On the paradox of grounded classes

1955 ◽  
Vol 20 (2) ◽  
pp. 140-140 ◽  
Author(s):  
Richard Montague
Keyword(s):  
Natural Number ◽  
Set Theory ◽  
Infinite Sequence ◽  
Axiom Of Choice ◽  
The Other ◽  
Other Hand ◽  
The Family ◽  
The One ◽  
The Axiom Of Choice ◽  
Regular Classes

Mr. Shen Yuting, in this Journal, vol. 18, no. 2 (June, 1953), stated a new paradox of intuitive set-theory. This paradox involves what Mr. Yuting calls the class of all grounded classes, that is, the family of all classes a for which there is no infinite sequence b such that … ϵ bn ϵ … ϵ b2ϵb1 ϵ a.Now it is possible to state this paradox without employing any complex set-theoretical notions (like those of a natural number or an infinite sequence). For let a class x be called regular if and only if (k)(x ϵ k ⊃ (∃y)(y ϵ k · ~(∃z)(z ϵ k · z ϵ y))). Let Reg be the class of all regular classes. I shall show that Reg is neither regular nor non-regular.Suppose, on the one hand, that Reg is regular. Then Reg ϵ Reg. Now Reg ϵ ẑ(z = Reg). Therefore, since Reg is regular, there is a y such that y ϵ ẑ(z = Reg) · ~(∃z)(z ϵ z(z = Reg) · z ϵ y). Hence ~(∃z)(z ϵ ẑ(z = Reg) · z ϵ Reg). But there is a z (namely Reg) such that z ϵ ẑ(z = Reg) · z ϵ Reg.On the other hand, suppose that Reg is not regular. Then, for some k, Reg ϵ k · [1] (y)(y ϵ k ⊃ (∃z)(z ϵ k · z ϵ y)). It follows that, for some z, z ϵ k · z ϵ Reg. But this implies that (ϵy)(y ϵ k · ~(ϵw)(w ϵ k · w ϵ y)), which contradicts [1].It can easily be shown, with the aid of the axiom of choice, that the regular classes are just Mr. Yuting's grounded classes.

scholarly journals A system of axiomatic set theory. Part IV. General set theory

1942 ◽  
Vol 7 (4) ◽  
pp. 133-145 ◽  
Author(s):  
Paul Bernays
Keyword(s):  
Set Theory ◽  
Axiom Of Choice ◽  
Point Of View ◽  
The Other ◽  
Von Neumann ◽  
Neumann System ◽  
Other Hand ◽  
The Axiom Of Choice ◽  
Axiomatic Set Theory

Our task in the treatment of general set theory will be to give a survey for the purpose of characterizing the different stages and the principal theorems with respect to their axiomatic requirements from the point of view of our system of axioms. The delimitation of “general set theory” which we have in view differs from that of Fraenkel's general set theory, and also from that of “standard logic” as understood by most logicians. It is adapted rather to the tendency of von Neumann's system of set theory—the von Neumann system having been the first in which the possibility appeared of separating the assumptions which are required for the conceptual formations from those which lead to the Cantor hierarchy of powers. Thus our intention is to obtain general set theory without use of the axioms V d, V c, VI.It will also be desirable to separate those proofs which can be made without the axiom of choice, and in doing this we shall have to use the axiom V*—i.e., the theorem of replacement taken as an axiom. From V*, as we saw in §4, we can immediately derive V a and V b as theorems, and also the theorem that a function whose domain is represented by a set is itself represented by a functional set; and on the other hand V* was found to be derivable from V a and V b in combination with the axiom of choice. (These statements on deducibility are of course all on the basis of the axioms I–III.)

scholarly journals High-order metaphysics as high-order abstractions and choice in set theory

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Set Theory ◽  
Axiom Of Choice ◽  
High Order ◽  
Precise Definition ◽  
The Other ◽  
Axiom Scheme ◽  
The One ◽  
Definition Of ◽  
The Axiom Of Choice ◽  
Comprehension Axiom

The link between the high-order metaphysics and abstractions, on the one hand, and choice in the foundation of set theory, on the other hand, can distinguish unambiguously the “good” principles of abstraction from the “bad” ones and thus resolve the “bad company problem” as to set theory. Thus it implies correspondingly a more precise definition of the relation between the axiom of choice and “all company” of axioms in set theory concerning directly or indirectly abstraction: the principle of abstraction, axiom of comprehension, axiom scheme of specification, axiom scheme of separation, subset axiom scheme, axiom scheme of replacement, axiom of unrestricted comprehension, axiom of extensionality, etc.

