Several proof-theoretic notions of validity have been proposed in the literature, for which completeness of intuitionistic logic has been conjectured. We define validity for intuitionistic propositional logic in a way which is common to many of these notions, emphasizing that an appropriate notion of validity must be closed under substitution. In this definition we consider atomic systems whose rules are not only production rules, but may include rules that allow one to discharge assumptions. Our central result shows that Harrop’s (...) class='Hi'>rule is valid under substitution, which refutes the completeness conjecture for intuitionistic logic. (shrink)

In this paper, we propose a computational interpretation of the generalized Kreisel–Putnam rule, also known as the generalized Harrop rule or simply the Split rule, in the style of BHK semantics. We will achieve this by exploiting the Curry–Howard correspondence between formulas and types. First, we inspect the inferential behavior of the Split rule in the setting of a natural deduction system for intuitionistic propositional logic. This will guide our process of formulating an appropriate program that (...) would capture the corresponding computational content of the typed Split rule. Our investigation can also be reframed as an effort to answer the following question: is the Split rule constructively valid in the sense of BHK semantics? Our answer is positive for the Split rule as well as for its newly proposed general version called the S rule. (shrink)

Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these (...) two properties. I also show how to use this fact to demonstrate that these logics seem to be constructive in previously unknown ways. (shrink)

I am concerned that the military’s Rules of Engagement (ROE) exclusively focus on prescribing permissible actions but fail to consider the servicemembers’ blameworthiness. In explaining this concern, I will illuminate how permissible actions do not necessarily yield blamelessness. While permissibility is generally a function of rules or good outcomes, blameworthiness is at least a function of an agent’s intentions. Why should we care about permissible actions done with blameworthy intentions? I offer two distinct motivations. Using a self-defense situation as an (...) example, I explain that neglecting to consider blame can increase the magnitude of harm done to an apparent but merely possible attacker. Secondly, we should certainly be concerned about the harms done to servicemembers, and I show that ROE that fail to prescribe a blameless intention may result in increased harm to servicemembers in the form of a “moral injury”. In even more general terms, I am advocating for a more robust in bello consideration of intentions. (shrink)

In the second chapter of her <i>Institutions de Physique</i> Emilie Du Chatelet gives two cosmological arguments for the existence of God. In this chapter I focus on the first of these arguments. I argue that, while it bears some significant similarities to arguments given by John Locke and Christian Wolff, it improves on these arguments in at least two ways. First, it avoids a potential equivocation in Locke's argument; and second, it avoids Wolff's mere stipulation that whoever claims that there (...) cannot be an infinite regress of contingent beings does not understand what a sufficient reason is. I finally argue that her argument avoids a related objection, considered by David Hume, on which to explain a causal chain is merely to explain each link in the chain. (shrink)

I examine the (mediated) correspondence between Spinoza and Robert Boyle concerning the latter’s account of fluidity and his experiments on reconstitution of niter in the light of the epistemology and doctrine of method contained in the Treatise on the Emendation of the Intellect. I argue that both the Treatise and the correspondence reveal that for Spinoza, the proper method of science is not experimental, and that he accepted a powerful under-determination thesis. I argue that, in contrast to modern versions, Spinoza’s (...) form of naturalism was a highly rationalist and anti-empirical one. I conclude with a brief account of the value of experience and experimentation for Spinoza’s scientific method. (shrink)

Many professional football clubs in Europe have youth academies. The business model of such academies is that a club invests resources in training a player and then, when the player is old enough to sign an adult contract, either sells the player or offers him an adult contract. According to Fédération Internationale De Football Association (FIFA), international transfers of players are only permitted if the player is over the age of 18. There are five exceptions to this rule. One (...) of them is that if the player is between 16 and 18 and the transfer takes place within the territory of the European Economic Area (EEA), then an international transfer is allowed. This article is a discussion of the FIFA rules that mandate non-uniform age limits for when players can first transfer to clubs within the EEA area. The conclusion of the article is that FIFA is morally unjustified in setting a higher minimum age for transfer to EEA clubs for non-EEA players than for EEA players. The article first develops an argument for its conclusion. It then discusses, and rejects, the five best objections to this argument. (shrink)

