It is argued that the Nash bargaining solution cannot serve as a principle of distributive justice because (i) it cannot secure stable cooperation in repeated interactions and (ii) it cannot capture our moral intuitions concerning distributive questions. In this article, I propose a solution to the first problem by amending the Nash bargaining solution so that it can maintain stable cooperation among rational bargainers. I call the resulting principle the stabilized Nash bargaining solution. The principle defends justice in the form (...) 'each according to her basic needs and above this level according to her relative bargaining power'. In response to the second problem, I argue that the stabilized Nash bargaining solution can serve as a principle of distributive justice in certain situations where moral reasoning is reduced to instrumental reasoning. In particular, I argue that rational individuals would choose the stabilized Nash bargaining solution in Rawls' original position. (shrink)

In everyday life we either express our beliefs in all-or-nothing terms or we resort to numerical probabilities: I believe it's going to rain or my chance of winning is one in a million. The Stability of Belief develops a theory of rational belief that allows us to reason with all-or-nothing belief and numerical belief simultaneously.

Much recent work on explanation in the interventionist tradition emphasizes the explanatory value of stable causal generalizations—i.e., causal generalizations that remain true in a wide range of background circumstances. We argue that two separate explanatory virtues are lumped together under the heading of `stability’. We call these two virtues breadth and guidance respectively. In our view, these two virtues are importantly distinct, but this fact is neglected or at least under-appreciated in the literature on stability. We argue that (...) an adequate theory of explanatory goodness should recognize breadth and guidance as distinct virtues, as breadth and guidance track different ideals of explanation, satisfy different cognitive and pragmatic ends, and play different theoretical roles in helping us understand the explanatory value of mechanisms. Thus keeping track of the distinction between these two forms of stability yields a more accurate and perspicuous picture of the role that stability considerations play in explanation. (shrink)

The distinguished philosopher Louis Loeb examines the epistemological framework of Scottish philosopher David Hume, as employed in his celebrated work A Treatise of Human Nature. Loeb's project is to advance an integrated interpretation of Hume's accounts of belief and justification. His thesis is that Hume, in his Treatise, has a "stability-based" theory of justification which posits that his belief is justified if it is the result of a belief producing mechanism that engenders stable beliefs. But Loeb argues that the (...) striking corollary to this theory is that no belief generating mechanism is fully stable - or fully justified - for a fully reflective person. This carefully argued and original interpretation of Hume makes sense of seemingly contradictory ideas and will provoke serious discussion among Hume scholars. (shrink)

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: Einstein’s static universe and Eddington’s demonstration of its instability, and the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems (...) theory and its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one. (shrink)

Despite great advances in recent scholarship on the political philosophy of John Rawls, Rawls’s conception of stability is not fully appreciated. This essay aims to remedy this by articulating a more complete understanding of stability and its role in Rawls’s theory of justice. I argue that even in A Theory of Justice Rawls maintains that within liberal democratic constitutionalism judgments of relative stability typically adjudicate decisively among conceptions of justice and is committed to more deeply than to (...) the substantive content of justice as fairness. This essay thus emphasizes the continuity of Rawls’s thought over time and motivates the position that Rawlsian stability is as philosophically significant and distinctively Rawlsian as justice as fairness itself. (shrink)

Grossberg and VanDieren have started a program to develop a stability theory for tame classes. We name some variants of tameness and prove the following. Let K be an AEC with Löwenheim-Skolem number ≤κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then K is Galois-stable in κ⁺ⁿ for all n<ω. With one further hypothesis we get a very strong conclusion in the countable case. Let K be an AEC satisfying the amalgamation (...) property and with Löwenheim-Skolem number ℵ₀ that is ω-local and ℵ₀-tame. If K is ℵ₀-Galois-stable then K is Galois-stable in all cardinalities. (shrink)

