This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the (...) semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property. (shrink)

The second volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents a deep exploration of the progress in uncertain combinatorics through innovative methodologies like graphization, hyperization, and uncertainization. This volume integrates foundational concepts from fuzzy, neutrosophic, soft, and rough set theory, among others, to further advance the field. Combinatorics and set theory, two central pillars of mathematics, focus on counting, arrangement, and the study of collections under defined rules. Combinatorics excels in handling (...) uncertainty, while set theory has evolved with concepts such as fuzzy and neutrosophic sets, which enable the modeling of complex real-world uncertainties by addressing truth, indeterminacy, and falsehood. These advancements, when combined with graph theory, give rise to novel forms of uncertain sets in "graphized" structures, including hypergraphs and superhypergraphs. Innovations such as Neutrosophic Oversets, Undersets, and Offsets, as well as the Nonstandard Real Set, build upon traditional graph concepts, pushing both theoretical and practical boundaries. The synthesis of combinatorics, set theory, and graph theory in this volume provides a robust framework for addressing the complexities and uncertainties inherent in both mathematical and real-world systems, paving the way for future research and application. In the first chapter, “A Review of the Hierarchy of Plithogenic, Neutrosophic, and Fuzzy Graphs: Survey and Applications”, the authors investigate the interrelationships among various graph classes, including Plithogenic graphs, and explore other related structures. Graph theory, a fundamental branch of mathematics, focuses on networks of nodes and edges, studying their paths, structures, and properties. A Fuzzy Graph extends this concept by assigning a membership degree between 0 and 1 to each edge and vertex, representing the level of uncertainty. The Turiyam Neutrosophic Graph is introduced as an extension of both Neutrosophic and Fuzzy Graphs, while Plithogenic graphs offer a potent method for managing uncertainty. The second chapter, “Review of Some Superhypergraph Classes: Directed, Bidirected, Soft, and Rough”, examines advanced graph structures such as directed superhypergraphs, bidirected hypergraphs, soft superhypergraphs, and rough superhypergraphs. Classical graph classes include undirected graphs, where edges lack orientation, and directed graphs, where edges have specific directions. Recent innovations, including bidirected graphs, have sparked ongoing research and significant advancements in the field. Soft Sets and their extension to Soft Graphs provide a flexible framework for managing uncertainty, while Rough Sets and Rough Graphs address uncertainty by using lower and upper approximations to handle imprecise data. Hypergraphs generalize traditional graphs by allowing edges, or hyperedges, to connect more than two vertices. Superhypergraphs further extend this by allowing both vertices and edges to represent subsets, facilitating the modeling of hierarchical and group-based relationships. The third chapter, “Survey of Intersection Graphs, Fuzzy Graphs, and Neutrosophic Graphs”, explores the intersection graph models within the realms of Fuzzy Graphs, Intuitionistic Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. The chapter highlights their mathematical properties and interrelationships, reflecting the growing number of graph classes being developed in these areas. Intersection graphs, such as Unit Square Graphs, Circle Graphs, and Ray Intersection Graphs, are crucial for understanding complex graph structures in uncertain environments. The fourth chapter, “Fundamental Computational Problems and Algorithms for SuperHyperGraphs”, addresses optimization problems within the SuperHypergraph framework, such as the SuperHypergraph Partition Problem, Reachability, and Minimum Spanning SuperHypertree. The chapter also adapts classical problems like the Traveling Salesman Problem and the Chinese Postman Problem to the SuperHypergraph context, exploring how hypergraphs, which allow hyperedges to connect more than two vertices, can be used to solve complex hierarchical and relational problems. The fifth chapter, “A Short Note on the Basic Graph Construction Algorithm for Plithogenic Graphs”, delves into algorithms designed for Plithogenic Graphs and Intuitionistic Plithogenic Graphs, analyzing their complexity and validity. Plithogenic Graphs model multi-valued attributes by incorporating membership and contradiction functions, offering a nuanced representation of complex relationships. The sixth chapter, “Short Note of Bunch Graph in Fuzzy, Neutrosophic, and Plithogenic Graphs”, generalizes traditional graph theory by representing nodes as groups (bunches) rather than individual entities. This approach enables the modeling of both competition and collaboration within a network. The chapter explores various uncertain models of bunch graphs, including Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. In the seventh chapter, “A Reconsideration of Advanced Concepts in Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, and Chemical Graphs”, the authors extend several fuzzy graph classes to Neutrosophic graphs and analyze their properties. Neutrosophic Graphs, a generalization of fuzzy graphs, incorporate degrees of truth, indeterminacy, and falsity to model uncertainty more effectively. The eighth chapter, “Short Note of Even-Hole-Graph for Uncertain Graph”, focuses on Even-Hole-Free and Meyniel Graphs analyzed within the frameworks of Fuzzy, Neutrosophic, Turiyam Neutrosophic, and Plithogenic Graphs. The study investigates the structure of these graphs, with an emphasis on their implications for uncertainty modeling. The ninth chapter, “Survey of Planar and Outerplanar Graphs in Fuzzy and Neutrosophic Graphs”, explores planar and outerplanar graphs, as well as apex graphs, within the contexts of fuzzy, neutrosophic, Turiyam Neutrosophic, and plithogenic graphs. The chapter examines how these types of graphs are used to model uncertain parameters and relationships in mathematical and real-world systems. The tenth chapter, “General Plithogenic Soft Rough Graphs and Some Related Graph Classes”, introduces and explores new concepts such as Turiyam Neutrosophic Soft Graphs and General Plithogenic Soft Graphs. The chapter also examines models of uncertain graphs, including Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Graphs, all designed to handle uncertainty in diverse contexts. The eleventh chapter, “Survey of Trees, Forests, and Paths in Fuzzy and Neutrosophic Graphs”, provides a comprehensive study of Trees, Forests, and Paths within the framework of Fuzzy and Neutrosophic Graphs. This chapter focuses on classifying and analyzing graph structures like trees and paths in uncertain environments, contributing to the ongoing development of graph theory in the context of uncertainty. (shrink)

