In The Empire of Chance, historians of science Gigerenzer et al. argue that statistical thinking has been “second to no other area of scientific endeavor” in its influence on “modern life and thought”. This article describes how quantitative descriptions of risk associated with industrialization and technological change became part of the mentality of ordinary Americans. It explains why Americans began counting accidents, tells what kinds of accidents they counted and how they counted them, and shows how statistical representations of risk (...) were used to justify prescriptions for public policy and individual behavior. On this frontier of the empire of chance, safety experts and self-styled “practical statisticians” were the principal colonizers. Distant from the centers of academic statistical science, they compromised rigorous scientific standards of methodology and accurate prediction in order to make convincing arguments outside their circles of expertise. To convey their point of view to audiences who were not literate in the field of statistics, they created a public language that conveyed statistical ideas through metaphors, graphic representations, and other rhetorical devices. They also engaged non-experts in collecting and analyzing data and, by the 1920s, even used quantitative self-measurement as a device to convince members of the public to alter their own risk-taking behaviors. (shrink)

There is a history of thinking that photographs provide a special kind of access to the objects depicted in them, beyond the access that would be provided by a painting or drawing. What is included in the photograph does not depend on the photographer’s beliefs about what is in front of the camera. This feature leads Kendall Walton to argue that photographs literally allow us to see the objects which appear in them. Current generative algorithms produce images in response to (...) users’ text prompts. Depending on the parameters, the output can resemble specific people or things which are named in the prompt. This resemblance does not depend on the user’s beliefs, so generated images are in this sense like photographs. Given this parallel, how should we think about AI-generated images? (shrink)

We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard natural numbers: -CA0 (...) (second-order number theory with a -comprehension axiom scheme) is insufficient. We briefly consider his claim to have produced a solution to the semantic paradoxes by introducing this conditional. We remark that the notion of a operator can be introduced in other settings. (shrink)

In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer's rule was applied to solve the system of symbolic 2-plithogenic linear equations. Also, provided enough examples for each case to enhance understanding.

A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic (...) 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR. (shrink)

We show how in the hierarchies${F_\alpha }$of Fieldian truth sets, and Herzberger’s${H_\alpha }$revision sequence starting from any hypothesis for${F_0}$ that essentially each${H_\alpha }$ carries within it a history of the whole prior revision process.As applications we provide a precise representation for, and a calculation of the length of, possiblepath independent determinateness hierarchiesof Field’s construction with a binary conditional operator. We demonstrate the existence of generalized liar sentences, that can be considered as diagonalizing past the determinateness hierarchies definable in Field’s recent (...) models. The ‘defectiveness’ of such diagonal sentences necessarily cannot be classified by any of the determinateness predicates of the model. They are ‘ineffable liars’. We may consider them a response to the claim of Field that ‘the conditional can be used to show that the theory is not subject to “revenge problems”.’. (shrink)

We formalize what it means to have permission to say something. We adapt the dynamic logic of permission by van der Meyden (J Log Comput 6(3):465–479, 1996 ) to the case where atomic actions are public truthful announcements. We also add a notion of obligation. Our logic is an extension of the logic of public announcements introduced by Plaza ( 1989 ) with dynamic modal operators for permission and for obligation. We axiomatize the logic and show that it is decidable.

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

We locate winning strategies for various ${\mathrm{\Sigma }}_{3}^{0}$ -games in the L-hierarchy in order to prove the following: Theorem 1. KP+Σ₂-Comprehension $\vdash \exists \alpha L_{\alpha}\ models"\Sigma _{2}-{\bf KP}+\Sigma _{3}^{0}-\text{Determinacy}."$ Alternatively: ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ "there is a β-model of ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17 em}}{\mathrm{\Sigma }}_{3}^{0}$ -Determinacy." The implication is not reversible. (The antecedent here may be replaced with ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left({\mathrm{\Pi }}_{3}^{1}\right)-{\mathrm{C}\mathrm{A}}_{0}:\text{\hspace{0.17em}}{\mathrm{\Pi }}_{3}^{1}$ instances of Comprehension with only ${\mathrm{\Pi }}_{3}^{1}$ -lightface definable parameters—or even weaker theories.) Theorem 2. KP +Δ₂-Comprehension +Σ₂-Replacement + ${\mathrm{\Sigma }}_{3}^{0}\phantom{\rule{0ex}{0ex}}$ -Determinacy. (Here AQI (...) is the assertion that every arithmetical quasi-inductive definition converges.) Alternatively: $\Delta _{3}^{1}{\rm CA}_{0}+{\rm AQI}\nvdash \Sigma _{3}^{0}$ -Determinacy. Hence the theories: ${\mathrm{\Pi }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0},\text{\hspace{0.17em}}{\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}+\text{\hspace{0.17em}}{\mathrm{\Sigma }}_{3}^{0}-\mathrm{D}\mathrm{e}\mathrm{t}\phantom{\rule{0ex}{0ex}}$ -Det, ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}+\mathrm{A}\mathrm{Q}\mathrm{I}$ , and ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ are in strictly descending order of strength. (shrink)