An attractive form of social stability is realized when the members of a well-ordered society give that society’s organizing principles their free and reflective endorsement. However, many political philosophers are skeptical that there is any requirement to show that their principles would engender this kind of stability. This skepticism is at the root of a number of objections to political liberalism, since arguments for political liberalism often appeal to its ability to be stable in this way. The aim (...) of this paper is to address skepticism about the stability condition by putting forward a novel defense of it. My defense builds on the claim that stable principles are necessary to secure the full autonomy of those who live under them. (shrink)

We address the question whether there is an explanation for the fact that as Fodor put it the micro-level “converges on stable macro-level properties”, and whether there are lessons from this explanation for other issues in the vicinity. We argue that stability in large systems can be understood in terms of statistical limit theorems. In the thermodynamic limit of infinite system size N → ∞ systems will have strictly stable macroscopic properties in the sense that transitions between different macroscopic (...) phases of matter (if there are any) will not occur in finite time. Indeed stability in this sense is a consequence of the absence of fluctuations, as (large) fluctuations would be required to induce such macroscopic transformations. These properties can be understood in terms of coarse-grained descriptions, and the statistical limit theorems for independent or weakly dependent random variable describing the behaviour averages and the statistics of fluctuations in the large system limit. We argue that RNG analyses applied to off-critical systems can provide a rationalization for the applicability of these limit theorems. Furthermore we discuss some related issues as, for example, the role of the infinite-system idealization. (shrink)

In this working paper, we discuss why researchers and policymakers need to better understand how different theoretical accounts of stability lead to different frameworks of analysis. Though ubiquitously mentioned, stability remains an under-theorized notion in security studies. Expert accounts tend to present stability as a generic description, readily applicable to most political phenomena Ð a stabilized state, a stable region, an unstable society. While seemingly equivocal, such uses exhibit different conceptualizations, exhibiting different features and demanding multiple research (...) programs. To date, most accounts of stability tend to take stability to be an (unconstructed) natural phenomenon or a non-derivative social construction. In this introductory paper, we claim that there is a third way to account for stability that remains unexplored in security studies. Simply put, it involves taking stability to be a derivative social construction (i.e., systemic fallout). We then argue that this alternative account should serve as the theoretical basis for an independent research program within stability studies. (shrink)

Several authors have investigated the question of whether canonical logic-based accounts of belief revision, and especially the theory of AGM revision operators, are compatible with the dynamics of Bayesian conditioning. Here we show that Leitgeb's stability rule for acceptance, which has been offered as a possible solution to the Lottery paradox, allows to bridge AGM revision and Bayesian update: using the stability rule, we prove that AGM revision operators emerge from Bayesian conditioning by an application of the principle (...) of maximum entropy. In situations of information loss, or whenever the agent relies on a qualitative description of her information state - such as a plausibility ranking over hypotheses, or a belief set - the dynamics of AGM belief revision are compatible with Bayesian conditioning; indeed, through the maximum entropy principle, conditioning naturally generated AGM revision operators. This mitigates an impossibility theorem of Lin and Kelly for tracking Bayesian conditioning with AGM revision, and suggests an approach to the compatibility problem that highlights the information loss incurred by acceptance rules in passing from probabilistic to qualitative representations of beliefs. (shrink)

In this paper I discuss the relation between various properties that have been regarded as important for determining whether or not a belief constitutes a piece of knowledge: its stability, strength and sensitivity to truth, as well as the strength of the epistemic position in which the subject is with respect to this belief. Attempts to explicate the relevant concepts more formally with the help of systems of spheres of possible worlds (à la Lewis and Grove) must take care (...) to keep apart the very different roles that systems of spheres can play. Nozicks sensitivity account turns out to be closer to the stability analysis of knowledge (versions of which I identify in Plato, Descartes, Klein and Lehrer) than one might have suspected. (shrink)

