The lottery paradox has been discussed widely. The standard solution to the lottery paradox is that a ticket holder is justified in believing each ticket will lose but the ticket holder is also justified in believing not all of the tickets will lose. If the standard solution is true, then we get the paradoxical result that it is possible for a person to have a justified set of beliefs that she knows is inconsistent. In this paper, I argue that the (...) best solution to the paradox is that a ticket holder is not justified in believing any of the tickets are losers. My solution avoids the paradoxical result of the standard solution. The solution I defend has been hastily rejected by other philosophers because it appears to lead to skepticism. I defend my solution from the threat of skepticism and give two arguments in favor of my conclusion that the ticket holder in the original lottery case is not justified in believing that his ticket will lose. (shrink)

Niko Kolodny It is often said that there is a special class of norms, ‘rational requirements’, that demand that our attitudes be related one another in certain ways, whatever else may be the case.1 In recent work, a special class of these rational requirements has attracted particular attention: what I will call ‘requirements of formal coherence as such’, which require just that our attitudes be formally coherent.2 For example, we are rationally required, if we believe something, to believe what it (...) entails. And we are rationally required, if we intend an end, to intend what we take to be necessary means to it. The intuitive idea is that formally incoherent attitudes give rise to a certain normative tension, or exert a kind of rational pressure on each another, and this tension, or pressure, is relieved just when one of the attitudes is revised. As John Broome observes, these requirements are, by their nature, ‘wide scope’, which is to say that there is no particular attitude that one must have or lack in order to satisfy them. This is because they require just formal coherence, and there is no particular attitude that one must have or lack in order to be formally coherent. (shrink)

In this paper, we propose the introduction of a neutrosophic chi-square-test for consistency, incorporating neutrosophic statistics. Our aim is to modify the existing chi-square -test for consistency in order to analyze imprecise data. We present a novel test statistic for the neutrosophic chi-square -test for consistency, which accounts for the uncertainties inherent in the data. To evaluate the performance of the proposed test, we compare it with the traditional chi-square -test for consistency based on classical statistics. (...) By conducting a comparative analysis, we assess the efficiency and effectiveness of our proposed neutrosophic chi-square-test for consistency. Furthermore, we illustrate the application of the proposed test through a numerical example, demonstrating how it can be utilized in practical scenarios. Through this implementation, we aim to provide empirical evidence of the improved performance of our proposed test when compared to the traditional chi-square-test for consistency based on classical statistics. We anticipate that the proposed neutrosophic chi-square-test for consistency will outperform its classical counterpart, offering enhanced accuracy and reliability when dealing with imprecise data. This advancement has the potential to contribute significantly to the field of statistical analysis, particularly in situations where data uncertainty and imprecision are prevalent. (shrink)

In the 1920s, Ackermann and von Neumann, in pursuit of Hilbert's programme, were working on consistency proofs for arithmetical systems. One proposed method of giving such proofs is Hilbert's epsilon-substitution method. There was, however, a second approach which was not reflected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert's first epsilon theorem and a certain "general consistency result" due to Bernays. An analysis of the form of this so-called (...) "failed proof" sheds further light on an interpretation of Hilbert's programme as an instrumentalist enterprise with the aim of showing that whenever a "real" proposition can be proved by ?ideal? means, it can also be proved by "real", finitary means. (shrink)

Pantheists commonly wish to hold three distinct theses: that God is identical with the universe as a whole, that God is to be found altogether in each part of the universe, and that some features of the universe are more divine than others. However, it might well be complained that these constitute an incompatible set of requirements on any theory. After outlining the three positions in question, this paper considers how successfully the four main species of pantheist metaphysic — the (...) substance monist model, the microcosmic-macrocosmic model, the universal-expressivist model, and the Absolute Idealist model — are able to respond to the problem of their compatibility. (shrink)

Thought: A Journal of Philosophy, EarlyView.

