ABSTRACTBernard Suits and other formalists endorse both the logical incompatibility thesis and the view that rule-breakings resulting in penalties can be a legitimate part of a game. This is what Fred D’Agostino calls ‘the problem of penalties’. In this paper, I reject both Suits’ and D’Agostino’s responses to the problem and argue instead that the solution is to abandon Suits’ view that the constitutive rules of all games are alike. Whereas the logical incompatibility thesis applies to games in which (...) players’ actions are perfectly controlled, it does not apply to sports. This insight not only justifies the rejection of formalism as a theory about the nature of sport but it also helps explain the greater normative complexity of sports, which in turn leads to the idea that in sports ‘cheating’ should be interpreted as a genus. (shrink)

Bernard Suits and other formalists endorse both the logical incompatibility thesis and the view that rule-breakings resulting in penalties can be a legitimate part of a game. This is what Fred D’Ag...

This book revisits the theory of the sources of international law from the perspective of formalism.

Judicial formalism is perceived as fully compliant with the requirements of the rule of law. With its reliance on plain meaning and its reluctance to apply historical, purposive and functional interpretative premises, it seems an ideal tool for constraining discretionary judicial powers and securing the predictability of law’s application, which latter is one of the main tenets of the rule of law. In this paper, I argue that judicial formalism is based on a misguided model of (...) language, and as such cannot deliver what it promises. In fact, judicial decisions based on formalistic reasoning are surprising to their addressees and instead of promoting predictability, they undermine it. A judicial strategy fully compliant with the rule of law requires a different vision of language than that proposed by judicial formalism, and as a consequence, a different, moderately non-formalistic conception of legal interpretation. (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)

Legal decisions and theories are frequently condemned as formalistic, yet little discussion has occurred regarding exactly what the term "'formalism" means. In this Article, Professor Schauer examines divergent uses of the term to elucidate its descriptive content. Conceptions offormalism, he argues, involve the notion that rules constrict the choice of the decisionmaker. Our aversion to formalism stems from denial that the language of rules either can or should constrict choice in this way. Yet Professor Schauer argues that this (...) aversion to formalism should be rethought: At times language both can and should restrict decisionmakers. Consequently, the term "'formalistic" should not be used as a blanket condemnation of a decisionmaking process; instead the debate regarding decision according to rules should be confronted on its own terms. (shrink)

When discussing Wilfrid Sellars’s philosophy, very little work has been done to offer a developmental account of his systematic views. More often than not, Sellars’s complex views are presented in a systematic and holistic fashion that ignores any periodization of his work. I argue that there is a metaphilosophical shift in Sellars’s early philosophy that results in substantive changes to his conception of language, linguistic rules, and normativity. Specifically, I claim that Sellars’s shift from a formalist metaphilosophy to one more (...) closely aligned with psychology allows for the construction of a normative conception of language. My central claim is that without his abandonment of earlier metaphilosophical commitments, Sellars could not hold what I call an external conception of normativity. It is this move away from a formalist notion of philosophy that allows Sellars to construct a normative picture of language. I conclude that because this substantive shift in philosophical commitments results from changes in Sellars’s metaphilosophical views, there is insight to be found in a meticulous periodization of his work. (shrink)

