In this paper, I examine Hume’s account of an important class of causal belief which he calls “general rules”. I argue that he understands general rules, like all causal beliefs, as lively ideas which are habitually associated with our impressions or memories. However, I argue, he believes that they are unlike any reflectively produced causal beliefs in that they are produced quickly and automatically, such that they occur independently of any other processes of reasoning. Given this, (...) I argue, Hume appears to understand general rules as relatively simple beliefs, expressible only via generic sentences, like “birds lay eggs”. (shrink)

An examination of the role played by general rules in Hume's positive (nonskeptical) epistemology. General rules for Hume are roughly just general beliefs. The difference between justified and unjustified belief is a matter of the influence of good versus bad general rules, the good general rules being the "extensive" and "constant" ones.

‘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)

Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for (...) bilateral proof rules has a reasonable claim to inferentially articulating the core meaning of all of the classical connectives. I propose this schema in the context of a bilateral sequent calculus in which each connective is given exactly two rules: a rule for affirmation and a rule for denial. Positive and negative rules for all of the classical connectives are given by a single rule schema, harmony between these positive and negative rules is established at the schematic level by a pair of elimination theorems, and the truth-conditions for all of the classical connectives are read off at once from the schema itself. (shrink)

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: "responsiveness", which requires (...) that revised beliefs incorporate what has been learnt, and "conservativeness", which requires that beliefs on which the learnt input is "silent" do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application. (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)

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)

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 studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and (...) that deductions in normal form have the subformula property. (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)

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)

Traditional rule consequentialism faces a problem sometimes called the ideal world objection—the worry that by looking only at the consequences in worlds where rules are universally adhered to, the theory fails to account for problems that arise because adherence to rules in the real world is inevitably imperfect. In response, recent theorists have defended sophisticated versions of rule consequentialism which are sensitive to the consequences in worlds with less utopian levels of adherence. In this paper, I argue that (...) these attempts underestimate the problem they are designed to avoid—the worry about ideal worlds is only one manifestation of a deeper and more general problem, the distant world objection, which threatens not only the sophisticated revisions of rule consequentialism, but any view which determines what we ought to do by evaluating worlds that differ from ours in more than what is up to us. (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)

In our thought, we employ rules of inference and belief-forming methods more generally. For instance, we (plausibly) employ deductive rules such as Modus Ponens, ampliative rules such as Inference to the Best Explanation, and perceptual methods that tell us to believe what perceptually appears to be the case. What explains our entitlement to employ these rules and methods? This chapter considers the motivations for broadly internalist answers to this question. It considers three such motivations—one based on (...) simple cases, one based on a general conception of epistemic responsibility, and one based on skeptical scenarios. The chapter argues that none of these motivations is successful. The first two motivations lead to forms of internalism—Extreme Method Internalism and Defense Internalism—that are too strong to be tenable. The third motivation motivates Mental Internalism (Mentalism), which does not fit with plausible accounts of entitlement. (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)

We can evaluate laws as better or worse relative to different normative standards. One might lament the fact that a law violates human rights or, in a different register, marvel at its ease of application. A question in legal philosophy is whether some standards for evaluating laws are fixed by—or grounded in—the very nature of law. I take Raz’s discussion of the distinctively legal virtues, those that fall under the rubric of the “Rule of Law” such as clarity, generality, and (...) non-retroactivity, as my starting point for exploring a very general puzzle about the relationship between law’s essence and its virtue. -/- The claim that there are some virtues that laws have qua laws invites a comparison between law and other “goodness-fixing kinds.” A kind is goodness-fixing if what it is to be a member of the kind fixes a standard for evaluating instances as better or worse. For example, if an object belongs to the kind CLOCK, whether it keeps time accurately provides a basis for evaluating it as better or worse as a clock. Furthermore, the relevant normative fact—if a clock does not keep time accurately, it is a bad clock—is at least partly explainable in terms of the nature of clocks (clocks are things that are supposed to be keep time accurately). Hence, for any goodness-fixing kind, K, that sets a standard, S, for evaluating Ks as Ks, we can ask: (1) How does the nature of Ks explain S? (2) Does being a K depend on meeting a minimum threshold of S-relative goodness? In the case of law and its constitutive standard defined by the Rule-of-Law virtues, these questions lack settled answers. Although Raz offers some discussion, I argue that his answers have the surprising upshot of rendering law sui generis relative to other goodness-fixing kinds, and that preserving continuity with other goodness-fixing kinds involves revising the general picture. (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)