Brad Hooker; II*—Rule-Consequentialism, Incoherence, Fairness1, Proceedings of the Aristotelian Society, Volume 95, Issue 1, 1 June 1995, Pages 19–36, https://d.

Rule-Consequentialism faces “the problem of partial acceptance”: How should the ideal code be selected given the possibility that its rules may not be universally accepted? A new contender, “Calculated Rates” Rule-Consequentialism claims to solve this problem. However, I argue that Calculated Rates merely relocates the partial acceptance question. Nevertheless, there is a significant lesson from this failure of Calculated Rates. Rule-Consequentialism’s problem of partial acceptance is more helpfully understood as an instance of the broader problem of selecting (...) the ideal code given various assumptions—assumptions about who will accept and comply with the rules, but also about how the rules will be taught and enforced, and how similar the future will be. Previous rich discussions about partial acceptance provide a taxonomy and groundwork for formulating the best version of Rule-Consequentialism. (shrink)

I introduce an account of when a rule normatively sustains a practice. My basic proposal is that a rule normatively sustains a practice when the value achieved by following the rule explains why agents continue following that rule, thus establishing and sustaining a pattern of activity. I apply this model to practices of belief management and identifies a substantive normative connection between knowledge and belief. More specifically, I proposes one special way that knowledge might set the (...) normative standard for belief: knowing is essentially the unique way of normatively sustaining cognition and, thereby, inquiry. In this respect, my proposal can be seen as one way of elaborating a “knowledge-first” normative theory. (shrink)

‘Rule-following’ is a name for a cluster of phenomena where we seem both guided and “normatively” constrained by something general in performing particular actions. Understanding the phenomenon is important because of its connection to meaning, representation, and content. This article gives an overview of the philosophical discussion of rule-following with emphasis on Kripke’s skeptical paradox and recent work on possible solutions. Part I of this two-part contribution is devoted to the basic issues from Wittgenstein to Kripke. Part II (...) will be about recent answers to the skeptical paradox and Boghossian’s and Wright’s new puzzles. (shrink)

What are rules? In this paper I develop a view of regulative rules which takes them to be a distinctive normative kind occupying a middle ground between orders and normative truths. The paradigmatic cases of regulative rules that I’m interested in are social rules like rules of etiquette and legal rules like traffic rules. On the view I’ll propose, a rule is a general normative content that is in force due to human activity: enactment by an authority or acceptance (...) by a community. Rules are unlike orders in being not necessarily communicative, not an expression’s of the giver’s will, not evaluable for sincerity, and in that they have propositional content. And they’re unlike normative truths in that they’re themselves not even truth-evaluable (though their contents are). This is because rules qua things that are in force are not like constatives which have a mind to world direction of fit, but more like performatives. Furthermore, they differ from normative truths in that their normativity is isolated from their background justification and is therefore not dependent on contributory notions like reasons coming together in a weighing explanation. As such, they occupy a middle ground between orders and normative truths, much like in H. L. A. Hart’s opinion law occupies a middle ground between “coercion” and “morality” (Hart 1961/1994). I also illustrate the virtues of this understanding of rules by showing how proper appreciation of how they differ from normative truths helps us defuse a common objection to Hart’s practice theory of rules. (shrink)

Many philosophers think that games like chess, languages like English, and speech acts like assertion are constituted by rules. Lots of others disagree. To argue over this productively, it would be first useful to know what it would be for these things to be rule-constituted. Searle famously claimed in Speech Acts that rules constitute things in the sense that they make possible the performance of actions related to those things (Searle 1969). On this view, rules constitute games, languages, and (...) speech acts in the sense that they make possible playing them, speaking them and performing them. This raises the question what it is to perform rule-constituted actions (e. g. play, speak, assert) and the question what makes constitutive rules distinctive such that only they make possible the performance of new actions (e. g. playing). In this paper I will criticize Searle’s answers to these questions. However, my main aim is to develop a better view, explain how it works in the case of each of games, language, and assertion and illustrate its appeal by showing how it enables rule-based views of these things to respond to various objections. (shrink)

Bioethics seems preoccupied with establishing, debating, promoting and sometimes debunking principles. While these tasks trade on the status of the word ‘principle’ in our ordinary language, scant attention is paid to the way principles operate in language. In this paper, we explore how principles relate to rules and practices so as to better understand their logic. We argue that principles gain their sense and power from the practices which give them sense. While general principles can be, and are, establishable in (...) abstraction from specific practices, as they are in principlist bioethics, such principles are impotent as moral guides to action. We show that the purchase any principle has as a moral guide to action emerges from its indexical properties as a principle which has sense in a specific practice. The meaning of any principle is internal to the practice and context in which it is invoked and, therefore, principles are not kinds of master rule which dictate moral judgement in new contexts but rather chameleon-like rules which change with the contexture in which they are invoked. (shrink)

