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.

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)

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)

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.

In this article, I argue that stability is one of the enabling conditions for epistocratic arrangements to function well and justify their claim right to rule. Against this backdrop, I demonstrate that advocates of strategies to allocate exclusive decision-making power to knowledgeable citizens fail to demonstrate that in a context marked by the fact of pluralism, liberal epistocracies will be stable. They could argue that liberal epistocracies will be stable because epistocratic arrangements are better equipped than democratic decision-making bodies (...) to produce outcomes that approximate the common good. They could argue that liberal epistocracies will be stable because there is a shared meritocratic set of values and ideas. Furthermore, they could opt for two standard liberal strategies, such as overlapping consensus and modus vivendi. Yet, in all cases, the argument for the stability of liberal epistocracies is not persuasive. (shrink)

The main goal of this paper is to introduce the notion of stabilizers in \(L\)-algebras and develop stabilizer theory in \(L\)-algebras. In this paper, we introduced the notions of left and right stabilizers and investigated some related properties of them. Then, we discussed the relations among stabilizers, ideal and co-annihilators. Also, we obtained that the set of all ideals of a \(CKL\)-algebra forms a relative pseudo-complemented lattice. In addition, we proved that right stabilizers in \(CKL\)-algebra are ideals. Then by using (...) the right stabilizers we produced a basis for a topology on \(L\)-algebra. We showed that the generated topology by this basis is Baire, connected, locally connected and separable and we investigated the other properties of this topology. (shrink)

In this chapter I investigate the kinds of changes that psychiatric kinds undergo when they become explanatory targets of areas of sciences that are not “mature” and are in the early stages of discovering mechanisms. The two areas of science that are the targets of my analysis are cognitive neuroscience and cognitive neurobiology.

The problem of identity is central to epistemic transference. However, relative identity appears to be the only way to work out an epistemic useful notion of identity. Relative identity, on its part, is either parasitic on strict identity or not identity at all. If, on the contrary, we ought for a strict concept of identity capable of satisfying its requirements, we end up with a tautologic and epistemic worthless category. The paper provides an answer to this problem, which, while working (...) with a strict notion, shows how it might still serve epistemic purposes. In doing so, it shows how a formal reconstruction of our objectual world and the identities we refer to poses a workable model upon which our messy epistemic one acquires stability. The paper focuses primarily on the Geach-Quine discussion on identity. (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)

Excerpt from The Stability of Truth: A Discussion of Reality as Related to Thought and Action The generalizations and principles of science, the significance of scientific facts, the consequences of recognizing and adopting in our daily life the knowledge of science: these are the subjects of this series of books, to be called the Philosophy of Nature Series. The science which will be most in evidence in these books is the science of living things, biology. And it is the (...) application of the scientific knowledge of living things in general to the conduct of human life in particular which will be the subject most conspicuous in the list of titles of the books of the series. This first book, then, a robust treatment of science in life, by a robust exponent of the life scientific, should be a most excellent introduction to the Series. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (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)

This chapter contains section titled: Introduction Emergence of the Stability‐Diversity—Complexity Debate Mathematization of Ecological Stability The End of the Consensus Contextualization and Classification of Ecological Stability Measures of Ecological Diversity and Complexity Evaluating Stability‐Diversity—Complexity Relationships Acknowledgments References Further Reading.

This chapter summarizes briefly what John Rawls meant by stability, the role it plays in Theory of Justice (TJ), and the outline of his main strategies for showing that a well‐ordered society based on his principles of justice would be relatively stable. It presents comments on Rawls's use of developmental moral psychology in support of his claim that societies based on justice as fairness would be relatively stable. The chapter discusses Rawls's conception of self‐respect, its role in his arguments (...) for justice as fairness, and whether it is subject to a certain Kantian objection that echoes in our contemporary political culture. It argues that if Rawls's turn to an overlapping consensus of reasonable comprehensive doctrines as the basis of stability in Political Liberalism (PL) was well motivated, then why not quietly bypass the earlier work on a sense of justice and self‐respect simply as an acknowledged failure. (shrink)

