The class approach to the problem of educating a comprehensively developed personality under the conditions of developed socialist society requires careful consideration of the full complexity of the social structure of contemporary socialist society and the resultant concrete connections and interrelations of classes, social strata, and groups. A class approach requires that social reality be evaluated from the standpoint of the objective tendencies it embodies and the progressive possibilities of historical development; it relies on real social strata capable (...) of and concerned with implementing these potentials. (shrink)

Aleksandar Ignjatović. Delineating Classes of Computational Complexity via Second Order Theories with Weak Set Existence Principles (I).

This is the text of a paper (along with appendixes) delivered at the 2019 annual meeting of the Minnesota Philosophical Society on Oct 26 in Cambridge, MN. -/- Beauchamp and Childress’s “Four Principles” (or “Principlism”) approach to bioethics has become something of a standard not only in bioethics classrooms and journals, but also within medicine itself. In this teaching-focused workshop, I’ll be doing the following: (1) Introducing the basics of the “Four Principles” approach, with a special focus on its relation (...) to the common morality and the importance to weighing and balancing of competing norms. (2) Comparing and contrasting this to other potential approaches, such as those provided by virtue ethics, act utilitarianism, casuistry, and competing versions of principles-based ethics. (3) Considering the ways in which the principles-based approach can best be implemented for lower-level, introductory bioethics classes, where the average student may have little background knowledge in either philosophy or medicine. I’ll be presenting sample activities, case studies, and lesson plans. There will be considerable time reserved for discussion at the end, so that participants can exchange ideas relating to the teaching of both bioethics and other varieties of applied ethics. (shrink)

We give a level-by-level analysis of the Weak Vopěnka Principle for definable classes of relational structures ( $\mathrm {WVP}$ ), in accordance with the complexity of their definition, and we determine the large-cardinal strength of each level. Thus, in particular, we show that $\mathrm {WVP}$ for $\Sigma _2$ -definable classes is equivalent to the existence of a strong cardinal. The main theorem (Theorem 5.11) shows, more generally, that $\mathrm {WVP}$ for $\Sigma _n$ -definable classes is equivalent to the existence (...) of a $\Sigma _n$ -strong cardinal (Definition 5.1). Hence, $\mathrm {WVP}$ is equivalent to the existence of a $\Sigma _n$ -strong cardinal for all $n<\omega $. (shrink)

We study various classes of maximality principles, \\), introduced by Hamkins :527–550, 2003), where \ defines a class of forcing posets and \ is an infinite cardinal. We explore the consistency strength and the relationship of \\) with various forcing axioms when \. In particular, we give a characterization of bounded forcing axioms for a class of forcings \ in terms of maximality principles MP\\) for \ formulas. A significant part of the paper is devoted to studying the (...) principle MP\\) where \ and \ defines the class of stationary set preserving forcings. We show that MP\\) has high consistency strength; on the other hand, if \ defines the class of proper forcings or semi-proper forcings, then by Hamkins, MP\\) is consistent relative to \. (shrink)

It is well known that S12 cannot prove the injective weak pigeonhole principle for polynomial time functions unless RSA is insecure. In this note we investigate the provability of the surjective weak pigeonhole principle in S12 for provably weaker function classes.

Open peer commentary on the article “Negotiating Between Learner and Mathematics: A Conceptual Framework to Analyze Teacher Sensitivity Toward Constructivism in a Mathematics Classroom” by Philip Borg, Dave Hewitt & Ian Jones. Upshot: The target article offers a method for teachers to reflect on their constructivist approach in classrooms. This commentary suggests ways to augment the approach for use with groups of teachers.

This paper investigates the semantic bases of class membership in the noun class system of Gújjolaay Eegimaa (Eegimaa henceforth), a Niger-Congo and Atlantic language of the BAK group spoken in Southern Senegal. The question of whether semantic principles underlie the overt classification of nouns in Niger-Congo languages is a controversial one. There is a common perception of Niger-Congo noun class systems as being mainly semantically arbitrary. The goal of the present paper is to show that physical properties (...) and culture-specific factors are central principles of semantic categorisation in the Eegimaa noun class system. I argue that the Eegimaa overt grammatical classification of nouns into classes is a semantic categorisation system whereby categories are structured according to prototypicality, family resemblance, metaphorical and metonymic extensions and chaining processes, as argued within the framework of Cognitive Linguistics. I show that the categorisation of entities in the Eegimaa nominal classification system productively makes use of physical properties such as shape as well as using culture-specific, less productive parameters for the semantic categorisation of entities denoted by nouns. The analysis proposed here also shows that the cases of multiple morphosyntactic classifications of nouns reflect multiple conceptual categorisation strategies. A detailed examination of the formal and semantic instances of multiple classification reveals the existence of conceptual correlations between the physical properties and the culture-specific semantic parameters of categorisation used in the Eegimaa noun class system. (shrink)

