Answering in negative a question of M. Hrušák, we construct a Borel ideal not extendable to any \(F_\sigma \) ideal and such that it is not Katětov above the ideal \(\mathrm {conv}\).

We show that there exist uncountably many pairwise nonisomorphic density-like ideals on $\omega $ which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by Borodulin-Nadzieja et al. in [this Journal, vol. 80, pp. 1268–1289]. Lastly, we provide sufficient conditions for a density-like ideal to be necessarily a generalized density ideal.

Answering in negative a question of M. Hrušák, we construct a Borel ideal not extendable to any Fσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_\sigma $$\end{document} ideal and such that it is not Katětov above the ideal conv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {conv}$$\end{document}.

Let $\mathcal {I}$ be an ideal on $\omega $. For $f,\,g\in \omega ^{\omega }$ we write $f \leq _{\mathcal {I}} g$ if $f(n) \leq g(n)$ for all $n\in \omega \setminus A$ with some $A\in \mathcal {I}$. Moreover, we denote $\mathcal {D}_{\mathcal {I}}=\{f\in \omega ^{\omega }: f^{-1}[\{n\}]\in \mathcal {I} \text { for every } n\in \omega \}$ (in particular, $\mathcal {D}_{\mathrm {Fin}}$ denotes the family of all finite-to-one functions).We examine cardinal numbers $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal (...) {I}}))$ and $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathrm {Fin}}\times \mathcal {D}_{\mathrm {Fin}}))$ describing the smallest sizes of unbounded from below with respect to the order $\leq _{\mathcal {I}}$ sets in $\mathcal {D}_{\mathrm {Fin}}$ and $\mathcal {D}_{\mathcal {I}}$, respectively. For a maximal ideal $\mathcal {I}$, these cardinals were investigated by M. Canjar in connection with coinitial and cofinal subsets of the ultrapowers.We show that $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathrm {Fin}} \times \mathcal {D}_{\mathrm {Fin}})) =\mathfrak {b}$ for all ideals $\mathcal {I}$ with the Baire property and that $\aleph _1 \leq \mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}})) \leq \mathfrak {b}$ for all coanalytic weak P-ideals (this class contains all $\bf {\Pi ^0_4}$ ideals). What is more, we give examples of Borel (even $\bf {\Sigma ^0_2}$ ) ideals $\mathcal {I}$ with $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}}))=\mathfrak {b}$ as well as with $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}})) =\aleph _1$.We also study cardinals $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {J}} \times \mathcal {D}_{\mathcal {K}}))$ describing the smallest sizes of sets in $\mathcal {D}_{\mathcal {K}}$ not bounded from below with respect to the preorder $\leq _{\mathcal {I}}$ by any member of $\mathcal {D}_{\mathcal {J}}\!$. Our research is partially motivated by the study of ideal-QN-spaces: those cardinals describe the smallest size of a space which is not ideal-QN. (shrink)

A family $$\mathcal {I}$$ I of subsets of a set X is an ideal on X if it is closed under taking subsets and finite unions of its elements. An ideal $$\mathcal {I}$$ I on X is below an ideal $$\mathcal {J}$$ J on Y in the Katětov order if there is a function $$f{: }Y\rightarrow X$$ f : Y → X such that $$f^{-1}[A]\in \mathcal {J}$$ f - 1 [ A ] ∈ J for every $$A\in \mathcal {I}$$ A (...) ∈ I. We show that the Hindman ideal, the Ramsey ideal and the summable ideal are pairwise incomparable in the Katětov order, where The Ramsey ideal consists of those sets of pairs of natural numbers which do not contain a set of all pairs of any infinite set (equivalently do not contain, in a sense, any infinite complete subgraph), The Hindman ideal consists of those sets of natural numbers which do not contain any infinite set together with all finite sums of its members (equivalently do not contain IP-sets that are considered in Ergodic Ramsey theory), The summable ideal consists of those sets of natural numbers such that the series of the reciprocals of its members is convergent. (shrink)

