Moral evaluation is concerned with the attribution of values whose distinction into two broad groups has become familiar. On the one hand, there are the most general moral values of lightness, wrongness, goodness, badness, and what ought to be or to be done. On the other, there is a great diversity of more specific moral values which these objects can have: of being a theft, for instance, or a thief; of honesty, reliability or callousness. Within the recent body of work (...) attempting to restore to the virtues a central place in ethical thinking, two claims stand out. One is that, of these two kinds of values, the specific ones are explanatorily prior to the general – that if an action is wrong, it is because it is wrong in one of those specific respects. A second claim, though, is now standardly made definitive of ‘Virtue ethics’: that amongst the specific values, the value of character is explanatorily prior to that of action – that if an action is callous, say, it is because it expresses callousness of character – and that in this sense, the moral value of action derives from that of character. This second claim has been widely attacked; in what follows, I present a reason for believing that, at least in the case of callousness, it is right. (shrink)

이 글의 주된 목적은 반복적 집합 개념을 검토하여 그 개념이 지니는 내부적인 문제들을 드러내고 그 개념에 대한 구성주의적 비판을 제시하는 것이다. 내부적인 문제는 고전수학자들에게 반복적 집합 개념이 불분명한 데에서 기인한다. 이 점은 불로스의 단계이론을 반복적 집합 개념에 관한 다른 설명과 비교하고 치환공리와 선택공리에 관한 논란을 검토하여 드러낼 것이다. 이보다 훨씬 심각한 문제는 구성주의적 비판이다. 특히, 고전적인 반복적 집합 개념에 내재한 무한에 관한 실재론적 이해에 대한 비판과, 집합론에서 고전논리의 사용에 대한 비판 및 비서술성에 관한 비판이 제기될 것이며, 반복적 집합 개념이 구성적으로 (...) 이해될 때, 어떤 원칙들이 정당화될 수 있는지 검토될 것이다. (shrink)

In referendum elections, voters are often required to register simultaneous votes on multiple proposals. The separability problem occurs when a voter’s preferred outcome on one proposal depends on the outcomes of other proposals. This type of interdependence can lead to unsatisfactory or even paradoxical election outcomes, such as a winning outcome that is the last choice of every voter. Here we propose an iterative voting scheme that allows voters to revise their voting strategies based on the outcomes of previous (...) iterations. Using a robust computer simulation, we investigate the potential of this approach to solve the separability problem. (shrink)

How should deontologists approach decision-making under uncertainty, for an iterated decision problem? In this paper I explore the shortcomings of a simple expected value approach, using a novel example to raise questions about attitudes to risk, the moral significance of tiny probabilities, the independent moral reasons against imposing risks, the morality of sunk costs, and the role of agent-relativity in iterated decision problems.

In this paper it is argued that, in order to solve the problem of iterated belief change, both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation. It is shown that the operation in question satisfies generalized versions of the Gärdenfors revision postulates. The account offered is motivated by Spohn's ordinal conditionalization (...) functions, and can be seen as the Jeffrization of a proposal considered by Rott. (shrink)

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be (...) reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a "virtual" manner, using uniterated revision. (shrink)

Positive thinkers love Watty Piper's The little engine that could. The story features a train laden with toys for deserving children on the other side of the mountain. After the locomotive breaks down, a sequence of snooty locomotives come up the track. Each engine refuses to pull the train up the mountain. They are followed by a weary old locomotive that declines, saying "I cannot. I cannot. I cannot." But then a bright blue engine comes up the track. He manages (...) to chug over the mountain by averring "I think I can. I think I can. I think can.". (shrink)

Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. For that, (...) we first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

Two of the major problems in AGM-style belief revision, namely the difficulties in accounting for iterated change and for Ramsey test conditionals, have satisfactory solutions in descriptor revision. In descriptor revision, the input is a metalinguistic sentence specifying the success condition of the operation. The choice mechanism selects one of the potential outcomes in which the success condition is satisfied. Iteration of this operation is unproblematic. Ramsey test conditionals can be introduced without giving rise to the paradoxical results that (...) they generate in other systems. In addition to standard Ramsey test conditionals, a more general variant of epistemic conditionals is defined, representing statements of the form ”if the belief state is changed to satisfy condition A then it will satisfy condition B”. An axiomatic characterization of such descriptor conditionals is presented. It is related in intricate ways to the KLM postulates for cumulative reasoning. (shrink)

This is a discussion of the problem of extending the basic AGM belief revision theory to iterated belief revision: the problem of formulating rules, not only for revising a basic belief state in response to potential new information, but also for revising one’s revision rules in response to potential new information. The emphasis in the paper is on foundational questions about the nature of and motivation for various constraints, and about the methodology of the evaluation of putative counterexamples (...) to proposed constraints. Some specific constraints that have been proposed are criticized. The paper emphasizes the importance of meta-information—information about one’s sources of information—and argues that little of substance can be said about constraints on iterated belief revision at a level of abstraction that lacks the resources for explicit representation of meta-information. (shrink)