This article argues that Brentano’s classification of mental phenomena is best understood against the background of the theories of natural classification held by Auguste Comte and John Stuart Mill. Section 1 offers a reconstruction of Brentano’s two-premise argument for his tripartite classification. Section 2 gives a brief overview of the reception and historical background of the classification project. Section 3 addresses the question as to why a classification of mental phenomena is needed at all and traces the answer back to (...) Mill’s view that psychological laws are class-specific. Section 4 and 5 connect the second premise of Brentano’s argument to Comte’s principle of comparative likeness and Mill’s insistance that class membership is determined by the possession of common characteristics. And section 6 briefly discusses the evidence Brentano provides for the first premise. (shrink)

This paper examines John Rawls' renowned theory of justice, which outlines two principles of justice and their respective significance. It explores how Rawls' notion of equality aligns with the philosophical concept of equity, emphasizing that his call for citizen equality inherently incorporates fairness. Additionally, the paper discusses the application of Rawls' "Difference Principle" to India's reservation policy. Rawls' principles, which aim to support the worst-off in society, are reflected in India's system of reservations for marginalized groups, including backward classes (...) and differently-abled individuals, to promote equitable opportunities. However, the paper cautions that excessive reservations could limit opportunities for more privileged groups. Ultimately, it is argued that Rawls' concept of social justice has contributed to the promotion of social justice in India. (shrink)

This study is in two parts. In the first part, various important principles of classical extensional mereology are derived on the basis of a nice axiomatization involving ‘part of’ and fusion. All results are proved here with full Fregean rigor. They are chosen because they are needed for the second part. In the second part, this natural-deduction framework is used in order to regiment David Lewis’s justification of his Division Thesis, which features prominently in his combination of mereology with (...) class='Hi'>class theory. The Division Thesis plays a crucial role in Lewis’s informal argument for his Second Thesis in his book Parts of Classes. In order to present Lewis’s argument in rigorous detail, an elegant new principle is offered for the theory that combines class theory and mereology. The new principle is called the Canonical Decomposition Thesis. It secures Lewis’s Division Thesis on the strong construal required in order for his argument to go through. The exercise illustrates how careful one has to be when setting up the details of an adequate foundational theory of parts and classes. The main aim behind this investigation is to determine whether an anti-realist, inferentialist theorist of meaning has the resources to exhibit Lewis’s argument for his Second Thesis—which is central to his marriage of class theory with mereology—as a purely conceptual one. The formal analysis shows that Lewis’s argument, despite its striking appearance to the contrary, can be given in the constructive, relevant logic IR. This is the logic that the author has argued, elsewhere, to be the correct logic from an anti-realist point of view. The anti-realist is therefore in a position to regard Lewis’s argument as purely conceptual. (shrink)

We study properties of certain subclasses of the Dedekind finite sets in set theory without the axiom of choice with respect to the comparability of their elements and to the boundedness of such classes, and we answer related open problems from Herrlich’s “The Finite and the Infinite.” The main results are as follows: 1. It is relatively consistent with ZF that the class of all finite sets is not the only finiteness class such that any two of its (...) elements are comparable. 2. The principle “Small Violations of Choice” —introduced by A. Blass—implies that the class of all Dedekind finite sets is bounded above. 3. “The class of all Dedekind finite sets is bounded above” is true in every permutation model of ZFA in which the class of atoms is a set, and in every symmetric model of ZF. 4. There exists a model of ZFA set theory in which the class of all atoms is a proper class and in which the class of all infinite Dedekind finite sets is not bounded above. 5. There exists a model of ZF in which the class of all infinite Dedekind finite sets is not bounded above. (shrink)

