-situational consistency’ to describe the aspect (...) of character traits that they are concerned with, but neither defines this phrase, and it is ambiguous: Doris uses it in one sense, Sreenivasan in another. Partly for this reason, the objections Sreenivasan raises fail to block the argument Doris provides. In particular, the most reliable data Doris employs, Milgram’s famous study of authority, is entirely immune to Sreenivasan’s objections. Sreenivasan has not shown, therefore, that Doris provides unsuitable evidence for his claim. (shrink)

Partial consistency statements can be expressed as polynomial-size propositional formulas. Frege proof systems have polynomial-size partial self-consistency proofs. Frege proof systems have polynomial-size proofs of partial consistency of extended Frege proof systems if and only if Frege proof systems polynomially simulate extended Frege proof systems. We give a new proof of Reckhow's theorem that any two Frege proof systems p-simulate each other. The proofs depend on polynomial size propositional formulas defining the truth of propositional formulas. These are (...) already known to exist since the Boolean formula value problem is in alternating logarithmic time; this paper presents a proof of this fact based on a construction which is somewhat simpler than the prior proofs of Buss and of Buss-Cook- Gupta-Ramachandran. (shrink)

Vindicating the claim that agents ought to be consistent has proved to be a difficult task. Recently, some have argued that we can use accuracy-dominance arguments to vindicate the normativity of such requirements. But what do these arguments prove, exactly? In this paper, I argue that we can make a distinction between two theses on the normativity of consistency: the view that one ought to be consistent and the view that one ought to avoid being inconsistent. I argue that (...) accuracy-dominance arguments for consistency support the latter view, but not necessarily the former. I also argue that the distinction between these two theses matters in the debate on the normativity of epistemic rationality. Specifically, the distinction suggests that there are interesting alternatives to vindicating the strong claim that one ought to be consistent. (shrink)

The relationship between logics with sets of theorems including contradictions (“inconsistent logics”) and theories closed under such logics is investigated. It is noted that if we take “theories” to be defined in terms of deductive closure understood in a way somewhat different from the standard, Tarskian, one, inconsistent logics can have consistent theories. That is, we can find some sets of formulas the closure of which under some inconsistent logic need not contain any contradictions. We prove this in a general (...) setting for a family of relevant connexive logics, extract the essential features of the proof in order to obtain a sufficient condition for the consistency of a theory in arbitrary logics, and finally consider some concrete examples of consistent mathematical theories in Abelian logic. The upshot is that on this way of understanding deductive closure, common to relevant logics, there is a rich and interesting kind of interaction between inconsistent logics and their theories. We argue that this suggests an important avenue for investigation of inconsistent logics, from both a technical and a philosophical perspective. (shrink)

On 17 July 2012, the European Commission formally adopted a proposal for a new European Union (EU) Directive regarding clinical trials, which will repeal and replace the existing Directive 2001/20/EC. The main reasons for the revision were: (1) the decreasing number of clinical trials in the region and (2) harsh criticism of the present version of the Directive. The proposed regulation could simplify the rules for conducting clinical trials and also rebuild the entire system of clinical trial assessment. However, it (...) seems that we probably have already lost our chance regarding the consistency and quality of functioning of research ethics committees in the EU. (shrink)

I argue that a particular restricted version of the Principle of Indiference is a consistent, indispensible tool for guiding our probabilistic judgements.

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differ...