Recent work has considered the problem of extending to the case of iterated belief change the so-called `Harper Identity' (HI), which defines single-shot contraction in terms of single-shot revision. The present paper considers the prospects of providing a similar extension of the Levi Identity (LI), in which the direction of definition runs the other way. We restrict our attention here to the three classic iterated revision operators--natural, restrained and lexicographic, for which we provide here the first collective characterisation in (...) the literature, under the appellation of `elementary' operators. We consider two prima facie plausible ways of extending (LI). The first proposal involves the use of the rational closure operator to offer a `reductive' account of iterated revision in terms of iterated contraction. The second, which doesn't commit to reductionism, was put forward some years ago by Nayak et al. We establish that, for elementary revision operators and under mild assumptions regarding contraction, Nayak's proposal is equivalent to a new set of postulates formalising the claim that contraction by ¬A should be considered to be a kind of `mild' revision by A. We then show that these, in turn, under slightly weaker assumptions, jointly amount to the conjunction of a pair of constraints on the extension of (HI) that were recently proposed in the literature. Finally, we consider the consequences of endorsing both suggestions and show that this would yield an identification of rational revision with natural revision. We close the paper by discussing the general prospects for defining iterated revision in terms of iterated contraction. (shrink)

Iterated admissibility embodies a minimal criterion of rationality in interactions. The epistemic characterization of this solution has been actively investigated in recent times: it has been shown that strategies surviving \ rounds of iterated admissibility may be identified as those that are obtained under a condition called rationality and m assumption of rationality in complete lexicographic type structures. On the other hand, it has been shown that its limit condition, with an infinity assumption of rationality ), might not be satisfied (...) by any state in the epistemic structure, if the class of types is complete and the types are continuous. In this paper we analyze the problem in a different framework. We redefine the notion of type as well as the epistemic notion of assumption. These new definitions are sufficient for the characterization of iterated admissibility as the class of strategies that indeed satisfy \. One of the key methodological innovations in our approach involves defining a new notion of generic types and employing these in conjunction with Cohen’s technique of forcing. (shrink)

In recent years, it becomes clear that ITER project in France, as one of the largest experimental fusion reactors underway, is far away from achieving net energy production. In this review article, we presented a short communication this week with Robert Neil Boyd, a senior physicist who happens to have his own working design of fusion reactor in the past. We hope that this transcript of our communication with him (as per 15-17th Nov. 2021) may be found useful for younger (...) scientists. (shrink)

In (Hertwig et al. , 2003) Hertwig et al. draw a distinction between decisions from experience and decisions from description. In a decision from experience an agent does not have a summary description of the possible outcomes or their likelihoods. A career choice, deciding whether to back up a computer hard drive, cross a busy street, etc., are typical examples of decisions from experience. In such decisions agents can rely only of their encounters with the corresponding prospects. By contrast, an (...) agent furnished with information sources such as drug-package inserts or mutual-fund brochures—all of which describe risky prospects—will often make decisions from description. In (Hertwig et al. , 2003) it is shown (empirically) that decisions from experience and decisions from description can lead to dramatically different choice behavior. Most of these results (summarized and analyzed in (Hertwig, 2009)) are concerned with the role of risk in decision making. This article presents some preliminary results concerning the role of uncertainty in decision-making. We focus on Ellsberg’s two-color problem and consider a chance setup based on double sampling. We report empirical results which indicate that decisions from description where subjects select between a clear urn, the chance setup based on double sampling and Ellsberg’s vague urn, are such that subjects perceive the chance setup at least as an intermediate option between clear and vague choices (and there is evidence indicating that the double sampling chance setup is seen as operationally indistinguishable from the vague urn). We then suggest how the iterated chance setup can be used in order to study decisions from experience in the case of uncertainty. (shrink)

A tracking control algorithm of nonlinear multiple agents with undirected communication is studied for each multiagent system affected by external interference and input saturation. A control design scheme combining iterative learning and adaptive control is proposed to perform parameter adaptive time-varying adjustment and prove the effectiveness of the control protocol by designing Lyapunov functions. Simulation results show that the high-precision tracking control problem of the nonlinear multiagent system based on adaptive iterative learning control can be well realized even when (...) the input is saturated. Finally, the validity of the proposed algorithm is verified by numerical analysis. (shrink)

