In this paper, we will prove that the plus cupping degrees generate a definable ideal on c.e. degrees different from other ones known so far, thus answering a question asked by Li and Yang (Proceedings of the 7th and the 8th Asian Logic Conferences. World Scientific Press, Singapore, 2003).

Let [NB]₁ denote the ideal generated by nonbounding c.e. degrees and NCup the ideal of noncuppable c.e. degrees. We show that both [NB]₁ ∪ NCup and the ideal generated by nonbounding and noncuppable degrees are new, in the sense that they are different from M, [NB]₁ and NCup—the only three known definable ideals so far.

We show that under $\mathsf {BMM}$ and “there exists a Woodin cardinal, $"$ the nonstationary ideal on $\omega _1$ cannot be defined by a $\Pi _1$ formula with parameter $A \subset \omega _1$. We show that the same conclusion holds under the assumption of Woodin’s $(\ast )$ -axiom. We further show that there are universes where $\mathsf {BPFA}$ holds and $\text {NS}_{\omega _1}$ is $\Pi _1(\{\omega _1\})$ -definable. Lastly we show that if the canonical inner model with one Woodin (...) cardinal $M_1$ exists, there is a generic extension of $M_1$ in which $\text {NS}_{\omega _1}$ is saturated and $\Pi _1(\{ \omega _1\} )$ -definable, and $\mathsf {MA_{\omega _1}}$ holds. (shrink)

You 遊 is a crucial term for understanding the Zhuangzi . Translated as “play,” “free play,” and “wandering,” it is usually defined as an ideal, playful Zhuangzian way of being. There are two problems with this definition. The first is logical: the Zhuangzi cannot consistently recommend playfulness as an ideal, since doing so vitiates the essence of you —it becomes an ethical imperative instead of an activity freely undertaken for its own sake. The second problem is performative: arguments for playful (...) Zhuangzi as exemplar resemble those of the logicians and philosophers who appear to come in for Zhuangzian criticism. This essay addresses these tensions by demonstrating how the Zhuangzi ambiguates the nature and value of you . Apparent endorsements of you are not freestanding, instead occurring in grudging replies of teachers to overly zealous students. In light of this recontextualization, a new version of you is offered that accommodates “non-playful” ways of being. (shrink)

In this note we consider subfamilies of the ideal s0 introduced by Marczewski-Szpilrajn and ideals sp0, l0 analogously defined using complete Laver trees and Laver trees respectively. We show that under some set-theoretical assumptions =c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${cov=\mathfrak{c}}$$\end{document} for example) in every uncountable Polish space X every family A⊆s0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{A}\subseteq s_0}$$\end{document} covering X has a subfamily with s-nonmeasurable union. We show the consistency of cov=ω1 (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${cov=\omega_1 < \mathfrak{c}}$$\end{document} with the existence of a partition A∈[s0]ω1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{A}\in[s_0]^{\omega_1}}$$\end{document} of the real line with a subfamily A′⊆A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{A}'\subseteq\mathcal{A}}$$\end{document} for which ⋃A′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bigcup\mathcal{A}'}$$\end{document} is s-nonmeasurable. We also show that it is relatively consistent with ZFC that ω1shrink)

We define in precise terms the basic properties that an ‘ideal propositional paraconsistent logic’ is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n > 2 there exists an extensive family of ideal n -valued logics, each one of which is not (...) equivalent to any k -valued logic with k < n. (shrink)

When we admire a person, we don’t just have a wow-response towards them, as we might towards a painting or a sunset. Rather, we construe them as realizing an ideal of the person in their lives to a conspicuous degree. To merit admiration, it is not enough simply to do something valuable or to possess desirable character traits. Rather, one’s achievements must manifest commitments and character traits that define a worthwhile ideal. Agential admiration, I argue, is a person-focused attitude like (...) shame, contempt, and hubristic pride, not an act-focused one like gratitude or guilt, not to mention mere evaluation as excellent. Given its holistic focus, its motivational effects permeate our interactions with its target, who is construed as an exemplar. Consequently, even if someone is admirable in some way, admiring them may be all-things-considered inappropriate, if they fall short of other ideals that we ought to care about. (shrink)

We present several naturally defined σ-ideals which have Borel bases but, unlike for the classical examples, these ideals are not of bounded Borel complexity. We investigate set-theoretic properties of such σ-ideals.