We provide a derivation of the Born Rule in the context of the Everett (Many-Worlds) approach to quantum mechanics. Our argument is based on the idea of self-locating uncertainty: in the period between the wave function branching via decoherence and an observer registering the outcome of the measurement, that observer can know the state of the universe precisely without knowing which branch they are on. We show that there is a uniquely rational way to apportion credence in such cases, which (...) leads directly to the Born Rule. Our analysis generalizes straightforwardly to cases of combined classical and quantum self-locating uncertainty, as in the cosmological multiverse. (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)

One of HLA Hart's main contributions to jurisprudence is his theory of social rules. Hart said, essentially, that a social rule exists if the members of a society act in some way and have a certain attitude. Most legal philosophers think that Hart's account of this attitude is too general, however, and that his theory is overinclusive as a result. In this article, I draw on recent work in the philosophy of action to propose a more precise account (...) of the relevant attitude, and a revised version of Hart's theory. I claim that a social rule exists if the members of a society act in some way and ‘accept’ they ought to act this way, independent of their beliefs about the matter. One of the implications of this idea is that the attitude that underlies a social rule is closely analogous to a presumption or fiction about what ought to be done. -/- . (shrink)

The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in (...) Posterior analytics is used to distinguish between conceptions that share the same name but are substantively different: for example the search for a broader genus including all mathematical objects; the search for a common character of different species of mathematical objects; and the effort to treat magnitudes as numbers. (shrink)

We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan’s Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular (...) we examine the Fréchet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction Cn+1 of n + 1 conditional events to the family {Cn,En+1|Hn+1}. We consider the relation with the notion of quasi-conjunction and we examine in detail the coherence of the prevision assessments related with the conjunction of three conditional events. Based on conjunction, we also give a characterization of p-consistency and of p-entailment, with applications to several inference rules in probabilistic nonmonotonic reasoning. Finally, we examine some non p-valid inference rules; then, we illustrate by an example two methods which allow to suitably modify non p-valid inference rules in order to get inferences which are p-valid. (shrink)

There is a fundamental disagreement about which norm regulates assertion. Proponents of factive accounts argue that only true propositions are assertable, whereas proponents of non-factive accounts insist that at least some false propositions are. Puzzlingly, both views are supported by equally plausible (but apparently incompatible) linguistic data. This paper delineates an alternative solution: to understand truth as the aim of assertion, and pair this view with a non-factive rule. The resulting account is able to explain all the relevant linguistic data, (...) and finds independent support from general considerations about the differences between rules and aims. (shrink)

Why do we have social norms—of fairness, cooperation, trust, property, or gender? Modern-day Humeans, as I call them, believe these norms are best accounted for in cultural evolutionary terms, as adaptive solutions to recurrent problems of social interaction. In this paper, I discuss a challenge to this “Humean Program.” Social norms involve widespread behaviors, but also distinctive psychological attitudes and dispositions. According to the challenge, Humean accounts of norms leave their psychological side unexplained. They explain, say, why we share equally, (...) but not why we disapprove of those who don’t. I defend the Humean Program against this challenge. In particular, I suggest an idea for how to extend the Program to account for the psychological side of norms. Socially adaptive behaviors aren’t just likely to emerge in a group; They are also likely to be widely taught within it. The transmission of these behaviors through instruction explains why they are associated with distinctive normative attitudes and dispositions. These attitudes play a pedagogical role in helping transmit these behaviors to children and newcomers. (shrink)