"Adam Wiegner's work belongs to Polish analytical philosophy, but it falls outside of its main current, the Lvov-Warsaw School, which was influenced by Hume's ideas. Wiegner, influenced by neo-Kantianism, developed a non-Humean conception of "holistic empiricism," which anticipates some of the ideas of K. R. Popper and W. V. O. Quine. Some of his ideas remain original to this day. His main research interests included epistemology, philosophy of mind, philosophy of science especially philosophy of psychology, analytical history of philosophy, (...) and interpretation of traditional logic in terms of mathematical logic."--BOOK JACKET. (shrink)

From folk tales to movies, stories possess features which naturally suit them to contribute to the growth of virtue. In this article I show that the fictional exemplars help the learner to grasp the moral importance of internal states and resolves a tension between existing kinds of exemplars discussed by virtue ethicists. Stories also increase the information conveyed by virtue terms and aid the growth of prudence. Stories can provide virtuous exemplars, inform learners as to the nature of the virtues (...) and offer practice in developing situational judgement. As such they are a significant resource for virtue ethics and moral education. (shrink)

W. Matthews Grant's "Dual Sources Account" aims at explaining how God causes all creaturely actions while leaving them free in a robust libertarian sense. It includes an account of predestination that is supposed to allow for the possibility that some created persons ultimately spend eternity in hell. I argue here that the resources Grant provides for understanding why God might permit created persons to end up in hell are, for two different reasons, insufficient. I then provide possible solutions to these (...) two problems, compatible with Grant's account overall, that help show why God might allow hell. (shrink)

In this paper I argue that both defence and criticism of the claim that humans act ‘under the guise of the good’ neglects the metaphysical roots of the theory. I begin with an overview of the theory and its modern commentators, with critics noting the apparent possibility of acting against the good, and supporters claiming that such actions are instances of error. These debates reduce the ‘guise of the good’ to a claim about intention and moral action, and in so (...) doing have become divorced from the theory's roots in classical and medieval philosophy. Aristotle and Aquinas’ ‘guise of the good’ is primarily a metaphysical claim resting on the equivalence between actuality and goodness, from which conclusions about moral action are derived. I show the reasoning behind their theory and how it forms the basis for the claims about intention and action at the centre of the modern debate. Finally, I argue that the absence of its original foundation is apparent in recent attacks on the ‘guise of the good’. It is unsurprising that modern action theory and ethics have not always been able to comfortably accommodate the ‘guise of the good’; they are only telling half of the story. (shrink)

Are animals moral agents? In this article, a theologian and an anthropologist unite to bring the resources of each field to bear on this question. Alas, not all interdisciplinary conversations end harmoniously, and after much discussion the two authors find themselves in substantial disagreement over the answer. The article is therefore presented in two halves, one for each side of the argument. As well as presenting two different positions, our hope is that this article clarifies the different understandings of morality (...) in our respective fields and will help to offset confusion in interdisciplinary dialogue. In what follows, we each present our case. In the first section, Adam Willows argues that moral activity necessarily involves the use of reason, symbolic thought, and language and is on that basis an exclusively human affair. In the second, Marcus Baynes-Rock discusses his experience of relationality with other creatures; a relationality which, he argues, creates a shared understanding of obligations which are characteristically moral. (shrink)

How should you take into account the opinions of an advisor? When you completely defer to the advisor's judgment, then you should treat the advisor as a guru. Roughly, that means you should believe what you expect she would believe, if supplied with your extra evidence. When the advisor is your own future self, the resulting principle amounts to a version of the Reflection Principle---a version amended to handle cases of information loss. When you count an advisor as an epistemic (...) peer, you should give her conclusions the same weight as your own. Denying that view---call it the ``equal weight view''---leads to absurdity: the absurdity that you could reasonably come to believe yourself to be an epistemic superior to an advisor simply by noting cases of disagreement with her, and taking it that she made most of the mistakes. Accepting the view seems to lead to another absurdity: that one should suspend judgment about everything that one's smart and well-informed friends disagree on, which means suspending judgment about almost everything interesting. But despite appearances, the equal weight view does not have this absurd consequence. Furthermore, the view can be generalized to handle cases involving not just epistemic peers, but also epistemic superiors and inferiors. (shrink)

The foundation for a system of morals, this 1749 work is a landmark of moral and political thought. Its highly original theories of conscience, moral judgment, and virtue offer a reconstruction of the Enlightenment concept of social science, embracing both political economy and theories of law and government.