Rondo Keele makes a foray into what he calls 'applied logic', investigating a complex argument strategy employed against Ockham by his greatest contemporary opponent, Walter Chatton. Chatton conceives a two-part strategy which attempts to force a kind of iteration of conceptual analysis, together with an infinite explanatory regress, in order to establish that one particular philosophical analysis is ultimately dependent on another. Chatton uses this strategy against Ockham in order to show that the latter's reductionist metaphysics depends ultimately upon (...) a deeper level of realist assumptions that he can neither evade nor explain away. Keele then shows how, earlier in his career, Chatton found himself on the receiving end of this same strategy, defending his own highly original solution to the problem of future contingents from the very iteration-regress attack he would subsequently use on Ockham. Keele concludes with an examination of Chatton's attempts to avoid the consequences of his own strategy, and draws some connections between this argument strategy and modal collapse in modern logics. (shrink)

Surveying and criticising attitudes towards the role and strength of the iterative conception of set—widely seen as the justificatory basis of Zermelo-Fraenkel set theory with Choice—this paper highlights a tension in both contemporary and historic accounts of the iterative conception’s justificatory role: on the one hand its advocates wish to claim that it justifies ZFC, but on the other hand they abstain from stating whether the preconditions for such justification exists. Expanding the number of axioms that the conception is standardly (...) charged with failing to justify, in the forms of the Emptyset and Powerset, this paper aims to extend the critique that the iterative conception does not justify ZFC to its subsystems. Exploring the historic and contemporary relationship between the iterative conception and set theory, the paper then attempts to defuse strategies that avoid the problems of intrinsic justification by weakening the iterative conception’s role to the ‘motivational’ or ‘heuristic’ by showing that what the iterative conception has been seen to motivate has changed over time. It is suggested that the conjunction of these arguments seriously weakens the programme of reasoning on an ‘atheoretic’ notion of set. (shrink)

The interpretation of the utilitarianism of John Stuart Mill has been a matter of controversy at least since J.O. Urmson published his well known paper over twenty-five years ago. Urmson attributed to Mill a form of “rule-utilitarianism”, contrasting his reading with the “received view” on which Mill held a form of “act-utilitarianism”. Since then, the interpretive problem has typically been seen to be that of determining which of these two types of theory should be attributed to Mill, or, at (...) least of determining whether Mill was a “rule-utilitarian”. However, as the distinction is typically made, it is possible to have a utilitarian theory which is neither an act- nor a rule-utilitarian theory. 1n particular, as I will attemptto show, Mill's theory is of neither type but is an example of a sophisticated type of utilitarianism which we might call “iterated-utilitarianism”, for reasons which will become clear in what follows. (shrink)

The problems that surround iterated contractions and expansions of beliefs are approached by studying hypertheories, a generalisation of Adam Grove's notion of systems of spheres. By using a language with dynamic and doxastic operators different ideas about the basic nature of belief change are axiomatised. It is shown that by imposing quite natural constraints on how hypertheories may change, the basic logics for belief change can be strengthened considerably to bring one closer to a theory of iterated belief change. It (...) is then argued that the logic of expansion, in particular, cannot without loss of generality be strengthened any further to allow for a full logic of iterated belief change. To remedy this situation a notion of directed expansion is introduced that allows for a full logic of iterated belief change. The new operation is given an axiomatisation that is complete for linear hypertheories. (shrink)

Many of the problems studied in cognitive science are inductive problems, requiring people to evaluate hypotheses in the light of data. The key to solving these problems successfully is having the right inductive biases—assumptions about the world that make it possible to choose between hypotheses that are equally consistent with the observed data. This article explores a novel experimental method for identifying the biases that guide human inductive inferences. The idea behind this method is simple: This article uses the responses (...) produced by a participant on one trial to generate the stimuli that either they or another participant will see on the next. A formal analysis of this “iterated learning” procedure, based on the assumption that the learners are Bayesian agents, predicts that it should reveal the inductive biases of these learners, as expressed in a prior probability distribution over hypotheses. This article presents a series of experiments using stimuli based on a well-studied set of category structures, demonstrating that iterated learning can be used to reveal the inductive biases of human learners. (shrink)

In dynamic epistemic logic and other fields, it is natural to consider relativization as an operator taking sentences to sentences. When using the ideas and methods of dynamic logic, one would like to iterate operators. This leads to iterated relativization. We are also concerned with the transitive closure operation, due to its connection to common knowledge. We show that for three fragments of the logic of iterated relativization and transitive closure, the satisfiability problems are fi1 11–complete. Two of these fragments (...) do not include transitive closure. We also show that the question of whether a sentence in these fragments has a finite (tree) model is fi0 01–complete. These results go via reduction to problems concerning domino systems. (shrink)