§1. Introduction. Ideals and filters of subsets of natural numbers have been studied by set theorists and topologists for a long time. There is a vast literature concerning various kinds of ultrafilters. There is also a substantial interest in nicely definable ideals—these by old results of Sierpiński are very far from being maximal— and the structure of such ideals will concern us in this announcement. In addition to being interesting in their own right, Borel and analytic (...) ideals occur naturally in the investigations of compact subsets of the space of all Baire class 1 functions on a Polish space, see [12, 18]. Also, certain objects associated with such ideals are of considerable interest and were quite extensively studied by several authors. Let us list here three examples; in all three of them I stands for an analytic or Borel ideal.1. The partial order induced by I on P: X ≥I Y iff X \ Y ϵ I and the partial order.2. Boolean algebras of the form P/I and their automorphisms.3. The equivalence relation associated with I: XEI Y iff X Δ ϵ I.In Section 4, we will have an opportunity to state some consequences of our results for equivalence relations as in 3. (shrink)

Idealization is commonly understood as distortion: representing things differently than how they actually are. In this paper, we outline an alternative artifactual approach that does not make misrepresentation central for the analysis of idealization. We examine the contrast between the Hodgkin-Huxley (1952a, b, c) and the Heimburg-Jackson (2005, 2006) models of the nerve impulse from the artifactual perspective, and argue that, since the two models draw upon different epistemic resources and research programs, it is often difficult to tell which features (...) of a system the central assumptions involved are supposed to distort. Many idealizations are holistic in nature. They cannot be locally undone without dismantling the model, as they occupy a central position in the entire research program. Nor is their holistic character mainly related to the use of mathematical and statistical modeling techniques as portrayed by Rice (2018, 2019). We suggest that holistic idealizations are implicit theoretical and representational assumptions that can only be understood in relation to the conceptual and representational tools exploited in modeling and experimental practices. Such holistic idealizations play a pivotal role not just in individual models, but also in defining research programs. -/- . (shrink)

Feminists, critical race scholars, and other social‐justice theorists sometimes object to “abstraction” in liberal normative theory. Arguing that oppression affects individual agents in powerful yet subtle ways, they contend that allegedly abstract theories often reinforce oppressive power structures. Here I critically examine and ultimately reject Onora O'Neill's “abstraction without idealization” as a solution to this problem. Because O'Neill defines abstraction as simply the “bracketing of certain predicates,” her methodology fails to guide decisions about what to bracket and what to include (...) in the theory. Moreover, it may not be possible to abstract without also relying on some particular ideals. While abstraction is unavoidable, I conclude that it must be employed with greater attention to sociopolitical hierarchies and by using ideals that do not collude with structures of oppression. I discuss the work of Susan Babbitt and Elizabeth Anderson as examples of how nonoppressive ideals might be incorporated into normative theory. (shrink)

We study two ideals which are naturally associated to independent families. The first of them, denoted \, is characterized by a diagonalization property which allows along a cofinal sequence of stages along a finite support iteration to adjoin a maximal independent family. The second ideal, denoted \\), originates in Shelah’s proof of \ in Shelah, 433–443, 1992). We show that for every independent family \, \\subseteq \mathcal {J}_\mathcal {A}\) and define a class of maximal independent families, to which we (...) refer as densely maximal, for which the two ideals coincide. Building upon the techniques of Shelah we characterize Sacks indestructibility for such families in terms of properties of \\) and devise a countably closed poset which adjoins a Sacks indestructible densely maximal independent family. (shrink)

Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F $\subseteq$ P(X) of size c, consisting of Borel sets which are not in I. Condition (M) states that there is a Borel function f: X → X with $f^{-1}[\{x\}] \not\in$ I for each x ∈ (...) X. Provided that X is a group and I is invariant, condition (D) states that there exist a Borel set B $\not\in$ I and a perfect set P $\subseteq$ X for which the family $\{B + x: x \in P\}$ is disjoint. The aim of the paper is to study whether the reverse implications in the chain (D) $\Rightarrow$ (M) $\Rightarrow$ (B) $\Rightarrow$ not-ccc can hold. We build a σ-ideal on the Cantor group witnessing (M) & ¬ (D) (Section 2). A modified version of that σ-ideal contains the whole space (Section 3). Some consistency results on deriving (M) from (B) for "nicely" defined ideals are established (Sections 4 and 5). We show that both ccc and (M) can fail (Theorems 1.3 and 5.6). Finally, some sharp versions of (M) for invariant ideals on Polish groups are investigated (Section 6). (shrink)

