We say that $\mathcal {I}$ is an ideal independent family if no element of ${\mathcal {I}}$ is a subset mod finite of a union of finitely many other elements of ${\mathcal {I}}.$ We will show that the minimum size of a maximal ideal independent family is consistently bigger than both $\mathfrak {d}$ and $\mathfrak {u},$ this answers a question of Donald Monk.

We show that after forcing with a countable support iteration or a finite product of Sacks or splitting forcing over L, every analytic hypergraph on a Polish space admits a $\mathbf {\Delta }^1_2$ maximal independent set. This extends an earlier result by Schrittesser (see [25]). As a main application we get the consistency of $\mathfrak {r} = \mathfrak {u} = \mathfrak {i} = \omega _2$ together with the existence of a $\Delta ^1_2$ ultrafilter, a $\Pi ^1_1$ maximal (...) independent family, and a $\Delta ^1_2$ Hamel basis. This solves open problems of Brendle, Fischer, and Khomskii [5] and the author [23]. We also show in ZFC that $\mathfrak {d} \leq \mathfrak {i}_{cl}$, addressing another question from [5]. (shrink)

We show that Miller partition forcing preserves selective independent families and P-points, which implies the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$. In addition, we show that Shelah’s poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$.

Shelah has shown that the number d, the smallest cardinality of a dominating family, is less than or equal to the number i, the smallest cardinality of a maximal independent family on ω. This was done using a downward Löwenheim-Skolem argument. Thus it is interesting to find a direct “elementary” proof. Here we show that this can be done.

We study higher analogues of the classical independence number on $\omega $. For $\kappa $ regular uncountable, we denote by $i(\kappa )$ the minimal size of a maximal $\kappa $ -independent family. We establish ZFC relations between $i(\kappa )$ and the standard higher analogues of some of the classical cardinal characteristics, e.g., $\mathfrak {r}(\kappa )\leq \mathfrak {i}(\kappa )$ and $\mathfrak {d}(\kappa )\leq \mathfrak {i}(\kappa )$. For $\kappa $ measurable, assuming that $2^{\kappa }=\kappa ^{+}$ we construct a (...) class='Hi'>maximal $\kappa $ -independent family which remains maximal after the $\kappa $ -support product of $\lambda $ many copies of $\kappa $ -Sacks forcing. Thus, we show the consistency of $\kappa ^{+}=\mathfrak {d}(\kappa )=\mathfrak {i}(\kappa )<2^{\kappa }$. We conclude the paper with interesting open questions and discuss difficulties regarding other natural approaches to higher independence. (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 (...) class='Hi'>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)

We study the set of possible sizes of maximal independent families to which we refer as spectrum of independence and denote \\). Here mif abbreviates maximal independent family. We show that:1.whenever \ are finitely many regular uncountable cardinals, it is consistent that \\); 2.whenever \ has uncountable cofinality, it is consistent that \=\{\aleph _1,\kappa =\mathfrak {c}\}\). Assuming large cardinals, in addition to above, we can provide that $$\begin{aligned} \cap \hbox {Spec}=\emptyset \end{aligned}$$for each i, \.

The tower number ${\mathfrak t}$ and the ultrafilter number $\mathfrak {u}$ are cardinal characteristics from set theory. They are based on combinatorial properties of classes of subsets of $\omega $ and the almost inclusion relation $\subseteq ^*$ between such subsets. We consider analogs of these cardinal characteristics in computability theory.We say that a sequence $(G_n)_{n \in {\mathbb N}}$ of computable sets is a tower if $G_0 = {\mathbb N}$, $G_{n+1} \subseteq ^* G_n$, and $G_n\smallsetminus G_{n+1}$ is infinite for each n. (...) A tower is maximal if there is no infinite computable set contained in all $G_n$. A tower ${\left \langle {G_n}\right \rangle }_{n\in \omega }$ is an ultrafilter base if for each computable R, there is n such that $G_n \subseteq ^* R$ or $G_n \subseteq ^* \overline R$ ; this property implies maximality of the tower. A sequence $(G_n)_{n \in {\mathbb N}}$ of sets can be encoded as the “columns” of a set $G\subseteq \mathbb N$. Our analogs of ${\mathfrak t}$ and ${\mathfrak u}$ are the mass problems of sets encoding maximal towers, and of sets encoding towers that are ultrafilter bases, respectively. The relative position of a cardinal characteristic broadly corresponds to the relative computational complexity of the mass problem. We use Medvedev reducibility to formalize relative computational complexity, and thus to compare such mass problems to known ones.We show that the mass problem of ultrafilter bases is equivalent to the mass problem of computing a function that dominates all computable functions, and hence, by Martin’s characterization, it captures highness. On the other hand, the mass problem for maximal towers is below the mass problem of computing a non-low set. We also show that some, but not all, noncomputable low sets compute maximal towers: Every noncomputable (low) c.e. set computes a maximal tower but no 1-generic $\Delta ^0_2$ -set does so.We finally consider the mass problems of maximal almost disjoint, and of maximal independent families. We show that they are Medvedev equivalent to maximal towers, and to ultrafilter bases, respectively. (shrink)