This article studies three most basic systems of truth as well as their subsystems over set theory ZF possibly with AC or the axiom of global choice GC, and then correlates them with subsystems of Morse–Kelley class theory MK. The article aims at making an initial step towards the axiomatic study of truth in set theory in connection with class theory. Some new results on the side of class theory, such as conservativity, forcing and some forms of (...) the reflection principle, are also presented. The equivalence results among systems of truth and classes obtained in this article are summarized in Theorem 104 , Theorem 107 and Theorem 108. (shrink)

A discussion of the philosophical prospects for basing a neo-Fregean theory of classes on a principle that attempts to articulate the limitation-of-size conception.

Social scientific reasoning (SSR) is essential to social science education and to a democratic society as a whole. Students are challenged to analyze and reason about social problems such as social inequality, crime, and poverty. However, students experience difficulties with SSR. This study addresses the research question: Which design principles can guide teachers in designing lessons that promote social scientific reasoning? In this design-based research, four social science teachers employed a conceptualization of SSR and its levels together with three initial (...) design principles to develop curriculum materials and activities. These design principles and curriculum materials were piloted in two secondary education classes (9th and 10th grades) and evaluated by four social science teachers, four social science teacher educators and 90 students. The study produced six design principles that can promote students’ SSR. In combination with the curriculum materials, those design principles can help develop teachers’ pedagogical content knowledge and guide the design of tasks and units that develop SSR. (shrink)

In his paper "Why a Class Can't Change Its Members," Richard Sharvy appears to establish the impossibility of the existence of a variable class—that is, a class that at one time has a member that is not a member of it at another time. I first indicate the importance of Sharvy's argument for our understanding of the concept of identity in the contexts of time and modality, and I summarize his argument. Sharvy says that a class (...) C that has one (non-variable) group of members at t2 and another (nonvariable) group of members at t2 would be identical with both the class C1 that always has the first group as members and the class C2 that always has the second group as members. This is an impossibility, since in general, one thing cannot be identical with two.I then criticize Sharvy's argument by pointing out a weakness in the defense of the claim that C = C1 and C = C2. This weakness is due to an ambiguity in Sharvy's Principle of Extensionality. (shrink)

Using Marcuse's theory of the total mobilization of advanced technology society along the lines of what he calls “the performance principle,” I attempt to describe the complex composition of class oppression in the classroom. Students conceive of themselves as economic units, customers pursuing neutral interests in a morally neutral, socio‐economic system of capitalist competition. The classic, unreflective conception of the classroom responds to this by implicitly endorsing individualism and ideals of humanist citizenship. While racism and cultural diversity have (...) come to count as elements of liberal intelligence in most college curricula, attempts to theorize these aspects of social and individual identity and place them in a broader content of class appear radical and inconsistent with the humanistic notion that we all have control over who we are and what we achieve. But tags such as “radical” and “unrealistic” mark a society based on the performance principle. Marcuse allows us to recognize a single author behind elements of psychology, metaphysics, and capitalism. The fact that bell hooks hits upon a similar notion suggests that we might use Marcuse's theory of the truly liberatory potential of imagination to transform and reconceive our classrooms so that the insidious effects of class, racism, and individualistic apathy might be subverted. Specifically, I outline and place into this theoretical context three concrete pedagogical practices: (a) the use of the physical space of the classroom; (b) the performance of community through group readings and short full‐class ceremonies, and (c) the symbolic modeling represented by interdisciplinary approaches to teaching. All three of these practices engage students in ways that co‐curricularly subvert class (and, incidentally, race divisions) and allow students to imagine, and so engage in, political action for justice as they see it. (shrink)

Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-conditional independence of features. This feature independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model that incorporates varying degrees of prior belief in class-conditional independence, learns whether or not (...) independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments—designed using optimal experimental design principles—were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-conditional independence, before adapting to the true environmental structure. Class-conditional independence may be a strong and useful default assumption in category learning tasks. (shrink)