Bourrat and Griffiths :33, 2018) have recently argued that most of the evidence presented by holobiont defenders to support the thesis that holobionts are evolutionary individuals is not to the point and is not even adequate to discriminate multispecies evolutionary individuals from other multispecies assemblages that would not be considered evolutionary individuals by most holobiont defenders. They further argue that an adequate criterion to distinguish the two categories is fitness alignment, presenting the notion of fitness boundedness as a criterion that (...) allows divorcing true multispecies evolutionary individuals from other multispecies assemblages and provides an adequate criterion to single out genuine evolutionary multispecies assemblages. A consequence of their criterion is that holobionts, as conventionally defined by hologenome defenders, are not evolutionary individuals except in very rare cases, and for very specific host-symbiont associations. This paper is a critical response to Bourrat and Griffiths’ arguments and a defence of the arguments presented by holobiont defenders. Drawing upon the case of the hologenomic basis of the evolution of sanguivory in vampire bats, I argue that Bourrat and Griffiths overlook some aspects of the biological nature of the microbiome that justifies the thesis that holobionts are evolutionarily different to other multispecies assemblages. I argue that the hologenome theory of evolution should not define the hologenome as a collection of genomes, but as the sum of the host genome plus some traits of the microbiome which together constitute an evolutionary individual, a conception I refer to as the stability of traits conception of the hologenome. Based on that conception I argue that the evidence presented by holobiont defenders is to the point, and supports the thesis that holobionts are evolutionary individuals. In this sense, the paper offers an account of the holobiont that aims to foster a dialogue between hologenome advocates and hologenome critics. (shrink)

This chapter contains section titled: Introduction:the European Union and the Law of Peoples The Argument of Law of Peoples Standards and Grounds for International Stability Human Rights in Federations The Argument of Law of Peoples for Inter‐people Inequality Distributive Justice in Federations Federal and Global Implications Toleration and Stability Reconsidered Acknowledgments Notes.

David Hume's A Treatise of Human Nature is famous for its extreme skepticism. Louis Loeb argues that Hume's destructive conclusions have in fact obscured a constructive stage that Hume abandons prematurely. Working within a philosophical tradition that values tranquillity, Hume favors an epistemology that links justification with settled belief. Hume appeals to psychological stability to support his own epistemological assessments, both favorable regarding causal inference, and unfavorable regarding imaginative propensities. The theory's success in explaining Hume's epistemic distinctions gives way (...) to pessimism, since Hume contends that reflection on beliefs is deeply destabilizing. So much the worse, Hume concludes, for placing a premium on reflection. Hume endorses and defends the position that stable beliefs of unreflective persons are justified, though they would not survive reflection. At the same time, Hume relishes the paradox that unreflective beliefs enjoy a preferred epistemic status and strains to establish it. Loeb introduces a series of amendments to the Treatise that secures a more positive result for justified belief while maintaining Hume's fundamental principles. In his review of Hume's applications of his epistemology, Loeb uncovers a stratum of psychological doctrine beyond associationism, a theory of conditions in which beliefs are felt to conflict and of the resolution of this uneasiness or dissonance. This theory of mental conflict is also essential to Hume's strategy for integrating empiricism about meaning with his naturalism. However, Hume fails to provide a general account of the conditions in which conflicting beliefs lead to persisting instability, so his theory is incomplete. Loeb explores Hume's concern with stability in reference to his discussions of belief, education, the probability of causes, unphilosophical probability, the belief in body, sympathy and moral judgment, and the passions, among other topics. (shrink)

We introduce tame abstract elementary classes as a generalization of all cases of abstract elementary classes that are known to permit development of stability-like theory. In this paper, we explore stability results in this new context. We assume that [Formula: see text] is a tame abstract elementary class satisfying the amalgamation property with no maximal model. The main results include:. Theorem 0.1. Suppose that [Formula: see text] is not only tame, but [Formula: see text]-tame. If [Formula: see text] (...) and [Formula: see text] is Galois stable in μ, then [Formula: see text], where [Formula: see text] is a relative of κ from first order logic. [Formula: see text] is the Hanf number of the class [Formula: see text]. It is known that [Formula: see text]. The theorem generalizes a result from [17]. It is used to prove both the existence of Morley sequences for non-splitting and the following initial step towards a stability spectrum theorem for tame classes:. Theorem 0.2. If [Formula: see text] is Galois-stable in some [Formula: see text], then [Formula: see text] is stable in every κ with κμ=κ. For example, under GCH we have that [Formula: see text] Galois-stable in μ implies that [Formula: see text] is Galois-stable in μ+n for all n < ω. (shrink)