The biinterpretability conjecture for the r.e. degrees asks whether, for each sufficiently large k, the [Formula: see text] relations on the r.e. degrees are uniformly definable from parameters. We solve a weaker version: for each k ≥ 7, the [Formula: see text] relations bounded from below by a nonzero degree are uniformly definable. As applications, we show that Low 1 is parameter definable, and we provide methods that lead to a new example of a ∅-definable ideal. (...) Moreover, we prove that automorphisms restricted to intervals [d, 1], d ≠ 0, are [Formula: see text]. We also show that, for each c ≠ 0, can be interpreted in [0, c] without parameters. (shrink)

We study normal ideals on Pκ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P_{\kappa} }$$\end{document} that are defined in terms of games of uncountable length.

In recent decades, attempts to explain autism have been frustrated by the heterogeneous nature of its behavioral symptoms and the underlying genetic, neural, and cognitive mechanisms that produce them. This has led some to propose eliminating the category altogether. The eliminativist inference relies on a conception of psychiatric categories as kinds defined by their underlying mechanistic structure. I review the evidence for eliminativism and propose an alternative model of the family of autisms. On this account, autism is a network category (...) defined by a set of idealized exemplars linked by multiple levels of theoretically significant properties. I argue that this network model better captures the empirical phenomena, the historical growth of the category, and the ways the category has been shaped by social norms and interests. Finally, I defend a realist interpretation of network categories against the challenge from eliminativists. (shrink)

This article reconsiders contemporary conservatism’s “libertarian” claim to economic and political liberty and related claims. It re‐examines the relation of conservatism and its supposed “libertarianism” to the principle or ideal of liberty in society and economy, respectively. The paper argues and demonstrates that since its inception out of medieval traditionalism, conservatism has continued to consistently oppose the ideal and practice of liberty defining liberalism, and to that extent modern liberal‐democratic society as a reality or project premised on that ideal. The (...) argument and inference is that conservative “libertarianism” is effectively the antithesis to the ideal of liberty, couched in and rationalized as antagonism toward liberalism identified as its original and continual antagonist. (shrink)

We study a normal ideal on Pκ that is defined in terms of games.

In lieu of an abstract, here is a brief excerpt of the content:The Ideal of Shared Decision Making Between Physicians and PatientsDan W. Brock (bio)IntroductionShared treatment decision making, with its division of labor between physician and patient, is a common ideal in medical ethics for the physician-patient relationship.1 Most simply put, the physician's role is to use his or her training, knowledge, and experience to provide the patient with facts about the diagnosis and about the prognoses without treatment and with (...) alternative treatments. The patient's role in this division of labor is to provide the values—his or her own conception of the good—with which to evaluate these alternatives, and to select the one that is best for himself or herself. As a rough guide to practice, this is a reasonable conception; most of the time it is likely to produce sound treatment decisions. However, as an ideal it is too simplistic, and is subject to several challenges that I will explore in this paper.Some challenges relate to the physician's role. This facts/values division of labor seems to assume that the physician can and should provide the facts about treatment alternatives in a value-neutral form. But some have questioned whether the sciences on which medicine is based are, or can be, value free. Moreover, the concepts of health and disease, and of the normal and pathological, are held by many to be value laden. And even if it is possible for physicians to provide only value-neutral facts to the patient, should the physicians' role be restricted in this way?Other challenges that I will present in the paper are to the patient's role [End Page 28] as provider of the values for the evaluation of the different treatment alternatives. One defense of this role is based on the claim that physicians are not in a position to know reliably what is in a patient's best interests (Buchanan, forthcoming). I believe at least as influential—even if often not explicitly stated—is an extreme subjectivism about values that assumes that the patient's own ultimate values, which define his or her own conception of the good, are incorrigible. By incorrigible, I mean they cannot be mistaken. In the standard case in which treatment is pursued for the patient's benefit, this extreme subjectivism is thought to support the patient's values guiding treatment decision making and treatment. I will explore this incorrigibility claim and will argue that on each of the main philosophical conceptions of the good for persons it is indefensible and should not be the basis for shared treatment decision making.Underlying this view of the physician-patient division of labor are assumptions and beliefs about the nature and relation of facts and values, and science and ethics, that are largely the legacy of a logical positivism that has long since been rejected by most philosophers. It is time that these unstable foundations for our normative ideal of the physician-patient relation were finally removed and replaced with more defensible underpinnings.Two Models of the Physician-Patient RelationshipPositivists insisted on a relatively sharp distinction between descriptive or empirical claims and science, on the one hand, and evaluative claims and ethics, on the other.2 Descriptive statements and the claims of science were to be true or false according to whether they in fact correctly described and explained the world. By remaining properly descriptive or empirical, science could, at least in principle, be entirely value neutral or value free.In its more extreme versions, positivism held that ethical judgments lacked cognitive content, but were instead expressions of emotions or attitudes, and as such could be neither true nor false, correct or mistaken. Because no evaluative statements were held to be logically entailed by any descriptive or empirical statements, moral reasoning was thought to be properly understood not as reasoning but as attempts at nonrational persuasion.3 Many drew from this an extreme subjectivism in ethics along the lines of what I have called above the incorrigibility thesis—there is no meaningful sense in which an individual's ultimate values defining his or her own conception of the good life could be mistaken, false, or unfounded.These... (shrink)

