scholarly journals Critical Plural Logic

2021 ◽  
pp. 267-296
Author(s):  
Salvatore Florio ◽  
Øystein Linnebo

This chapter develops and motivates an alternative, more critical plural logic, thus exploring the third horn of the trilemma from the previous chapter. First, a liberal view of mathematical definitions is defended, according to which any objects can be used to define a set. This entails that the traditional plural comprehension scheme needs to be restricted. Some successor principles are then formulated on the basis of the idea that any plurality needs to be circumscribed. Finally, the resulting critical plural logic is shown to give rise to a natural and elegant approach to set theory.

Author(s):  
C. Claire Thomson

Building on the picture of post-war Anglo-Danish documentary collaboration established in the previous chapter, this chapter examines three cases of international collaboration in which Dansk Kulturfilm and Ministeriernes Filmudvalg were involved in the late 1940s and 1950s. They Guide You Across (Ingolf Boisen, 1949) was commissioned to showcase Scandinavian cooperation in the realm of aviation (SAS) and was adopted by the newly-established United Nations Film Board. The complexities of this film’s production, funding and distribution are illustrative of the activities of the UN Film Board in its first years of operation. The second case study considers Alle mine Skibe (All My Ships, Theodor Christensen, 1951) as an example of a film commissioned and funded under the auspices of the Marshall Plan. This US initiative sponsored informational films across Europe, emphasising national solutions to post-war reconstruction. The third case study, Bent Barfod’s animated film Noget om Norden (Somethin’ about Scandinavia, 1956) explains Nordic cooperation for an international audience, but ironically exposed some gaps in inter-Nordic collaboration in the realm of film.


Author(s):  
Tim Button ◽  
Sean Walsh

In this chapter, the focus shifts from numbers to sets. Again, no first-order set theory can hope to get anywhere near categoricity, but Zermelo famously proved the quasi-categoricity of second-order set theory. As in the previous chapter, we must ask who is entitled to invoke full second-order logic. That question is as subtle as before, and raises the same problem for moderate modelists. However, the quasi-categorical nature of Zermelo's Theorem gives rise to some specific questions concerning the aims of axiomatic set theories. Given the status of Zermelo's Theorem in the philosophy of set theory, we include a stand-alone proof of this theorem. We also prove a similar quasi-categoricity for Scott-Potter set theory, a theory which axiomatises the idea of an arbitrary stage of the iterative hierarchy.


2006 ◽  
Vol 15 (1) ◽  
pp. 79-93 ◽  
Author(s):  
O. Linnebo
Keyword(s):  

2020 ◽  
Vol 16 (2) ◽  
pp. 379-414
Author(s):  
Siswoyo Aris Munandar ◽  
Elia Malikhaturrahmah

The fact is that many young Javanese today do not know wayang characters, wayang stories, folk songs, and children's games. This proves the lack of appreciation of the younger generation for studying literature and culture in their region. They consider that regional literature is ancient and out of date. This causes regional literature and culture to gradually become extinct. Syi'ir Jawi Budi Utami is oral literature written by Kiai Djamal. This research was conducted as an effort to understand syi'ir Kiai Djamal by using the Levi-Strauss structuralism analysis which examines literary works not only from the literary field but also from the field of anthropology. The author focuses this research on two problem formulations, namely, why did Kiai Djamal write syi'ir Jawi Budi Utami and what is the structure of syir Jawi Budi Utami. The method used for data collection is documentation and is processed by descriptive-analytical methods. The purpose of this research is to enrich the discourse and insight into the study of the concept of Levi-Strauss structuralism as well as as a reference or preliminary review for the development of studies on the Sufistic syi'ir of Kiai Djamal in Levi-Strauss structuralism, on the one hand, the application of Levi-Strauss structuralism analysis to other objects. This research found that the principles of writing syi'ir Kiai Djamal consist of five episodes, namely: first Kiai Djamal introduces the phases of a Muslim, namely syari'ah, thoriqoh, and haqiqoh. The second episode of Kiai Djamal introduces one of the tarekat, namely the Syadziliyyah Tarekat, followed by the following chapters regarding the explanation of the Syadziliyyah Tarekat. The third episode is the Qodiriyah Order. The fourth episode is the Tarekat An-Naqsabandiyah in brief. The fifth episode is a continuous explanation of the previous chapter. This shows the structure of writing Syi'ir Kiai Djamal. Also, the researcher sees that the context in syi'ir Kiai Djamal is an unconscious reflection of Kiai Djamal with the discovery of signifier and signified, langue and parole, form and content and phonemes in syi'ir Kiai Sufistik Djamal. Faktanya anak-anak muda Jawa saat ini banyak yang tidak mengenal tokoh-tokoh wayang, cerita wayang, lagu daerah, dan dolanan anak. Hal ini membuktikan kurangnya apresiasi generasi muda untuk mempelajari sastra dan budaya daerahnya sendiri. Mereka menganggap bahwa sastra daerah bersifat kuno dan ketinggalan zaman.  Hal ini menyebabkan sastra dan budaya daerah lambat laun akan mengalami kepunahan. Syi’ir Jawi Budi Utami merupakan salah satu sastra lisan yang ditulis oleh Kiai Djamal. Penelitian ini dilakukan sebagai upaya untuk memahami syi’ir Kiai Djamal dengan menggunakan analisis strukturalisme Levi-Strauss yang mengkaji karya sastra tidak hanya dari bidang sastra saja tetapi juga dari bidang antropologi. Penulis memfokuskan penelitian ini pada dua rumusan masalah yaitu, mengapa Kiai Djamal menulis syi’ir Jawi Budi Utami dan bagaimana struktur dalam syir Jawi Budi Utami. Metode yang digunakan untuk pengumpulan data adalah dokumentasi, dan diolah dengan metode deskriptif analitis. Tujuan penelitian ini adalah memperkaya wacana dan wawasan tentang kajian konsep strukturalisme Levi-Strauss serta sebagai referensi atau tinjauan awal untuk pengembangan kajian atas syi’ir sufistik Kiai Djamal dalam strukturalisme Levi-Strauss di satu sisi, aplikasi analisis strukturalisme Levi-Strauss terhadap objek lain.  Penelitian ini menemukan bahwa prinsip penulisan syi’ir Kiai Djamal terdapat lima episode, yaitu: pertama Kiai Djamal memperkenalkan fase-fase seorang muslim yaitu syari’ah, thoriqoh dan haqiqoh. Episode kedua Kiai Djamal memperkenalkan salah satu tarekat yaitu Tarekat Syadziliyyah disusul bab-bab setelahnya mengenai penjelasan Tarekat Syadziliyyah. Episode ketiga adalah Tarekat Qodiriyah. Episode keempat adalah Tarekat An-Naqsabandiyah secara singkat. Episode kelima adalah penjelasan bab sebelumnya secara sambung  menyambung. Hal ini menunjukkan struktur dari penulisan Syi’ir Kiai Djamal. Selain itu peneliti melihat bahwa konteks yang ada dalam syi’ir Kiai Djamal merupakan cerminan nirsadar dari Kiai Djamal dengan ditemukannya signifier dan signified, langue dan parole, form dan content serta fonem dalam syi’ir Kiai Sufistik Djamal.  