Compares formalism and instrumentalism and evaluates their general claims. “Part of what is meant by formalism is this: The law provides sufficient basis for deciding any case that arises. There are no “gaps” within the law, and there is but one sound legal decision for each case.” The formalist also holds that law is traceable to an authoritative source. “…sound legal decisions can be justified as the conclusions of valid deductive syllogisms. Because law is believed to be complete (...) and univocal, all cases that arise can in principle be decided in this way. This is the formalistic model for legal justifications.” Moderate instrumentalism also accepts the notion that the law has sources and that past political events can determine what the law is for the future. However, they also maintain that the law has gaps. “Moderate instrumentalists and positivists alike embrace a source-based conception of the law as well as a formalistic model for legal justification; partly because of this combination, they reject the formalistic notion that law is complete and univocal. Instrumentalists, like positivists, emphasize that because the interpretation of authoritative legal texts and their application to cases are often controversial, reasonable arguments are often possible on both sides of a legal issue. Since there are no hard and fast rules for adjudicating such disputes, positivists conclude that law in such cases is indeterminate – not yet fully formed, needing judicial legislation. Instrumentalists most likely have a similar view of the law. They assume that law is determinate on an issue at a given time only if its identification and application are, roughly speaking, mechanical.” [Must keep in mind the distinction between determinate and conclusive.] “The instrumentalists make the decisive assumption that law is not determinate if it is controversial, for law is thought to be gappy and indeterminate only when reasonable legal arguments are possible on both sides of a legal question…This reasoning exposes a more fundamental assumption of formalism, instrumentalism, and positivism: Nondeductive reasoning is incapable of adequately establishing any conclusion.” This, though, is a radical thesis given that all scientific hypotheses are unproven deductively. [But it might be a claim restricted to legal reasoning. Moreover, it seems legitimate to wonder whether legal reasoning is really comparable to offering scientific hypotheses.] We should, however, reject the mechanistic model of legal and judicial reasoning that assumes a given major premise captured in authoritative legal texts that deductively produces conclusions in a situation to which a law applies. Take a law that requires some activity to be “economically efficient” but fails to specify economic efficiency. The text assumes that there is such a thing as economic efficiency, that some activities are so efficient and others not, that some judgments about economic efficiency are true and others false, and that the criteria of efficiency are determinable in principle. “[I]f there really are reasons for preferring one conception of economic efficiency to others in a given context, the assumption of the law in question would be true; if the court correctly identifies and applies that conception, it is simply carrying out its legal mandate. It would be faithful to the text, but it would not be limited to the four corners of the text and its literal implications.” Thus, a judge may employ non-mechanical reasoning in arriving at the meaning of legal requirements such as economic efficiency. Moral reasons are constitutive of the law. A judge must, in deciding the appropriate conc ption of economic efficiency, offer reasons for preferring that conception in the given context. (shrink)

Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. (...) I argue that for Thomae, the formal standpoint is an _algebraic perspective_ on a domain of objects, and a "sign" is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae's chess analogy is intended to provide a model for such shifts in perspective. (shrink)

This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences. The formalism is to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity. ;A modal conditional approach is taken to formalize the nonmonotonic reasoning in general at the level of object language. A serial of logic systems---MN, NID, NCUM, N STCUM---are constructed in an increasing strength of the characterized nonmonotonic inference relation. In (...) these systems, two binary modal operators ⩾ and > are introduced in their syntax, and a ⊛ function lifted from the traditional * function is deployed in their semantics. These systems are shown to be sound and complete with respect to certain classes of frames defined in the semantics. They are decidable as well. The nonmonotonic inference is argued to be a ternary relation "[phi], Gamma |∼ alpha", and is defined in the system NSTCUM. Many widely discussed nonmonotonic inference patterns such as Defeasible Modus Ponens, Defeasible Transitivity, the Penguin Principle etc. are justified. The specificity rule is proved to be a theorem of the system N STCUM. The impact of negated defaults on an inference is also investigated and accounted for. ;A canonical form to read off generics is proposed: All generic sentences with subject-predicate structure can be re-written into their canonical form S . If S is a plural noun phrase, it can be further refined to be . Normal objects are selected based on the "meaning" of the subject and predicate terms. The second parameter provides an aspect with respect to which certain objects of a kind are considered normal. Due to such a way to select normal objects, the drowning problem is solved. ;The inference behaviors of generics are axiomatized in the system G, which is a quantificational extension of the system NSTCUM. It is proved to be sound and complete with respect to the class of L⩾,G -frames. Those benchmark examples of generic inferences are examined in the system G. (shrink)