Threats to the stability of liberal democracies are of obvious contemporary import. Concern with stability runs through John Rawls’s work. The stability that concerned him was that of fundamental terms of cooperation. Rawls long believed that the terms which would be stable were his two principles, but he eventually conceded that even a well-ordered society was more likely to be characterized by “justice pluralism” than by consensus on his own conception of justice. Contemporary liberal democracies, too, are (...) divided about what justice demands. I believe Rawls’s treatment of stability can help us understand the conditions under which fundamental terms of cooperation can be stable under non-ideal conditions such as ours. But because Rawls never worked through the consequences of his concession, his view needs to be developed before we can draw on it. Rawls’s treatment makes use of elementary game theory. Thus in _Theory of Justice_ he said -- and in _Political Liberalism_ he implied -- that stability would result from citizens with a sense of justice “playing” strategies which combined for what was, in effect, a Nash equilibrium. I argue that his concession requires a new conception of stability and implies that Rawls cannot appeal to a Nash equilibrium to show how stability would be maintained. His concession therefore forces open a troubling gap in his analysis. I fill that gap by proposing a weaker equilibrium concept that serves Rawlsian purposes. I conclude with what this project suggests for challenges facing the fragile liberal democracies of our own time. (shrink)

This paper offers a critique of an account of explanatory integration that claims that explanations of cognitive capacities by functional analyses and mechanistic explanations can be seamlessly integrated. It is shown that achieving such explanatory integration requires that the terms designating cognitive capacities in the two forms of explanation are stable but that experimental practice in the mind-brain sciences currently is not directed at achieving such stability. A positive proposal for changing experimental practice so as to promote such (...) class='Hi'>stability is put forward and its implications for explanatory integration are briefly considered. (shrink)

The topic of moral diversity is not only prevalent in contemporary moral and political philosophy, it is also practically relevant. Moral diversity, however, poses a significant challenge for moral theory building. John Thrasher, in his discussion of public reason theory, which includes social contract theory, argues that if one seriously considers the goal of moral constructivism and considerations of representation and stability, then moral diversity poses an insurmountable problem for most public reason theories. I agree with Thrasher that moral (...) diversity poses a significant challenge for orthodox multistage social contract theories. In fact, I even add a further problem for such theories under the assumption of deep moral diversity. Nevertheless, I argue that my recently developed multilevel social contract theory overcomes these problems. I focus on some of the underexplored features of this theory to show that multilevel social contract theory offers one conceptually coherent and plausible way to render social contract theory viable and relevant for modern diverse societies. (shrink)

One important thesis Ásta defends in Categories We Live By is that social properties and categories are somehow dependent on our thoughts, attitudes, or practices—that they are inventions of the mind, projected onto the world. Another important aspect of her view is that the social properties are related to certain base properties; an individual is placed in a category when the relevant base properties are thought to hold of them. I see the relationship between the social and the base as (...) connected to the problem of explaining how the social properties are sufficiently stable so as to be taken seriously, both in theoretical endeavors as well as in practical matters of how we relate to each other. In this light, I identify stability constraints for an adequate account of social categories. I argue that certain distinctive aspects of Ásta's conferralist view of social categories, such as the radical contextualism in her account of gender, undermine the stability of categories and are at odds with taking social categories seriously. I end with the suggestion that a distinctive “sheltered” form of normativity might help us do justice to Ásta's insights while avoiding some of the destabilizing elements of conferralism. (shrink)