I address the question of whether naturalism can provide adequate means for the scientific study of rules and rule-following behavior. As the term "naturalism" is used in many different ways in the contemporary debate, I will first spell out which version of naturalism I am targeting. Then I will recall a classical argument against naturalism in a version presented by Husserl. In the main part of the paper I will sketch a conception of rule-following behavior that is influenced (...) by Sellars and Haugeland. I will argue that rule-following is an essential part of human nature and insist in the social dimension of rules. Moreover, I will focus on the often overlooked fact that genuine rule-following behavior requires resilience and presupposes an inclination to calibrate one's own behavior to that of the other members of the community. Rule-following, I will argue, is possible only for social creatures who follow shared rules, which in turn presupposes a shared (first-person plural) perspective. This implies, however, that our scientific understanding of human nature has to remain incomplete as long as it does not take this perspective, which prima facie seems alien to it, into account. (shrink)

I frame my argument by way of Hayek's tendency to treat Hume and Smith as central articulations of the rule of law. The rest of the paper explores their defense of clientelism. First, I introduce Hume’s ideas on the utility of patronage in his essay, “Of the Independency of Parliament.” I argue that in Hume clientelism just is a feature of parliamentary business. It seems ineliminable. I then contextualize Hume’s account by comparing it to Montesquieu’s account of this system (...) of patronage in Book XIX, chapter 27 of The Spirit of the Laws. Montesquieu primarily treats it as a species of bad corruption. However, he also sees some benefits to it. I then turn to Smith and I show that he echoes Hume’s analysis of corruption in an easily ignored passage in Wealth of Nations. I then show that for Smith one argument in favor of a kind of federal parliamentary union between Great Brittain and her American colonies lies in its ability to facilitate and make more efficient the system of patronage by the Crown. While Smith’s account of these matters is quite Humean, one can discern in Smith a distinct cost-benefit argument for the acceptance of the necessity of a system of patronage in the service of the peaceful expansion and entrenchment of the rule of law in his proposal for parliamentary union. (shrink)

In the middle of the 20th century, it was a common Wittgenstein-inspired idea in philosophy that for a linguistic expression to have a meaning is for it to be governed by a rule of use. In other words, it was widely believed that meanings are to be identified with use-conditions. However, as things stand, this idea is widely taken to be vague and mysterious, inconsistent with “truth-conditional semantics”, and subject to the Frege-Geach problem. In this paper I reinvigorate the (...) ideas that meaningfulness is a matter of being governed by rules of use and that meanings are best thought of in terms of use-conditions. I will do this by sketching the Rule-Governance view of the nature of linguistic meaningfulness, showing that the view isn’t by itself subject to the two problems, and explain why the idea has had a lasting appeal to philosophers from Strawson to Kaplan and why we should find it continually attractive. (shrink)

This paper discusses the prospects of a dispositional solution to the Kripke–Wittgenstein rule-following puzzle. Recent attempts to employ dispositional approaches to this puzzle have appealed to the ideas of finks and antidotes—interfering dispositions and conditions—to explain why the rule-following disposition is not always manifested. We argue that this approach fails: agents cannot be supposed to have straightforward dispositions to follow a rule which are in some fashion masked by other, contrary dispositions of the agent, because in all (...) cases, at least some of the interfering dispositions are both relatively permanent and intrinsic to the agent. The presence of these intrinsic and relatively permanent states renders the ascription of a rule-following disposition to the agent false. (shrink)

Most plausible moral theories must address problems of partial acceptance or partial compliance. The aim of this paper is to examine some proposed ways of dealing with partial acceptance problems as well as to introduce a new Rule Utilitarian suggestion. Here I survey three forms of Rule Utilitarianism, each of which represents a distinct approach to solving partial acceptance issues. I examine Fixed Rate, Variable Rate, and Optimum Rate Rule Utilitarianism, and argue that a new approach, Maximizing (...) Expectation Rate Rule Utilitarianism, better solves partial acceptance problems. (shrink)

This paper describes and defends a novel and distinctively egalitarian conception of the rule of law. Official behavior is to be governed by preexisting, public rules that do not draw irrelevant distinctions between the subjects of law. If these demands are satisfied, a state achieves vertical equality between officials and ordinary people and horizontal legal equality among ordinary people.