One of the ways our legal system has avoided confronting this ugly reality is through a commitment to legal formalism. Legal formalism allows us to ignore the social determinants that my AUSA friend saw every day as he prosecuted federal drug cases. As my colleague Professor Michael Seidman has suggested, legal formalism, which has been effectively critiqued and displaced by legal realism in many other areas of law, continues to exercise considerable influence over the way we think (...) about criminal law. This formalist approach, in my view, has strongly affected the way we approach the drug problem. One consequence is that we continue to pursue an increasingly futile war on drugs and refuse to see the issue in its broader, realist dimension. A little realism on the subject of drugs, I suggest, would go a long way. There is much to be said for formalism in the criminal law. Formalism, with its commitment to fair procedures, clear rules, and restricted discretion, is a necessary part of any fair system of criminal law. The sanctions involved in the criminal system are too severe to permit them to be allocated in an open ended discretionary or regulatory manner. The criminal law's commitment to formalism is thus not a fault, but a strength. Discretionary regulatory schemes too often invite subjective judgments susceptible to abuse, prejudice, and favoritism. Formalist rules, by contrast, are built on the promise of treating likes alike. Precisely for this reason, however, we ought to reconsider whether the criminal approach makes sense when there is substantial evidence that the commitment to equality has been seriously compromised. Our dual commitments to equality and to the reduction of the human damage that drug abuse inflicts suggest that we should reduce our reliance on the criminal justice system. Alternative approaches, such as treatment and rehabilitation, promise to be both more effective and more fair. (shrink)

. This paper endeavors to formalize imperatives that convey actions. Imperatives, unlike propositions, do not hold the value of true or false. Peter Vranas proposed an alternate logical formalism in the literature of imperative logic with three values, namely: Satisfaction (), Violation () and Avoidance (). Although this formalism takes into account the conditional imperatives, it does not address imperatives from the perspective of actions. According to Mīmāṁsā, the prime motive of an imperative is to carry out action (...) so as to reach the goal. This paper modifies the notion of Vranas' imperative logic using Mīmāṁsā principles. The resulting imperative formalism, focusing on action representation, is presented with syntax, deduction rules and semantic tables. The effectiveness of this representation is demonstrated in the area of artificial intelligence planning. (shrink)

In his work, Bernard Suits presents and pursues a stated objective: to define ‘game’ or, more precisely, ‘game-playing’. In The Grasshopper: Games, Life and Utopia, the author seeks a definition not as a ‘commitment to the universal fruitfulness of definition construction’, but rather with the idea ‘that some things are definable, and some are not’. This is something he believed could resolve many of the issues surrounding the debate on ‘game’ and ‘play’, such as those with Huizinga (in Homo Ludens) (...) or proposed by the anti-definitionism of Wittgenstein, a philosopher who did not accept that it was possible to define ‘game’. In this article, we will trace Suits’ definitional steps and aim to critique his resolution as a kind of ‘formalism’, as it tended to prioritize rules. Furthermore, notwithstanding the merit of his theoretical endeavor – seen in the attempt to define a social component that is so complex and the target of the most diverse interpretations and misconceptions –, it seems to us that, with his theoretical unifying element (lusory attitude), the author has summoned another problem to the debate, that of ‘subjectivism’, rather than a solution (especially to his formalism), even subjecting himself to comparisons with other conceptions (e.g. Fichte) that are also problematic. This aspect will also be criticized. The attention of this article will shift to these two lines of critique, drawing on an insightful analysis of Malaby’s work at a specific juncture, aiming to delve further into the subject and taking an additional step. (shrink)

Several writers have argued recently that optimal rules of law authorize morally suboptimal decisions in certain cases.1 Larry Alexander calls these “gap cases.”2 Should judges in gap cases defer to legal rules or deviate from them? Philosophers known as “formalists” favor deference, “particularists” favor deviation.

Recent literature in experimental philosophy has postulated the existence of the abstract/concrete paradox : the tendency to activate inconsistent intuitions depending on whether a problem to be analyzed is framed in abstract terms or is described as a concrete case. One recent study supports the thesis that this effect influences judicial decision-making, including decision-making by professional judges, in areas such as interpretation of constitutional principles and application of clear-cut rules. Here, following the existing literature in legal theory, we argue that (...) the susceptibility to such an effect might depend on whether decision-makers operate in a legal system characterized by the formalist or particularist approach to legal interpretation, with formalist systems being less susceptible to the effect. To test this hypothesis, we compare the results of experimental studies on ACP run on samples from two countries differing in legal culture: Poland and Brazil. The lack of significant differences between those results suggests that ACP is a robust effect in the legal context. (shrink)