Without doubt, terrorism is one of the most vehemently debated subjects in current political affairs as well as in academic discourse. Yet, although it constitutes an issue of general socio-political interest, neither in everyday language nor in professional (political, legal, or academic) contexts does there exist a generally accepted definition of terrorism. The question of how it should be defined has been answered countless times, with as much variety as quantity in the answers. In academic discourse, it is difficult to (...) find two scholars who use the term ‘terrorism’ in the same way. -/- While it is impossible to formulate a definition which satisfies everyone, discussing the definition question is indispensable. The necessity to review existing definitions with a view to improving them is especially obvious in legal and political contexts. How terrorism is defined in these contexts has serious consequences, and if we lack clear definitions we run into problems. How can we have laws or take political measures against something we have not clearly defined? Without doubt, there exists a practical necessity for a definition in these fields. It is important to have clear standards for defining terrorism. -/- In my view, the definition should meet three basic criteria: first, it should cover those cases that we concurrently consider to be instances of terrorism (such as the attacks on the World Trade Center in New York and the Pentagon in September 2001 or those on commuting trains in Madrid Atocha in March 2004). That is, ideally, our definition of terrorism remains close to uncontroversial usages of the term. Second, the definition should abstain from morally judging the act in question. Later I will say more about so called “moral” definitions of terrorism. For now, it suffices to say that defining an action and evaluating it are distinct tasks and should remain so. Third, the definition must identify characteristics that are specific to terrorism alone, characteristics which clearly distinguish it from other phenomena. (shrink)

Let J be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal J * ∣B as follows: X ∈ J * ∣B if there exists a Borel set $B \subset R \times R$ such that $X \subset B$ and for any x ∈ R we have $\{y \in R: \langle x,y\rangle \in B\} \in \mathscr{J}$ . We show that there exists a family $\mathscr{A} \subset \mathscr{J}^\ast\mid\mathscr{B}$ of power ω (...) 1 such that $\bigcup\mathscr{A} \not\in \mathscr{J}^\ast\mid\mathscr{B}$ . In the last section we investigate properties of ideals of Lebesgue measure zero sets and meager sets in Cohen extensions of models of set theory. (shrink)

An ideal I defined on a group G is called idempotent if for every $A \in I, \{g \in G: Ag^{-1} \not\in I\} \in I$ . We show that a countably complete idempotent ideal on an abelian group cannot be prime but may have strong saturation properties.

What grounds the truth of modal statements? And how do we get to know about what is possible or necessary? One of the most prominent anti-realist perspectives on the nature of modality, due to Peter Menzies, is the response-dependent account of modal concepts. Typically, offering a response-dependent account of a concept means defining it in terms of dispositions to elicit certain mental states from suitable agents under suitable circumstances. Menzies grounded possibility and necessity in the conceivability-response of ideal conceivers: P (...) is possible iff an ideal conceiver could conceive that P. I will draw attention to three major objections that can be identified in the modal metaphysics and epistemology literature: Chalmers’ Incoherency Objection, Sherratt’s Transparency Objection and Geirsson’s Irrelevancy Objection. Each of these objections raises a different worry regarding Menzies’ account: that the notion of an ideal conceiver is incoherent, that the account implies a controversial thesis, and that it fails to offer an explanation of our knowledge of modality. The aim of this paper is to defend the response-dependent account of modality against these three objections. (shrink)

Ideal families defined on a cardinalk often exhibit reflection properties. IfC ⫅k is a club, for example, thenC∩α is a club-in-α club-in-k often. In this paper we generalize this notion to ideal families defined on℘ kλ and exhibit some examples.