A growing body of empirical research suggests that people's concrete‐case intuitions are unstable—i.e., vulnerable to biasing influences—with no way of anticipating the instability. This has led some to challenge the use of intuitions in philosophical practice. In this chapter, I consider responses to this challenge. One is that the empirical research cited has no bearing on the epistemic status of intuitions because it fails to actually test intuitions. While this is a worry worth taking seriously, there is another response available—namely, (...) that even if we grant that these studies successfully elicited intuitions, in the midst of the instability uncovered there was also a fair amount of stability. And an investigation into the features of unstable vs. stable judgments, and the contexts within which they are generated, suggests that the instability in question may not actually be intuitional. (shrink)

This paper deals with the exponential stabilization problem for a class of nonlinear switched systems with mixed delays under asynchronous switching. The switching signal of the switched controller involves delay, which results in the asynchronous switching between the candidate controllers and subsystems. By constructing the parameter-dependent Lyapunov-Krasovskii functional and the average dwell time approach, some sufficient conditions in forms of linear matrix inequalities are presented to ensure the exponential stability of the switched nonlinear system under arbitrary switching signals. In (...) addition, through the special deformation of the matrix and Schur complement, the controllers with asynchronous switching are designed. Finally, a numerical example and a practical example of river pollution control are provided to show the validity and potential of the developed results. (shrink)

The Stability of Belief: How Rational Belief Coheres with Probability, by LeitgebHannes. Oxford: Oxford University Press, 2017. Pp. xiv + 365.

Anthropogenic climate change poses a direct and imminent threat to the stability of modern society. Recent reports of the probable consequences of climate change paint a grim picture; they describe a world environmentally much less stable than the world to which we have become accustomed. As we begin to adapt to our changing climate, we will need to identify new sources for the stability necessary for a flourishing society. I suggest that this stability should come from the (...) ideals of the good life we seek to promote when we focus on capabilities, on the substantial freedoms humans need to flourish. These ideals serve as a stable foundation for well-being in a time of great environmental and social instability; they should serve as guides for our policies, practices and institutions. I conclude by appealing to capabilities as a means of integrating well-being into our adaptation strategies, and show how doing so may well provide a way of formulating a powerful moral justification for adaptation strategies appropriate for both the developed and the developing world. (shrink)

How individuals reason deductively has concerned researchers for many years. Yet, it is still unclear whether, and if so how, participants’ reasoning performance changes over time. In two test sessions one week apart, we examined how the syllogistic reasoning performance of 100 participants changed within and between sessions. Participants’ reasoning performance increased during the first session. A week later, they started off at the same level of reasoning performance but did not further improve. The reported performance gains were only found (...) for logically valid, but not for invalid syllogisms indicating a bias against responding that ‘no valid conclusion’ follows from the premises. Importantly, we demonstrate that participants substantially varied in the strength of the temporal performance changes and explored how individual characteristics, such as participants’ personality and cognitive ability, relate to these interindividual differences. Together, our findings contradict common assumptions that reasoning performance only reflects a stable inherent ability. (shrink)

There are two prominent ways of formally modelling human belief. One is in terms of plain beliefs, i.e., sets of propositions. The second one is in terms of degrees of beliefs, which are commonly taken to be representable by subjective probability functions. In relating these two ways of modelling human belief, the most natural idea is a thesis frequently attributed to John Locke: a proposition is or ought to be believed just in case its subjective probability exceeds a contextually fixed (...) probability threshold \. This idea is known to have two serious drawbacks: first, it denies that beliefs are closed under conjunction, and second, it may easily lead to sets of beliefs that are logically inconsistent. In this paper I present two recent accounts of aligning plain belief with subjective probability: the Stability Theory of Leitgeb (2013, 2014, 2015, 2017) and the Probalogical Theory of Lin and Kelly (2012a, 2012b). I argue that Leitgeb’s theory may be too sceptical for the purposes of real life. (shrink)

In this article, I explain why stabilizing constructs is important to the success of the Research Domain Criteria Project and identify one measure for facilitating such stability.