Legal formalism is the foil for many theories of law. Yet formalism remains controversial, meaning that its critics focus on claims that are not central. This paper sets out a view of formalism using a methodology that embraces one of formalism’s most distinct claims, that formalism is a scientific theory of law. This naturalistic view of formalism helps to distinguish two distinct types of formalism, “doctrinal formalism,” the view that judicial behaviour can (...) be represented using rules, and “rule formalism,” the view that judges follow external rules when they are deciding cases. Doctrinal formalism, understood in naturalistic terms, overcomes many of the criticisms that have been levelled at formalism and can also be used to rehabilitate the currently out‐of‐favour “declaratory theory of law.” Doctrinal formalism is also a longstanding view of law, reflecting both what the original formalists thought of law, and what many present‐day doctrinal lawyers seem to believe. The naturalistic methodology is used to show that the main dispute between doctrinal formalism and American legal realism can be explained by a difference of assumptions concerning whether the values of judges are relative to society, or relative to other judges. (shrink)

In the article, philosophical and methodological analysis of the program of Hilbert’s formalism as a really working direction for consideration of the bases of modern mathematics is presented. For the professional mathematicians methodological advantages of the program of formalism advanced by David Hilbert, consist primarily in the fact that the highest possible level of theoretical rigor of modern mathematical theories was practically represented there. To resolve the fundamental difficulties of the problem of bases of mathematics, according to Hilbert, (...) the theory of mathematical proof is needed, but contrary to popular belief rigorous formalization of the proof is not a synonym of reliability and rigor of mathematical reasoning from the point of view of the philosophy of the foundations of mathematics. In fact, the consistency of the theories is "more important" than their logical consistency because not every statement, which does not contradict to the reasonable ones, can be attributed to a true statement. However, for working mathematicians, Hilbert is logical and consistent and the axiomatic method and formalism are an essential part of their rules of thinking. (shrink)

This article defends a formalist interpretation of Wittgenstein’s later thought on music by comparing it with Eduard Hanslick’s musical formalism. In doing so, it returns to a disagreement I have had with Bela Szabados who, in his book Wittgenstein as a Philosophical Tone-Poet, claims that the attribution of formalism obscures the role that music played in the development of Wittgenstein’s thought. The paper scrutinizes the four arguments Szabados presents to defend his claim, pertaining to alleged differences between Wittgenstein (...) and Hanslick on their accounts of theory, beauty, rules, and the broader significance of music. I will argue that in each case the similarities between Wittgenstein’s and Hanslick’s respective views outshine possible differences. Ultimately, I will argue that instead of rendering music a marginal phenomenon suited for mere entertainment, formalism –as presented by Hanslick and Wittgenstein, whom I read as influenced by Kant’s aesthetics– underscores music’s ability to show fundamental features of reality and our relation to it. Music does this precisely by being treated as a sensuous yet structured medium that is irreducible to any conceptually determined domain. (shrink)

We present and defend a view labeled “practiceism” which provides a solution to the incompatibility problems. The classic incompatibility problem is inconsistency of:1. Someone who intentionally violates the rules of a game is not playing the game.2. In many cases, players intentionally violate the rules as part of playing the game.The problem has a normative counterpart:1’. In normal cases, it is wrong for a player to intentionally violate the rules of the game.2’. In many normal cases, it is not wrong (...) for a player to intentionally violate the rules of the game.According to both formalism and informalism, the rules of the game include the formal rules of the game. Both traditional positions avoid the incompatibility problems by rejecting 1 and 1'. Practiceism rejects 2 and 2’: it maintains that the rules are the rules manifested in playing the game, not the formal rules.Practiceism presents two theses: (... (shrink)

In this article, I consider whether a suitably stripped-down version of Kant's aesthetic theory could nevertheless provide philosophical foundations for musical formalism. I begin by distinguishing between formalism as a view about the nature of music and formalism as an approach to music criticism, arguing that Kant's aesthetics only rules out the former. Then, using an example from the work of musicologist and composer Edward T. Cone, I isolate the characteristics of formalist music criticism. With this characterization (...) in mind, I conclude by showing that even if Kant's aesthetic theory is reduced to its most fundamental claims, the logic of formalist music criticism precludes its practice within even a kantian perspective. (shrink)