We show that the non-existence of mad families is equiconsistent with \, answering an old question of Mathias. We also consider the above result in the general context of maximal independent sets in Borel graphs, and we construct a Borel graph G such that \ “there is no maximal independent set in G” is equiconsistent with \ “there exists an inaccessible cardinal”.

In lieu of an abstract, here is a brief excerpt of the content: Unmasking the Maxim: An Ancient Genre And Why It Matters Now W. ROBERT CONNOR We live surrounded by maxims, often without even noticing them. They are easily dismissed as platitudes, banalities or harmless clichés, but even in an age of big data and number crunching we put them to work almost every day. A Silicon Valley whiz kid says, Move Fast and Break Things. Investors try to Buy (...) Low and Sell High. Investigative reporters Follow the Money. Others Follow their Bliss. The lavish host thinks, The More the Merrier, while the Modernist architect is sure that Less is More. Captains of Industry whisper to themselves, Me First; captains of sinking ships shout, Women and Children First. Be Prepared was the Boy Scouts’ marching song, while the Proud Boys Stand Down and Stand By, awaiting their marching orders. Maxims are perhaps the smallest members in a large family of speech acts, which among the Greeks included proverbs, oracles, riddles, blessings, curses and lamentations. Not all of these continue in use, but maxims have found companions—mottos, mantras, advertising tag lines and jingles, slogans, political rallying cries, hashtags, three- or four-letter acronyms and 280 character tweets from the goddess Twitter. Familiarity, however, can breed contempt, or at least inattentiveness to the full range of their influence. Sometimes what sounds at first like empty verbiage turns into action. Bruce Lee adapted an old Taoist saying when he said, Be Water, and thereby provided what was for a while a surprisingly effective strategy for protesters in Hong Kong. arion 28.3 winter 2021 6 unmasking the maxim Maxims empower, for good or ill. In the hands of bigots or ideologues, they can turn deadly. Sic Semper Tyrannis shouted John Wilkes Booth after shooting Abraham Lincoln. A manufacturer of assault rifles urged potential customers to Earn Your Man Card. How better to earn it than to obey 8chan, a web site favored by white nationalists, with its own maxim, Embrace Infamy. A devotee of the site did just that, perpetrating a mass shooting in El Paso, Texas. Maxims, then, should not be lightly dismissed. Since the ancient Greeks so relished maxims, they should surely be interrogated to help us better understand the power of these often underestimated speech acts. Before turning to the Greeks, however, the English word maxim needs a closer look. english “maxim” english borrowed maxim from a Latin phrase and boiled it down for everyday use. In Latin writings about logic, the expression maxima propositio, biggest proposition, denoted a statement that did not need to be proved, but could provide the basis for proof of other, lesser propositions. This phraseology goes back at least to Boethius in the sixth century of our era. It’s the equivalent of the generalizations that serve as the major premises in syllogistic logic. If this makes maxims sound like the axioms of geometry, that is historically right. The starting points of plane geometry are propositions that deserve to be accepted; even without proof that they are worthy of belief. That’s the meaning of the term axiōma. No one needs to prove that things equal to the same thing are equal to each other. Think about it; after a while it seems self-evident. It is worthy of assent. We might equally well call such an axiom a maxim; indeed, the earliest (1426) attested use of maxim in English is described in the Oxford English Dictionary as “an axiom; a self-evident proposition assumed as a premise in mathematical, or dialectical reasoning.” W. Robert Connor 7 This usage is now obsolete, but Thomas Jefferson understood the idea behind it, since he believed that there were such truths, waiting to be put to work in building a society where all people were equal and possess certain inalienable rights. He did not feel he had to prove these propositions; they were in his view self-evident. In using these ideas in his draft of the Declaration of Independence, he was, in effect, transferring to politics what Euclid had done in geometry. It was a swift, strategic stroke on his part, for, since self-evident truths require no argument or explanation, they focus discussion not on... (shrink)

We prove here the consistency of u>i where: u=Min{|X|:X⫅P(ω) generates a non-principle ultrafilter}, i=Min{|A|:A is a maximal independent family of subsets of ω}In this we continue Goldstern and Shelah [G1Sh388] where Con(r>u) was proved using a similar but different forcing. We were motivated by Vaughan [V] (which consists of a survey and a list of open problems). For more information on the subject see [V] and [G1Sh388].