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)

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)

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)

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)

Assuming the existence of a monster model, tameness, and continuity of nonsplitting in an abstract elementary class (AEC), we extend known superstability results: let $\mu>\operatorname {LS}(\mathbf {K})$ be a regular stability cardinal and let $\chi $ be the local character of $\mu $ -nonsplitting. The following holds: 1.When $\mu $ -nonforking is restricted to $(\mu,\geq \chi )$ -limit models ordered by universal extensions, it enjoys invariance, monotonicity, uniqueness, existence, extension, and continuity. It also has local character $\chi $. This (...) generalizes Vasey’s result [37, Corollary 13.16] which assumed $\mu $ -superstability to obtain same properties but with local character $\aleph _0$.2.There is $\lambda \in [\mu,h(\mu ))$ such that if $\mathbf {K}$ is stable in every cardinal between $\mu $ and $\lambda $, then $\mathbf {K}$ has $\mu $ -symmetry while $\mu $ -nonforking in (1) has symmetry. In this case:(a) $\mathbf {K}$ has the uniqueness of $(\mu,\geq \chi )$ -limit models: if $M_1,M_2$ are both $(\mu,\geq \chi )$ -limit over some $M_0\in K_{\mu }$, then $M_1\cong _{M_0}M_2$ ;(b)any increasing chain of $\mu ^+$ -saturated models of length $\geq \chi $ has a $\mu ^+$ -saturated union. These generalize [31] and remove the symmetry assumption in [10, 38].Under $(<\mu )$ -tameness, the conclusions of (1), (2)(a)(b) are equivalent to $\mathbf {K}$ having the $\chi $ -local character of $\mu $ -nonsplitting.Grossberg and Vasey [18, 38] gave eventual superstability criteria for tame AECs with a monster model. We remove the high cardinal threshold and reduce the cardinal jump between equivalent superstability criteria. We also add two new superstability criteria to the list: a weaker version of solvability and the boundedness of the U-rank. (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.

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 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)

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)

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)

Spekkens has introduced a toy theory (Spekkens in Phys. Rev. A 75(3):032110, 2007) in order to argue for an epistemic view of quantum states. I describe a notation for the theory (excluding certain joint measurements) which makes its similarities and differences with the quantum mechanics of stabilizer states clear. Given an application of the qubit stabilizer formalism, it is often entirely straightforward to construct an analogous application of the notation to the toy theory. This assists calculations within the toy theory, (...) for example of the number of possible states and transformations, and enables superpositions to be defined for composite systems. (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)

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)

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)

In his Treatise, Hume confronted the tensions between his project of uncovering the causal operations of the human mind and the extreme skeptical tendencies of his system. Louis Loeb argues that Hume overreaches, and he advances a controversial interpretation of Hume's epistemological framework that shows how Hume could have avoided the more destructive positions in his work.

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)

Seidenfeld (Seidenfeld, T. [1988a], Decision theory without 'Independence' or without 'Ordering', Economics and Philosophy 4: 267-290) gave an argument for Independence based on a supposition that admissibility of a sequential option is preserved under substitution of indifferents at choice nodes (S). To avoid a natural complaint that (S) begs the question against a critic of Independence, he provided an independent proof of (S) in his (Seidenfeld, T. [1988b], Rejoinder [to Hammond and McClennen], Economics and Philosophy 4: 309-315). In reply to (...) my (Rabinowicz, W. [1995], To have one's cake and eat it too: Sequential choice and expected-utility violations, The Journal of Philosophy 92: 586-620), in which I argue that the proof is invalid, Seidenfeld (Seidenfeld, T. [2000], Substitution of indifferent options at choice nodes and admissibility: A reply to Rabinowicz, Theory and Decision 48: 305–310 this issue) submits that I fail to give due consideration to one of the underlying assumptions of his derivation: it is meant to apply only to those cases in which the agent's preferences are stable throughout the sequential decision process. The purpose of this note is to clarify the notion of preference stability so as meet this objection. (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)