Liberalism and the Family

Family Values ◽  
2014 ◽  
Author(s):  
Harry Brighouse ◽  
Adam Swift
Keyword(s):  
The Other ◽  
Parental Rights ◽  
Moral Concern ◽  
The Core ◽  
Other Hand ◽  
The Family ◽  
Exit Option ◽  
The One ◽  
Parent Child Relationships ◽  
Parent Child

This chapter sets out the ways in which the family might be thought to pose problems for the liberal framework, and defends the adoption of that framework from the objection that it simply cannot do justice to—or, perhaps, fails adequately to care about—the ethically significant phenomena attending parent–child relationships. On the one hand, liberalism takes individuals to be the fundamental objects of moral concern, and the rights it claims people have are primarily rights of individuals over their own lives: the core liberal idea is that it is important for individuals to exercise their own judgment about how they are to live. On the other hand, parental rights are rights over others, they are rights over others who have no realistic exit option, and they are rights over others whose capacity to make their own judgments about how they are to live their lives is no less important than that of the adults raising them.

scholarly journals Contesting “Conversion” and “Reversion” among Young Adult Asian American Buddhists

Religions ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 261
Author(s):  
Chenxing Han
Keyword(s):  
Young Adults ◽  
Young Adult ◽  
Predominantly White ◽  
Asian American ◽  
Lived Experiences ◽  
The Other ◽  
The West ◽  
Other Hand ◽  
The Family ◽  
The One

This paper engages the perspectives of thirty young adult Asian American Buddhists (YAAABs) raised in non-Buddhist households. Grounded in semi-structured, one-on-one in-person and email interviews, my research reveals the family tensions and challenges of belonging faced by a group straddling multiple religious and cultural worlds. These young adults articulate their alienation from both predominantly white and predominantly Asian Buddhist communities in America. On the one hand, they express ambivalence over adopting the label of “convert” because of its Christian connotations as well as its associations with whiteness in the American Buddhist context. On the other hand, they lack the familiarity with Asian Buddhist cultures experienced by second- or multi-generation YAAABs who grew up in Buddhist families. In their nuanced responses to arguments that (1) American convert Buddhism is a non-Asian phenomenon, and (2) Asians in the West can only “revert” to Buddhism, these young adults assert the plurality and hybridity of their lived experiences as representative of all American Buddhists, rather than incidental characteristics of a fringe group within a white-dominated category.

Aspects of Marriage in Three South-western Villages

1992 ◽  
Vol 130 ◽  
pp. 323-337 ◽  
Author(s):  
Stevan Harrell
Keyword(s):  
Rural China ◽  
The Other ◽  
Other Hand ◽  
The Family ◽  
The One

In their effect on marriage and the family, as in so many other domains, the reforms can be seen as having a dual thrust. On the one hand, by giving the land in long-term leases back to the family, and allowing it to invest in a variety of small and medium-sized ventures, they have restored something like the situation in rural China before the collectivization of 1956, when the family estate was the source of income and investment in opportunity for most rural Chinese. On the other hand, the reforms have been undertaken explicitly in the name of modernization, and the increases in both agricultural and rural industrial yields, along with the rise in household entrepreneurship, have taken China in some ways even further from the feudalism of pre-revolutionary days than it was during the collective era.

An Interview with Judy G. Barber: Prenuptial Agreements, Intimacy, Trust and Control

1997 ◽  
Vol 10 (2) ◽  
pp. 173-178 ◽  
Author(s):  
Drew S. Mendoza ◽  
Sharon P. Krone
Keyword(s):  
The Other ◽  
Good Chance ◽  
Marriage And Family ◽  
Other Hand ◽  
The Family ◽  
Emotional Commitment ◽  
The One ◽  
And Control ◽  
Relationship Of ◽  
The Relationship

A business-owning family and a soon-to-be-wed couple often face two mutually exclusive goals that seem impossible to reconcile. On the one hand, a couple considering marriage wants to believe that love alone will keep them together. On the other hand, statistics today say there is a good chance the relationship will not last. A prenuptial agreement provides the protection an individual or the family may want against a possible divorce, but the process by which the document is introduced and negotiated can deplete the relationship of intimacy. How can a woman from a wealthy business-owning family express and reinforce the emotional commitment and trust she has for her partner while presenting a prenuptial agreement] How can a son administer a prenuptial agreement to his fiancee without controlling the process or outcome of his spouse's financial welfare] How can a family require a prenuptial agreement without jeopardizing their future relationship with the newlyweds] In the following interview, Judy Barber, a consultant and licensed marriage and family counselor specializing in the psychology of money, outlines several recommendations for families and couples who are considering a prenuptial agreement.

scholarly journals On Some Sources of the Life of Alexander Oshevensky (The Theme of the Family in the Hagiography)

Scrinium ◽  
2015 ◽  
Vol 11 (1) ◽  
pp. 281-294
Author(s):  
Alexander V. Pigin
Keyword(s):  
The Other ◽  
Other Hand ◽  
Christian Morality ◽  
Literary Sources ◽  
The Family ◽  
The One ◽  
The Relationship ◽  
The Town