In a recent paper, Tim Henning argues that the result that we should save the greatest number in rescue cases can be established on procedural grounds without making use of the aggregation of interests. He first argues that we ought to respect the affected persons' equal claims to have a say in the rescue decision and that this can only be achieved by the majority rule, which consists in giving each affected person an equal vote. Then he argues for (...) the second claim that if everyone votes in their self-interest, then the greatest number will be saved. I present a class of cases in which the second claim fails. This establishes that even if self-interested voting is assumed, the majority rule does not always lead to the greatest number being saved. (shrink)

Free trade agreements are about reducing tariffs, market access in services, protection of intellectual property rights, streamlining customs procedures, trade remedy measures, and dispute settlement mechanism. Equally important if not even more important than these provisions is the designation of rules of origin. Many benefits can be lost if restrictive rules of origin are incorporated. Rules of origin are supposed to be straightforward and easy-to-follow methods used to determine origin of imported goods. The policy question that arises is how to (...) improve trade integration among Arab countries through more effective rules of origin. (shrink)

Foundational theories of mental content seek to identify the conditions under which a mental representation expresses, in the mind of a particular thinker, a particular content. Normativists endorse the following general sort of foundational theory of mental content: A mental representation r expresses concept C for agent S just in case S ought to use r in conformity with some particular pattern of use associated with C. In response to Normativist theories of content, Kathrin Glüer-Pagin and Åsa Wikforss propose a (...) dilemma, alleging that Normativism either entails a vicious regress or falls prey to a charge of idleness. In this paper, I respond to this argument. I argue that Normativism can avoid the commitments that generate the regress and does not propose the sort of explanation required to charge that its explanation has been shown to be problematically idle. The regress-generating commitment to be avoided is, roughly, that tokened, contentful mental states are the product of rule-following. The explanatory task Normativists should disavow is that of explaining how it is that beliefs and other contentful mental states are produced. I argue that Normativism, properly understood as a theory of content, does not provide this kind of psychological explanation, and therefore does not entail that such explanations are to be given in terms of rule-following. If this is correct, Normativism is not the proper target of the dilemma offered by Glüer-Pagin and Wikforss. Understanding why one might construe Normativism in the way Glüer-Pagin and Wikforss must, and how, properly understood, it avoids their dilemma, can help us to appreciate the attractiveness of a genuinely normative theory of content and the importance of paying careful attention to the sort of normativity involved in norm-based theories of content. (shrink)

I criticize Yamada's account of rule-following. Yamada's conditions are not necessary. And he misses the deepest level of the rule-following considerations: how meaning rules come about.

‘Rule-following’ is a name for a cluster of phenomena where we seem both guided and “normatively” constrained by something general in performing particular actions. Understanding the phenomenon is important because of its connection to meaning, representation, and content. This article gives an overview of the philosophical discussion of rule-following with emphasis on Kripke’s skeptical paradox and recent work on possible solutions. Part I of this two-part contribution was devoted to the basic issues from Wittgenstein to Kripke. Part II (...) is about recent answers to the skeptical paradox and Boghossian’s and Wright’s new puzzles. (shrink)

Ideas on meaning, rules and mathematical proofs abound in Wittgenstein’s writings. The undeniable fact that they are present together, sometimes intertwined in the same passage of Philosophical Investigations or Remarks on the Foundations of Mathematics, does not show, however, that the connection between these ideas is necessary or inextricable. The possibility remains, and ought to be checked, that they can be plausibly and consistently separated. I am going to examine two views detectable in Wittgenstein’s works: one about proofs, the other (...) about meaning and rules. The first is the denial of the objectivity of proof. The second is a conception of meaning stemming from the rule-following considerations. I shall argue that, though Wittgenstein seems to conjoin the two views, they can be, and should be, separated1. (shrink)

According to Amie Thomasson's Modal Normativism (MN), knowledge of metaphysical modality is to be explained in terms of a speaker’s mastery of semantic rules, as opposed to one’s epistemic grasp of independent modal facts. In this chapter, I outline (MN)'s account of modal knowledge (§1) and argue that more than semantic mastery is needed for knowledge of metaphysical modality. Specifically (§2), in reasoning aimed at gaining such knowledge, a competent speaker needs to further deploy essentialist principles and information. In response, (...) normativists might contend that a competent speaker will only need to appeal to specific independence counterfactuals, on analogy with quasi-realism about morality. These conditionals fix the meaning of our terms at the actual world, independently of the particular context in which a statement is evaluated. However, I show that this strategy causes several problems for the account (§3). While those problems might perhaps be avoided by endorsing a certain picture of modal metaphysics (Modal Monism), such a picture involves notorious issues that normativists will have to address (§4). It is thus doubtful that (MN) can explain knowledge of metaphysical modality. Still, it may explain some modal knowledge without committing to Modal Monism. As I show (§5), semantic mastery may suffice for gaining knowledge of logical-conceptual modality or analyticity. (shrink)

In her seminal article ‘Modern Moral Philosophy’ (1958) Elizabeth Anscombe argued that we need a new ethics, one that uses virtue terms to generate absolute prohibitions against certain act-types. Leading contemporary virtue ethicists have not taken up Anscombe's challenge in justifying absolute prohibitions and have generally downplayed the role of rule-following in their normative theories. That they have not done so is primarily because contemporary virtue ethicists have focused on what is sufficient for characterizing the deliberation and action of (...) the fully virtuous person, and rule-following is inadequate for this task. In this article, I take up Anscombe's challenge by showing that rule-following is necessary for virtuous agency, and that virtue ethics can justify absolute prohibitions. First, I offer a possibility proof by showing how virtue ethics can generate absolute prohibitions in three ways: by considering actions that directly manifest vice or that cannot be performed virtuously; actions that are prohibited by one's institutional roles and practical identities; and actions that are prohibited by the prescriptions of the wise. I then seek to show why virtue ethicists should incorporate rule-following and absolute prohibitions into their theories. I emphasize the central role that rules have in the development of virtue, then motivate the stronger view that fully virtuous agents follow moral rules by considering the importance of hope, uncertainty about consequences, and taking responsibility for what eventuates. Finally, I provide an account of what Anscombe called a ‘corrupt mind’, explaining how our understanding of virtue is corrupted if we think that virtue may require us to do vicious actions. (shrink)