The research is devoted to the problem of philosophically justifying rationality, which inevitably takes the form of a circular argument: to define what rationality is, we must refrain from referring to its criteria, which must be rationally defined beforehand. This epistemic circle is compared to the so-called “experimenter’s regress”. The experimenter’s regress involves reasoning in which judging the correctness of obtained scientific results can only be based on the correctness of the procedure of obtaining them and judging the correctness of (...) the procedure of obtaining them can only be done by relying on the obtained results. From the perspective of social researchers of science, the experimenter’s (and the theoretician’s) regress casts a shadow on traditional theories of rationality that take science as a model of rational knowledge. The research analyzes the experimenter’s regress in the context of virtuous and vicious circles. It is shown that the experimenter’s regress is overcome by turning to external factors. These factors are proposed to be interpreted in terms of extended rationality. By analyzing the experimenter’s regress, social epistemologists consciously or unconsciously rationalize these “external” factors and enrich the concept of rationality. This allows qualifying the circle described by rationality in defining itself as virtuous and the work of the epistemologist as a progressive activity, during which both epistemology and its subject undergo qualitative changes. (shrink)

This paper examines the nomic covariationist strategy of using idealization to define representation. While the literature has focused upon the possibility of defining ideal conditions for perception, I argue that nomic covariationist appeals to idealization are pseudoscientific and contrary to a foundational and empirically well-supported methodological presupposition in cognitive science. Moreover, one major figure in this camp fails to come to grips with its role and its problems in mainstream science. Thus he forwards a false dichotomy of the sciences and (...) treats idealization as a blank check written by scientists on an unknown bank. Finally, I consider and reject alternative formulations of the nomic covariationist's idealization strategy. (shrink)

. The author aims at defining the borderlines of the concept “rule of law.” This has been often inflated to encompass several dimensions of an ideal legal order. The author on the contrary believes that the “rule of law” ought to be a “thin” ideal. As a matter of fact, when the “rule of law” signifies almost any dimension of an ideal legal order, it comes to stand for nothing essential in particular. Deflation is then advocated for the rehabilitation of (...) the normative content of the “rule of law.” This means that the “rule of law” should be defined as a concept covering only some well delimited dimensions of an ideal legal order. (shrink)

The author aims at defining the borderlines of the concept “rule of law.” This has been often inflated to encompass several dimensions of an ideal legal order. The author on the contrary believes that the “rule of law” ought to be a “thin” ideal. As a matter of fact, when the “rule of law” signifies almost any dimension of an ideal legal order, it comes to stand for nothing essential in particular. Deflation is then advocated for the rehabilitation of the (...) normative content of the “rule of law.” This means that the “rule of law” should be defined as a concept covering only some well delimited dimensions of an ideal legal order. (shrink)

Background As our society is ageing, nursing homes are finding it increasingly difficult to deal with an expanding population of patients with dementia and a decreasing workforce. A potential answer to this problem might lie in the use of technology. However, the use and application of surveillance technology in dementia care has led to considerable ethical debate among healthcare professionals and ethicists, with no clear consensus to date. Aim To explore how surveillance technology is viewed by care professionals and ethicists (...) working in the field, by investigating the ideal application of surveillance technology in the residential care of people with dementia. Methods Use was made of the concept mapping method, a computer-assisted procedure consisting of five steps: brainstorming, prioritising, clustering, processing by the computer and analysis. Various participants (ranging from ethicists to physicians and nurses) were invited on the basis of their professional background. Results The views generated are grouped into six categories ranging from the need for a right balance between freedom and security, to be beneficial and tailored to the resident, and clearly defined procedures to competent and caring personnel, active monitoring and clear normative guidance. The results are presented in the form of a graphic chart. Conclusions There appears to be an inherent duality in the views on using surveillance technology which is rooted in the moral conflict between safety and freedom. Elaboration of this ethical issue has proved to be very difficult. (shrink)

Here we work in an arbitrary o-minimal expansion of a divisible ordered abelian group. We say that a definable ring is definably semiprime if squares of nontrivial two-sided ideals definable in the expansion are nontrivial. We prove a definable version of Wedderburn–Artin theorem and give a characterization of definably semiprime rings.

Here I reply to a recent exchange between Edgar Danielyan and Brian Garrett regarding Alvin Plantinga’s assessment of Gaunilo’s ‘ideal island’ objection to Anselm’s ontological argument. I argue that an ideal island is conceivable if it’s defined as any island exhibiting an ideal ratio of great-making island properties.