(1567) is a Northern Russian hagiographical work devoted to the founder of the St. Niсholas Alexander-Oshevensky Monastery, which was located nearby the town of Kargopol. The article analyses hagiographer Theodosius’ techniques for dealing with literary sources, especially with two Byzantine texts, The Ladder by John Climacus and The Life of Alexis the Man of God. Theodosius uses these sources to develop one of the major themes of his own work, that is, the relationship between St. Alexander and his family. The family theme bears ambiguous meaning. On the one hand, the family is rejected from the standpoint of monastic asceticism, but on the other hand, it is rendered as the ultimate value and stronghold of Christian morality.


scholarly journals Guidance Behind Criticisms: The Good Parenting as Portrayed in the First Malay Autobiography

2019 ◽  
Vol 15 (2) ◽  
pp. 116
Author(s):  
Rahimah Hamdan ◽  
Arba’ie Sujud
Keyword(s):  
19Th Century ◽  
The Other ◽  
Single Study ◽  
Other Hand ◽  
The Family ◽  
New Form ◽  
The One ◽  
Harsh Criticism ◽  
The 19Th Century

This paper was aimed at identifying the guidance to parenting that emerged in the first Malay autobiography, the Hikayat Abdullah, and subsequently, to analyse those instructions on parenting in the context of the traditional Malay society of the 19th century. The recognition accorded to Abdullah Munshi as the Father of Modern Malay Literature has attracted various reactions from scholars. Some scholars regard Abdullah Munshi as the one who brought renewal to Malay literature through his courageous criticism of the customs and culture that had been in practice for generations. On the other hand, there are scholars who disapprove of that recognition being given to him and who consider Abdullah Munshi’s criticisms in his works as a deviation from the reality expressed in previous works. Nevertheless, not a single study has suggested that perhaps Abdullah Munshi firmly emphasized those criticisms with the intention of providing some sort of guidance. Hence, by analysing certain texts in the Hikayat Abdullah and by reviewing the evidence from the perspective of Swettenham (1895), who objectively evaluated the thinking and culture of the Malay community, this study was able to rectify the image of Abdullah Munshi, who, all this while, was considered to be pro-British because of his harsh criticism of the Malay community. Moreover, those criticisms were meant to provide guidance for the family institution, especially for parents. This indirectly proves that Abdullah Munshi took a serious view of parenting and believed that improvements were necessary to produce a dignified and civilized generation. In conclusion, the autobiography, the Hikayat Abdullah, was not just a new form of writing that deviated from the conventions of traditional Malay literature, but was the fruit of the wisdom of the author that was meant to benefit his readers.

scholarly journals Salva Phaenomenis. Phenomenological Dimension of Subjectivity in the Frame of the Reductionist Paradigm of the Cognitive Sciences

Studia Humana ◽  
2015 ◽  
Vol 4 (2) ◽  
pp. 3-12
Author(s):  
Filip Kobiela
Keyword(s):  
Future Development ◽  
The Other ◽  
Cognitive Sciences ◽  
Adequate Model ◽  
Other Hand ◽  
The Family ◽  
Methodological Approaches ◽  
Phenomenological Dimension ◽  
The One ◽  
Research Domain

Abstract The paper addresses the family of questions that arose from the field of interactions between phenomenology and the cognitive sciences. On the one hand, apparently partial coextensivity of research domain of phenomenology and the cognitive sciences sets the goal of their cooperation and mutual inspiration. On the other hand, there are some obstacles on the path to achieve this goal: phenomenology and the cognitive sciences have different traditions, they speak different languages, they have adopted different methodological approaches, and last but not least, their prominent exponents exhibits different styles of thinking. In order to clarify this complicated area of tensions, the paper presents the results of philosophical reflections of such topics as: 1) philosophical presuppositions and postulates of the cognitive sciences 2) abstraction of some phenomena during idealisation and the dialectical model of science's development 3) argumentation based on prediction of future development of the cognitive sciences. This finally leads to the formulation of a phenomenology-based postulate for adequate model of mind and the discussion of humanistic dimension of cognitive sciences.

scholarly journals PERAN KELUARGA DALAM PEMBENTURAN MORAL BANGSA DITINIAU DART SUDUT PANDANG AGAMA ISLAM

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
M. Atho Mudzhar
Keyword(s):  
Social Life ◽  
National Character ◽  
The Other ◽  
Other Hand ◽  
The Family ◽  
The One ◽  
Modern Era

The interest in the role of family in social life in this modern era is growing stronger. On the one hand, this is the result of the declining degree of cohesiveness and disorientation of the family due to industrialization and individualization. On the other hand, it is the effect of the increasing expectation of society toward family institution as the result of the failure of the institutions outside family circles to implant and defend some values in life. This article is trying to see how a family can play a role in building national character, viewed especially from Islamicperspectives. In a specific way, this article shows how Islamic teachings give guidance concerning matters relating to the functions of the family.

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