This paper proposes an approach to investigate norm-governed learning agents which combines a logic-based formalism with an equation-based counterpart. This dual formalism enables us to describe the reasoning of such agents and their interactions using argumentation, and, at the same time, to capture systemic features using equations. The approach is applied to norm emergence and internalisation in systems of learning agents. The logical formalism is rooted into a probabilistic defeasible logic instantiating Dung’s argumentation framework. Rules of this (...) logic are attached with probabilities to describe the agents’ minds and behaviours as well as uncertain environments. Then, the equation-based model for reinforcement learning, defined over this probability distribution, allows agents to adapt to their environment and self-organise. (shrink)

The analysis of atomic sentences and their subatomic components poses a special problem for proof-theoretic approaches to natural language semantics, as it is far from clear how their semantics could be explained by means of proofs rather than denotations. The paper develops a proof-theoretic semantics for a fragment of English within a type-theoretical formalism that combines subatomic systems for natural deduction [20] with constructive (or Martin-Löf) type theory [8, 9] by stating rules for the formation, introduction, elimination and equality (...) of atomic propositions understood as types (or sets) of subatomic proof-objects. The formalism is extended with dependent types to admit an interpretation of non-atomic sentences. The paper concludes with applications to natural language including internally nested proper names, anaphoric pronouns, simple identity sentences, and intensional transitive verbs. (shrink)

This paper analyses the impact of the Law and Economics movement on legal decision making. Focussing on the position of the leading intellectual figure of this movement, Richard Posner, the author shows how his theories imply a silent revolution in American jurisprudence. Starting from the criteria of economic efficiency and wealth maximization, seen in the light of American pragmatism, Posner upholds anti‐formalist interpretation of statutor law by judges based on the principles of free market economics. His theory starts from the (...) assumption that statutor law has become more and more ambiguous and open‐ended and thus, as in the case of antitrust law, judges can freely interpret legal provisions on the basis of free market postulates. This position has broader implications in the debate about the meaning of the rule of law: Posner's position implies abandoning the emancipatory core of the liberal tradition. (shrink)

The hydrodynamical formalism for the quantum theory of a nonrelativistic particle is considered, together with a reformulation of it which makes use of the methods of kinetic theory and is based on the existence of the Wigner phase-space distribution. It is argued that this reformulation provides strong evidence in favor of the statistical interpretation of quantum mechanics, and it is suggested that this latter could be better understood as an almost classical statistical theory. Moreover, it is shown how, within (...) this context, the Wigner and the Margenau-Hill functions are not equivalent, and that the latter is essentially unsatisfactory, as well as the associated symmetrization rule. Arguments in favor of a stochastic picture of the phenomena at the microscopic level are also presented. (shrink)

The overaraching goal of this paper is to elucidate the nature of superselection rules in a manner that is accessible to philosophers of science and that brings out the connections between superselection and some of the most fundamental interpretational issues in quantum physics. The formalism of von Neumann algebras is used to characterize three different senses of superselection rules (dubbed, weak, strong, and very strong) and to provide useful necessary and sufficient conditions for each sense. It is then shown (...) how the Haag–Kastler algebraic approach to quantum physics holds the promise of a uniform and comprehensive account of the origin of superselection rules. Some of the challenges that must be met before this promise can be kept are discussed. The focus then turns to the role of superselection rules in solutions to the measurement problem and the emergence of classical properties. It is claimed that the role for “hard” superselection rules is limited, but “soft” (a.k.a. environmental) superselection rules or N. P. Landsman’s situational superselection rules may have a major role to play. Finally, an assessment is given of the recently revived attempts to deconstruct superselection rules. (shrink)

This paper deals with Frege’s early critique of formalism in the philosophy of mathematics. Frege opposes meaningful arithmetic, according to which arithmetical formulas express a sense and arithmetical rules are grounded in the reference of the signs, to formal arithmetic, exemplified in particular by J. Thomae, whose “formal standpoint”, according to Frege, is that arithmetic should be understood as a manipulation of meaningless figures. However, Frege’s discussion of Thomae’s analogy between arithmetic and chess shows that Frege does not understand (...) his main point, which is that we must distinguish conceptually between statements about chess figures, and the chess pieces they represent. Indeed, Thomae’s fruitful use of this comparison undermines the ontological conception of arithmetic represented by Frege. The chess pieces do not go proxy for anything, but playing chess is not for that reason just manipulation of physical chess figures. This is also Wittgenstein’s point when he criticizes Frege for not seeing the “justified side of formalism”. Thomae’s formalism can be clarified by using the distinction between sign and symbol. Symbols are never meaningless or empty forms or signs, since they have a role or function in a symbolism, which one may call their meaning. The discussion of the chess analogy shows that Frege fails to see this operative aspect of the symbolism. We can conclude that the “formal standpoint” that Frege criticizes is his fabrication, rather than anything we can attribute to Thomae. (shrink)