In an incendiary 2010 Nature article, M. A. Nowak, C. E. Tarnita, and E. O. Wilson present a savage critique of the best-known and most widely used framework for the study of social evolution, W. D. Hamilton’s theory of kin selection. More than a hundred biologists have since rallied to the theory’s defence, but Nowak et al. maintain that their arguments ‘stand unrefuted’. Here I consider the most contentious claim Nowak et al. defend: that Hamilton’s rule, the core explanatory (...) principle of kin selection theory, ‘almost never holds’. I first distinguish two versions of Hamilton’s rule in contemporary theory: a special version (HRS) that requires restrictive assumptions, and a general version (HRG) that does not. I then show that Nowak et al. are most charitably construed as arguing that HRS almost never holds, while HRG buys its generality at the expense of explanatory power. While their arguments against HRS are fairly uncontroversial, their arguments against HRG are more contentious, yet these have been largely overlooked in the ensuing furore. I consider the arguments for and against the explanatory value of HRG, with a view to assessing what exactly is at stake in the debate. I suggest that the debate hinges on issues concerning the causal interpretability of regression coefficients, and concerning the explanatory function Hamilton’s rule is intended to serve. (shrink)

Kearns (2021) argues that there is a parody version of Anselm's ontological argument (a "gontological argument") which shows that God does not exist. I show that Anselm considers one of the key premises in Kearns' gontological argument, and explicitly gives an argument which entails its falsity, and hence the unsoundness of the supposed parody argument. -/- .

Richard Jeffrey's generalization of Bayes' rule of conditioning follows, within the theory of belief functions, from Dempster's rule of combination and the rule of minimal extension. Both Jeffrey's rule and the theory of belief functions can and should be construed constructively, rather than normatively or descriptively. The theory of belief functions gives a more thorough analysis of how beliefs might be constructed than Jeffrey's rule does. The inadequacy of Bayesian conditioning is much more general than (...) Jeffrey's examples of uncertain perception might suggest. The ``parameter α '' that Hartry Field has introduced into Jeffrey's rule corresponds to the "weight of evidence" of the theory of belief functions. (shrink)

Ruling Passions is Simon Blackburn’s latest attempt to defend a theory of practical reason which he calls “expressivism”.2 In the first three chapters Blackburn outlines an account of how we should understand statements of right, good and virtue, as well as their negative counterparts (“the Ethical [or Moral] Proposition”, as he terms this amalgam). This he calls “quasi-realism”. I shall describe what this position entails in the first section. Secondly I shall consider the opposition to this view advanced by McDowell (...) (1987), who in turn takes his inspiration from Wiggins (1976a, 1976b). Finally I shall assess Blackburn’s reply to McDowell and Wiggins (found in Chapter 4 of RP), and argue that it is inadequate. (shrink)

Gupta’s Rule of Revision theory of truth builds on insights to be found in Martin and Woodruff and Kripke in order to permanently deepen our understanding of truth, of paradox, and of how we work our language while our language is working us. His concept of a predicate deriving its meaning by way of a Rule of Revision ought to impact significantly on the philosophy of language. Still, fortunately, he has left me something to.

This essay explores the implications of H.L.A. Hart's rule of recognition for identifying ultimate standards of law in the United States. The effort reveals that these standards are much more complex than is commonly supposed. Not all of the federal constitution is part of the “ultimate” rule of recognition, and much else must be included in that rule. The analysis uncovers many possibilities for how ultimate standards relate to derivative standards that are omitted or barely hinted at (...) in Hart's account. Some of these possibilities pose genuine difficulty for Hart's basic theory and help illuminate the relation of conventional and normative elements in an adequate account of law, a subject addressed in the final section of the essay. (shrink)

Chapter 5 addresses the provisional morality of the Treatise on the Emendation of the Intellect (TIE). The young Spinoza proposes that even as one works at emending the intellect, one should live by certain rules, which one must assume to be good. One should accommodate ordinary ways of speaking and living to the extent that one can without compromising one’s project. One should enjoy pleasures in moderation. Finally, one should seek instrumental goods only insofar as they are necessary for health (...) and social acceptability. In order to explain shifts in Spinoza’s views about the way that individuals should live while pursuing the good, the chapter traces developments in his accounts of ideas and of the relationship between the philosopher and society. (shrink)