This review essay of Economics Rules situates Dani Rodrik’s contribution with respect to the 2007–2008 global economic crisis. This financial meltdown, which the eurozone did not fully recover from before the Covid-19 pandemic, led to soul- searching among economists as well as a call for heterodox economic approaches. Yet, over the past decade, instead the economics profession has maintained its orthodoxy. Rodrik’s Economics Rules offers a critique of the economics profession that is castigating but mild. It calls for (...) economists to use more and diverse models without becoming wedded to any single model or an overarching vision. Yet Rodrik ratifies many of the benchmark models standard to orthodox economics and provides little ground for a fundamental rethinking of the discipline. This essay analyses the conservatism underlying Rodrik’s approach, which upholds general equilibrium theory and rational expectations underlying the efficient market hypothesis. It argues that the economics discipline’s scope-creep to maintain its applicability to all human decision-making, and its acceptance of all-inclusive utility functions, crowds out moral sentiments and civic virtue. Thus. it argues that rather than urging economists simply to be more cautious in their application of models to address particular social concerns, instead economists must recognise their discipline’s inherent limitations. (shrink)

As an indirect ethical theory, rule consequentialism first evaluates moral codes in terms of how good the consequences of their general adoption are and then individual actions in terms of whether or not the optimific code authorises them. There are three well-known and powerful objections to rule consequentialism’s indirect structure: the ideal world objection, the rule worship objection, and the incoherence objection. These objections are all based on cases in which following the optimific code has suboptimal consequences in the (...) real world. After outlining the traditional objections and the cases used to support them, this paper first constructs a new hybrid version of consequentialism that combines elements of both act and rule consequentialism. It then argues that this novel view has sufficient resources for responding to the previous traditional objections to pure rule consequentialism. (shrink)

Abstract This paper offers an appraisal of Phillip Pettit's approach to the problem how a merely finite set of examples can serve to represent a determinate rule, given that indefinitely many rules can be extrapolated from any such set. I argue that Pettit's so-called ethnocentric theory of rule-following fails to deliver the solution to this problem he sets out to provide. More constructively, I consider what further provisions are needed in order to advance Pettit's general approach to the (...) problem. I conclude that what is needed is an account that, whilst it affirms the view that agents' responses are constitutively involved in the exemplification of rules, does not allow such responses the pride of place they have in Pettit's theory. (shrink)

A certain type of inference rules in modal logics, generalizing Gabbay's Irreflexivity rule, is introduced and some general completeness results about modal logics axiomatized with such rules are proved.

As the ongoing literature on the paradoxes of the Lottery and the Preface reminds us, the nature of the relation between probability and rational acceptability remains far from settled. This article provides a novel perspective on the matter by exploiting a recently noted structural parallel with the problem of judgment aggregation. After offering a number of general desiderata on the relation between finite probability models and sets of accepted sentences in a Boolean sentential language, it is noted that a (...) number of these constraints will be satisfied if and only if acceptable sentences are true under all valuations in a distinguished non-empty set W. Drawing inspiration from distance-based aggregation procedures, various scoring rule based membership conditions for W are discussed and a possible point of contact with ranking theory is considered. The paper closes with various suggestions for further research. (shrink)

This essay formulates a moral principle I call sustainability’s golden rule. This principle, I will argue, goes a long way in providing correct moral guidance for sustainable development. In laying out these ideas, the essay proceeds as follows: first, a very basic, oft-privileged definition of sustainable development is put forward; second, I make clear how sustainability’s golden rule is formulable from basic moral considerations that explain why sustainable development should be pursued at all; and lastly, I deduce some of the (...) general implications sustainability’s golden rule has for sustainable development. (shrink)

This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both logically and (...) probabilistically. The statistical relevance of one function in determining another is put forward as a way of defining the value of information: The statistical relevance of a function F to a function G is the absolute value of the change in one's information about the value of G afforded by specifying the value of F. This theory provides normative justifications for conclusions projected by analogy from one case to another, and for generalization from an instance to a rule. The soundness of such conclusions, in either the logical or the probabilistic case, can be identified with the extent to which the corresponding criteria (determination and uniformity) actually hold for the features being related. (shrink)