The article contains a critical analysis of the skeptical solution to the rule- following problem. The skeptical solution denies the existence of “superlative” R-facts that would make statements of the form “P means R by ‘+’ ” true. The role of the sources for the meaning of ‘+’ here is played by the patterns of solidarity behavior of members of some community to which P belongs. The correct use of ‘+’ would be one that is approved by the competent (...) majority of this community, and there can be no other sense in which it would be correct or wrong. Boyd’s hypothesis denies the communal character of the ‘+’ meaning. While there are no “superlative” R-facts, there should be C-facts not about the R as the standard that P or its community follows in their practice of using ‘+’, but about whether they do it correctly. The proof of the Boyd hypothesis is based on the example of an imaginary Ω-community, whose agents use a finite set of simple symbols for the needs of their arithmetic: ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘J’. Each symbol denotes a subset of identical, from the Ω-community point of view, numerical values. The symbol ‘A’ is used, for ex- ample, for a subset of the natural numbers 1, 10, 19, 28, 37, 46, etc.; ‘B’ for 2, 11, 20, 29, 38, 47, etc.; ‘C’ for 3, 12, 21, 30, 39, 48, etc. The Ω-community’s arithmetic uses the only local function ⊕ whose range of values forms a finite set of mathematical propositions {α} that are true. The Ω-community’s arithmetic, like our own, is open to many skeptical challenges. Is there a fact that determines the meaning of ‘⊕’? What do agents do when they calculate with ‘⊕’ (say, solve examples ‘A⊕B = ?’, ‘C⊕E=?’, etc.)? Do they Add, Badd or Dadd? To answer them would require a “superlative” R-fact. For the calculation practice with ‘⊕’, it could be a certain R-fact that determines the only possible order for the sequence of numerals ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘J’ such that {α} is true. An analysis of the calculation practice using the local arithmetic function ⊕ shows that for it there are no such R-facts that would determine the only correct standard R – even if the agents in the Ω-community were trained in such calculations on a full set of cases for the application of that function. However, for such practice there are C-facts (independent in their existence from R-facts) that make it possible to distinguish between what seems to be right and what is right. The solitary agent P and the Ω-community are in the same position regarding the knowledge of C-facts. The Ω-community’s point of view has no advantage in matters of C-facts knowledge over the solitary agent P’s point of view. The Ω-community arithmetic shows that if a solitary agent P had the suitable knowledge of C-facts about the practice of calculations with ‘⊕’, it would allow him/her to disagree with the not correct answers of other members of the community even when they would constitute an absolute majority. (shrink)

Are norms of inquiry in tension with epistemic norms? I provide a (largely) negative answer, turning to a picture of epistemic practices as rule-governed games. The idea is that, while epistemic norms are correctness standards for the attitudes involved in epistemic games, norms of inquiry derive from the aims of those games. Attitudes that, despite being epistemically correct, are inadvisable regarding the goals of some inquiry are just like bad (but legal) moves in basketball or chess. I further consider (...) cases in which the aims of inquiry recommend breaking epistemic norms. I compare them to strategic infractions, which are common in many coherent games. Finally, I explore the connections between rules and aims in games and in inquiry. I show that in both cases respecting the rules is constitutively required for satisfying the aims of the practice. (shrink)

Normativists about belief hold that belief formation is essentially rule- or norm-guided. On this view, certain norms are constitutive of or essential to belief in such a way that no mental state not guided by those norms counts as a belief, properly construed. In recent influential work, Kathrin Glüer and Åsa Wikforss develop novel arguments against normativism. According to their regress of motivations argument, not all belief formation can be rule- or norm-guided, on pain of a vicious infinite (...) regress. I argue that the regress of motivations argument is unsuccessful: an appeal to the notion of blind rule-following, drawn from a plausible interpretation of Ludwig Wittgenstein’s remarks on rule-following, stops the regress of motivations in its tracks. (shrink)

Rule-following is a normative doing and therefore needs to be reconsidered in a metaethical framework. Rule-following will be discussed in the light of cognitivism and non-cognitivism. It will be shown that neither cognitivism nor non-cognitivism are sufficiently good accounts for conceptualizing rule-following, because they are held captive by a quasi-mechanistical picture of rule-following. This idea stems from Stanley Cavell´s and John McDowell´s approach to rule-following. McDowell appeals to the idea that we participate in “shared forms (...) of life” and therefore are able to follow rules correctly. I believe that his quietist view can be amplified by conceptualizing different modes of following a rule. We can also follow a rule e.g. ironically and still grasp the conceptual content of the rule adequately. (shrink)

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also consider sequential (...) quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (shrink)