According to Brad Hooker's rule-consequentialism, as well as ordinary moral prohibitions against lying, stealing, killing, and harming others, the optimific code will include an over-riding “prevent disaster clause”. This paper explores two issues related to the disaster clause. The first issue is whether the disaster clause is vague—and whether this is a problem for rule-consequentialism. I argue that on Hooker's rule-consequentialism, there will be cases where it is indeterminate whether a given outcome counts as a disaster such (...) that it is permissible to infringe a given prohibition to avoid that outcome. I argue that it counts in favour of Hooker's rule-consequentialism that it makes this space for vagueness. The second issue is how to understand the disaster clause so that it does not make rule-consequentialism intolerably demanding—and more particularly whether avoiding over-demandingness requires the rule-consequentialist to place a counterintuitive limit on requirements to aid. I will argue that rule-consequentialism can avoid over-demandingness without placing a counterintuitive limit on requirements to aid. (shrink)

Brad Hooker’s rule-consequentialism and T.M. Scanlon’s contractualism have been some of the most debated ethical theories in normative ethics during the last twenty years or so. This article suggests that these theories can be compared at two levels. Firstly, what are the deep, structural differences between the rule-consequentialist and contractualist frameworks in which Hooker and Scanlon formulate their views? Secondly, what are the more superficial differences between Hooker’s and Scanlon’s formulations of these theories? Based on exploring these questions (...) and several purported differences between Hooker’s and Scanlon’s views, this article argues that, at the structural level, the two theories are more similar than previous recognised. It suggests that there is only one candidate for a deeper difference and even it may not be that significant. This insight sheds new light on both contractualism and rule-consequentialism, and it will also help us to formulate better versions of the views. (shrink)

This note corrects a lemma in the recent paper 1] of one of the authors by rst correcting problems with Poole's rule for speci city of arguments. It also responds to the criticism of Touretzky, et al. 9].

Change happens to us. It's measured in gains or losses: you find a spouse or lose a loved one; you receive a promotion or lose a job. Change happens around us. It's marked by natural and social factors: a good harvest, a natural disaster; an economic boom, a stock market plunge. Change is initiated by us. It's weighed by its outcome: you make a decision that improves your life; you make a choice that shatters your dreams. Transitional tides-whether personal or (...) cultural-can bring on stress, confusion, and even panic. Only a small percentage of people respond to change in truly effective ways. Yet how we deal with change determines whether it will ultimately be a positive or negative force in our lives. Best-selling author Dr. Myles Munroe explains how we can tap into the positive power of change-no matter what the source of that change-enabling us to thrive while fulfilling our God-given purposes in life. (shrink)

In the 1950s, Alan Turing proposed his influential test for machine intelligence, which involved a teletyped dialogue between a human player, a machine, and an interrogator. Two readings of Turing's rules for the test have been given. According to the standard reading of Turing's words, the goal of the interrogator was to discover which was the human being and which was the machine, while the goal of the machine was to be indistinguishable from a human being. According to the literal (...) reading, the goal of the machine was to simulate a man imitating a woman, while the interrogator – unaware of the real purpose of the test – was attempting to determine which of the two contestants was the woman and which was the man. The present work offers a study of Turing's rules for the test in the context of his advocated purpose and his other texts. The conclusion is that there are several independent and mutually reinforcing lines of evidence that support the standard reading, while fitting the literal reading in Turing's work faces severe interpretative difficulties. So, the controversy over Turing's rules should be settled in favor of the standard reading. (shrink)

