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)

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.

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)

It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive (...) diagnoses of the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible. (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.

The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in mathematical formulation and in intended scope, into the principle of maximum relative entropy or of minimum information. It has been claimed that these principles are singled out as unique methods of statistical inference that agree with (...) certain compelling consistency requirements. This paper reviews these consistency arguments and the surrounding controversy. It is shown that the uniqueness proofs are flawed, or rest on unreasonably strong assumptions. A more general class of inference rules, maximizing the so-called Re[acute ]nyi entropies, is exhibited which also fulfill the reasonable part of the consistency assumptions. (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 generalize a previous result about dynamically consistent menu preferences to the case where preferences are not necessarily complete. We show that, as it is the case when preferences are complete, a subjective state space version of dynamic consistency is linked to a comparative theory of preference for flexibility. In words, an objective signal is interpreted as an event in the agent’s subjective state space and the agent acts in a dynamically consistent way after that if and only if (...) we can attribute all the differences between the agent’s preferences before and after the signal to the fact that the agent values flexibility more before the signal than after. (shrink)

We consider the problem about the length of proofs of the sentences $\operatorname{Con}_S(\underline{n})$ saying that there is no proof of contradiction in S whose length is ≤ n. We show the relation of this problem to some problems about propositional proof systems.

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)

Cross-cultural comparisons often investigate values that are assumed to have long-lasting influence on human conduct and thought. To capture and compare cultural values across cultures, Geert Hofstede's Cultural Dimensions Theory has offered an influential framework. Hofstede also provided a survey instrument, the Values Survey Module (VSM), for measuring cultural values as outlined in his Cultural Dimensions Theory. The VSM has since been subject to a series of revisions. Yet, data on countries have been derived from the original VSM — and (...) not on one of the revised versions of VSM. We tested three scales (indulgence, power distance, and individualism) from the latest version, the VSM 2013, as part of a larger survey across 57 countries. Two main findings emerged. For one thing, country scores based on the VSM 2013 scales correlated only weakly with country scores of the same cultural dimensions obtained in a large previous study. Thus, the validity of the VSM 2013 is in doubt. For another thing, the internal consistency of the VSM 2013 scales was overall poor, indicating that the scales did not reliably measure well-defined constructs. We discuss implications for cross-cultural research. (shrink)

Thought: A Journal of Philosophy, EarlyView.

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)

In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the “generalized positive” theory GPK∞+. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK∞+ interprets the Kelley Morse class theory. Here we prove that GPK∞+ + ACWF and the Kelley-Morse class theory with the axiom of global choice and the axiom “On is ramifiable” are mutually interpretable. This shows that GPK∞+ + ACWF is a “strong” theory since “On (...) is ramifiable” implies the existence of a proper class of inaccessible cardinals. (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)

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.

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)

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)

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)

In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency (_LFI_) a more appealing formalism for reasoning under uncertainty, it is important to develop the proof theory of the first-order versions of such _LFI_s. Here, we intend to make a first step in this direction. On the other hand, the logic _Ciore_ was developed to provide new logical systems in the study of inconsistent databases from the point of view of _LFI_s. (...) An interesting fact about _Ciore_ is that it has a _strong_ consistency operator, that is, a consistency operator which (forward/backward) propagates inconsistency. Also, it turns out to be an algebraizable logic (in the sense of Blok and Pigozzi) that can be characterized by means of a 3-valued logical matrix. Recently, a first-order version of _Ciore_, namely _QCiore_, was defined preserving the spirit of _Ciore_, that is, without introducing unexpected relationships between the quantifiers. Besides, some important model-theoretic results were obtained for this logic. In this paper we study some proof–theoretic aspects of both _Ciore_ and _QCiore_ respectively. In first place, we introduce a two-sided sequent system for _Ciore_. Later, we prove that this system enjoys the cut-elimination property and apply it to derive some interesting properties. Later, we extend the above-mentioned system to first-order languages and prove completeness and cut-elimination property using the well-known Shütte’s technique. (shrink)

We have avoided here the term \false", since we do not want to commit ourselves to the view that A is false precisely when it is not true. Our formulation of the intuition is therefore obviously circular, but this is unavoidable in intuitive informal characterizations of basic connectives and quanti ers.

The 1-consistency of arithmetic is shown to be equivalent to the existence of fixed points of a certain type of update procedure, which is implicit in the epsilon-substitution method.

In order to handle inconsistent knowledge bases in a reasonable way, one needs a logic which allows nontrivial inconsistent theories. Logics of this sort are called paraconsistent. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa’s approach, which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely differently when contradictions are involved. Da Costa’s approach has led to the family of logics (...) of formal (in)consistency (LFIs). In this paper we provide in a modular way simple non-deterministic semantics for 64 of the most important logics from this family. Our semantics is 3-valued for some of the systems, and infinite-valued for the others. We prove that these results cannot be improved: neither of the systems with a three-valued non-deterministic semantics has either a finite characteristic ordinary matrix or a two-valued characteristic non-deterministic matrix, and neither of the other systems we investigate has a finite characteristic non-deterministic matrix. Still, our semantics provides decision procedures for all the systems investigated, as well as easy proofs of important proof-theoretical properties of them. (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.

This paper connects veritistic teleological epistemology, VTE, with the epistemological dimension of the scientific realism debate. VTE sees our epistemic activities as a tradeoff between believing truths and avoiding error. I argue that van Fraassen’s epistemology is not suited to give a justification for a crucial presupposition of his Bad Lot objection to inference to the best explanation (IBE), the presupposition that believing that p is linked to p being more likely to be true. This makes him vulnerable to a (...) counterargument, tailored after Musgrave’s defense of IBE, which would result in a stalemate between them about presuppositions of rationality. I will, however, show that switching to VTE can justify van Fraassen’s presupposition. This leads to a dismissal of common IBE arguments for realism as presented by Boyd and Musgrave, but I also argue that a more cautious version of realism can be rescued from the Bad Lot objection. Finally, I raise some worries about epistemic risk-attitude consistency for constructive empiricists and develop an alternative anti-realist position.1. (shrink)

In this paper I present a new way of understanding Dutch Book Arguments: the idea is that an agent is shown to be incoherent iff he would accept as fair a set of bets that would result in a loss under any interpretation of the claims involved. This draws on a standard definition of logical inconsistency. On this new understanding, the Dutch Book Arguments for the probability axioms go through, but the Dutch Book Argument for Reflection fails. The question of (...) whether we have a Dutch Book Argument for Conditionalization is left open. (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)

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)

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)