The interpretation of the utilitarianism of John Stuart Mill has been a matter of controversy at least since J.O. Urmson published his well known paper over twenty-five years ago. Urmson attributed to Mill a form of “rule-utilitarianism”, contrasting his reading with the “received view” on which Mill held a form of “act-utilitarianism”. Since then, the interpretive problem has typically been seen to be that of determining which of these two types of theory should be attributed to Mill, or, at (...) least of determining whether Mill was a “rule-utilitarian”. However, as the distinction is typically made, it is possible to have a utilitarian theory which is neither an act- nor a rule-utilitarian theory. 1n particular, as I will attemptto show, Mill's theory is of neither type but is an example of a sophisticated type of utilitarianism which we might call “iterated-utilitarianism”, for reasons which will become clear in what follows. (shrink)

In this paper, we consider the iterative algorithm for a boundary value problem of n -order fractional differential equation with mixed integral and multipoint boundary conditions. Using an iterative technique, we derive an existence result of the uniqueness of the positive solution, then construct the iterative scheme to approximate the positive solution of the equation, and further establish some numerical results on the estimation of the convergence rate and the approximation error.

This paper considers the consensus control problem of nonlinear spatial-temporal hyperbolic partial difference multiagent systems and parabolic partial difference multiagent systems with time delay. Based on the system’s own fixed topology and the method of generating the desired trajectory by introducing virtual leader, using the consensus tracking error between the agent and the virtual leader agent and neighbor agents in the last iteration, an iterative learning algorithm is proposed. The sufficient condition for the system consensus error to converge (...) along the iterative axis is given. When the iterative learning number k approaches infinity, the consensus error in the sense of the L 2 norm between all agents in the system will converge to zero. Furthermore, simulation results illustrate the effectiveness of the algorithm. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 38.2 (2000) 221-238 [Access article in PDF] Hume's Iterative Probability Argument: A Pernicious Reductio Kevin Meeker University of South Alabama In this essay I want to look afresh at David Hume's iterative probability argument, found in the section entitled "Of Scepticism with regard to Reason" in his A Treatise of Human Nature.1 Interestingly enough, after years of comparative neglect,2 this argument has been (...) basking in the glow of scholarly sunshine lately.3 But to what can we attribute its extended hiatus? The convergence of three major factors seems responsible. First, philosophers have oftentimes flung this argument into the ocean of obscurity because of its perceived inadequacies.4 Second, and on a related note, many assume that Hume himself permitted this argument to drown because it never resurfaces again in his writings. Most suspiciously, Hume's Enquiry Concerning Human Understanding, which is his popular (and preferred) presentation of the epistemological sections [End Page 221] of the Treatise, does not contain this argument.5 Last, but certainly not least, for a long time this argument sat uncomfortably with the naturalist interpretation of Hume6 that has gained ascendancy in the twentieth century. For prior to this century, Hume was almost unanimously regarded as a sceptic. Despite a few waves from those who interpreted Hume as a logical positivist earlier in this century, Norman Kemp Smith charted a new course for Humean interpretations with his emphasis on Hume's naturalism.7 And this is the current according to which most Hume interpreters set their sails today.Because the naturalist reading of Hume relies so heavily on the system he attempts to set forth in the Treatise, though, naturalists have come to see the importance of reading this argument in a naturalistically acceptable way. William E. Morris best expresses the significance of this argument from a naturalistic perspective in the following manner: If we ever are to understand Hume's view of the role of reason, it stands to reason that we should first figure out how to integrate "Of scepticism with regard to reason" into the picture. Only then will we be ready to move to a consideration of Hume's positive views about reason. These views are the least understood of any of Hume's doctrines. Gaining an adequate understanding of them is both the most pressing and the most difficult problem facing Hume studies today.8While I agree with Morris about the importance of getting a clear understanding of the reasoning of I, iv, 1, I will argue that a correct reading of this section reveals the implausibility of major naturalistic interpretations of Hume.This paper has four major sections. In the first important section, I will highlight the crucial aspects of the iterative argument that will be the focus of this paper and deal with a preliminary but important interpretive issue. In the second section, I will briefly look at Annette Baier's naturalistic reading of Hume's philosophy to show how this particular passage bears on broader [End Page 222] interpretive issues. The third main section will focus on explicating Morris' similar but more detailed interpretation. Finally in the last part I will show that while it is legitimate to characterize the argument here as a reductio (as Baier and Morris both do), the argument still yields, contrary to what naturalists have recently suggested, a very sceptical conclusion. 1. The Arguments of Section I, IV, 1 of the TreatiseHume's "Of Scepticism with regard to Reason" contains at least two important arguments. While Hume agrees that knowledge involves certainty (whereas beliefs based on probability are by their very nature uncertain9 ), the conclusion of his first argument is that "all knowledge resolves itself into probability" (Treatise, 181). His point here is simply that all of our beliefs are fallible. That is, nothing is absolutely certain; thus none of our beliefs attain the exalted status of certain knowledge. But once this consequence of our fallibility is recognized, he then argues roughly that the probability that any particular belief... (shrink)