Bergmann’s rule and Allen’s rule played important roles in mid-twentieth century discussions of adaptation, variation, and geographical distribution. Although inherited from the nineteenth-century natural history tradition these rules gained significance during the consolidation of the modern synthesis as evolutionary theorists focused attention on populations as units of evolution. For systematists, the rules provided a compelling rationale for identifying geographical races or subspecies, a function that was also picked up by some physical anthropologists. More generally, the rules provided strong (...) evidence for adaptation by natural selection. Supporters of the rules tacitly, or often explicitly, assumed that the clines described by the rules reflected adaptations for thermoregulation. This assumption was challenged by the physiologists Laurence Irving and Per Scholander based on their arctic research conducted after World War II. Their critique spurred a controversy played out in a series of articles in Evolution, in Ernst Mayr’s Animal Species and Evolution, and in the writings of other prominent evolutionary biologists and physical anthropologists. Considering this episode highlights the complexity and ambiguity of important biological concepts such as adaptation, homeostasis, and self-regulation. It also demonstrates how different disciplinary orientations and styles of scientific research influenced evolutionary explanations, and the consequent difficulties of constructing a truly synthetic evolutionary biology in the decades immediately following World War II. (shrink)

Two readings of Wittgenstein's rule-following paradox dominate the literature: either his arguments lead to skepticism, and thus to the view that only a deflated account of meaning is available, or they lead to quietism, and thus to the view that no philosophical account of meaning is called for. I argue, against both these positions, that a proper diagnosis of the paradox points the way towards a constructive, non-sceptical account of meaning.

We consider HA*, that is Heyting's Arithmetic extended with transfinite induction over all recursive well orderings, which may be viewed as defining constructive truth, since PA* agrees with classical truth. We prove that Markov's Principle, as a schema, is not provable in HA*, but that HA* is closed under Markov's Rule.

Hamilton’s theory of inclusive fitness is a widely used framework for studying the evolution of social behavior, but controversy surrounds its status. Hamilton originally derived his famous rb > c rule for the spread of a social gene by assuming additivity of costs and benefits. However, it has recently been argued that the additivity assumption can be dispensed with, so long as the −c and b terms are suitably defined, as partial regression coefficients. I argue that this way of (...) generalizing Hamilton’s rule to the nonadditive case, while formally correct, faces conceptual problems. (shrink)

It is proved that Ackermann’s rule δ is admissible in a wide spectrum of relevant logics satisfying certain syntactical properties.

Hamilton’s theory of inclusive fitness is a widely used framework for studying the evolution of social behavior, but controversy surrounds its status. Hamilton originally derived his famous rb > c rule for the spread of a social gene by assuming additivity of costs and benefits. However, it has recently been argued that the additivity assumption can be dispensed with, so long as the −c and b terms are suitably defined, as partial regression coefficients. I argue that this way of (...) generalizing Hamilton’s rule to the nonadditive case, while formally correct, faces conceptual problems. (shrink)

Patricia Crone's _God's Rule_ is a fundamental reconstruction and analysis of Islamic political thought focusing on its intellectual development during the six centuries from the rise of Islam to the Mongol invasions. Based on a wide variety of primary sources--including some not previously considered from the point of view of political thought--this is the first book to examine the medieval Muslim answers to questions crucial to any Western understanding of Middle Eastern politics today, such as why states are necessary, what (...) functions they are meant to fulfill, and whether or why they must be based on religious law. The character of Muslim political thought differs fundamentally from its counterpart in the West. The Christian West started with the conviction that truth (both cognitive and moral) and political power belonged to separate spheres. Ultimately, both power and truth originated with God, but they had distinct historical trajectories and regulated different aspects of life. The Muslims started with the opposite conviction: truth and power appeared at the same time in history and regulated the same aspects of life. In medieval Europe, the disagreement over the relationship between religious authority and political power took the form of a protracted controversy regarding the roles of church and state. In the medieval Middle East, religious authority and political power were embedded in a single, divinely sanctioned Islamic community--a congregation and state made one. The disagreement, therefore, took the form of a protracted controversy over the nature and function of the leadership of Islam itself. Crone makes Islamic political thought accessible by relating it to the contexts in which it was formulated, analyzing it in terms familiar to today's reader, and, where possible, comparing it with medieval European and modern political thought. By examining the ideological point of departure for medieval Islamic political thought, Crone provides an invaluable foundation for a better understanding of contemporary Middle Eastern politics and current world events. (shrink)