This article analyses the role of ideas about class in the conceptualization of citizenship in twentieth-century Britain. It argues that the way in which citizenship was conceptualized involved a process of ideological engagement, by which a specific interpretation of the concept of class was asserted, and other possible interpretations closed off, as a result of particular preferences and priorities. The analysis is pursued through a comparative case study of the way in which two particular thinkers -- Henry Jones (...) and T.H. Marshall -- developed their ideas about citizenship within two different historical contexts in Britain: the late nineteenth century through to the 1910s, and the 1940s through to the 1970s. Jones and Marshall defined their conceptions of citizenship in opposition to notions of class as a basis for social organization, and both saw citizenship as a means by which individuals could trans- cend the boundaries of class. The specific way in which each interpreted the concept of class, however, led to different conclusions as to the process by which this would be achieved, which, in turn, determined the principles upon which they based their conceptions of citizenship. (shrink)

What are moral principles? The assumption underlying much of the generalism–particularism debate in ethics is that they are (or would be) moral laws: generalizations or some special class thereof, such as explanatory or counterfactual-supporting generalizations. I argue that this law conception of moral principles is mistaken. For moral principles do at least three things that moral laws cannot do, at least not in their own right: explain certain phenomena, provide particular kinds of support for counterfactuals, and ground moral necessities, (...) “necessary connections” between obligating reasons and obligations. Moreover, neither a best-systems theory of moral principles nor any of the competing theories of moral principles proposed by Sean McKeever and Michael Ridge, Pekka Väyrynen, and Mark Lance and Margaret Little could vindicate the law conception of moral principles. I conclude with some brief remarks about what moral principles might be if they are not moral laws. (shrink)

A dispute in epistemology has arisen over whether some class of things epistemic (things known or justified, for example) is closed under some operation involving the notion of what follows deductively from members of this class. Very few philosophers these days believe that if you know that p, and p entails q, then you know that q. But many philosophers think that something weaker holds, for instance that if you know that p, and p entails q, then you (...) are in a position to know that p, or if you know that p and you competently deduce p from q, then you know that q. However there are some considerations tracing back to Wittgenstein’s On Certainty and some early work by Fred Dretske that suggests even these weaker principles are false. (shrink)

The obligation to inform and obtain the consent of human subjects is axiomatic in social and medical research. Yet educational researchers are often reluctant to inform their subjects: class teachers and headteachers, for example, are often used as gatekeepers, and investigators sometimes do not so much seek consent as assume it. This chapter discusses the principle of informed consent, in particular that of children. It proposes guidelines for gatekeepers who may be called upon to authorise research and to (...) grant to investigators access to children in their care. (shrink)

According to the class of de minimis decision principles, risks can be ignored (or at least treated very differently from other risks) if the risk is sufficiently small. In this article, we argue that a de minimis threshold has no place in a normative theory of decision making, because the application of the principle will either recommend ignoring risks that should not be ignored (e.g., the sure death of a person) or it cannot be used by ordinary bounded (...) and information-constrained agents. (shrink)

Assume. Let κ be a cardinal. A ‐ground is a transitive proper class W modelling such that V is a generic extension of W via a forcing of cardinality. The κ‐mantle is the intersection of all ‐grounds. We prove that certain partial choice principles in are the consequence of κ being inaccessible/weakly compact, and some other related facts.

In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information for (...) more specific reference classes yields personal probabilities whose accuracy is optimal, according to all proper scoring rules, in situations where all of the relevant frequency information is point-valued. Assuming that frequency information for narrower reference classes is preferred, when the relevant frequency statements are point-valued, a dilemma arises when choosing whether to make a direct inference based upon relatively precise-valued frequency information for a broad reference class, R, or upon relatively imprecise-valued frequency information for a more specific reference class, R*. I address such cases, by showing that it is often possible to make a precise-valued frequency judgment regarding R* based on precise-valued frequency information for R, using standard principles of direct inference. Having made such a frequency judgment, the dilemma of choosing between and is removed, and one may proceed by using the precise-valued frequency estimate for the more specific reference class as a premise for direct inference. (shrink)