Proponents of the rule of law argue about whether that ideal should be conceived formalistically or in terms of substantive values. Formalistically, the rule of law is associated with principles like generality, clarity, prospectivity, consistency, etc. Substantively, it is associated with market values, with constitutional rights, and with freedom and human dignity. In this paper, I argue for a third layer of complexity: the procedural aspect of the rule of law; the aspects of rule-of-law requirements that (...) have to do with "natural Justice" or "procedural due process." These I believe have been neglected in the jurisprudential literature devoted specifically to the idea of the rule of law and they deserve much greater emphasis. Moreover procedural values go beyond elementary principles like the guarantee of an unbiased tribunal or the opportunity to present and confront evidence. They include the right to argue in a court about what the law is and what its bearing should be on one's situation. The provision that law makes for argument is necessarily unsettling, and so this emphasis on the procedural aspect highlights the point predictability should not be regarded as the be-all and end-all of the rule of law. (shrink)

This paper argues that the problematic of rule following in Wittgenstein's Philosophical Investigations and Heidegger's analysis of anxiety in Being and Time have analogous structures. Working through these analogies helps our interpretation of both of these authors. Contrasting sceptical and anti-sceptical readings of Wittgenstein helps us to resolve an interpretive puzzle about what an authentic response to anxiety looks like for Heidegger. And considering the importance of anxiety to Heidegger's conception of authenticity allows us to locate in Wittgenstein's later (...) philosophy a covert appeal to something resembling Heideggerian authenticity. (shrink)

At the core of republican thought, on Philip Pettit’s account, lies the conception of freedom as non-domination, as opposed to freedom as noninterference in the liberal sense. I revisit the distinction between liberal and republican freedom and argue that republican freedom incorporates a particular rule-of-law requirement, whereas liberal freedom does not. Liberals may also endorse such a requirement, but not as part of their conception of freedom itself. I offer a formal analysis of this rule-of-law requirement and compare (...) liberal and republican freedom on its basis. While I agree with Pettit that republican freedom has broader implications than liberal freedom, I conclude that we face a trade-off between two dimensions of freedom (scope and robustness) and that it is harder for republicans to solve that trade-off than it is for liberals. Key Words: freedom • republicanism • liberalism • noninterference • non-domination • rule of law • robustness • liberal paradox. (shrink)

1. Do models formulated in programming languages use explicit rules where connectionist models do not? 2. Are rules as found in programming languages hard, precise, and exceptionless, where connectionist rules are not? 3. Do connectionist models use rules operating on distributed representations where models formulated in programming languages do not? 4. Do connectionist models fail to use structure sensitive rules of the sort found in "classical" computer architectures? In this chapter we argue that the answer to each of these questions (...) is negative. (shrink)

There is an increase in the use of in-door wireless networking solutions via Wi-Fi and this increase infiltrated and utilized Wi-Fi enable devices, as well as smart mobiles, games consoles, security systems, tablet PCs and smart TVs. Thus the demand on Wi-Fi connections increased rapidly. Rule Based System is an essential method in helping using the human expertise in many challenging fields. In this paper, a Rule Based System was designed and developed for diagnosing the wireless connection problems (...) and attain a precise decision about the cause of the problem. SL5 Object expert system language was used in developing the rule based system. An Evaluation of the rule based system was carried out to test its accuracy and the results were promising. (shrink)

The level of enjoyment in participating in sports activities is one component that causes young athletes to decide to stop or become more motivated to pursue sports activities. Practicing and participating in competitions are the main activities in sports coaching interactions towards optimal performance. This study aims to determine the effect of modifying the match rules implemented in youth soccer competitions on the level of enjoyment of players. Using an experimental method with 20 soccer schools participating in a competition with (...) modified game rules. Players registered by his team amounted to an average of 13.8 players aged 9-12 years. The number of players who are willing to fill out the pleasure level questionnaire is 238 players. Each player was asked to fill out a questionnaire before and after the competition, the questionnaire was analyzed using the mean and percentage test technique. The results of data analysis showed the average score before participating in the competition was 4.10 while after participating in the competition it was 4.47, which means an increase of 8.88%. The results showed that the level of enjoyment of the players increased after participating in the competition. Modification of the rule of the game in competition affects the level of enjoyment of players in the interaction of youth soccer coaching. Coaches, administrators, and match organizers are expected to have a positive paradigm of thinking and policy making towards the organization of competitions for young soccer players. (shrink)

This article takes up the question of whether legal rules are reasons for action. They are commonly regarded in this way, yet are legal rules reasons for action themselves (the reflexivity thesis) or are they instead merely statements of other reasons that we may already have (the paraphrastic thesis)? I argue for a version of the paraphrastic thesis. In doing so, considerable attention is given to the neglected but important puzzle of the opaqueness of rules, which arises out of what (...) some regard as the gap between the evaluative grounds of legal rules and what makes them into reasons for action. After examining an important articulation of the puzzle in the work of Joseph Raz, I argue that the reflexivity thesis is (i) undermined by certain features of rule making and (ii) defeated by the principle of presumptive sufficiency. The result is that it is possible for legal rules to be paraphrastic statements of reasons but, conversely, impossible for them to be reasons in themselves. (shrink)