An open formalism for arithmetic is presented based on first-order logic supplemented by a very strictly controlled constructive form of the omega-rule. This formalism (which contains Peano Arithmetic) is proved (nonconstructively, of course) to be complete. Besides this main formalism, two other complete open formalisms are presented, in which the only inference rule is modus ponens. Any closure of any theorem of the main formalism is a theorem of each of these other two. This (...) fact is proved constructively for the stronger of them and nonconstructively for the weaker one. There is, though, an interesting counterpart: the consistency of the weaker formalism can be proved finitarily. (shrink)

Musical formalism is often portrayed as the enemy of artistic freedom. Its main representative, Eduard Hanslick, is seen as a purist who, by emphasizing musical rules, aims at restricting music criticism and even musical practices themselves. It may also seem that formalism is depriving music of its ability to have moral significance, as the semantic connection to the extramusical is denied by the formalistic view. In my paper, I defend formalism by placing Hanslick’s argument in a Kantian (...) framework. It is not hard to find Kantian elements in Hanslick’s work, such as his emphasis on the contemplative and disinterested nature of the aesthetic judgment, the nonconceptuality of music’s content, and his insistence that “beauty has no purpose.” I argue further that Hanslick’s formalism is in fact motivated by and manifests the Kantian conception of freedom as self-legislation. Thus understood, the kind of moral significance music may have rests upon its own autonomous rules. (shrink)

The essays in this volume are all concerned with the arguments about law as a system of rule-based decision-making,particularly the ideas advanced by legal philosopher Frederick Schauer. Schauer's work has not only helped revive interest in legal formalism but has also helped relocate arguments about the relationship between posited rules and morality. The contributors to this volume, themselves distinguished theorists, have concentrated on three aspects of Schauer's work: the nature of jurisprudential description; his theory of presumptive positivism; and (...) the application of his theory of rule-based decision-making to other areas of legal and moral thought. Contributors: Larry Alexander, Brian Bix, Philip Bobbitt, Marianne Constable, Michael C. Dorf, Jeremy Elkins, Claire Oakes Finkelstein, Leo Katz, Jason Johnston, Dennis Patterson. (shrink)

Information is a peculiar quantity. Unlike matter and energy, which are conserved by the laws of physics, the aggregation of knowledge from many sources can in fact produce more information (synergy) or less (redundancy) than the sum of its parts. This feature can endow groups with problem‐solving strategies that are superior to those possible among noninteracting individuals and, in turn, may provide a selection drive toward collective cooperation and coordination. Here we explore the formal properties of information aggregation as a (...) general principle for explaining features of social organization. We quantify information in terms of the general formalism of information theory, which also prescribes the rules of how different pieces of evidence inform the solution of a given problem. We then show how several canonical examples of collective cognition and coordination can be understood through principles of minimization of uncertainty (maximization of predictability) under information pooling over many individuals. We discuss in some detail how collective coordination in swarms, markets, natural language processing, and collaborative filtering may be guided by the optimal aggregation of information in social collectives. We also identify circumstances when these processes fail, leading, for example, to inefficient markets. The contrast to approaches to understand coordination and collaboration via decision and game theory is also briefly discussed. (shrink)

Both Holmes and Langdell believed that science was the model for all human inquiry and the source of all human progress. Langdell was influenced by an unsophisticated scientism, which led him to attempt to identify the true meaning of legal doctrines. Holmes was influenced by the sophisticated positivism of John Stuart Mill, which led him to attempt to reduce legal rules and doctrines to scientific laws of antecedence and consequence, justified only by their social consequences. Both Holmes and Langdell concluded (...) that judges ought to decide a case by applying the rules established by precedent, without appeal to any special claims of justice and without appeal to any higher‐order normative principle. (shrink)

This is an attempt to understand the ethics of leonard nelson as dealing with some of the same problems arising from kant's moral philosophy as have concerned the rule utilitarians in anglo-American philosophy. In particular, They share the attempt to provide a rationale for specific duties in terms of ends to be achieved, And they try to correct what they see as excessive rigidity and formalism in the kantian imperatives.