The aim of this study was to investigate the consistency between the self-reports and teacher ratings of students’ emotional and social inclusion at school as well as for their academic self-concept. The German version of the Perceptions of Inclusion Questionnaire (PIQ) was administered to 329 grade 8 students (50.8% female, Mage = 14.5 years, SDage = 0.5 years) and their teachers. First, the three-dimensional structure of both PIQ versions was confirmed by confirmatory item factor analysis. The  and  (...) coefficients demonstrated good reliability for all scales. Second, a correlated trait-correlated method minus one model provided evidence that the method-specificity of teacher ratings was larger than the consistency between the self-reports and teacher ratings. Third, the results of a latent difference model indicated that general method effects can partly be explained by a student’s gender or special educational needs. Finally, the low consistency between self-reports and teacher rating is discussed. (shrink)

Tragic choices arise during the COVID-19 pandemic when the limited resources made available in acute medical settings cannot be accessed by all patients who need them. In these circumstances, healthcare rationing is unavoidable. It is important in any healthcare rationing process that the interests of the community are recognised, and that decision-making upholds these interests through a fair and consistent process of decision-making. Responding to recent calls to safeguard individuals’ legal rights in decision-making in intensive care, and for new authoritative (...) national guidance for decision-making, this paper seeks to clarify what consistency and fairness demand in healthcare rationing during the COVID-19 pandemic, from both a legal and ethical standpoint. The paper begins with a brief review of UK law concerning healthcare resource allocation, considering how community interests and individual rights have been marshalled in judicial deliberation about the use of limited health resources within the National Health Service. It is then argued that an important distinction needs to be drawn between procedural and outcome consistency, and that a procedurally consistent decision-making process ought to be favoured. Congruent with the position that UK courts have adopted for resource allocation decision-making in the NHS more generally, specific requirements for a procedural framework and substantive triage criteria to be applied within that framework during the COVID-19 pandemic are considered in detail. (shrink)

A moral dilemma is a situation in which an agent ought to do each of two actions, Both of which he cannot do. If there are genuine moral dilemmas, The ethical theorist is presented with a problem: he must reject several very plausible principles of standard deontic logic. The main reasons usually given to show that there are moral dilemmas are examined, And it is argued that they are not sufficient. Several positive arguments are then presented, Arguments which try to (...) show that an adequate moral theory must rule out the possibility of genuine dilemmas. (shrink)

Moore and Donnelly argue in the paper ‘The job of “ethics committees”’ that research ethics committees should be renamed and that their job should be specified as “review of proposals for consistency with the duly established and applicable code” only.1 They raise a large number of issues, but in this comment I briefly want to suggest that two of their arguments are fundamentally flawed. The first flawed argument is the argument related to the separation of powers. Moore and Donnelly (...) proceed from the premise that it is pro tanto better to have an institutional arrangement that separates code-making powers and decisional powers, and then proceed to argue that this separation is not feasible for what they call ‘ethics consistency review’ because “no matter who established any prespecified review standards, the review decision maker must be empowered at review to revise those standards when this would make for an ethical improvement. This is because any understanding of ethics-consistency standards themselves and of their implications for any case is fallible and improvable in …. (shrink)

Stephen Yablo [23,24] introduces a new informal paradox, constituted by an infinite list of semi-formalized sentences. It has been shown that, formalized in a first-order language, Yablo’s piece of reasoning is invalid, for it is impossible to derive falsum from the sequence, due mainly to the Compactness Theorem. This result casts doubts on the paradoxical character of the list of sentences. After identifying two usual senses in which an expression or set of expressions is said to be paradoxical, since second-order (...) languages are not compact, I study the paradoxicality of Yablo’s list within these languages. While non-paradoxical in the first sense, the second-order version of the list is a paradox in our second sense. I conclude that this suffices for regarding Yablo’s original list as paradoxical and his informal argument as valid. (shrink)

R. Jay Wallace argues that the normativity of instrumental rationality can be traced to the independent rational requirement to hold consistent beliefs. I present three objections to this view. John Broome argues that there is a structural similarity between the rational requirements of instrumental rationality and belief consistency. Since he does not reduce the former to the latter, his view can avoid the objections to Wallace’s view. However, we should not think Broome’s account explains the whole of instrumental rationality (...) since agents with consistent intentions can still fail in their instrumental reasoning. This consideration makes Broome’s approach vulnerable to a line of criticism that both he and Wallace present against Christine Korsgaard’s conception of instrumental rationality. (shrink)