RésuméLa théorie des expressions incomplétes dans Principia Mathematica, se fonde sur le principe déja appliqué par Russell dans “On Denoting”, selon lequel il est souhaitable dans certains cas, ?on;établir le statut syntaxique des expressions catégorématiques. Grâce à la théorie intensionnelle ramifyée des types, les expressions incomplétes réféientiellement pourront être logiquement caractérisées par un mode de dérivation principalement basé sur la quantification non‐objectuelle. Ľintroduction des classes cependant, n'est en aucune façon reliée à ce mode intensionnel de dérivation; il en résulte qu'elles (...) fonctionnent en réalité dans ce contexte comme des expressions pourvues de dénotation et ce n'est que par une analogie grammaticale que Russell peut les comparer, du point de vue de leur élimination, aux expressions incomplétes de Principia Mathematica.SummaryThe theory of incomplete symbols in Principia Mathematica is founded on the principle already applied by Russell in “On Denoting“ that it is desirable in certain cases, to establish the syntactical status of “categorematic” expressions. Thanks to the intensional ramified theory of types, the referentially incomplete expressions could be logically caracterised by a mode of derivation primarily based on non‐objectual quantification. The introduction of classes, however, is by no way linked to that intensional mode of derivation; as a result, they function, in that context, like denotative expressions and it is only by a “grammatical” analogy that Russell can compare them, as regards their elimination, to the incomplete symbols in Principia Mathematica.ZusammenfassungDie Theorie der unvollstandigen Symbole in den Principia Mathematica gründet auf dem von Russell schon in “On Denoting” angewendeten Prinzip, wonach es in gewissen Fällen wün‐schenswert ist, den syntaktischen Status kategorematischer Ausdrücke festzulegen. Aufgrund der intensionalen verzweigten Typentheorie könnte man die referentiell unvollständigen Ausdrücke logisch durch eine im wesentlichen auf die nicht objektuelle Quantifi‐kation abstellende Ableitungsart charakterisieren. Die Einführung der Klassen dagegen hüngt keineswegs von dieser intensionalen Ableitungsart ab; daraus geht hervor, dass sie in diesem Kontext wie denotative Ausdrücke funktionieren, und es gelingt Russell nur vermittels einer grammatische Analogie, sie hinsichtlich ihrer Elimination mit den unvollständigen Symbolen der Principia Mathematica zu vergleichen. (shrink)

We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded subclasses $P, Q, {\langle L[P],\in,P \rangle }$ and ${\langle L[Q],\in,Q \rangle }$ possess the same reals, satisfy the Generalised Continuum Hypothesis, and moreover are elementarily equivalent. Examples of such P are Card, the class of uncountable cardinals, I the uniform indiscernibles, or for any n the class $C^{n}{=_{{\operatorname {df}}}}\{ \lambda (...) \, | \, V_{\lambda } \prec _{{\Sigma }_{n}}V\}$ ; moreover the theory of such models is invariant under ZFC-preserving extensions. They also all have a rich structure satisfying many of the usual combinatorial principles and a definable wellorder of the reals. The inner model constructed using definability in the language augmented by the Härtig quantifier is thus also characterized. (shrink)

This article argues that all-affected principle needs to be reconceptualized to account for the differences in the historical and current social position of those who are or who should be making legitimacy claims. Drawing on Butler’s theory of vulnerability, this article advances a new and more robust all-affected principle that affords a stronger claim to legitimacy to those most-deeply affected by both the current decision in question and the historical process and practices shaping the choices available. In particular, (...) this article identifies three sets of exclusions of groups and claims that drive this reformulation: first, cases of historical injustice such as indigenous peoples; second, cases of current processes of minoritization which silence or render some groups and opinions as marginal such as women, ethnic minorities or even people in lower economic classes; and third, cases of state establishment of boundaries and ‘worthy’ citizenship such as refugees making claims for relocation and asylum. (shrink)

A class of theories which satisfy the Relativity Principle has been overlooked. The kinematics for these theories is derived by relaxing the 'boost isotropy' symmetry normally invoked, and the role the dynamical fields play in determining the inertial coordinate systems is emphasised, leading to a criticism of Friedman's (1983) practice of identifying them via the absolute objects of a spacetime theory alone. Some theories complete with 'boost anisotropic' dynamics are given.