Forster and Sober introduced the “sub-family problem” for model selection criteria that recommend balancing goodness-of-fit against simplicity. This problem arises when a maximally simple model is artificially constructed to have excellent fit with the data. We argue that the problem arises because of a violation of the general maxim that balancing goodness-of-fit against simplicity leads to desirable inferences only if one is comparing models for the consideration of which one has a positive reason independently of the current data.

An important objection to signaling approaches to representation is that, if signaling behavior is driven by the maximization of usefulness, then signals will typically carry much more information about agent-dependent usefulness than about objective features of the world. This sort of considerations are sometimes taken to provide support for an anti-realist stance on representation itself. The author examines the game-theoretic version of this skeptical line of argument developed by Donald Hoffman and his colleagues. It is shown that their argument only (...) works under an extremely impoverished picture of the informational connections that hold between agent and world. In particular, it only works for cue-driven agents, in Kim Sterelny’s sense. In cases in which the agents’ understanding of what is useful results from combining pieces of information that reach them in different ways, and that complement one another, maximizing usefulness involves construing first a picture of agent-independent, objective matters of fact. (shrink)

In \(\textbf{ZF}\), the well-known Fichtenholz–Kantorovich–Hausdorff theorem concerning the existence of independent families of _X_ of size \(|{\mathcal {P}} (X)|\) is equivalent to the following portion of the equally well-known Hewitt–Marczewski–Pondiczery theorem concerning the density of product spaces: “The product \({\textbf{2}}^{{\mathcal {P}}(X)}\) has a dense subset of size |_X_|”. However, the latter statement turns out to be strictly weaker than \(\textbf{AC}\) while the full Hewitt–Marczewski–Pondiczery theorem is equivalent to \(\textbf{AC}\). We study the relative strengths in \(\textbf{ZF}\) between the statement “_X_ (...) has no independent family of size \(|{\mathcal {P}}(X)|\) ” and some of the definitions of “_X_ is finite” studied in Levy’s classic paper, observing that the former statement implies one such definition, is implied by another, and incomparable with some others. (shrink)

We study independent families of functions and permutations and associated cardinal characteristics and. In this paper, we show that these cardinals lie between the cardinals and and give some related consistency results.

Recall that a subset X of a Boolean algebra A is independent if for any two finite disjoint subsets F , G of X we have ∏ x∈F x ∏ y∈G −y≠0. The independence of a BA A , denoted by Ind, is the supremum of cardinalities of its independent subsets. We can also consider the maximal independent subsets. The smallest size of an infinite maximal independent subset is the cardinal invariant i , well (...) known in the case A= P / fin . In this article we consider the collection of all cardinalities of infinite maximal independent subsets of a BA A ; we call this set the spectrum of infinite maximal independent subsets , denoted by Spind. Note that infinite maximal independent subsets exist in any BA which is not superatomic. The main result is that any set of infinite cardinals can occur as Spind for some infinite BA A . Beyond this we give results concerning the way that Spind changes under various algebraic operations. However, the basic components of most algebras that we deal with are free algebras. (shrink)

The purpose of the study is to test the pedagogical potential of design and research activities in the context of the formation of research independence of cadets of a military higher educational institution through experimental work. The article reveals the technological aspect of the implementation of design and research activities by cadets of a military university. Scientific novelty lies in the identification and verification of the effectiveness of the pedagogical conditions that contribute to the formation of research independence of cadets (...) of a military higher educational institution. The article presents the author's edition of the thematic focus and content of the design and research assignments. As a result of the study, the empirical method proved the effectiveness of the revealed pedagogical conditions on the process of forming the research independence of cadets of a military higher educational institution. (shrink)