The resemblance is plain to see between Kripke’s Wittgenstein introducing bizarre rules such as quaddition (in illustrating the sceptical paradox against theories of meaning) and Goodman’s introducing the equally bizarre grue (in generating the new riddle of induction). But the two sorts of bizarre cases also differ in interesting respects. For those familiar with Goodman’s case, this similarity sparks a strong temptation to enlist to the meaning sceptic’s cause key elements of Goodman’s new riddle, which are missing from Kripke’s case. (...) In this essay, I characterize a natural way of doing just this, which targets dispositionalist solutions to the sceptical paradox. I also show that, despite initial appearances, this new objection to dispositionalism (the symmetry problem) is not nearly as worrisome as originally thought. The solution offered on behalf of semantic dispositionalists does require a trade-off, though, from the severe form of indeterminacy advanced by the meaning sceptic to a much milder thesis. (shrink)

A scholarly edition of a work by Adam Smith. The edition presents an authoritative text, together with an introduction, commentary notes, and scholarly apparatus.

Theorists have had less success in analyzing the truth conditions of generics. Philosophers of language have offered a number of theories. This chapter surveys several semantic accounts of generics. However, the focus is on generics and experimental philosophy. It briefly reviews empirical work that bears on these semantic accounts. While generics constitute an interesting linguistic phenomenon worthy of study in their own right, the study of generics also has wide‐ranging implications for questions beyond the philosophy of language, including questions in (...) social psychology and cognitive science more generally. The chapter also reviews empirical work on the relationship between generics and cognition. Existing empirical work strongly supports the generics‐as‐defaults hypothesis: the hypothesis that generics reflect a cognitively default, fundamental mode of generalizing in humans. Finally, the chapter elucidates evidence that generic language and generic modes of generalizing play an important role in stereotyping and prejudice. (shrink)

Constituent power is an idea with a long tradition in modern political thought but has been largely abandoned since the middle of the twentieth century. Here I offer a new account of constituent power that avoids problems of the classical account, including the paradox of constitutionalism, and clarifies how individuals contribute to creating their shared political order. I argue that constituent power should be understood as an individual power-with: the agential power to constitute a legal order with others. Our individual, (...) banal acts of law-abidingness each partially effect the collective outcome. We generally exercise constituent power unconsciously and automatically, guiding our actions to succeed as defined by law and relying on the legal system to take up our contributions and effectively combine them with others. (shrink)

This thoughtful new abridgment is enriched by the brilliant commentary which accompanies it. In it, Laurence Dickey argues that the _Wealth of Nations_ contains--and conceals--a great deal of how Smith actually thought a commercial society works. Guided by his conviction that the so-called Adam Smith Problem--the relationship between ethics and economics in Smith's thinking--is a core element in the argument of the work itself, Dickey's commentary focuses on the devices Smith uses to ground his economics in broadly ethical and (...) social categories. An unparalleled guide to an often difficult and perplexing work. (shrink)

Heritable personality traits often predict fundamental philosophical disagreement. This conclusion is based on studies of more than 15,000 people sampled from diverse cultures and educational backgrounds, including verifiable experts. In this chapter, we review some of this research showing links between personality and philosophical bias in free will, intentional action, and ethics. Our discussion focuses on serious challenges that these philosophical biases pose (e.g., limits on the use of philosophical intuitions as evidence). We close with discussion of the Philosophical Personality (...) Argument and brief consideration of emerging projects in applied experimental philosophy. (shrink)

In addition to being uncertain about what the world is like, one can also be uncertain about one’s own spatial or temporal location in the world. My aim is to pose a problem arising from the interaction between these two sorts of uncertainty, solve the problem, and draw two lessons from the solution.

It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as an agent's (...) attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient. (shrink)

In order to predict and explain behavior, one cannot specify the mental state of an agent merely by saying what information she possesses. Instead one must specify what information is available to an agent relative to various purposes. Specifying mental states in this way allows us to accommodate cases of imperfect recall, cognitive accomplishments involved in logical deduction, the mental states of confused or fragmented subjects, and the difference between propositional knowledge and know-how .