The aim of this paper is to give an account of what it is to internalize a rule. I claim that internalization is the process of redistributing the burden of instruction from the teacher to the student. The process is complete when instruction is no longer needed, and the rule has reshaped perceptual classification of the circumstances in which it applies. Teaching a rule is the initiation of this process. We internalize rules by simulating instruction coming from (...) someone else. Running these simulations enables us to toggle between the perspective of the instructor and our own perspective. By doing this we coordinate our perspectives with that of the teacher. The account given here provides a deeper explanation of why internalizing a rule involves the dispositions and reactive attitudes proponents of Rule Consequentialism often say it does, why moral reflection is variably demanding, how intergenerational moral progress is made possible by our cognitive architectures, and why the adoption of a rule should be understood in terms of teaching that rule. (shrink)

In this paper, I present a game-theoretic solution to the rule-following paradox in terms of what I will call basic constitutive practices. The structure of such a practice P constitutes what it is to take part in P by defining the correctness conditions of our most basic concepts as those actions that lie on the correlated equilibrium of P itself. Accordingly, an agent S meant addition by his use of the term ‘+’ because S is taking part in a (...) basic constitutive practice of adding where quus-like answers are ruled out by not lying on the equilibrium. The resulting picture of language will preserve the objectivity and correctness conditions of meaning, all the while providing room for the community as a whole to make a mistake. I also argue that by accepting the account presented, we have a strong reason to reject the idea that language is rule-governed. (shrink)

The going-on problem (GOP) is the central concern of Wittgenstein's later philosophy. It informs not only his epistemology and philosophy of mind, but also his views on mathematics, universals, and religion. In section I, I frame this issue as a matter of accounting for intentionality. Here I follow Saul Kripke's lead. My departure therefrom follows: first, a criticism of Wittgenstein's “straight” conventionalism and, secondly, a defense of a solution Kripke rejects. I proceed under the assumption, borne out in the end, (...) that statements of rule-following have truth-conditions and are not, as Kripke seems willing to concede, merely "assertible" in circumstances of a specified sort. Ultimately, my goal is to demonstrate that intending can be understood in terms of an individual's dispositions rather than those of the community to which she belongs. (shrink)

In this article, it is argued that existing democracies might establish popular rule even if Joseph Schumpeter’s notoriously unflattering picture of ordinary citizens is accurate. Some degree of popular rule is in principle compatible with apathetic, ignorant and suggestible citizens, contrary to what Schumpeter and others have maintained. The people may have control over policy, and their control may constitute popular rule, even if citizens lack definite policy opinions and even if their opinions result in part from (...) elites’ efforts to manipulate these opinions. Thus, even a purely descriptive, ‘realist’ account of democracy of the kind that Schumpeter professed to offer may need to concede that there is no democracy without some degree of popular rule. (shrink)

Over the last decade, philosophers of science have extensively criticized the epistemic superiority of randomized controlled trials for testing safety and effectiveness of new drugs, defending instead various forms of evidential pluralism. We argue that scientific methods in regulatory decision-making cannot be assessed in epistemic terms only: there are costs involved. Drawing on the legal distinction between rules and standards, we show that drug regulation based on evidential pluralism has much higher costs than our current RCT-based system. We analyze these (...) costs and advocate for evaluating any scheme for drug regulatory tests in terms of concrete empirical benchmarks, like the error rates of regulatory decisions. (shrink)

This paper employs some outcomes (for the most part due to David Lewis) of the contemporary debate on the metaphysics of dispositions to evaluate those dispositional analyses of meaning that make use of the concept of a disposition in ideal conditions. The first section of the paper explains why one may find appealing the notion of an ideal-condition dispositional analysis of meaning and argues that Saul Kripke’s well-known argument against such analyses is wanting. The second section focuses on Lewis’ work (...) in the metaphysics of dispositions in order to call attention to some intuitions about the nature of dispositions that we all seem to share. In particular, I stress the role of what I call "Actuality Constraint". The third section of the paper maintains that the Actuality Constraint can be used to show that the dispositions with which ideal-condition dispositional analyses identify my meaning addition by "+" do not exist (in so doing, I develop a suggestion put forward by Paul Boghossian). This immediately implies that ideal-condition dispositional analyses of meaning cannot work. The last section discusses a possible objection to my argument. The point of the objection is that the argument depends on an illicit assumption. I show (1) that, in fact, the assumption in question is far from illicit and (2) that even without this assumption it is possible to argue that the dispositions with which ideal-condition dispositional analyses identify my meaning addition by "+" do not exist. (shrink)

This paper presents a new reconstruction of Wittgenstein’s famous (and controversial) rule-following arguments. Two are the novel features offered by our reconstruction. In the first place, we propose a shift of the central focus of the discussion, from the general semantics and the philosophy of mind to the philosophy of mathematics and the rejection of the notion of a function. The second new feature is positive: we argue that Wittgenstein offers us a new alternative notion of a rule (...) (to replace the rejected functions), a notion reminiscent of Category Theory’s notion of a morphism. (shrink)

Recently two distinct forms of rule-utilitarianism have been introduced that differ on how to measure the consequences of rules. Brad Hooker advocates fixed-rate rule-utilitarianism, while Michael Ridge advocates variable-rate rule-utilitarianism. I argue that both of these are inferior to a new proposal, optimum-rate rule-utilitarianism. According to optimum-rate rule-utilitarianism, an ideal code is the code whose optimum acceptance level is no lower than that of any alternative code. I then argue that all three forms of (...) class='Hi'>rule-utilitarianism fall prey to two fatal problems that leave us without any viable form of rule-utilitarianism. (shrink)