In the advent of communication, Derrida finds that meaning through signification carries with it the possibility of mis-communication in which the intended meaning behind the text becomes undecidable and inevitably polysemic in its transference. In a short, yet fecund essay “Signature Event Context,” Derrida tackles the problem of communication and the supposed claim of the classical notion of writing’s conception of virtual permanence within the text. The classical notion of writing claims that writing as a medium or a species (...) of communication implies that the transference of meaning is conducted in a homogenous fashion. In the absence, of the author who has abandoned the fleeting singular instance of inscription, the text, according to the classical notion of writing, must be able to transfer meaning within the interplay of the text itself, for if it fails to do so, writing would cease to become useful in its intention to transfer meaning. (shrink)

This paper is about what I call the Question of Iterated Causation (QIC): for any instance of causation in which c1…ck cause effect e, what are the causes of c1…ck’s causing of e? In short: what causes instances of causation or, as I will refer to these instances, the “causal goings‐on”? A natural response (which I call “dismissivism”) is that this is a bad question because causal goings‐on aren’t apt to be caused. After rebutting several versions of dismissivism, I consider (...) the view that QIC, though not illegitimate, is easy to answer: the causal goings‐on are apt to be caused but are plainly uncaused (“brutism”). However, I will argue that brutism too has a serious problem: namely, it leads to a highly implausible kind of armchair indeterminism. Next I consider some substantive candidate answers to QIC, none of which, I argue, is particularly promising. The paper’s final conclusion is twofold: QIC is at least as difficult as the more well‐known Question of Iterated Grounding; moreover, the largely overlooked regress problem that it raises gives us at least some defeasible reason to avoid causation in theory‐building. (shrink)

ABSTRACT We consider in this work the problem of iterated belief revision. We propose a family of belief revision operators called revision with memory operators and we give a logical (both syntactical and semantical) characterization of these operators. They obey what we call the principle of strong primacy of update: when one revises his beliefs by a new evidence, then all possible worlds that satisfy this new evidence become more reliable than those that do not. We show that those (...) operators have a satisfying behaviour concerning the iteration of the revision process. Then we provide four particular operators of this family. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 38.2 (2000) 221-238 [Access article in PDF] Hume's Iterative Probability Argument: A Pernicious Reductio Kevin Meeker University of South Alabama In this essay I want to look afresh at David Hume's iterative probability argument, found in the section entitled "Of Scepticism with regard to Reason" in his A Treatise of Human Nature.1 Interestingly enough, after years of comparative neglect,2 this argument has been (...) basking in the glow of scholarly sunshine lately.3 But to what can we attribute its extended hiatus? The convergence of three major factors seems responsible. First, philosophers have oftentimes flung this argument into the ocean of obscurity because of its perceived inadequacies.4 Second, and on a related note, many assume that Hume himself permitted this argument to drown because it never resurfaces again in his writings. Most suspiciously, Hume's Enquiry Concerning Human Understanding, which is his popular (and preferred) presentation of the epistemological sections [End Page 221] of the Treatise, does not contain this argument.5 Last, but certainly not least, for a long time this argument sat uncomfortably with the naturalist interpretation of Hume6 that has gained ascendancy in the twentieth century. For prior to this century, Hume was almost unanimously regarded as a sceptic. Despite a few waves from those who interpreted Hume as a logical positivist earlier in this century, Norman Kemp Smith charted a new course for Humean interpretations with his emphasis on Hume's naturalism.7 And this is the current according to which most Hume interpreters set their sails today.Because the naturalist reading of Hume relies so heavily on the system he attempts to set forth in the Treatise, though, naturalists have come to see the importance of reading this argument in a naturalistically acceptable way. William E. Morris best expresses the significance of this argument from a naturalistic perspective in the following manner: If we ever are to understand Hume's view of the role of reason, it stands to reason that we should first figure out how to integrate "Of scepticism with regard to reason" into the picture. Only then will we be ready to move to a consideration of Hume's positive views about reason. These views are the least understood of any of Hume's doctrines. Gaining an adequate understanding of them is both the most pressing and the most difficult problem facing Hume studies today.8While I agree with Morris about the importance of getting a clear understanding of the reasoning of I, iv, 1, I will argue that a correct reading of this section reveals the implausibility of major naturalistic interpretations of Hume.This paper has four major sections. In the first important section, I will highlight the crucial aspects of the iterative argument that will be the focus of this paper and deal with a preliminary but important interpretive issue. In the second section, I will briefly look at Annette Baier's naturalistic reading of Hume's philosophy to show how this particular passage bears on broader [End Page 222] interpretive issues. The third main section will focus on explicating Morris' similar but more detailed interpretation. Finally in the last part I will show that while it is legitimate to characterize the argument here as a reductio (as Baier and Morris both do), the argument still yields, contrary to what naturalists have recently suggested, a very sceptical conclusion. 1. The Arguments of Section I, IV, 1 of the TreatiseHume's "Of Scepticism with regard to Reason" contains at least two important arguments. While Hume agrees that knowledge involves certainty (whereas beliefs based on probability are by their very nature uncertain9 ), the conclusion of his first argument is that "all knowledge resolves itself into probability" (Treatise, 181). His point here is simply that all of our beliefs are fallible. That is, nothing is absolutely certain; thus none of our beliefs attain the exalted status of certain knowledge. But once this consequence of our fallibility is recognized, he then argues roughly that the probability that any particular belief... (shrink)