This book offers a new definition of metaphor-as an ontological and visual construction, whose roots are external visual forms, and its motivation is our attachment to forms. This definition, which Michalle Gal names “visualist,” challenges the ruling conceptualist theory of metaphors and places a new emphasis on how we experience rather than understand metaphors. In doing so, she responds to the visual turn that is taking place in literature and the media, demanding that the visual become a site of philosophical (...) analysis. This focus on the external visual world allows Gal to employ visual theories to capture the essence of metaphor. She looks beyond conceptual or semantic mechanism, and returns to theories of Arnheim and Gombrich and the current evolution of ideas about the visual or material and embodied cognition. Proposing to see visual metaphors in their basic form, she uses a new externalist terminology of ontology, visuality, composition, affordance, construction, and emergence. Setting out a new theory that takes into account that humans are visual no less than cognitive creatures, Visual Metaphors and Aesthetics lays the foundation for a new vocabulary to talk about metaphors. (shrink)

This book offers a detailed account and discussion of Ludwig Wittgenstein's philosophy of mathematics. In Part I, the stage is set with a brief presentation of Frege's logicist attempt to provide arithmetic with a foundation and Wittgenstein's criticisms of it, followed by sketches of Wittgenstein's early views of mathematics, in the Tractatus and in the early 1930s. Then (in Part II), Wittgenstein's mature philosophy of mathematics (1937-44) is carefully presented and examined. Schroeder explains that it is based on two key (...) ideas: the calculus view and the grammar view. On the one hand, mathematics is seen as a human activity - calculation - rather than a theory. On the other hand, the results of mathematical calculations serve as grammatical norms. The following chapters (on mathematics as grammar; rule-following; conventionalism; the empirical basis of mathematics; the role of proof) explore the tension between those two key ideas and suggest a way in which it can be resolved. Finally, there are chapters analysing and defending Wittgenstein's provocative views on Hilbert's Formalism and the quest for consistency proofs and on Gödel's incompleteness theorems. (shrink)

The intention here is that of giving a formal underpinning to the idea of 'meaning-is-use' which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett-Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i. e. the so-called reduction rules. For that we suggest an (...) extension to the Curry-Howard interpretation which draws on the idea of labelled deduction, and brings back Frege's device of variable-abstraction to operate on the labels (i. e., proof-terms) alongside formulas of predicate logic. (shrink)

It is shown that the Hilbert space formalism of quantum mechanics can be derived as a corrected form of probability theory. These constructions yield the Schrödinger equation for a particle in an electromagnetic field and exhibit a relationship of this equation to Markov processes. The operator formalism for expectation values is shown to be related to anL 2 representation of marginal distributions and a relationship of the commutation rules for canonically conjugate observables to a topological relationship of two (...) manifolds is indicated. (shrink)

We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to classical constraints, based on a question-and-answer procedure. The problem is posed from a particular batch of queries while the constraints are represented by the truth table of a set of Boolean functions. The Bayesian inference technique consists in assigning a probability distribution within a real-valued (...) probability space to the joint set of queries in order to satisfy the constraints. The initial query batch is not unique and alternative batches can be considered at will. They are enabled mechanically from the initial batch, quite simply by transcribing the probability space into an auxiliary Hilbert space. It turns out that this sole procedure leads to exactly rediscover the standard quantum information theory and thus provides an information-theoretic rationale to its technical rules. In this framework, the great challenges of quantum mechanics become simple platitudes: Why is the theory probabilistic? Why is the theory linear? Where does the Hilbert space come from? In addition, most of the paradoxes, such as uncertainty principle, entanglement, contextuality, nonsignaling correlation, measurement problem, etc., become straightforward features. In the end, our major conclusion is that quantum information is nothing but classical information processed by a mature form of Bayesian inference technique and, as such, consubstantial with Aristotelian logic. (shrink)

