We have seen that despite Feferman's results Gödel's second theorem vitiates the use of Hilbert-type epistemological programs and consistency proofs as a response to mathematical skepticism. Thus consistency proofs fail to have the philosophical significance often attributed to them.This does not mean that consistency proofs are of no interest to philosophers. We know that a ‘non-pathological’ consistency proof for a system S will use methods which are not available in S. When S is as strong a (...) system as we are willing to entertain seriously then a consistency proof for it will yield no epistemological gain. But in other cases philosophers might argue that the proof uses methods which are merely different rather than stronger than those available in the system in question. This claim has been made, for example, in the case of the constructive consistency proofs for elementary number theory. Similar philosophical investigations can be made on relative consistency proofs, since these differ from each other in the principles they employ. For example, most relative consistency proofs can be carried out within elementary number theory, but without using the theory of real numbers, no one has been able to prove the consistency of Quine's ML relative to that of his NF.What about the consistency of all mathematics or of some strong system for set theory? How do we answer the skeptic? Since here a convincing proof is not possible, we have established that the skeptic demands too much. We cannot be certain that our axioms are free from contradiction and must treat them as hypotheses which may be abandoned or modified in the face of further mathematical experience. This attitude is taken by many foundational workers who also go on to voice opinions about thelikelihood that various systems are consistent. Since these opinions are variously supported by appeals to the clarity of the mathematical concept formalized, the existence or non-existence of ‘weird’ models for the system and actual empirical experience with the system, this is surely a fruitful area for philosophical research. (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)

The last section of “Lecture at Zilsel’s” [9, §4] contains an interesting but quite condensed discussion of Gentzen’s first version of his consistency proof for P A [8], reformulating it as what has come to be called the no-counterexample interpretation. I will describe Gentzen’s result (in game-theoretic terms), fill in the details (with some corrections) of Godel's reformulation, and discuss the relation between the two proofs.

In *Cognition and Commitment in Hume's Philosophy*, Don Garrett argues for the coherence of Hume's philosophy when it is viewed as work in cognitive psychology. Without denying this, I argue that there is more to Hume's standpoint than cognitive psychology. Specifically, Hume's standpoint shifts as the level of inquiry changes. A descriptive cognitive psychology is one standpoint that he occupies. However, he occupies other standpoints as well: the commonsense standpoint of the vulgar is one; the radical doubt of the skeptic (...) is another. Such a radical perspectivism is central to Hume's writings. (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)

This book reconstructs the history of skepticism ranging from ancient to contemporary times, from Pyrrho to Kripke. The main skeptical stances and the historical reconstruction of the concept of skepticism are connected with an analysis of their recurrent inconsistency. The author reveals that this inconsistency is not a logical contradiction but a pragmatic one. She shows that it is a contradiction between the content of the skeptical position and the implicit presumption of the act of its assertion. The thesis of (...) global skepticism cannot be accepted as true without falling into the pragmatic inconsistency. The author explains, how skepticism was important for exposing the limits of human knowledge and inspired its development. (shrink)

The business practices of multinational corporations raise many provocative moral issues and offer a touchstone for some fundamental ethical concepts. This essay identifies a wide range of problems but centers on the matter of consistency in corporate policy between foreign and domestic practices and the kind of generality of standards that is required to achieve consistency. Two considerations are singled out for illustrative discussion: wage scales and bribes. Proposals are offered for achieving consistency and generality in each (...) case, the principle of contextual generality for the first and the notion of structural universals for the second. (shrink)

An ambitious ethical theory ---Alan Gewirth's "Principle of Generic Consistency"--- is encoded and analysed in Isabelle/HOL. Gewirth's theory has stirred much attention in philosophy and ethics and has been proposed as a potential means to bound the impact of artificial general intelligence.

Alan Gewirth's _Reason and Morality_, in which he set forth the Principle of Generic Consistency, is a major work of modern ethical theory that, though much debated and highly respected, has yet to gain full acceptance. Deryck Beyleveld contends that this resistance stems from misunderstanding of the method and logical operations of Gewirth's central argument. In this book Beyleveld seeks to remedy this deficiency. His rigorous reconstruction of Gewirth's argument gives its various parts their most compelling formulation and clarifies (...) its essential logical structure. Beyleveld then classifies all the criticisms that Gewirth's argument has received and measures them against his reconstruction of the argument. The overall result is an immensely rich picture of the argument, in which all of its complex issues and key moves are clearly displayed and its validity can finally be discerned. The comprehensiveness of Beyleveld's treatment provides ready access to the entire debate surrounding the foundational argument of _Reason and Morality_. It will be required reading for all who are interested in Gewirth's theory and deontological ethics and will be of central importance to moral and legal theorists. (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)

This study adopts an intrapersonal perspective to explore how and when employees shift roles from help giver to help seeker by investigating the relationship between their help-giving and following help-seeking behavior. Based on self-regulation theory, we hypothesize two contradictory psychological processes (i.e., consistency vs. licensing) via which employees determine whether to seek help after giving help. Importantly, we differentiate autonomous help-seeking from dependent help-seeking and propose stronger effects of help-giving on dependent help-seeking. Further, we identify leader respect as a (...) moderator to solve the opposite effects of employees’ help-giving on their subsequent help-seeking indicated by the two contradictory mechanisms. Results of two field studies consistently showed that the negative (positive) relationship between help-giving and dependent help-seeking was serially mediated by personal reputation and reputation maintenance concerns (perceived increase of moral credits and help-seeking justification). Results regarding autonomous help-seeking were inconsistent and help-giving only positively affected autonomous help-seeking via perceived increase of moral credits and help-seeking justification in Study 2. Leader respect weakened the positive (in Study 1) but strengthened the negative relationship (in Study 1 and 2). We discuss theoretical implications for helping literature, self-regulation theory, and moral behavior research. (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)