In order to clarify the problems of iterated (global) belief change it is useful to study simple cases, in particular consecutive contractions by sentences that are both logically and epistemically independent. Models in which the selection mechanism is kept constant are much more plausible in this case than what they are in general. One such model, namely uniform specified meet contraction, has the advantage of being closely connected with the AGM model. Its properties seem fairly adequate for the intended type (...) of contraction. However, the revision operator based on it via the Levi identity collapses into an implausible operation that loses all old information when revising by new information. A weaker version, semi-uniform specified meet contraction, avoids the collapse but has the disadvantage of a remarkably weak logic. It is left as an open issue whether there is an intermediate class of contraction operators that yields a more satisfactory logic. (shrink)

The Theme. Strong forcing axioms like Martin’s Maximum give a reasonably satisfactory structural analysis of $H(\omega _2)$. A broad program in modern Set Theory is searching for strong forcing axioms beyond $\omega _1$. In other words, one would like to figure out the structural properties of taller initial segments of the universe. However, the classical techniques of forcing iterations seem unable to bypass the obstacles, as the resulting forcings axioms beyond $\omega _1$ have not thus far been strong enough! However, (...) with his celebrated work on generalised side conditions, I. Neeman introduced us to a novel paradigm to iterate forcings. In particular, he could, among other things, reprove the consistency of the Proper Forcing Axiom using an iterated forcing with finite supports. In 2015, using his technology of virtual models, Veličković built up an iteration of semi-proper forcings with finite supports, hence reproving the consistency of Martin’s Maximum, an achievement leading to the notion of a virtual model.In this thesis, we are interested in constructing forcing notions with finitely many virtual models as side conditions to preserve three uncountable cardinals. The thesis constitutes six chapters and three appendices that amount to 118 pages, where Section 1 is devoted to preliminaries, and Section 2 is a warm-up about the scaffolding poset of a proper forcing. In Section 3, we present the general theory of virtual models in the context of forcing with sets of models of two types, where we, e.g., define the “meet” between two virtual models and prove its properties.The main results are joint with Boban Veličković, and partly appeared in Guessing models and the approachability ideal, J. Math. Log. 21 (2021).Pure Side Conditions. In Section 4, we use two types of virtual models (countable and large non-transitive ones induced by a supercompact cardinal, which we call Magidor models) to construct our forcing with pure side conditions. The forcing covertly uses a third type of models that are transitive. We also add decorations to the conditions to add many clubs in the generic $\omega _2$. In contrast to Neeman’s method, we do not have a single chain, but $\alpha $ -chains, for an ordinal $\alpha $ with $V_\alpha \prec V_\lambda $. Thus, starting from suitable large cardinals $\kappa <\lambda $, we construct a forcing notion whose conditions are finite sets of virtual models described earlier. The forcing is strongly proper, preserves $\kappa $, and has the $\lambda $ -Knaster property. The relevant quotients of the forcing are strongly proper, which helps us prove strong guessing model principles. The construction is generalisable to a ${<}\mu $ -closed forcing, for any given cardinal $\mu $ with $\mu ^{<\mu }=\mu <\kappa $.The Iteration Theorem. In Section 5, we use the forcing with pure side conditions to iterate a subclass of proper and $\aleph _2$ -c.c. forcings and obtain a forcing axiom at the level of $\aleph _2$. The iterable class is closely related to Asperó–Mota’s forcing axiom for finitely proper forcings.Guessing Model Principles. Section 6 encompasses the main parts of the thesis. We prove the consistency of the guessing principle $\mathrm {GMP}^+(\omega _3,\omega _1)$ that states for any cardinal ${\theta \geq \omega _3}$, the set of $\aleph _2$ -sized elementary submodels M of $H(\theta )$, which are the union of an $\omega _1$ -continuous $\in $ -chain of $\omega _1$ -guessing, I.C. models is stationary in $\mathcal P_{\omega _3}(H(\theta ))$. The consistency and consequences of this principle are demonstrated in the following diagram. We also prove that one can obtain the above guessing models in a way that the $\omega _1$ -sized $\omega _1$ -guessing models remain $\omega _1$ -guessing model in any outer transitive model with the same $\omega _1$, and we denote this principle by $\rm{SGMP}^+(\omega_3,\omega_1)$.In the following diagram, $\mathrm{TP}$ stands for the tree property; $w\mathrm{KH}$ stands for the weak Kurepa Hypothesis; $\mathrm{MP}$ stands for Mitchell property, i.e., the approachability ideal is trivial modulo the nonstationary ideal; $\mathrm{AP}$ stands for the approachability property; $\mathrm {AMTP}(\kappa ^+)$ states that if $2^\kappa <\aleph _{\kappa ^+}$, then every forcing which adds a new subset of $\kappa ^+$ whose initial segments are in the ground model, collapses some cardinal $\leq 2^{\kappa }$. The dotted arrow denotes the relative consistency, while others are logical implications.Appendices. Appendix A includes merely the above diagram. Appendix B presents a proof of the Mapping Reflection Principle with finite conditions under $\mathrm {PFA}$. Appendix C contains open problems. Finally, the thesis’s bibliography consists of 42 items.Abstract prepared by Rahman MohammadpourE-mail: [email protected]: https://theses.hal.science/tel-03209264. (shrink)