The traditional approach to the covariance problem in quantum mechanics is inverted and the space-time transformations are assumed as the basicunknowns, according to the prescription that the correspondence principle and the commutation rules must becovariant. It is shown that the only solutions are either Galilean or Lorentzian (including the possibility of an imaginary light-velocity c2<0). The Dirac formalism for the wave-equation and the condition c2>0 are obtained simoultaneously as theunique solution, provided that the Hamiltonian is Hermitean (in the usual (...) sense), and the internal degrees of freedom allow for afinite-dimensional representation. Infinite-dimensional representations are introduced in order to extend the Hamiltonian formalism to other spinors. (shrink)

There has been considerable discussion in the past about the assumptions and basis of different ethical rules. For instance, it is commonplace to say that ethical rules are defaults rules, which means that they tolerate exceptions. Some authors argue that morality can only be grounded in particular cases while others defend the existence of general principles related to ethical rules. Our purpose here is not to justify either position, but to try to model general ethical rules with artificial intelligence formalisms (...) and to compute logical consequences of different ethical theories. More precisely, this is an attempt to show that progress in non-monotonic logics, which simulates default reasoning, could provide a way to formalize different ethical conceptions. From a technical point of view, the model developed in this paper makes use of the Answer Set Programming (ASP) formalism. It is applied comparatively to different ethical systems with respect to their attitude towards lying. The advantages of such formalization are two-fold: firstly, to clarify ideas and assumptions, and, secondly, to use solvers to derive consequences of different ethical conceptions automatically, which can help in a rigorous comparison of ethical theories. (shrink)

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an extension (...) to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. (shrink)

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an extension (...) to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. (shrink)

In recent articles, Zangari (1994) and Karakostas (1997) observe that while an &unknown;-extended version of the proper orthochronous Lorentz group O + (1,3) exists for values of &unknown; not equal to zero, no similar &unknown;-extended version of its double covering group SL(2, C) exists (where &unknown;=1-2&unknown; R , with &unknown; R the non-standard simultaneity parameter of Reichenbach). Thus, they maintain, since SL(2, C) is essential in describing the rotational behaviour of half-integer spin fields, and since there is empirical evidence for (...) such behaviour, &unknown;-coordinate transformations for any value of &unknown;<>0 are ruled out empirically. In this article, I make two observations:(a)There is an isomorphism between even-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions of such spinor fields.(b)There is a 2-1 isomorphism between odd-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions for such spinor fields up to a sign. Evidence that the components of such fields do take unique values is not decisive in favour of the realist in the debate over the conventionality of simultaneity in so far as such fields do not play a role in clock synchrony experiments in general, and determinations of the one-way speed of light in particular.I claim that these observations are made clear when one considers the coordinate-independent 2-spinor formalism. They are less evident if one restricts oneself to earlier coordinate-dependent formalisms. I end by distinguishing these conclusions from those drawn by the critique of Zangari given by Gunn and Vetharaniam (1995). (shrink)

The debate between Glymour and Fine hinges in part on a comparison of the width of the incoming wave packet in momentum space with the angles intercepted by the detectors in the Cross-Ramsey experiment. As Fine argues, it follows from the quantum formalism that the initial dispersion will be conserved in Compton scattering, and he allows that the Sum Rule is constrained by the statistical results of quantum mechanics. The Sum Rule may fail, but it will not (...) fail in any way that violates quantum mechanics. Thus most of the time the individual momentum value does not change more than the width of the initial wave packet: usually the value of Qγe at t must equal the value of Qγ at t′ plus the value of Qe at t′ ± Δp/2, where Δp represents the dispersion in momentum for the initial gamma ray. Thus in order to refute Fine's thesis, the detectors must discriminate finely enough to pick out changeovers of individual values within Δp. (shrink)

Appraising the worth of others’ testimony is always complex; appraising the worth of expert testimony is even harder; appraising the worth of expert testimony in a legal context is harder yet. Legal efforts to assess the reliability of expert testimony—I’ll focus on evolving U.S. law governing the admissibility of such testimony—seem far from adequate, offering little effective practical guidance. My purpose in this paper is to think through what might be done to offer courts more real, operational help. The first (...) step is to explain why the legal formulae that have evolved over the years may seem reassuring, but aren’t really of much practical use. The next is to suggest that we might do better not by amending evidentiary rules but by helping judges and attorneys understand what questions they should ask about expert evidence. I focus here on (i) epidemiological testimony, and (ii) the process of peer review. (shrink)