Knill, Kersten, & Mamassian (Chapter 6) provide an interesting discussion of how the Bayesian formulation can be used to help investigate human vision. In their view, computational theories can be based on an ideal observer that uses Bayesian inference to make optimal use of available information. Four factors are important here: the image information used, the output structures estimated, the priors assumed (i.e., knowledge about the structure of the world), and the likelihood function used (i.e., knowledge about the projection of (...) the world onto the sensors). Knill & Kersten argue that such a framework not only helps analyze a perceptual task, but can also help investigators to define it. Two examples are provided (the interpretation of surface contour and the perception of moving shadows) to show how this approach can be used in practice. As the authors admit, most (if not all) perceptual processes are ill-suited to a "strong" Bayesian approach based on a single consistent model of the world. Instead, they argue for a "weak" variant that assumes Bayesian inference to be carried out in modules of more limited scope. But how weak is "weak"? Are such approaches suitable for only a few relatively low-level tasks, or can they be applied more generally? Could a weak Bayesian approach, for example, explain how we would recognize the return of Elvis Presley? The formal modelling of human perception To help get a fix on things, it is useful to examine the fate of an earlier attempt to formalize human perception: the application of information theory. It was once hoped that this theory—a close cousin of the Bayesian formulation—would provide a way to uncover information-handling laws that were largely independent of physical implementation. In this approach, the human nervous system was assumed to have.. (shrink)

The modern social world is unjust. It is also complex. What does this latter fact imply about the kind of approach that should be used in ameliorating the injustice expressed in the former fact? One answer, recently put forth by Jacob Barrett, is that _ideal theory_, which he understands as being fundamentally defined by the identification and subsequent pursuit of an aspirational macro-level institutional goal, lacks a place in social reform. The reason he thinks ideal theory lacks a place has (...) to do with its inability to deal with complexity. _Pace_ Barrett, I argue that ideal theory, suitably understood, can play a valuable role in social reform in a complex world. While some ideal theorists have underappreciated the extent to which complexity considerations complicate social reform, this does not mean that there is no place for it. This paper surveys the resources ideal theory has available to cope with what I call _the challenge of complexity_. Although the coping techniques will be successful to varying degrees, I believe, in aggregate, a compelling case can be made that ideal theory can combat the challenge of complexity. Still, one may worry that even if ideal theory can adequately deal with complexity, it cannot adequately deal with ever-changing social circumstances. Call this _the dancing landscape objection_. A static ideal theory cannot overcome it, but a _dynamic ideal theory_ could. In sum, dynamic ideal theory can contribute to social reform in a complex and mutable social world. (shrink)

My research into Virtual Reality technology and its central property of immersion has indicated that immersion in Virtual Reality (VR) electronic systems is a significant key to the understanding of contemporary culture as well as considerable aspects of previous culture as detected in the histories of philosophy and the visual arts. The fundamental change in aesthetic perception engendered by immersion, a perception which is connected to the ideal of total-immersion in virtual space, identifies certain shifts in ontology which are relevant (...) to a better understanding of the human being. This understanding was achieved through a broad inquiry into the histories of Virtual Reality, philosophy, and the visual arts and has lead to the formulation of an aesthetic theory of immersive consciousness indicative of immersive culture. The primary subject of this discourse is immersion then: an experience which will be identified within the dissertation as the indispensable characteristic of Virtual Reality. The understanding of immersion arrived at here will be used to fashion a synchronous theory of art particularly informed by encounters and concepts of immersion into virtuality. To sufficiently address this subject in a scholarly fashion, I have researched, found and accumulated aesthetic and philosophic examples of immersive tendencies, as found within the histories of art and philosophy, which subsequently contributed towards the articulation of what I have come to call immersive consciousness. As a result of formulating such an immersive consciousness, a good deal of the basis for the questioning of the Western ontological tradition has been found in the Western tradition itself when we look with new eyes and ask new uncertain questions. Moreover, this immersive consciousness will be used to propose some abstract questions encircling today's electronic-based culture. Through the structuring of the argument within the thesis - and overtly within the conclusion - I have articulated a non-teleological creative strategy which provides the basis for an unconstraining integration of noologies (ways of semblancing the thinking process). This strategy provides a means of exemplifying - and for honoring - various methods of thinking. This structuring strategy is consistent with the 'hacker ethic' as defined by Steven Levy, as a demand that access to computers - and anything which might teach us something about the way the world works - should be unlimited and total. To follow this strategy, this dissertation has set out to understand how topical conceptions of virtual immersion connect to pre-existing systems of thought as revealed in art as they have extended out of antecedent ontological self-understandings, historical human self-understandings which have evidenced themselves in the elaboration of technological objectives. To do this I have forged a certain rhizomatic paternity/maternity for Virtual Reality within this dissertation by joining choice immersive examples of simulacra technology into mental connections with the relevant examples culled from the histories of art, architecture, information-technology, sex, myth, space, consciousness and philosophy. (shrink)