Fractal art graphics are the product of the fusion of mathematics and art, relying on the computing power of a computer to iteratively calculate mathematical formulas and present the results in a graphical rendering. The selection of the initial value of the first iteration has a greater impact on the final calculation result. If the initial value of the iteration is not selected properly, the iteration will not converge or will converge to the wrong result, which will (...) affect the accuracy of the fractal art graphic design. Aiming at this problem, this paper proposes an improved optimization method for selecting the initial value of the Gauss-Newton iteration method. Through the area division method of the system composed of the sensor array, the effective initial value of iterative calculation is selected in the corresponding area for subsequent iterative calculation. Using the special skeleton structure of Newton’s iterative graphics, such as infinitely finely inlaid chain-like, scattered-point-like composition, combined with the use of graphic secondary design methods, we conduct fractal art graphics design research with special texture effects. On this basis, the Newton iterative graphics are processed by dithering and MATLAB-based mathematical morphology to obtain graphics and then processed with the help of weaving CAD to directly form fractal art graphics with special texture effects. Design experiments with the help of electronic Jacquard machines proved that it is feasible to transform special texture effects based on Newton's iterative graphic design into Jacquard fractal art graphics. (shrink)

In his Reportatio super Sententias (ca. 1321–1323), Walter Chatton proposes a solution to the problem of future contingents based on propositional analysis. Future-tense statements must be disambiguated with the help of a scope distinction between temporal and truth operators, such that a statement like “Socrates will sit” comes out either as (1) “it is true now that Socrates will sit,” or (2) “it will be true that Socrates sits.” On the first analysis, Socrates’s action is necessitated, whereas on the (...) second it remains contingent. In his later Quodlibet (ca. 1330), Chatton maintains his original analysis but augments it with an ingenious use of the traditional distinction between actus exercitus and actus significatus. His use of the distinction enables him both to give some speech-act-theoretical content to the scope analysis, which had been open to the charge of mere formalism, and to defend it cogently against an apparently strong counterargument. (shrink)

Maximizers in isolated Prisoner's Dilemmas are doomed to frustration. But in Braybrooke's view maximizers might do better in a series, securing Pareto-optimal arrangements if not from the very beginning, at least eventually. Given certain favourable special conditions, it can be shown according to Braybrooke and shown even without question-begging motivational or value assumptions, that in a series of Dilemmas maximizers could manage to communicate a readiness to reciprocate, generate thereby expectations of reciprocation, and so give rise to optimizing reciprocations which, (...) in due course, would reinforce expectations, the net result of all this being an increasingly stable practice to mutual benefit. In this way neighbours could learn to be good neighbours: they could learn to respect each other's property, to engage in reciprocal assistance, and perhaps even to make and keep promises covering a range of activities. So maximizers are, Braybrooke holds, capable of a society of sorts. Out of the ashes they might build something. But even under favourable conditions they could not build much and most conditions would defeat them almost entirely, for many-person Dilemmas whether isolated or in series would be quite beyond them, question-begging motivational assumptions aside. In settings at all like those in which we live, utility maximization assuming only ‘traditional’ motivation is self-defeating without remedy, and most certainly not an adequate basis for social life.' The probable inference from as a conception of individual rationality: for surely truly rational agents would be if not perfectly well designed at least better designed for communal living than utility maximizers would be assuming only ‘traditional’, non-question-begging values or motivation. Or, if this inference is denied and maximization is not challenged as a conception of rationality, we can conclude instead, Braybrooke has more recently suggested, that the advice, ‘Be rational,’ is incomplete, and when addressed to groups should be supplemented by, ‘And be somewhat ‘untraditional’ in your values; respect at least some rules that would make coordination and cooperation possible even in many-person interaction problems.’. (shrink)