In this paper I try to 'rethink' consistency as an educational quality for the 3rd millennium, following Italo Calvino's choice to take it up in his lecture series Memos for the Next Millennium, and despite the fact that the (final) lecture devoted to this quality remained unwritten. After reflecting on how consistency already plays a certain role in Calvino's other lectures, I expand on the specific educational implications of this role's unresolved ambivalence, in order to argue that this (...) ambivalence, properly understood, might be fully constitutive of the educational significance of consistency. To achieve such an understanding I turn to Gilles Deleuze and his concept of style as a 'practice' of consistency. Not only does a stylistic understanding of consistency offer interesting possibilities for a more constructive approach to the said ambivalence—between consistency as static stability and dynamic keeping-together- but as such it also speaks to a number of issues that are directly and fundamentally educational in nature. (shrink)

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)

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)

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)

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)

Medeiros et al. implement a mixed methods approach to explore the mechanisms underlying individual transformation during mindfulness-based interventions. We provide critiques, questions and ….

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)

I argue that the medieval form of dialectical disputation known as obligationes can be viewed as a logical game of consistency maintenance. The game has two participants, Opponent and Respondent. Opponent puts forward a proposition P; Respondent must concede, deny or doubt, on the basis of inferential relations between P and previously accepted or denied propositions, or, in case there is none, on the basis of the common set of beliefs. Respondent loses the game if he concedes a contradictory (...) set of propositions. Opponent loses the game if Respondent is able to maintain consistency during the stipulated period of time. The obligational rules are here formalised by means of familiar notational devices, and the application of some game-theoretical concepts, such as (winning) strategy, moves, motivation, allows for an analysis of some crucial properties of the game. In particular, the primacy of inferential (syntactic) relations over semantic aspects and the dynamic character of obligations are outlined. (shrink)

We examined the relation between home literacy environment (HLE) and early literacy development in a sample of children learning four alphabetic orthographies varying in orthographic consistency (English, Dutch, German, and Greek). Seven hundred and fourteen children were followed from Grade 1 to Grade 2 and tested on emergent literacy skills (vocabulary, letter knowledge, and phonological awareness) at the beginning of Grade 1 and on word reading fluency and spelling at the end of Grade 1, the beginning of Grade 2, (...) and the end of Grade 2. Their parents responded to a questionnaire assessing HLE [parent teaching (PT), shared book reading (SBR), access to literacy resources (ALR)] at the beginning of Grade 1. Results showed first that PT was associated with letter knowledge or phonological awareness in Dutch and Greek, while ALR was associated with emergent literacy skills in all languages. SBR did not predict any cognitive or early literacy skills in any language. Second, PT and ALR had indirect effects on literacy outcomes via different emergent literacy skills in all languages. These findings suggest that not all HLE components are equally important for emergent literacy skills, reading fluency, and spelling. No specific trend in the role of orthographic consistency in the aforementioned relations emerged, which suggests that other factors may account for the observed differences across languages when children start receiving formal reading instruction in Grade 1. (shrink)

It is argued that accepting that there are human rights, or that there are categorically binding requirements of any kind on action, logically requires accepting the PGC (Principle of Generic Consistency) as the supreme criterion of practical reasonableness.Consequently, all legal systems that recognise human rights (hence, the English legal system), all who view law as a matter of obligation, and all who consider that there are categorically binding requirements on action, must take the PGC to be a necessary criterion (...) of legal validity. Conventions on human rights must, as conventions on human rights, be interpreted to conform with the PGC. (shrink)

The paper investigates inaccessible set axioms and their consistency strength in constructive set theory. In ZFC inaccessible sets are of the form Vκ where κ is a strongly inaccessible cardinal and Vκ denotes the κth level of the von Neumann hierarchy. Inaccessible sets figure prominently in category theory as Grothendieck universes and are related to universes in type theory. The objective of this paper is to show that the consistency strength of inaccessible set axioms heavily depend on the (...) context in which they are embedded. The context here will be the theory CZF− of constructive Zermelo–Fraenkel set theory but without -Induction . Let INAC be the statement that for every set there is an inaccessible set containing it. CZF−+INAC is a mathematically rich theory in which one can easily formalize Bishop style constructive mathematics and a great deal of category theory. CZF−+INAC also has a realizability interpretation in type theory which gives its theorems a direct computational meaning. The main result presented here is that the proof theoretic ordinal of CZF−+INAC is a small ordinal known as the Feferman–Schütte ordinal Γ0. (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)

We give a simple and direct proof that super-consistency implies the cut-elimination property in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes ideas from the semantic proofs of cut elimination that proceed by proving the completeness of the cut-free calculus. As an application, we compare our work with the cut-elimination theorems in higher-order logic that involve V-complexes.

This paper is a critical analysis of Putnam’s “consistency objection,” an objection made against a particular reading of Wittgenstein’s philosophy of mathematics (“up-to-us-ism”). I show that Putnam’s objection presupposes a rather unlikely version of Wittgenstein’s “up-to-us-ism” and is unable to undermine a more likely anti-Platonist version. I also show that a companion argument, (the “something more” argument) is unable to overturn this more sophisticated anti-Platonist version of Wittgenstein’s up-to-us-ism. Along the way I try to clarify Wittgenstein’s anti-Plalonist account of (...) mathematics, so that others do not repeat Putnam’s mistake. (shrink)