Proponents of epistocracy worry that high levels of voter ignorance can harm democracies. To combat such ignorance, they recommend allocating comparatively more political power to more politically knowledgeable citizens. In response, some recent critics of epistocracy contend that epistocratic institutions risk causing even more harm, since much evidence from political psychology indicates that more politically knowledgeable citizens are typically more biased, less open-minded, and more prone to motivated reasoning about political matters than their less knowledgeable counterparts. If so, perhaps epistocratic (...) institutions will perform worse epistemically than corresponding democratic institutions. Call this 'the problem of epistocratic irrationality'. This paper argues that the problem of epistocratic irrationality can be overcome. First, I argue that critics of epistocracy have overlooked several complications regarding the psychological data they claim shows that more knowledgeable citizens are less politically rational. Second, I argue that appropriately designed epistocratic institutions could overcome the problem of epistocratic irrationality even if such critics have interpreted the data correctly. I first explore whether refined selection mechanisms could allow epistocrats to avoid empowering less rational citizens, before assessing the prospects of implementing only those epistocratic institutions with a solid track record of reliable performance. (shrink)

Many have claimed that unspecific evidence sometimes demands unsharp, indeterminate, imprecise, vague, or interval-valued probabilities. Against this, a variant of the diachronic Dutch Book argument shows that perfectly rational agents always have perfectly sharp probabilities.

Our purpose in this article is to identify and suggest resolution for two core problematics of grounded theory. First, while grounded theory provides transparency to one part of the conceptualization process, where codes emerge directly from the data, it provides no such systematic or transparent way for gaining insight into the conceptual relationships between discovered codes. Producing a grounded theory depends not only on the definition of conceptual pieces, but the delineation of a relationship between at least two of those (...) pieces. Second, the conceptualization process of grounded theory is done in hierarchical fashion, where individual codes emerge from the data but then are used to generate insight into more general concepts and thematic statements. But various works on grounded theory have failed to provide any systematic way of using data specific levels of scale (the codes) to gain insight into more macro levels of scale (concepts and themes). We offer fractal concept analysis as a means of resolving both of these issues. By using a logic structure generator, fractal concept analysis delineates self-similar conceptual frameworks at various levels of abstraction, yielding a method for linking concepts together within and between levels of scale encountered in the grounded theory coding and categorization process. We conclude that this fractal analytic technique can bolster the aims of grounded theory as a formalized and systematic process for generating theory from empirical data. (shrink)

When one encounters disagreement about the truth of a factual claim from a trusted advisor who has access to all of one's evidence, should that move one in the direction of the advisor's view? Conciliatory views on disagreement say "yes, at least a little." Such views are extremely natural, but they can give incoherent advice when the issue under dispute is disagreement itself. So conciliatory views stand refuted. But despite first appearances, this makes no trouble for *partly* conciliatory views: views (...) that recommend giving ground in the face of disagreement about many matters, but not about disagreement itself. (shrink)

The “puzzle of the unmarked clock” derives from a conflict between the following: (1) a plausible principle of epistemic modesty, and (2) “Rational Reflection”, a principle saying how one’s beliefs about what it is rational to believe constrain the rest of one’s beliefs. An independently motivated improvement to Rational Reflection preserves its spirit while resolving the conflict.

Coercion is morally objectionable: it’s bad to be coerced and it’s wrong to coerce people. But why is coercion objectionable? In this paper, I advance an egalitarian account of what’s objectionable about coercion. The account is rooted in the idea that certain relationships, like those of master to slave and lord to peasant, are relationships of subordination or domination. These relationships are morally objectionable. Moreover, such relationships are in part constituted by asymmetries of power. A master subordinates a slave because (...) the master has more power over the slave than vice versa. The account says that coercion is objectionable because it creates such asymmetries of power, and so creates relationships of subordination. I show how this account can address its most serious problems, and how it can illuminate what’s wrong with blackmail, exploitation, withholding aid, and compulsion. (shrink)

Politics is full of people who don’t care about the facts. Still, while not caring about the facts, they are often concerned to present themselves as caring about them. Politics, in other words, is full of bullshitters. But why? In this paper I develop an incentives-based analysis of bullshit in politics, arguing that it is often a rational response to the incentives facing different groups of agents. In a slogan: bullshit in politics pays, sometimes literally. After first outlining an account (...) of bullshit (Section 1), I discuss the incentives driving three different groups of agents to bullshit: politicians, the media, and voters (Section 2). I then examine several existing proposals to combat bullshit in politics, arguing that each will fail because they ignore the relevant underlying incentives (Section 3). I conclude somewhat pessimistically that a certain amount of bullshit in politics is inevitable (Section 4). (shrink)