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using \emph{fully varied revision} sequences yields a complete \Pi13 set of integers; (iii) the set of \emph{stably categorical} sentences using their revision operator ψ is similarly \Pi13 and which (...) is complete in Gödel’s universe of constructible sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points. (shrink)

How should a liberal state treat its citizens who subscribe to religion and enjoy its component goods? This thesis explores the possibility of reconciling religion and justice. It argues for (1) a proper understanding of religion and the kind of good it constitutes; (2) the possibility of a liberal theory of justice which takes fully into account the claims of believers; and (3) an arrangement of social institutions which protects the engagement of citizens with faith with the goods of religion. (...) There have been several recent liberal approaches to the question which promise to accommodate the claims of believers in societies characterized by pluralism. They aim at the coexistence of citizens with faith with other citizens who are either non-adherents or even opposed to religion. However, so this thesis argues, these approaches are not successful. In particular, they fail to establish more than a mere doctrine of non-discrimination against believers. As a result, these liberal frameworks fail to address the central question of how liberal justice ought to treat religious goods. In reaction, some theorists of religion have claimed that there is a deep incompatibility between liberalism and a proper understanding of what a life devoted to religion is. In contrast, this thesis proposes a novel approach which starts from a unified view of religion, and proceeds to develop a liberal framework to accommodate the claims of believers. It argues that whilst non-discrimination is obviously necessary and fundamental, a more ambitious, proper understanding of religious goods and religious needs can contribute to a more coherent liberal strategy towards citizens with faith. It could also help motivate social policies and institutions to treat believers and non-believers in a just and fair manner. (shrink)

The author clarifies the existential philosophy that is implicit in Kurt Goldstein's philosophy of organism (Goldstein, 1963; 1995). Situated in response to the growing trend that psychological phenomena are reducible to the nervous system, the author argues for the reverse: that the significance of nervous system activity can only be understood by viewing it as background to foreground performances. Like the organization of perception into meaningful figure-- ground Gestalts, the existential modes of embodiment, sociality, temporality, spatiality, and attunement are organized (...) together to accomplish foreground performances. It is only within this context that the activity of the nervous system may be understood as significant or insignificant. Speech is given as an example. The article concludes with a commentary on how the trend of reducing psychological phenomena to neurological phenomena has impaired our understanding of brain disorders and psychological disorders. (shrink)

We consider notions of truth and logical validity defined in various recent constructions of Hartry Field. We try to explicate his notion of determinate truth by clarifying the path-dependent hierarchies of his determinateness operator.

In response to criticisms of the use of the Ideological Surround Model to analyze Tolerance of Ambiguity, emphasis is placed on how the methodologies of this model operate from Christian pacifist assumptions. This model seeks to promote social scientific methodologies that will allow competing perspectives to obtain increasing clarity on points of conflict.

The problem of resource allocation in health has stimulated much thought and research, in attempts to provide objective, rational methods by which necessary choices can be made. One such method was proposed in a paper in this journal. The authors argued for a utilitarian approach, which they claimed to demonstrate was acceptable to society at large. This paper argues that the evidence supporting such a claim was flawed; such a utilitarian approach is not socially acceptable, and is therefore not relevant. (...) Rather more relevant directions for research are discussed, based on the assertion that a degree of realism is essential when considering the problems of resource allocation. (shrink)

Lenin's work "On the Significance of Militant Materialism," written in the spring of 1922, is justly regarded as the philosophical testament of our leader. In it, the tasks of the day were merged with the tasks of the entire epoch on the basis of a profound analysis of reality.

The Secret Doctrine comprises a virtual encyclopaedia of the "anciently universal wisdom-tradition" -- scarcely an issue of consequence in the broad range of human experience is left untouched. As part of the Secret Doctrine Centenary project, this 441-page Index provides ready access to the vast quantity of material from many cultures set forth in the SD's original two volumes published in 1888. Due to the topics covered, it is as much an index of ideas as it is of subjects, works, (...) persons, and proper names. To aid the reader, major subject entries are cross-referenced; foreign terms are identified by language and, where possible, given in both their 1888 spelling(s) and as modernly transliterated, often with one or two word definitions. Subentries are arranged alphabetically. Cited works and authors, whose titles or names are not given in the SD are placed in brackets for convenient identification. Also included is an Appendix of foreign phrases with translation and source reference -- all helping to make this Index an invaluable reference tool for students of The Secret Doctrine. (shrink)