We examine a general class of variable-value population principles. Our particular focus is on the extent to which such principles can avoid the repugnant and sadistic conclusions. We show that if a mild limit property is imposed, avoidance of the repugnant conclusion implies the sadistic conclusion. This result generalizes earlier observations by showing that they apply to a substantially larger class of principles. Our second theorem states that, under the limit property, the axiom of mere addition also conflicts (...) with avoidance of the repugnant conclusion. This result is a consequence of a similar observation that appears in the earlier literature. (shrink)

A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated with arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the corresponding forcing axioms and the corresponding fragments of the strong reflection principle, are analyzed, and consequences are presented. Some of these consequences are “exact” versions of diagonal stationary reflection principles of sets of ordinals. We also separate some of these diagonal strong reflection principles from (...) related axioms. (shrink)

This paper argues that race and class inequalities cannot be fully understood in isolation: their intersectional quality is explored through an analysis of how the White working class were portrayed in popular and political discourse during late 2008 (the timing is highly significant). While global capitalism reeled on the edge of financial melt-down, the essential values of neo-liberalism were reasserted as natural, moral and efficient through two apparently contrasting discourses. First, a victim discourse presented White working people, and (...) their children in particular, as suffering educationally because of minoritised racial groups and their advocates. Second a discourse of degeneracy presented an immoral and barbaric underclass as a threat to social and economic order. Applying the 'interest-convergence principle', from Critical Race Theory, the discourses amount to a strategic mobilisation of White interests where the 'White, but not quite' status of the working class (Allen, 2009) provides a buffer zone at a time of economic and cultural crisis which secures societal White supremacy and provides a further setback to progressive reforms that focus on race, gender and disability equality. The existence of poor Whites, therefore, is not only consistent with a regime of White supremacy — they are actually an essential part of the processes that sustain it. (shrink)

Recent findings suggest that medical students’ moral competence decreases throughout medical school. This pilot study gives preliminary insights into the effects of two educational interventions in ethics classes on moral competence among medical students in Munich, Germany. Between 2012 and 2013, medical students were tested using Lind’s Moral Competence Test prior to and after completing different ethics classes. The experimental group participated in principle-based structured case discussions and was compared with a control group with theory-based case discussions. The pre/post (...) C-scores were compared using a Wilcoxon Test, ANOVA and effect-size calculation. The C-score improved by around 3.2 C-points in the EG, and by 0.2 C-points in the CG. The mean C-score difference was not statistically significant for the EG or between the two groups. There was no statistical significance for the teachers’ influence on C-score. In both groups, students with below-average C-scores improved and students with above-average C-scores regressed. The increase of the C-Index was greater in the EG than in the CG. The absolute effect-size of the EG compared with the CG was 3.0 C-points, indicating a relevant effect. Teaching ethics with PBSCDs did not provide a statistically significant influence on students’ moral competence, compared with TBCDs. Yet, the effect size suggests that PBSCDs may improve moral competence among medical students more effectively. Further research with larger and completely randomized samples is needed to gain definite explanations for the results. (shrink)

The current paper studies the formal properties of the Global Reflection Principle, to wit the assertion “All theorems of$\mathrm {Th}$are true,” where$\mathrm {Th}$is a theory in the language of arithmetic and the truth predicate satisfies the usual Tarskian inductive conditions for formulae in the language of arithmetic. We fix the gap in Kotlarski’s proof from [15], showing that the Global Reflection Principle for Peano Arithmetic is provable in the theory of compositional truth with bounded induction only ($\mathrm {CT}_0$). (...) Furthermore, we extend the above result showing that$\Sigma _1$-uniform reflection over a theory of uniform Tarski biconditionals ($\mathrm {UTB}^-$) is provable in$\mathrm {CT}_0$, thus answering the question of Beklemishev and Pakhomov [2]. Finally, we introduce the notion of a prolongable satisfaction class and use it to study the structure of models of$\mathrm {CT}_0$. In particular, we provide a new model-theoretical characterization of theories of finite iterations of uniform reflection and present a new proof characterizing the arithmetical consequences of$\mathrm {CT}_0$. (shrink)

The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in mathematical formulation and in intended scope, into the principle of maximum relative entropy or of minimum information. It has been claimed that these principles are singled out as unique methods of statistical (...) inference that agree with certain compelling consistency requirements. This paper reviews these consistency arguments and the surrounding controversy. It is shown that the uniqueness proofs are flawed, or rest on unreasonably strong assumptions. A more general class of inference rules, maximizing the so-called Re[acute ]nyi entropies, is exhibited which also fulfill the reasonable part of the consistency assumptions. (shrink)