The book’s core argument is that an artificial intelligence that could equal or exceed human intelligence—sometimes called artificial general intelligence (AGI)—is for mathematical reasons impossible. It offers two specific reasons for this claim: Human intelligence is a capability of a complex dynamic system—the human brain and central nervous system. Systems of this sort cannot be modelled mathematically in a way that allows them to operate inside a computer. In supporting their claim, the authors, Jobst Landgrebe and Barry Smith, marshal (...) evidence from mathematics, physics, computer science, philosophy, linguistics, and biology, setting up their book around three central questions: What are the essential marks of human intelligence? What is it that researchers try to do when they attempt to achieve "artificial intelligence" (AI)? And why, after more than 50 years, are our most common interactions with AI, for example with our bank’s computers, still so unsatisfactory? Landgrebe and Smith show how a widespread fear about AI’s potential to bring about radical changes in the nature of human beings and in the human social order is founded on an error. There is still, as they demonstrate in a final chapter, a great deal that AI can achieve which will benefit humanity. But these benefits will be achieved without the aid of systems that are more powerful than humans, which are as impossible as AI systems that are intrinsically "evil" or able to "will" a takeover of human society. (shrink)

The majority rule has caught much attention in recent debate about the aggregation of judgments. But its role in finding the truth is limited. A majority of expert judgments is not necessarily authoritative, even if all experts are equally competent, if they make their judgments independently of each other, and if all the judgments are based on the same source of (good) evidence. In this paper I demonstrate this limitation by presenting a simple counterexample and a related general result. (...) I pave the way for this argument by introducing a Bayesian model of evidence and expert judgment in order to give a precise account of the basic problem. (shrink)

Plato’s idea of the second-best state is the first appearance of the rule of law. It is considered as a realistic alternative to the government of the Philosopher King, differ-ing formally from it on the employment of general rules. The aim of this paper is to elaborate an articulation of both proposals and to better understand that of the rule of law within Plato’s thought. The main differences between it and the modern theories of the rule of law (...) will be assessed. Plato conceives the rule of law as a remedy directed to avoid tyranny, in which the idea of generality, characteristically associated with the rule of law. The law that rules the polis is a reasoned thought accepted by the citizenship, directed to avoid the ruling of the will of the tyrant. (shrink)

Aboriginal claims for self-government in the Americas and Australasia are distinctive for being less about secession—at least so far—than about demanding an innovative rethinking of the regulative norms and institutions within and between already established nation-states. Recent cases in Australia (and Canada) provide an opportunity to consider the nature of such claims, and some of the theoretical implications for regulative conceptions of sovereignty and the rule of law. A general question informing the entire discussion here is: how do particular (...) conceptions of the rule of law affect Aboriginal claims? Can a distinctive body of Aboriginal law survive in a liberal constitutional state already constituted in part by regulative ideals of the rule of law? (shrink)

Call it the Skynet hypothesis, Artificial General Intelligence, or the advent of the Singularity — for years, AI experts and non-experts alike have fretted (and, for a small group, celebrated) the idea that artificial intelligence may one day become smarter than humans. -/- According to the theory, advances in AI — specifically of the machine learning type that’s able to take on new information and rewrite its code accordingly — will eventually catch up with the wetware of the biological (...) brain. In this interpretation of events, every AI advance from Jeopardy-winning IBM machines to the massive AI language model GPT-3 is taking humanity one step closer to an existential threat. We’re literally building our soon-to-be-sentient successors. -/- Except that it will never happen. At least, according to the authors of the new book Why Machines Will Never Rule the World: Artificial Intelligence without Fear. (shrink)