The use of artificial intelligence (AI) to aid legal decision making has become prominent. This paper investigates the use of AI in a critical issue in employment law, the determination of a worker’s status—employee vs. independent contractor—in two common law countries (the U.S. and Canada). This legal question has been a contentious labor issue insofar as independent contractors are not eligible for the same benefits as employees. It has become an important societal issue due to the ubiquity of (...) the gig economy and the recent disruptions in employment arrangements. To address this problem, we collected, annotated, and structured the data for all Canadian and Californian court cases related to this legal question between 2002 and 2021, resulting in 538 Canadian cases and 217 U.S. cases. In contrast to legal literature focusing on complex and correlated characteristics of the employment relationship, our statistical analyses of the data show very strong correlations between the worker’s status and a small subset of quantifiable characteristics of the employment relationship. In fact, despite the variety of situations in the case law, we show that simple, off-the-shelf AI models classify the cases with an out-of-sample accuracy of more than 90%. Interestingly, the analysis of misclassified cases reveals consistent misclassification patterns by most algorithms. Legal analyses of these cases led us to identify how equity is ensured by judges in ambiguous situations. Finally, our findings have practical implications for access to legal advice and justice. We deployed our AI model via the open-access platform, https://MyOpenCourt.org/, to help users answer employment legal questions. This platform has already assisted many Canadian users, and we hope it will help democratize access to legal advice to large crowds. (shrink)

Le présent article s’appuie sur une pratique psychologique dans le cadre de visites médiatisées. Il cible notamment les entretiens cliniques réalisés par le psychologue avec les parents dans l’après-coup des visites médiatisées et a pour objectif de saisir l’enjeu clinique de ces temps d’entretiens. Deux vignettes cliniques permettent d’esquisser les potentialités des rencontres en l’absence des enfants. Il apparaît que ces entretiens favorisent le rétablissement d’une activité de mentalisation et de symbolisation. Enfin, une discussion métapsychologique éclaire les études de cas.

The exponential Papapetrou metric induced by scalar field conforms to observational data not worse than the vacuum Schwarzschild solution. Here, we analyze the origin of this metric as a peculiar space-time within a wide class of scalar and antiscalar solutions of the Einstein equations parameterized by scalar charge. Generalizing the three families of static solutions obtained by Fisher, Janis et al. :878. https://doi.org/10.1103/PhysRevLett.20.878, 1968), and Xanthopoulos and Zannias :2564, 1989), we prove that all three reduce to the same exponential metric (...) provided that scalar charge is equal to central mass, thereby suggesting the universal character of such background scalar field. (shrink)

A few years ago, an illusionist theory of consciousness appeared in the philosophy of consciousness. It makes an unexpected statement – there is actually no phenomenal consciousness, it is illusory. This illusion is created introspective distortion of physical processes in the brain, which seem to us to have special phenomenal properties. However, an equally strong form of physicalism in the philosophy of consciousness has already appeared more than fifty years ago – identity theory of the mental and physical. Moreover, the (...) proponents of illusionism themselves admit their connection with the identity theorists. As a result, it is reasonable to ask whether illusionism is simply a modern adaptation of the identity theory, and not a new independent theory. This article is devoted to this issue. First, the author presents both theories, focusing on their key statements, arguments and advantages described by the followers of the respective approaches. Then the author makes a comparison, highlighting common places and differences for the approaches. Among the former, the following are noted: the physicalist spirit of both theories; their denial of the existence of a special mental properties metaphysically different from physical ones; argumentation in favor of the pragmatic attractiveness of a theory; defending their key theses as primarily hypotheses that may turn out to be true; a similar strategy for explaining the error, as a result of which we come to the conclusion about the existence of the mental. However, the author also points out a number of serious differences: different attitudes to the possibility of neutral notion for properties of experience; differences in the vision of the content of the mind-body problem; illusionist denial of the real referent of the language of phenomenality; the development of the concept of illusion, which entails a number of new solutions and problems; the epistemological significance of the main arguments of illusionism is more influential in comparison with identity theory. As a result, the author comes to the conclusion that, despite the fact that a significant part of the content of the theories coincides, illusionism has a number of key differences. This testifies, on the one hand, to the skillful use of past achievements of the physicalist-oriented philosophy of consciousness, and, on the other, to the fundamental novelty and independence of illusionism. (shrink)

Summary The author is of the opinion that as a result of Alexander the Great’s conquest of Syria, which had been a single administrative entity under the Achaemenids, it was divided into two satrapies – the northern and the southern one. He believes that Menon, son of Cerdimmas, was appointed as the first head of the northern satrapy, to be replaced by Arimmas, who, in his turn, was succeeded by Asclepiodorus, son of Eunicus. Besides, it seems that Andromachus became the (...) first head of the southern satrapy, and after he was killed, Menon, transferred from the north to the south, took his place. Already in Alexander’s lifetime, probably in 329/328, Syria was once again merged into one satrapy. It is unclear who was installed as satrap of the unified region. At any rate, it could not have been Menes, son of Dionysius: the hypothesis that in winter 331/330 he was made satrap of the new province including Syria and Cilicia does not stand scrutiny. In the author’s view, the main task Alexander assigned to Menes was to take control and then to keep open and organized the sea communications with the coast of Syria, Phoenicia and Cilicia, and in the matters concerning these activities Menes was fully independent of the local satraps. (shrink)