The ancient problems of bankruptcy, contested garment, and rights arbitration have generated many studies, debates, and controversy. The objective of this paper is to show that the Shapley value from game theory, measuring the power of each player in a game, may be consistently applied for getting the general one-step solution of all these three problems viewed as -person games. The decision making is based on the same tool, namely the game theory logic based on the use of the Shapley (...) value, but the specific games involved are slightly different in each problem. The kind of claims of the players, the relationship between the given claims and the given resources available, and the particular way of calculating the generalized characteristic function of the game determine the specific type of game which has to be solved in each of the three ancient problems mentioned. The iterative use of the Shapley value may also justify the well-known Aumann-Maschler step-by-step procedure for solving the bankruptcy problem. (shrink)

While Rawls himself put contractualism to work at the national level, his more cosmopolitan followers have argued that the full requirements of international justice can be reached only by way of a global contractualist argument. Both positions neglect a resource from within the contractualist tradition, The need for iteration of the nation-level contract gives rise to strong and reasonably definite moral requirements. A good-faith adoption of the contractual argument entails, first, a duty to assist those whose potential recourse to (...) just arrangements is blocked by tyranny or political collapse. Second, understood as a net risk-reducing project, a nation-level contract entails a duty not to impede the iterated risk-reduction projects of other national soceties. Envisaging the duty in this contractualist way avoids problems that beset both "natural duty" and "interactionist" approaches to international justice. The non-impedance requirement bears especially on international economic arrangements. The institutional representation of those affected by such arrangements would connect this abstract requirement with practical conclusions. (shrink)

Actualists who believe in possible worlds typically regard them as "abstract" objects of some special sort. For example, Alvin Plantinga takes worlds to be maximal possible states-of-affairs, all of which "exist", as actualism requires, but only one of which "obtains". Views like Plantinga's run into difficulty in the interpretation of statements of "iterated" modality, statements about what is "possible" for individuals that "could" exist but that do not actually exist. These statements seem to require the existence of "singular" states-Of-affairs that (...) have nonactual individuals as constituents, a requirement that is incompatible with actualism. One can try to avoid the troublesome singular states-of-affairs by introducing "unexemplified individual essences" and maintaining that these are the true constituents of the required states-of-affairs, rather than the nonactual possibles themselves. However, serious arguments are raised against this employment of individual essences. (shrink)

The paper is essentially a short version Spohn "Strategic Rationality" which emphasizes in particular how the ideas developed there may be used to shed new light on the iterated prisoner's dilemma (and on iterated Newcomb's problem).

This article reflects on the problem of false belief produced by the integrated psychological and algorithmic landscape humans now inhabit. Following the work of scholars such as Lee McIntyre (Post-Truth, MIT Press, 2018) or Cailin O’Connor and James Weatherall (The Misinformation Age: How False Beliefs Spread, Yale University Press, 2019) it combines recent discussions of fake news, post-truth, and science denialism across the disciplines of political science, computer science, sociology, psychology, and the history and philosophy of science that variously (...) address the ineffectiveness, in a digital era, of countering individual falsehoods with facts. Truth and falsehood, it argues, rather than being seen as properties or conditions attached to individual instances of content, should now be seen as collective, performative, and above all persuasive phenomena. They should be practically evaluated as networked systems and mechanisms of sharing in which individually targeted actions are combining with structural tendencies (both human and mechanical) in unprecedented ways. For example, the persuasive agency of apparent consensus (clicks, likes, bots, trolls) is newly important in a fractured environment that only appears to be, but is no longer ‘public’; the control of narratives, labels, and associations is a live, time-sensitive issue, a continuous contest, or ongoing cusp. Taking a social approach to truth yields observations of new relevance; from how current strategies of negative cohesion, blame, and enemy-creation depend crucially on binary ways of constructing the world, to how the offer of identity/community powerfully cooperates with the structural tendencies of algorithm-driven advertiser platforms towards polarisation. Remedies for these machine-learned and psychological tendencies lie in end-user education. So the Arts and Humanities, whether via comparisons with previous historical periods, or via principles of critical thinking and active reading, offer crucial resources to help counter what since 1997 silicon valley executives and scholars have called ‘persuasive technology’ (Fogg in Persuasive Technology: Using Computers to Change What we Think and Do, Morgan Kaufmann, 2003; Hamari et al. (eds) in Persuasive Technology, Springer International Publishing, 2014; Harris in How a Handful of Tech Companies Control Billions of Minds Every Day, 2017; Lanier in Who Owns the Future? Simon & Schuster, 2014 and Ten Arguments for Deleting your Social Media Accounts Right Now, Picador, 2019). The article proposes a paradigm shift in public understandings of this new social environment: from a culture of discovery, where what matters is what exists or is in fact the case, to a culture of iteration, where what matters is what gets repeated. (shrink)