The concepts of supportive evidence and of relevant evidence seem very closely related to each other. Supportive evidence is clearly always relevant as well. But must relevant evidence be defined as evidence which is either supportive or weakeking? In an explicit or implicit manner, this is indeed the position of many philosophers. The paradox of ideal evidence, however, shows us that this is to restrictive. Besides increasing or decreasing the probability attached to some hypothesis, evidence can alter or interact with (...) the background assumptions underlying the hypothesis.In most circumstances, the (post hoc) relevance of evidence can indeed be judged by its effect on the confidence one attaches to hypotheses. Occasionally, as in the circumstances described by Example I, and more generally called “the Paradox of Ideal Evidence”, the relevance of evidence to an hypothesis can only be understood by appeal to a broader sense. (shrink)

Questions concerning the epistemological status of computer science are, in this paper, answered from the point of view of the formal verification framework. State space reduction techniques adopted to simplify computational models in model checking are analysed in terms of Aristotelian abstractions and Galilean idealizations characterizing the inquiry of empirical systems. Methodological considerations drawn here are employed to argue in favour of the scientific understanding of computer science as a discipline. Specifically, reduced models gained by Dataion are acknowledged as Aristotelian (...) abstractions that include only data which are sufficient to examine the interested executions. The present study highlights how the need to maximize incompatible properties is at the basis of both Abstraction Refinement, the process of generating a cascade of computational models to achieve a balance between simplicity and informativeness, and the Multiple Model Idealization approach in biology. Finally, fairness constraints, imposed to computational models to allow fair behaviours only, are defined as ceteris paribus conditions under which temporal formulas, formalizing software requirements, acquire the status of law-like statements about the software systems executions. (shrink)

The volume aims to clarify and argue in support of the distinction between ideal and nonideal theory, as it is defined and used especially by (some of) the political philosophers working on the topic of social justice. In the process of trying to achieve this aim, the volume proposes, as well, a series of analyses concerning the other major problem raised by the ideal-nonideal distinction in political theory: the problem of the soundness of ideal theory as a method of specifying (...) the concept of justice and/or as a guide for political action, institutions and policies. Except for the foreword (which sets its scene and explorative framework) and the afterword (which concludes its argumentative approach and reminds some of its key explanations and observations), the volume is organized in three chapters. The first chapter discusses John Rawls` view on the distinction between ideal and nonideal theory. Its basic intention is to clarify, assess and synthetize the main claims and theses specific to the Rawlsian outlook. This analysis is followed, in the second chapter, by an investigation of the main post-Rawlsian contributions to the project of clarifying the ideal-nonideal distinction in theorizing justice. The third chapter rejects the claim according to which the distinction between ideal and nonideal theory is unjustified or, at least, not categorical. Based on its argumentative and explanatory undertaking, the book proposes the following simple definition of the ideal-nonideal distinction in theorizing justice: ideal theory is the theory aiming to offer an (adequate) answer to the question “what is social justice?”. In other words, ideal theory is the theory of defining or specifying the concept of social justice. Nonideal theory is, instead, the area of academic research interested in answering (and bound to answer) all the other imperative questions about justice and injustice: „is social justice an achievable ideal here and now?”, „which are the best policies in correcting or mitigating the current social injustices?”, „which is the most appropriate strategy for achieving the institutional design that best realizes the principles of justice?”, „in what way are the duties of justice affected when the others fail to conform to these duties?”, „which are the requirements of retributive justice?” or „which are the principles of rectificatory justice?”. (shrink)

Let K be an infinite Galois extension of the rationals such that every finite subextension has odd degree over the rationals and its prime ideals dividing 2 are unramified. We show that its ring of integers is first-order definable in K. As an application we prove that equation image together with all its Galois subextensions are undecidable, where Δ is the set of all the prime integers which are congruent to −1 modulo 4.