IN C.Q. N.S. xiii , 1578ff., M. L. West discusses various non-Greek traditions which throw light on the interpretation of Pherecydes. Of course problems remain, but one of these the comparative material may yet solve. Is West correct in suggesting that we emend the Suda entry on Pherecydesand so reduce the seven recesses to five ? A convincing analogy can help us here. G. S. Kirk has already compared the seven gates which Ishtar has to penetrate when she descends into (...) the underworld. Despite all his reluctance to admit oriental influence on Pherecydes, he sees this as a possible source. (shrink)

One of the gains to be reckoned from the study of nomenclature in the sepulchral inscriptions of the early empire is the gradual abandonment of attempts to distinguish between slave and freeborn on the basis of personal name or cognomen alone, especially when this is of Latin derivation. Nevertheless, one still finds personal cognomina in undated inscriptions adduced as sole evidence for the origin or status of individuals below senatorial rank. Thus in a standard work on freedmen in the early (...) empire, recently reprinted, names such as Agilis, Amandus, Auctus, Communis, Donatus, Faustus, Felix, etc., are said to be commonly servile, but others such as Aquila, Bassus, Capito, Cams, Celer, Crescens, etc., are taken as ingenuous. The criteria used in making such a distinction are subjective and arbitrary and the statistics based on them are largely valueless. It is the purpose of this note to consider briefly on this question the evidence of the personal nomenclature of the Imperial slaves and freedmen. In this group, the Familia Caesaris, no problem of status arises, and the fact that the majority of their inscriptions can be dated, at least approximately, makes it possible to trace the chronological development of the use of cognomina ingenua by one important group of servile origin from the first to the early third century A.D. Moreover, such a development is useful evidence for change in the social structure of the early empire. (shrink)

This paper tries to clarify the logical structure of the relationship between labor values and prices from an axiomatic perspective. The famous “transformation problem” is interpreted as an impossibility result for a specific interpretation of value theory based on specific assumptions and definitions. A comprehensive review of recent literature is provided, which shows that there are various theoretically relevant and logically consistent alternative interpretations based on different assumptions and definitions.

Suppose a computer prints out the following little "poem": The shooting of the hunters she heardBut to pity it moved her not. What can we say about the meaning of this "poem"? We can say that it is ambiguous. It could mean: She heard the hunters shooting at animals, people, etc., but she had no pity for the victims. . . . She heard the hunters being shot but did not pity them. . . . She heard the hunters shooting (...) at someone or something and she heard the hunters being shot but did not pity either. An author could use the above word sequence to convey either , , or . But since we cannot treat the text produced by the computer as anyone's use of the words in question, it would not make sense to decide among its linguistically possible readings, just as it would not make sense to choose among the linguistically possible readings of an ambiguous sentence if it is considered in abstraction from its use by a speaker on a particular occasion. For example, it would not make sense to say of the sentence "He saw the man carrying the suitcase" that it just means "He saw the man who is carrying the suitcase" if we know that and in which what ways the sentence is ambiguous. If someone did say this, we would be inclined to think either that he does not know that the sentence is ambiguous or that he is talking not about the sentence but about an utterance of that sentence by a speaker on some occasion. Hence all we can do in interpreting the computer "poem" is to specify the set of its linguistically possible readings, namely, {, , }. But it would not make sense to select , for example, and say, "That is what the computer poem means, not , nor ." P. D. Juhl is an assistant professor of German at Princeton University. The present essay, in a different form, will appear in his forthcoming book, The Nature of Literary Interpretation. See also: "Against Theory" by Steven Knapp and Walter Benn Michaels in Vol. 8, No. 4. (shrink)

As humans we are constantly engaging not only with other humans but with plants, animals, and matter. This article examines the way we view our engagement with the materiality of the world around us, by looking at the work of philosopher Jane Bennet on vibrant materiality and author Tove Jansson. Bennet presents an argument that matter can be analysed as active and vibrant. While Western philosophers are used to viewing matter as passive and dead, seeing it as active makes space (...) for different engagement with matter. One of the ways we can start engaging with matter, once we stop thinking of it as passive and dead, is through the lens of ethics. Jansson in her children’s book Moominpappa at Sea shows a possibility for looking at the material world through this ethical lens. This article will put these works in conversation by reading both as philosophical works that have nuanced engagement with the topic of how we can be in community with the things that surround us. Jansson’s work provides a helpful addition to Vibrant Matter by showing how we are inextricably entangled in harm, and providing a possible way to live with this reality. (shrink)