Summary The article substantiates the possibility and meaningfulness of a coherent theoretical system for psychotherapy, as it is strived for in Gestalt Theoretical Psychotherapy and presented in several articles in this issue of the journal "Gestalt Theory". The necessity of consistency in the theoretical assumptions and concepts of a psychotherapy method is not derived from scientific considerations alone, but already arises from the elementary role of consistency in human life. This also results in the requirements for the (...) class='Hi'>consistency of theoretical foundations of psychotherapy. It is not fulfilled in a mere internal, logical consistency of its models, but only in the actual fitting together with the critical-phenomenal and naive-phenomenal worlds of the therapists and their clients in the reality test of life. (shrink)

We introduce a nonstandard arithmetic $NQA^-$ based on the theory developed by R. Chuaqui and P. Suppes in [2] (we will denote it by $NQA^+$ ), with a weakened external open minimization schema. A finitary consistency proof for $NQA^-$ formalizable in PRA is presented. We also show interesting facts about the strength of the theories $NQA^-$ and $NQA^+$ ; $NQA^-$ is mutually interpretable with $I\Delta_0 + EXP$ , and on the other hand, $NQA^+$ interprets the theories IΣ1 and $WKL_0$.

In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic BKc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending BKc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent logics.

Branching theories are popular frameworks for modeling objective indeterminism in the form of a future of open possibilities. In such theories, the notion of a history plays a crucial role: it is both a basic ingredient in the axiomatic definition of the framework, and it is used as a parameter of truth in semantics for languages with a future tense. Furthermore, histories—complete possible courses of events—ground the notion of modal consistency: a set of events is modally consistent iff there (...) is a history containing that set. We will explain these roles of histories and highlight some critical aspects having to do with the fact that histories are global and, in a relevant sense, “big” objects. The notion of modal consistency, on the other hand, has both local and global aspects. We ask in how far a local notion of modal consistency can serve as an alternative to the common uses of histories, and work out two recent approaches to alternatives to histories. Combining these approaches, we develop a novel semantics for branching time. (shrink)

We prove an institutional version of A. Robinson ’s Consistency Theorem. This result is then appliedto the institution of many-sorted first-order predicate logic and to two of its variations, infinitary and partial, obtaining very general syntactic criteria sufficient for a signature square in order to satisfy the Robinson consistency and Craig interpolation properties.

For “natural enough” systems of ordinal notation we show that α times iterated local reflection schema over a sufficiently strong arithmetic T proves the same Π 1 0 -sentences as ω α times iterated consistency. A corollary is that the two hierarchies catch up modulo relative interpretability exactly at ε-numbers. We also derive the following more general “mixed” formulas estimating the consistency strength of iterated local reflection: for all ordinals α ⩾ 1 and all β, β ≡ Π (...) 1 0 T ω α · , α ≡ Π 1 0 T β + ω α . Here T α stands for α times iterated local reflection over T , T β stands for β times iterated consistency, and ≡ Π 1 0 denotes mutual Π 1 0 -conservativity. In an appendix to this paper we develop our notion of “natural enough” system of ordinal notation and show that such systems do exist for every recursive ordinal. (shrink)

Immanuel Kant is one of Alain Badiou’s principle philosophical enemies. Kant’s critical philosophy is anathema to Badiou not only because of the latter’s openly aired hatred of the motif of finitude so omnipresent in post-Kantian European intellectual traditions—Badiou blames Kant for inventing this motif—but also because of its idealism. For Badiou-the-materialist, as for any serious philosophical materialist writing in Kant’s wake, transcendental idealism must be dismantled and overcome. In his most recent works, Badiou attempts to invent a non-Kantian notion of (...) the transcendental, a notion compatible with the basic tenets of materialism. However, from 1988’s Being and Event up through the present, Badiou’s oeuvre contains indications that he hasn’t managed fully to purge the traces of Kantian transcendental idealism that arguably continue to haunt his system—with these traces clustering around a concept Badiou christens “counting-for-one”. The result is that, in the end, Kant’s shadow still falls over Badiouian philosophy—this is despite Badiou’s admirable, sophisticated, and instructive attempts to step out from under it—thus calling into question this philosophy’s self-proclaimed status as materialist through and through. (shrink)