Visser's rules form a basis for the admissible rules of . Here we show that this result can be generalized to arbitrary intermediate logics: Visser's rules form a basis for the admissible rules of any intermediate logic for which they are admissible. This implies that if Visser's rules are derivable for then has no nonderivable admissible rules. We also provide a necessary and sufficient condition for the admissibility of Visser's rules. We apply these results to some specific intermediate logics and (...) obtain that Visser's rules form a basis for the admissible rules of, for example, De Morgan logic, and that Dummett's logic and the propositional Gödel logics do not have nonderivable admissible rules. (shrink)

Usual derivations of Lilders's projection rule show that Liuders's rule is the rule required by quantum statistics to calculate the final state after an ideal (minimally disturbing) measurement. These derivations are at best inconclusive, however, when it comes to interpreting Liuders's rule as a description of individual state transformations. In this paper, I show a natural way of deriving Liiders's rule from well-motivated and explicit physical assumptions referring to individual systems. This requires, however, the introduction (...) of a concept of individual state which is not standard. (shrink)

Retrospective rule-making has few supporters and many opponents. Defenders of retrospective laws generally do so on the basis that they are a necessary evil in specific or limited circumstances, for example to close tax loopholes, to deal with terrorists or to prosecute fallen tyrants. Yet the reality of retrospective rule making is far more widespread than this, and ranges from ’corrective’ legislation to ’interpretive regulations’ to judicial decision making. The search for a rational justification for retrospective rule-making (...) necessitates a reconsideration of the very nature of the rule of law and the kind of law that can rule, and will provide new insights into the nature of law and the parameters of societal order. This book examines the various ways in which laws may be seen as retrospective and analyses the problems in defining retrospectivity. In his analysis Dr Charles Sampford asserts that the definitive argument against retrospective rule-making is the expectation of individuals that, if their actions today are considered by a future court, the applicable law was discoverable at the time the action was performed. The book goes on to suggest that although the strength of this ’rule of law’ argument should prevail in general, exceptions are sometimes necessary, and that there may even be occasions when analysis of the rule of law may provide the foundation for the application of retrospective laws. (shrink)

Probabilities in quantum theory are traditionally given by Born’s rule as the expectation values of projection operators. Here it is shown that Born’s rule is insufficient in universes so large that they contain identical multiple copies of observers, because one does not have definite projection operators to apply. Possible replacements for Born’s rule include using the expectation value of various operators that are not projection operators, or using vari-.

In 1870–75 Markovnikov enunciatedan empirical Rule which generalized theregiochemical outcome of addition reactions tounsymmetrical alkenes. This Rule remaineduseful for about 75 years, until suchreactions came to be better understood inmechanistic terms. Thereafter the Rule couldbe deduced from principles of relativecarbocation stabilization and ceased to servean independent purpose. Nevertheless, mostorganic textbooks continue to cite it (oftenin a historically inaccurate, anachronisticway), thereby distracting student attentionfrom the underlying principles. This paperadvocates doing away with the Rule in organicchemistry textbooks and (...) classrooms. (shrink)

The rule of rescue describes the powerful human proclivity to rescue identified endangered lives, regardless of cost or risk. Deciding whether or not to perform a decompressive craniectomy as a life-saving or ‘rescue’ procedure for a young person with a severe traumatic brain injury provides a good example of the ethical tensions that occur in these situations. Unfortunately, there comes a point when the primary brain injury is so severe that if the patient survives they are likely to remain (...) severely disabled and fully dependent. The health resource implications of this outcome are significant. By using a web-based outcome prediction model this study compares the long-term outcome and designation of two groups of patients. One group had a very severe injury as adjudged by the model and the other group a less severe injury. At 18 month follow-up there were significant differences in outcome and healthcare requirements. This raises important ethical issues when considering life-saving but non-restorative surgical intervention. The discussion about realistic outcome cannot be dichotomised into simply life or death so that the outcome for the patient must enter the equation. As in other ‘rescue situations’, the utility of the procedure cannot be rationalised on a mere cost–benefit analysis. A compromise has to be reached to determine at what point either the likely outcome would be unacceptable to the person on whom the procedure is being performed or the social utility gained from the rule of rescue intervention fails to justify the utilitarian value and justice of equitable resource allocation. (shrink)

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