In the theory of meaning, it is common to contrast truth-conditional theories of meaning with theories which identify the meaning of an expression with its use. One rather exact version of the somewhat vague use-theoretic picture is the view that the standard rules of inference determine the meanings of logical constants. Often this idea also functions as a paradigm for more general use-theoretic approaches to meaning. In particular, the idea plays a key role in the anti-realist program of Dummett and (...) his followers. In the theory of truth, a key distinction now is made between substantial theories and minimalist or deflationist views. According to the former, truth is a genuine substantial property of the truth-bearers, whereas according to the latter, truth does not have any deeper essence, but all that can be said about truth is contained in T-sentences (sentences having the form: ‘P’ is true if and only if P). There is no necessary analytic connection between the above theories of meaning and truth, but they have nevertheless some connections. Realists often favour some kind of truth-conditional theory of meaning and a substantial theory of truth (in particular, the correspondence theory). Minimalists and deflationists on truth characteristically advocate the use theory of meaning (e.g. Horwich). Semantical anti-realism (e.g. Dummett, Prawitz) forms an interesting middle case: its starting point is the use theory of meaning, but it usually accepts a substantial view on truth, namely that truth is to be equated with verifiability or warranted assertability. When truth is so understood, it is also possible to accept the idea that meaning is closely related to truth-conditions, and hence the conflict between use theories and truth-conditional theories in a sense disappears in this view. (shrink)

On the developmental reading, Descartes first praised his method in the first instance of Rule VIII of the Regulae ad directionem ingenii, but then demoted it to provisional in the “blacksmith” analogy, and then found his discrete method could not resolve his “finest example,” his inquiry into the essence and scope of human knowledge, an event that, on this reading, resulted in him dropping his method. In this paper, I explain how Rule VIII can be read as a (...) coherent title and commentary that is a further development of the method of the Regulae. (shrink)

Mental content normativists hold that the mind’s conceptual contents are essentially normative. Many hold the view because they think that facts of the form “subject S possesses concept c” imply that S is enjoined by rules concerning the application of c in theoretical judgments. Some opponents independently raise an intuitive objection: even if there are such rules, S’s possession of the concept is not the source of the enjoinment. Hence, these rules do not support mental content normativism. Call this the (...) “Source Objection.” This paper refutes the Source Objection, outlining a key strand of the relationship between judgments and their contents in the process. Theoretical judgment and mental conceptual content are equally the source of enjoinment; norms for judging with contents do not derive from one at the expense of the other. (shrink)

I briefly consider why Descartes stopped work on the _Rules_ towards the end of my paper. My main concern is to accurately characterize the project represented in the _Rules_, especially in its relation to early-modern logic.

This paper is about what we call Deontically-flavored Nominal Constructions (DNCs) in English, such as "No ice cream" or "Dogs on leash only". DNCs are often perceived as commands and have been argued to be a type of non-canonical imperative, much like root infinitives in German or Russian. We argue instead that DNCs at their core are declaratives that cite a rule but can be used performatively in the right context. We propose that DNCs contain an elided deontic modal, (...) i.e., allowed, whose presence explains their distributional restrictions and interpretational properties. Among other things, we speculate on the licensing conditions of DNCs (the presence of 'only' or the negative determiner 'no'), suggesting that these are tied to the properties of discourses in which rules can be used naturally. (shrink)

What is the American rule of law? Is it a paradigm case of the strong constitutionalism concept of the rule of law or has it fallen short of its rule of law ambitions? -/- This open access book traces the promise and paradox of the American rule of law in three interwoven ways. -/- It focuses on explicating the ideals of the American rule of law by asking: how do we interpret its history and the (...) goals of its constitutional framers to see the rule of law ambitions its foundational institutions express? -/- It considers those constitutional institutions as inextricable from the problem of race in the United States and the tensions between the rule of law as a protector of property rights and the rule of law as a restrictor on arbitrary power and a guarantor of legal equality. In that context, it explores the distinctive role of Black liberation movements in developing the American rule of law. -/- Finally, it considers the extent to which the American rule of law is compromised at its frontiers, and the extent that those compromises undermine legal protections Americans enjoy in the interior. It asks how America reflects the legal contradictions of capitalism and empire outside its borders, and the impact of those contradictions on its external goals. (shrink)

This self-contained one page paper produces one valid two-premise premise-conclusion argument that is a counterexample to the entire three traditional rules of distribution. These three rules were previously thought to be generally applicable criteria for invalidity of premise-conclusion arguments. No longer can a three-term argument be dismissed as invalid simply on the ground that its middle is undistributed, for example. The following question seems never to have been raised: how does having an undistributed middle show that an argument's conclusion does (...) not follow from its premises? This result does nothing to vitiate the theories of distribution developed over the period beginning in medieval times. What it does vitiate is many if not all attempts to use distribution in tests of invalidity outside of the standard two-premise categorical arguments—where they were verified on a case-by-case basis without further theoretical grounding. In addition it shows that there was no theoretical basis for many if not all claims of fundamental status of rules of distribution. These results are further support for approaching historical texts using mathematical archeology. (shrink)