We construct a consistent theory of a quantum massive Weyl field. We start with the formulation of the classical field theory approach for the description of massive Weyl fields. It is demonstrated that the standard Lagrange formalism cannot be applied for the studies of massive first-quantized Weyl spinors. Nevertheless we show that the classical field theory description of massive Weyl fields can be implemented in frames of the Hamilton formalism or using the extended Lagrange formalism. Then we carry out a (...) canonical quantization of the system. The independent ways for the quantization of a massive Weyl field are discussed. We also compare our results with the previous approaches for the treatment of massive Weyl spinors. Finally the new interpretation of the Majorana condition is proposed. (shrink)

In his collection of essays Having the World in View (2009), John McDowell draws a distinction between empirical experience (conceived as the conceptual activity relevant to judgment) and empirical judgment (i.e., the full-fledged assertoric content itself ). McDowell’s latest proposal is that the form of empirical experience is transferable into judgment, but it is not itself a judgment. Taking back the view he advanced in Mind and World, McDowell now believes that perception does not have propositional content as such, but (...) the content of perception can, however, always be actualized in a judgment. There is, in other words, a strict parallelism between the deliverances of sensibility and potential future judgments of experience. The early Husserl disagrees with this and recognizesexplicitly the existence of coherent forms of perceptual engagement with the world that is independent of the mastery of language and the use of concepts.Perception constitutes—together with certain other embodied practices—our primary mode of access to the world, and this occurs before and independently ofour thinking activity. However, the realization of the centrality of time for intentionality will lead Husserl after 1905 to recognize a kind of lawfulness internal tothe sensuous materials themselves, prior to any egoical achievement. The most immediate consequence of this paradigm change is that the very idea of non-conceptual content now seems unwarranted. Indeed, if time is that which keeps the process of sense formation unified even at the lowest levels of constitution, then the world-disclosing activity of the ego cannot be discontinuous with the conceptual realm. Against this background, it will be argued that the dialectic between the conceptual and non-conceptual ultimately makes no sense on a phenomenological basis. Once temporality has entered the scene, the only meaningful opposition that stands is that between the conceptual and pre-conceptual spheres. (shrink)

Bhagavadacharya was the central figure in the Renaissance of Ramanandi tradition in the 20th century. He dedicated his life to gaining independence for his school from Ramanuja Sampradaya, whose leaders regarded Ramanandis as “third-class” members of the movement mostly because of the lack of shastric scholarship and inter-caste commensalities among the latter. To achieve this goal, Bhagavadacharya wrote commentaries on most of the Prasthāna-traya as well as many other works popularizing the Ramanandi version of Vishishtadvaita. He widely used his knowledge (...) of philosophy in shastric debates with his opponents among whom were not only followers of Ramanuja but also a famous Advaitin guru and political activist Swami Karpatri whom he allegedly defeated in a dispute which concerned the rights of Harijans initiated into Vaishnava tradition to enter temples and share communalities with the so-called “pure Hindus”. In my paper, I will present key philosophical and practical ideas of Bhagavadacharya based on my research conducted in the library of Bhagavadacharya Smarak Bhavan in August 2021. It will include basic details related to the acharya’s background and activities as well as analysis of his teachings within the frames of his main scope of Vishishtadvaita’s propagation among Hindus in general and Ramanandis in particular. (shrink)