This paper defends the claim that mere temporal proximity always and without exception strengthens certain moral duties, including the duty to save – call this view Robust Temporalism. Although almost all other moral philosophers dismiss Robust Temporalism out of hand, I argue that it is prima facie intuitively plausible, and that it is analogous to a view about special obligations that many philosophers already accept. I also defend Robust Temporalism against several common objections, and I highlight its relevance to a (...) number of practical policy debates, including longtermism. My conclusion is that Robust Temporalism is a moral live option, that deserves to be taken much more seriously in the future. (shrink)

Imagine a sculptor who molds a lump of clay to create a statue. Hylomorphism claims that the statue and the lump of clay are two different colocated objects that have different forms, even though they share the same matter. Recently, there has been some discussion on the requirements of consistency for hylomorphist theories. In this paper, we focus on an argument presented by Maegan Fairchild, according to which a minimal version of hylomorphism is inconsistent. We argue that the argument (...) is unsound or, at best, it just points to a well-known problem for hylmorphist theories. Additionally, we explore some general consequences of this fact. (shrink)

Rule-consequentialism has been accused of either collapsing into act-consequentialism or being internally inconsistent. I have tried to develop a form of rule-consequentialism without these flaws. In this June's issue of Utilitas, Robert Card argued that I have failed. Here I assess his arguments.

Moral conflicts are real, and while a deontic logic containing a modified "agglomeration rule" may be able to accommodate this fact, even the most sophisticated logic will still overlook much of what everyday normative reasoning involves.

It is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.

In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not necessarily related to the notion (...) of formal consistency. (shrink)

This paper attempts to address the question of how multilingualism in the EU might affect the consistency of private enforcement of competition law. In the literature, there have been concerns raised about the consistency of public enforcement of competition law, so in this paper attention has shifted to concerns about consistency of private enforcement. For the purposes of this paper, a distinction is drawn between rule-making and the application of competition law. The latter falls outside the scope (...) of this paper. The article starts by going straight into aspects of public versus private enforcement of EU competition law and consistency of private enforcement of competition law. Next, by looking at examples of national rules implementing the EU Damages Directive, the author is going to discern what challenges for consistency of private enforcement of competition law are associated with the multilingualism in the EU. (shrink)

We consider a society whose members have to choose not only an outcome from a given set of outcomes but also a subset of agents that will remain members of the society. We study the extensions of approval voting, scoring methods and the Condorcet winner to our setting from the point of view of their internal stability and consistency properties.

This article explores Alan Gewirth’s argument for a secular foundation for the idea 2 of human rights as a possible response to Michael J. Perry’s claim “that the idea of 3 human rights is…ineliminably religious.” I examine Gewirth’s reasoning for constructing 3 a theory, namely that existing theories are fundamentally flawed and leave the idea of human rights without a logically consistent foundation, before considering in detail his claims for the Principle of Generic Consistency (PGC). Having looked at his (...) critique of numerous other theories, as well as at his own argument about human action grounding basic rights to freedom and well-being, I then offer a critique of Gewirth’s PGC. Ultimately my conclusion is that Gewrith's 3 theory relies too heavily on the notions, first that we have a meta-desire not to contradict ourselves and, second, that we are unable to find persuasive justifications for our behavior that might allow us to avoid self-contradiction. If one is not troubled by charges of self-contradiction or, as is more often the case, one does not recognize that one’s victim is as much a human being as oneself, Gewirth’s theory 5 V 3 will not seem particularly persuasive. *** DIRECT SUPPORT *** A28BB025 00003. (shrink)