When faced with a rule that they take to be true, and a recalcitrant example, people are apt to say: “The exception proves the rule”. When pressed on what they mean by this though, things are often less than clear. A common response is to dredge up some once-heard etymology: ‘proves’ here, it is often said, means ‘tests’. But this response—its frequent appearance even in some reference works notwithstanding1—makes no sense of the way in which the expression is used. To (...) insist that the exception proves the rule is to insist that whilst this is an exception, the rule still stands; and furthermore, that, rather than undermining the rule, the exception serves to confirm it. This second claim may seem paradoxical, but it should not, once it is realized that what does the confirming is not the exception itself, but rather the fact that we judge it to be an exception; and that what is confirmed is not the rule itself, but rather the fact that we judge it to be a rule. To treat something as an exception is not to treat it as a counterexample that refutes the existence of the rule. Rather it is to treat it as special, and so to concede the rule from which it is excepted. The point comes clearly in the original (probably 17th Century) Latin form: Exceptio probat (figit2) regulam in casibus non exceptis. Exception (i.e. the act of excepting) proves (establishes) the rule in the cases not excepted. Clearly this form of reasoning cannot apply when the rule that we are considering has the form of a simple universal generalization. Here there can be no exceptions, only counterexamples. So what we need, and what will be developed.. (shrink)

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. (...) These acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy. (shrink)

Assuming that votes are independent, the epistemically optimal procedure in a binary collective choice problem is known to be a weighted supermajority rule with weights given by personal log-likelihood-ratios. It is shown here that an analogous result holds in a much more general model. Firstly, the result follows from a more basic principle than expected-utility maximisation, namely from an axiom (Epistemic Monotonicity) which requires neither utilities nor prior probabilities of the ‘correctness’ of alternatives. Secondly, a person’s input need not (...) be a vote for an alternative, it may be any type of input, for instance a subjective degree of belief or probability of the correctness of one of the alternatives. The case of a profile of subjective degrees of belief is particularly appealing, since here no parameters such as competence parameters need to be known. (shrink)

Epistemic rationality is typically taken to be immodest at least in this sense: a rational epistemic state should always take itself to be doing at least as well, epistemically and by its own light, than any alternative epistemic state. If epistemic states are probability functions and their alternatives are other probability functions defined over the same collection of proposition, we can capture the relevant sense of immodesty by claiming that epistemic utility functions are (strictly) proper. In this paper I examine (...) what happens if we allow for the alternatives to an epistemic state to include probability functions with different domains. I first prove an impossibility result: on minimal assumptions, I show that there is no way of vindicating strong immodesty principles to the effect that any probability function should take itself to be doing at least as well than any alternative probability function, regardless of its domain. I then consider alternative, weaker generalizations of the traditional immodesty principle and prove some characterization results for some classes of epistemic utility functions satisfying each of the relevant principles. (shrink)

The Golden Rule is (roughly) as follows: treat others as you would have others treat you. Philosophical reactions to it vary; it has both supporters and detractors. In any case, almost nobody who things critically about morality takes the literal version of the Golden Rule seriously, since there are just too many problems with it. To demonstrate this, I will look at a literal version of the Golden Rule espoused by John C. Maxwell, a well-known and influential motivational speaker, and (...) briefly discuss some of the obvious problems that it faces. I will then examine a more sophisticated version of the Golden Rule espoused by philosopher Harry Gensler. While able to overcome some of the problems of the literal Golden Rule, Gensler's version nevertheless shares a common difficulty with it: in both cases, the moral agent is asked to imagine themselves in the place of another. Maxwell things this is easily done, and Gensler asks for vividness and accuracy in this act of imagination. I wish to show that any version of the Golden Rule that takes seriously the need to imagine oneself in the place of another is to ask one to do the impossible, so any versions of the Golden Rule that require this should be rejected. (shrink)

Whether it was John Searle’s Chinese Room argument (Searle, 1980) or Roger Penrose’s argument of the non-computable nature of a mathematician’s insight – an argument that was based on Gödel’s Incompleteness theorem (Penrose, 1989), we have always had skeptics that questioned the possibility of realizing strong Artificial Intelligence (AI), or what has become known by Artificial General Intelligence (AGI). But this new book by Landgrebe and Smith (henceforth, L&S) is perhaps the strongest argument ever made against strong AI. It (...) is a very extensive review of what building a mind essentially amounts to drawing on insights and results from biology, physics, linguistics, computability, philosophy, and mathematics. (shrink)