The black hole information loss paradox is a catch-all term for a family of puzzles related to black hole evaporation. For almost 50 years, the quest to elucidate the implications of black hole evaporation has not only sustained momentum, but has also become increasingly populated with proposals that seem to generate more questions than they purport to answer. Scholars often neglect to acknowledge ongoing discussions within black hole thermodynamics and statistical mechanics when analyzing the paradox, including the interpretation of (...) Bekenstein-Hawking entropy, which is far from settled. To remedy the dialectical gridlock, I have formulated an overarching, unified framework, which I call ``Black Hole Paradoxes'', that integrates the debates and taxonomizes the relevant `camps' or philosophical positions. -/- I demonstrate that black hole evaporation within Hawking's semi-classical framework insinuates how late-time Hawking radiation is an entangled global system, a contradiction in terms. The relevant forms of information loss are associated with a decrease in maximal Boltzmann entropy and an increase in global von Neumann entropy respectively, which engender what I've branded the ``paradox of phantom entanglement''. Prospective solutions are then tasked with demonstrating how late-time Hawking radiation is either exclusively an entangled subsystem, in which a black hole remnant lingers as an information safehouse, or exclusively an unentangled global system, in which information is evacuated to the exterior. -/- The disagreement between safehouse and evacuation solutions boils down to the statistical interpretation of thermodynamic black hole entropy, i.e., Bekenstein-Hawking entropy. Safehouse solutions attribute Bekenstein-Hawking entropy to a minority of black hole degrees of freedom, those that are associated with the horizon. Evacuation solutions, in contrast, attribute Bekenstein-Hawking entropy to all black hole degrees of freedom. I argue that the interpretation of Bekenstein-Hawking entropy is the litmus test to vet the overpopulated proposal space. So long as any proposal rejecting Hawking's original calculation independently derives black hole evaporation, globally conserves degrees of freedom and entanglement, preserves a version of semi-classical gravity at sub-Planckian scales, and describes black hole thermodynamics in statistical terms, then it counts as a genuine solution to the paradox. (shrink)

We consider human performance on an optimal stopping problem where people are presented with a list of numbers independently chosen from a uniform distribution. People are told how many numbers are in the list, and how they were chosen. People are then shown the numbers one at a time, and are instructed to choose the maximum, subject to the constraint that they must choose a number at the time it is presented, and any choice below the maximum is incorrect. We (...) present empirical evidence that suggests people use threshold-based models to make decisions, choosing the first currently maximal number that exceeds a fixed threshold for that position in the list. We then develop a hierarchical generative account of this model family, and use Bayesian methods to learn about the parameters of the generative process, making inferences about the threshold decision models people use. We discuss the interesting aspects of human performance on the task, including the lack of learning, and the presence of large individual differences, and consider the possibility of extending the modeling framework to account for individual differences. We also use the modeling results to discuss the merits of hierarchical, generative and Bayesian models of cognitive processes more generally. (shrink)

Natural selection is often envisaged as the ultimate cause of the apparent rationality exhibited by organisms in their specific habitat. Given the equivalence between selection and rationality as maximizing processes, one would indeed expect organisms to implement rational decision-makers. Yet, many violations of the clauses of rationality have been witnessed in various species such as starlings, hummingbirds, amoebas and honeybees. This paper attempts to interpret such discrepancies between economic rationality and biological rationality. After having distinguished two kinds of rationality we (...) introduce irrationality as a negation of economic rationality by biologically rational decision-makers. Focusing mainly on those instances of irrationalities that can be understood as exhibiting inconsistency in making choices, i.e. as non-conformity of a given behaviour to axioms such as transitivity or independence of irrelevant alternatives, we propose two possible families of Darwinian explanations that may account for these apparent irrationalities. First, we consider cases where natural selection may have been an indirect cause of irrationality. Second, we consider putative cases where violations of rationality axioms may have been directly favored by natural selection. Though the latter cases seem to clearly contradict our intuitive representation of natural selection as a process that maximizes fitness, we argue that they are actually unproblematic; for often, they can be redescribed as cases where no rationality axiom is violated, or as situations where no adaptive solution exists in the first place. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume XXI, Number 2, November 1995, pp. 315-332 Robertson, Hume, and the Balance of Power FREDERICK G. WHELAN William Robertson, like his Scottish Enlightenment colleague David Hume, practiced a kind of philosophic history which, although it appears to consist mainly of narratives of political and military events, is also designed to teach moral and political lessons of general significance and utility. The principal theme of Hume's History (...) of England, for example, is the growth of legal and constitutional government in connection with the emergence of modern society; Hume's narrative implicitly justifies both such a government and the moderate politics on which it depends. A theme of comparable importance in Robertson's History of Charles V (1769) is the emergence of a balance of power and thence a relatively stable international system among European states in the early sixteenth century, when the policy of balance first clearly appeared. As he declares in his Preface: The political principles and maxims then established still continue to operate. The ideas concerning the balance of power, then introduced or rendered general, still influence the councils of nations. (R 307)1 Robertson both describes the relevant policy decisions (especially the alliance between the traditional enemies, England and France, to counter the threat posed by Charles Vs unprecedentedly large empire) and justifies such policies as reasonable and beneficial.2 Frederick G. Whelan is at the Political Science Department, University of Pittsburgh, Pittsburgh PA 15260 USA. 316 Frederick G. Whelan In treating this theme, Robertson was taking up a topic that was of interest to Hume as well. Hume refers on a number of occasions to the sixteenth century balance of power in his History chapters on the reign of Henry VIII (1759),3 especially in the portion extending through the 1520s, and he treats the topic more systematically in his earlier essay "Of the Balance of Power" (1752).4 Hume like Robertson defends balance of power policies in general, and Hume certainly (Robertson probably) had a more particular reason for doing so: to justify contemporary British (Whig) foreign policy (and several wars), which since the reign of Louis XIV had aimed at maintaining a European counterbalance to France.5 Hume's and Robertson's favorable descriptions of the sixteenth century anti-Habsburg policy provide a useful background for defending the eighteenth century anti-Bourbon policy.6 Indeed, both Hume and Robertson probably exaggerated the prevalence of the balance of power, at least as a conscious policy, in the early sixteenth century; although they were no doubt correct in noting that something like the modern state system first began to take shape at that time, they seem to have projected the eighteenth century emphasis on balance backwards in time as a way of legitimizing it.7 Robertson sums up the fifty year period he covers by observing that the similar stage of development of the states of Europe at that time, together with the policy of balance, permitted the preservation of a fairly stable system of independent states that has lasted until the present: But the advantages possessed by one state were counterbalanced by circumstances favourable to others; and thus prevented any from attaining such superiority as might have been fatal to all. The nations of Europe in that age, as in the present, were like one great family.... There was not among them that wide diversity of character and of genius which, in almost every period of history, hath exalted the Europeans above the inhabitants of the other quarters of the globe, and seems to have destined the one to rule and the others to obey. (R 704) Hume's concern with contemporary policy, and with France, is more conspicuous: Europe has now, for above a century, remained on the defensive against the greatest force that ever, perhaps, was formed by the civil or political combination of mankind. And such is the influence of the maxim here treated of, that tho' that ambitious nation, in the five last general wars, have been victorious in four, and unsuccessful only in one, they have not much enlarged their dominions, nor acquired a total ascendant over EUROPE.... In the last three of these general Hume... (shrink)