I investigate the extent to which perspectival realism agrees with frequentist statistical methodology and philosophy, with an emphasis on J. Neyman’s views. Based on the example of the stopping rule problem, I show how PR can naturally be associated with frequentist statistics in general. I also show that there are some aspects of Neyman’s thought that seem to confirm PR and others that disconfirm it. I argue that epistemic PR is consistent with Neyman’s frequentism to a satisfactory degree and that (...) on the grounds of Neyman’s frequentist methodology one is dealing with genuine and non-trivial perspectives. I also argue that universality and normativity of PR are weakened when analysed from the point of view of Neyman’s statistical methodology. (shrink)

Introduction i. Adam Smith's Lectures at Glasgow University Adam Smith was elected to the Chair of Logic at Glasgow University on 9 January, and admitted to ...

Despite their many virtues, democracies suffer from well-known problems with high levels of voter ignorance. Such ignorance, one might think, leads democracies to occasionally produce bad outcomes. Proponents of epistocracy claim that allocating comparatively greater amounts of political power to citizens who possess more politically relevant knowledge may help us to mitigate the bad effects of voter ignorance. An important challenge to epistocracy rejects the claim that we can reliably identify a subset of citizens who possess more politically relevant knowledge (...) than others. Roughly put, such knowledge should involve knowledge of various politically relevant social-scientific facts. But since the social sciences are mired in controversy, it’s not clear what the politically relevant facts are. Accordingly, we cannot definitively say of some citizens that they possess more politically relevant knowledge than others. Call this the Argument from Political Disagreement. In this paper I respond to the Argument from Political Disagreement. First, I argue that it conflates social-scientific knowledge with politically relevant knowledge. Even if there were no uncontroversial social-scientific knowledge, there is much uncontroversial politically relevant knowledge. Second, I establish the importance of such non-social-scientific knowledge for political decision-making. I conclude that this knowledge constitutes the minimal body of knowledge which epistocrats need to make their case. (shrink)

In the Law of Civilisation and Decay, Adams considers various societies and civilisations by the symbolism, manner and influence of their coinage, and concludes that a society or civilisation becomes sapped of its culture-vigour, when entering a cycle where money becomes the dominant factor rather than merely serving as a mechanism.

In "Counterfactual Dependence and Time's Arrow", David Lewis defends an analysis of counterfactuals intended to yield the asymmetry of counterfactual dependence: that later affairs depend counterfactually on earlier ones, and not the other way around. I argue that careful attention to the dynamical properties of thermodynamically irreversible processes shows that in many ordinary cases, Lewis's analysis fails to yield this asymmetry. Furthermore, the analysis fails in an instructive way: it teaches us something about the connection between the asymmetry of overdetermination (...) and the asymmetry of entropy. (shrink)

I discuss aspects of Freudian theory that have entered folk psychology.

This paper explores the ways in which truth is better than falsehood, and suggests that, among other things, it depends on the kinds of proposition to which these values are attached. Ordinary singular propositions like “It is raining” seem to fit best the bivalent “scheme” of classical logic, the general proposition “It is always raining” is more appropriately rated according to how often it rains, and a “practically vague” proposition like “The lecture will start at 1” is appropriately rated according (...) to its nearness to exactness. Implications for logic of this “rating system” are commented on. (shrink)

Robert Merrihew Adams has been a leader in renewing philosophical respect for the idea that moral obligation may be founded on the commands of God. This collection of Adams' essays, two of which are previously unpublished, draws from his extensive writings on philosophical theology that discuss metaphysical, epistemological, and ethical issues surrounding the concept of God--whether God exists or not, what God is or would be like, and how we ought to relate ourselves to such a being. Adams studies the (...) relation between religion and ethics, delving into an analysis of moral arguments for theistic belief. In several essays, he applies contemporary studies in the metaphysics of individuality, possibility and necessity, and counterfactual conditionals to issues surrounding the existence of God and problems of evil. (shrink)