We describe (essential features and an axiomatization of) a new metamathematical (cognitive) ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions, and playing a fundamental role in Artificial Mathematical Intelligence (or Cognitive-computational metamathematics). Furthermore, we present an initial (first-order) formalization of this mechanism together with its characterizing relation with classic notions like primitive positive definability and Diophantiveness. Additionally, we analyze the semantic variability of functional conceptual substratum when small syntactic modifications are done. Finally, (...) we describe cognitively natural inference rules for (mathematical) definitions inspired by functional conceptual substratum and we show that they are sound and complete w.r.t.\ standard calculi. (shrink)

Some readers of Wittgenstein---I discuss Robert Brandom---think that his writings contain a regress argument showing that the notion of participating in a practice is more basic than the notion of following a rule, in explanations of linguistic correctness. But the regress argument bears equally on both these notions: if there is an explanatory regress of rules, then there is an explanatory regress of practices as well. Why then does Wittgenstein invoke the notion of a practice, apparently by way of (...) diagnosing the error on which the regress argument rests? I suggest that he invokes that notion to emphasize certain aspects of rule-following which we are apt to neglect, when we forget that rule-following is---not, rests upon---participating in a practice. When we appreciate those aspects of rule/practice-following we see the flaw in both regress arguments. (shrink)

In this perspective paper, I tried to explain that what will be the possible prospect of multiple functions in one and another through the chain rule of differentiation? The chain rule is a formula to compute the derivative of the functional composition of two or more functions. The chain rule provides us a technique for finding the derivative of composite functions, with the number of functions that make up the composition determining how many differentiation steps are necessary. The chain rule (...) in that what changes I noted, how it can be modified to reduce the differentiation process of multiple functions in one and another and implementing that process in the inverse of multiple functions in one and another, further proceedings them through the chain rule of differentiation with all prospects. Here I claim that the differentiation’s chain rule is not changed but the sequences of finding the derivative of multiple functions are changed. (shrink)

A reply to Melissa Lane's "Antianarchia: interpreting political thought in Plato" In these comments I focus on how to think of antianarchia as an element of Plato's political thought, and in doing so raise some methodological questions about how to read Plato’s dialogues, focusing on what is involved in attributing views to Plato in general.

The Born’s rule to interpret the square of wave function as the probability to get a specific value in measurement has been accepted as a postulate in foundations of quantum mechanics. Although there have been so many attempts at deriving this rule theoretically using different approaches such as frequency operator approach, many-world theory, Bayesian probability and envariance, literature shows that arguments in each of these methods are circular. In view of absence of a convincing theoretical proof, recently some researchers have (...) carried out experiments to validate the rule up-to maximum possible accuracy using multi-order interference (Sinha et al, Science, 329, 418 [2010]). But, a convincing analytical proof of Born’s rule will make us understand the basic process responsible for exact square dependency of probability on wave function. In this paper, by generalizing the method of calculating probability in common experience into quantum mechanics, we prove the Born’s rule for statistical interpretation of wave function. (shrink)

After providing a brief overview of the economic theory of judicial decisions this paper presents an argument for why not only the economic theory of judicial decisions, but also the rational approach in general, most often fails in explaining decision-making. Work done within the research program of New Institutionalism is presented as a possible alternative. Within this research program judicial activity is conceptualized as the activity of "interpreting the rules of the game", i.e. the institutions that frame the (...) economic and political interaction in a society. Such a conceptualization of judicial interpretation and judicial decision-making would have to depart from rational choice modes of reasoning, and should instead focus on how human beings actually reason, learn and choose drawing from research in cognitive science. (shrink)

Recent work in judgment and decisionmaking has stressed that institutions, like individuals, often rely on decisionmaking heuristics. But most of the institutional decisionmaking heuristics studied to date are highly firm- and industry-specific. This contrasts to the individual case, in which many heuristics are general-purpose rules suitable for a wide range of decision problems. Are there also general-purpose heuristics for institutional decisionmaking? In this paper, I argue that a number of methods recently developed for decisionmaking under deep uncertainty (...) have a good claim to be understood as general-purpose decisionmaking heuristics suitable for a broad range of institutional decision problems. (shrink)