Extending the language of the intuitionistic propositional logic Int with additional logical constants, we construct a wide family of extensions of Int with the following properties: (a) every member of this family is a maximal conservative extension of Int; (b) additional constants are independent in each of them.

We study the notion of [Formula: see text]-MAD families where [Formula: see text] is a Borel ideal on [Formula: see text]. We show that if [Formula: see text] is any finite or countably iterated Fubini product of the ideal of finite sets [Formula: see text], then there are no analytic infinite [Formula: see text]-MAD families, and assuming Projective Determinacy and Dependent Choice there are no infinite projective [Formula: see text]-MAD families; and under the full Axiom of Determinacy [Formula: see text][Formula: (...) see text] or under [Formula: see text] there are no infinite [Formula: see text]-mad families. Similar results are obtained in Solovay’s model. These results apply in particular to the ideal [Formula: see text], which corresponds to the classical notion of MAD families, as well as to the ideal [Formula: see text]. The proofs combine ideas from invariant descriptive set theory and forcing. (shrink)

The presence of stigmatizing language in the electronic health record (EHR) has been used to measure implicit biases that underlie health inequities. The purpose of this study was to identify the presence of stigmatizing language in the clinical notes of pregnant people during the birth admission. We conducted a qualitative analysis on N = 1117 birth admission EHR notes from two urban hospitals in 2017. We identified stigmatizing language categories, such as Disapproval (39.3%), Questioning patient credibility (37.7%), Difficult patient (21.3%), (...) Stereotyping (1.6%), and Unilateral decisions (1.6%) in 61 notes (5.4%). We also defined a new stigmatizing language category indicating Power/privilege. This was present in 37 notes (3.3%) and signaled approval of social status, upholding a hierarchy of bias. The stigmatizing language was most frequently identified in birth admission triage notes (16%) and least frequently in social work initial assessments (13.7%). We found that clinicians from various disciplines recorded stigmatizing language in the medical records of birthing people. This language was used to question birthing people's credibility and convey disapproval of decision‐making abilities for themselves or their newborns. We reported a Power/privilege language bias in the inconsistent documentation of traits considered favorable for patient outcomes (e.g., employment status). Future work on stigmatizing language may inform tailored interventions to improve perinatal outcomes for all birthing people and their families. (shrink)