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (shrink)

The replicator dynamics and Moran process are the main deterministic and stochastic models of evolutionary game theory. The models are connected by a mean-field relationship—the former describes the expected behavior of the latter. However, there are conditions under which their predictions diverge. I demonstrate that the divergence between their predictions is a function of standard techniques used in their analysis and of differences in the idealizations involved in each. My analysis reveals problems for stochastic stability analysis in a broad (...) class of games, demonstrates a novel domain of agreement between the dynamics, and indicates a broader moral for evolutionary modeling. (shrink)

In the work of both Ludwik Fleck and Thomas Kuhn the scientific literature plays important roles for stability and change of scientific phenomenal worlds. In this article we shall introduce the analyses of scientific literature provided by Fleck and Kuhn, respectively. From this background we shall discuss the problem of how divergent thinking can emerge in a dogmatic atmosphere. We shall argue that in their accounts of the factors inducing changes of scientific phenomenal worlds Fleck and Kuhn offer substantially (...) different approaches, and we shall discuss in which respects their approaches may be compatible. (shrink)

John Rawls argued in A Theory of Justice that “justice as fairness…is likely to have greater stability than the traditional alternatives since it is more in line with the principles of moral psychology”. In support, he presented a psychology of moral development that was informed by a comprehensive liberalism. In Political Liberalism, Rawls confessed that the argument was “unrealistic and must be recast”. Rawls, however, never provided a psychology of moral development informed by a specifically political liberalism, leaving it (...) at a disadvantage with respect to comprehensive liberalism itself. I argue that no coherent account is available. But, because Rawls’s Liberal Principle of Legitimacy, along with its implied stricture against “indoctrination in the pejorative sense,” is a creature of ideal rather than non-ideal theory, the deficiency is far less significant than many would assume. In non-ideal circumstances -- such as ours -- political liberalism does not disallow, and in fact requires, compulsory, free early education informed by the best available comprehensive liberal philosophy. (shrink)

John Rawls argued in A Theory of Justice that ‘justice as fairness … is likely to have greater stability than the traditional alternatives since it is more in line with the principles of moral psychology'. In support, he presented a psychology of moral development that was informed by a comprehensive liberalism. In Political Liberalism, Rawls confessed that the argument was 'unrealistic and must be recast'. Rawls, however, never provided a psychology of moral development informed by a specifically political liberalism, (...) leaving it at a disadvantage with respect to comprehensive liberalism itself. I argue that no coherent account is available. But, because Rawls’s Liberal Principle of Legitimacy, along with its implied stricture against 'indoctrination in the pejorative sense', is a creature of ideal rather than non-ideal theory, the deficiency is far less significant than many would assume. (shrink)

Let p be an odd prime. A method is described which given a structure M of finite similarity type produces a nilpotent group of class 2 and exponent p which is in the same stability class as M. Theorem. There are nilpotent groups of class 2 and exponent p in all stability classes. Theorem. The problem of characterizing a stability class is equivalent to characterizing the (nilpotent, class 2, exponent p) groups in that class.

In Stability and Justification in Hume’s Treatise, Louis Loeb ascribes to Hume a naturalistic account of justified belief, one on which Hume is fundamentally concerned with the question whether stable belief can be achieved. Loeb’s interpretation is systematic, richly explanatory, and powerfully argued. He makes a compelling case that stability plays a central role in Hume’s epistemology. Loeb’s case is so compelling indeed that anyone who wants to defend an alternative interpretation will now have to assimilate or deflect (...) the massive textual evidence in favor of the stability interpretation. I will argue here that, for some passages Loeb cites in favor of the stability interpretation, a veritistic interpretation explains the text at least as well as the stability interpretation does. (shrink)

The symposiasts press from a number of directions. Erin Kelly contends that Hume’s stability-based sentimentalist ethics cannot do justice to our considered normative moral judgements. Schmitt and Williams criticize my account of Hume’s epistemology proper. I will have to give ground: my book does overstate the extent to which Hume reaches a destructive result, in large part because I overlook significant variants of a stability account of justification. I make other concessions—in regard to the country gentlemen passage and (...) Hume’s 1.3.9 treatment of resemblance—but believe these have limited repercussions. (shrink)