The article discusses Ilyenkov's conception of the ideal, which has its roots in Marx's concept of human as a sociohistorical being, yet goes beyond Marx by developing a concrete understanding of human social activity. Defined dialectically as a form of the subjective activity of social man that has objective meaning and significance, the ideal in Ilyenkov is not simply a form of "social representation" , but it rather exists as man's ideal activity toward realization of his own goals, and as (...) such it guides creative activity in the world, opening up new horizons for human development. (shrink)

The growing significance of social media in research demands new ethical standards and practices. Although a substantial body of literature on social media ethics exists, studies on the ethics of conducting research using social media are scarce. The emergence of new evidence sources, like social media, requires innovative methods and renewed consideration of research ethics. Therefore, we pose the following question: What are the defining characteristics of ethics papers on social media research? Following a modified version of the Preferred Reporting (...) Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol, we analyzed 34 publications based on ten variables: author gender, publication year, region, academic discipline, type, design, methodology, social media platform in focus, positionality statement, and ethical issues. Our findings suggest contemporary social media research ethics primarily reflects the ethical ideals of the Global North, with limited representation from the Global South. Women authors have published more papers than men authors. Previous studies have prioritized ethical concerns such as privacy, informed consent, and anonymity while overlooking researchers’ risks and the ethics of social media sites. We particularly emphasized the lack of researchers’ positionality statements in research. Our findings will pave the way to understanding social media ethics better, especially with the rapid growth of social media research in global scholarship. (shrink)

The purpose of this communication is to announce some recent results on the computably enumerable sets. There are two disjoint sets of results; the first involves invariant classes and the second involves automorphisms of the computably enumerable sets. What these results have in common is that the guts of the proofs of these theorems uses a new form of definable coding for the computably enumerable sets.We will work in the structure of the computably enumerable sets. The language is just (...) inclusion, ⊆. This structure is called ε.All sets will be computably enumerable non-computable sets and all degrees will be computably enumerable and non-computable, unless otherwise noted. Our notation and definitions are standard and follow Soare [1987]; however we will warm up with some definitions and notation issues so the reader need not consult Soare [1987]. Some historical remarks follow in Section 2.1 and throughout Section 3.We will also consider the quotient structure ε modulo the ideal of finite sets, ε*. ε* is a definable quotient structure of ε since “Χ is finite” is definable in ε; “Χ is finite” iff all subsets of Χ are computable. We use A* to denote the equivalent class of A under the ideal of finite sets. (shrink)

Probabilistic coherence is not an absolute requirement of rationality; nevertheless, it is an ideal of rationality with substantive normative import. An idealized rational agent who avoided making implicit logical errors in forming his preferences would be coherent. In response to the challenge, recently made by epistemologists such as Foley and Plantinga, that appeals to ideal rationality render probabilism either irrelevant or implausible, I argue that idealized requirements can be normatively relevant even when the ideals are unattainable, so long as (...) they define a structure that links imperfect and perfect rationality in a way that enables us to make sense of the notion of better approximations to the ideal. I then analyze the notion of approximation to the ideal of coherence by developing a generalized theory of belief functions that allows for incoherence, and showing how such belief functions can be ordered with regard to greater or lesser coherence. (shrink)

With every σ-ideal I on a Polish space we associate the σ-ideal I* generated by the closed sets in I. We study the forcing notions of Borel sets modulo the respective σ-ideals I and I* and find connections between their forcing properties. To this end, we associate to a σ-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of the ideal. We also study the 1—1 (...) or constant property of σ-ideals, i.e., the property that every Borel function defined on a Borel positive set can be restricted to a positive Borel set on which it either 1—1 or constant. We prove the following dichotomy: if I is a σ-ideal generated by closed sets, then either the forcing P I adds a Cohen real, or else I has the 1—1 or constant property. (shrink)

Husserl’s concept of an “historical apriori” is marked by a tension: It simultaneously departs from, and develops his long-standing commitment to philosophy as transcendental phenomenology. This paper looks at some reasons for this tension in the context of Husserl’s attempt to determine philosophy as a “tradition” in The Origin of Geometry. Husserl is convinced that philosophy is a scientific tradition, and the historical apriori serves in the analysis of the conditions that define a distinctively scientific “handing down.” The key here (...) is a kind of writing—mathematics—thanks to which the participants in the tradition can be certain that they are in essential connection with the “original” idealities of that tradition. But Husserl’s discovery about the individual philosopher’s relation to the philosophical tradition—namely, that it is always mediated by a kind of “poetic invention”—undermines his conviction that philosophy can be a scientific tradition. This is Husserl’s “existentialism.”. (shrink)