© The Author 2018. Published by Oxford University Press. All rights reserved. Logical geometry provides a broad framework for systematically studying the logical properties of Aristotelian diagrams. The main aim of this paper is to present and illustrate the foundations of a computational approach to logical geometry. In particular, after briefly discussing some key notions from logical geometry, I describe a logical problem concerning Aristotelian diagrams that is of considerable theoretical importance, viz. the task of finding the maximal Boolean (...) complexity of a given family of Aristotelian diagrams, and I then present and discuss a simple algorithm for automatically solving this task. This algorithm is naturally implemented within the paradigm of logic programming. In order to illustrate the theoretical fruitfulness of this algorithm, I also show how it sheds new light on several well-known families of Aristotelian diagrams. (shrink)

This article aims at giving insight into Norwegian mental health service by exploring the ideologies of two diametrical philosophers, the American Robert Nozick (1938–2002) and the German Axel Honneth (1949‐). Nozick proposes as an ideal a minimal state in which citizens have a “negative right” to the absence of interference and to follow their own interests without restriction from the state. On the other side, Axel Honneth claims that there is no freedom without state interference. In his view, governmental involvement (...) is understood as a prerequisite for personal freedom. We may call this state an opposite of the minimal state; a maximal state. To get a better understanding of these opposite philosophies, we use texts written from conversations with people suffering from mental health problems, nurses and other caregivers in four Norwegian municipalities. Nozick's notion of the minimal state and Honneth's political philosophy of freedom and recognition were used as analytical tools. Among patients and helpers, there were different opinions about good care and how much caregivers should intervene. Some emphasized autonomy, independency, minimal involvement in human contact by nurses and other caregivers, similar a minimal state. Others perceived good care as bonding between helpers and service‐users. They underlined equal and personal relationships, as well as helping with practicalities, similar a maximal state. In the discussion, we focus on how people with chronic illnesses are supposed to transform themselves into self‐cared individuals, able to manage their own condition successfully with minimal help from public welfare and at a lower cost. Finally, we express concerns about who will care for disempowered patients without family and other resources in a minimal state. (shrink)

We provide results allowing to state, by the simple inspection of suitable classes of posets , that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of (...) choice, of the cardinality of the set of the maximal intermediate propositional logics with the disjunction property. (shrink)

Partitioner algebras are defined by Baumgartner and Weese 619) as a natural tool for studying the properties of maximal almost disjoint families of subsets of ω. We prove from PFA+ and that there exists a partitioner algebra which contains a subalgebra which is not representable as a partitioner algebra.

An ordering (≤K) on maximal almost disjoint (MAD) families closely related to destructibility of MAD families by forcing is introduced and studied. It is shown that the order has antichains of size.

The article is a reappraisal of the requirement of maximal specificity (RMS) proposed by the author as a means of avoiding "ambiguity" in probabilistic explanation. The author argues that RMS is not, as he had held in one earlier publication, a rough substitute for the requirement of total evidence, but is independent of it and has quite a different rationale. A group of recent objections to RMS is answered by stressing that the statistical generalizations invoked in probabilistic explanations (...) must be lawlike, and by arguing that predicates fit for occurrence in lawlike statistical probability statements must meet two conditions, at least one of which is violated in each of the counterexamples adduced in the objections. These considerations suggest the conception that probabilistic-statistical laws concern the long-run frequency of some characteristic within a reference class as characterized by some particular "description" or predicate expression, and that replacement of such a description by a coextensive one may turn a statement that is lawlike into another that is not. Finally, to repair a defect noted by Grandy, the author's earlier formulation of RMS is replaced by a modified version. (shrink)

We continue with the study of the Katětov order on MAD families. We prove that Katětov maximal MAD families exist under $\mathfrak {b=c}$ and that there are no Katětov-top MAD families assuming $\mathfrak {s\leq b}.$ This improves previously known results from the literature. We also answer a problem form Arciga, Hrušák, and Martínez regarding Katětov maximal MAD families.

Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We show that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in our strong sense. This applies to practically (...) all three-valued paraconsistent logics that have been considered in the literature, including a large family of logics which were developed by da Costa's school. Then we show that in contrast, paraconsistent logics based on three-valued properly nondeterministic matrices are not maximal, except for a few special cases (which are fully characterized). However, these non-deterministic matrices are useful for representing in a clear and concise way the vast variety of the (deterministic) three-valued maximally paraconsistent matrices. The corresponding weaker notion of maximality, called premaximal paraconsistency, captures the "core" of maximal paraconsistency of all possible paraconsistent determinizations of a non-deterministic matrix, thus representing what is really essential for their maximal paraconsistency. (shrink)