2020 ◽  
pp. 43-56
Author(s):  
Zoe Adams

The chapter builds on the analysis in Chapter 1 with a view to exploring the nature of law and its relationship with capitalist society in more detail. The previous chapter used an analysis of capitalism’s deep structures to explore the nature of law’s role(s) in capitalism, engaging with the various legal ‘functions’ that capitalism presupposes. The purpose of this chapter is to explore the implications of this understanding of law’s role (or function) when it comes to understanding law’s form. The first section begins by developing a theory of the legal form by engaging with the work of Evgeny Pashukanis. The second section teases out the implications of this analysis for our understanding of the relationship between the legal form and capitalism’s contradictions. The third section draws on this analysis to shed light on the relationship between legal form and content. The fourth section makes some tentative conclusions about the implications of this analysis for our understanding of labour law.


Author(s):  
John Collins

This chapter has three major tasks. Firstly, I show how the conception of linguistic pragmatism on offer squares with certain features of standard truth-conditional approaches to meaning, especially as regards compositionality. Secondly, pace some recent semantic proposals, I argue that the properties of the Saxon genitive (e.g., Sally’s car) and adnominal adjectival attributions (e.g., red pen) are referentially open in the way I argued in the previous chapter. The third task involves sketching the kind of role I take syntax to play in fixing linguistic meaning and how the argument-adjunct distinction operates in regards to my core claims.


Author(s):  
Yang Zhu ◽  
Miroslav Krstic

This chapter investigates adaptive control for uncertain multi-input LTI systems with distinct discrete actuator delays. In parallel with the single-input case in the third chapter, four types of basic uncertainties come with multi-input LTI time-delay systems. Different combinations of the four uncertainties above result in different design difficulties. For example, when the full-state measurement of the transport PDE state is available, the global stabilization is acquired, whereas when the actuator state is not measurable and the delay value is unknown at the same time, the problem is not solvable globally, since the problem is not linearly parameterized. The chapter then summarizes the different collections of uncertainties for the multi-input case. When some of the four variables are unknown or unmeasured, the basic idea of certainty-equivalence-based adaptive control is to use an estimator (a parameter estimator or a state estimator) to replace the unknown variables in the PDE-based framework in the previous chapter, and carefully select their adaptive update laws based on Lyapunov-based analysis.


2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Zhaohao Wang ◽  
Lan Shu ◽  
Xiuyong Ding

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper discusses five types of existing neighborhood-based generalized rough sets. The concepts of minimal neighborhood description and maximal neighborhood description of an element are defined, and by means of the two concepts, the properties and structures of the third and the fourth types of neighborhood-based rough sets are deeply explored. Furthermore, we systematically study the covering reduction of the third and the fourth types of neighborhood-based rough sets in terms of the two concepts. Finally, two open problems proposed by Yun et al. (2011) are solved.


2016 ◽  
Vol 81 (3) ◽  
pp. 972-996 ◽  
Author(s):  
GUNTER FUCHS ◽  
RALF SCHINDLER

AbstractOne of the basic concepts of set theoretic geology is the mantle of a model of set theory V: it is the intersection of all grounds of V, that is, of all inner models M of V such that V is a set-forcing extension of M. The main theme of the present paper is to identify situations in which the mantle turns out to be a fine structural extender model. The first main result is that this is the case when the universe is constructible from a set and there is an inner model with a Woodin cardinal. The second situation like that arises if L[E] is an extender model that is iterable in V but not internally iterable, as guided by P-constructions, L[E] has no strong cardinal, and the extender sequence E is ordinal definable in L[E] and its forcing extensions by collapsing a cutpoint to ω (in an appropriate sense). The third main result concerns the Solid Core of a model of set theory. This is the union of all sets that are constructible from a set of ordinals that cannot be added by set-forcing to an inner model. The main result here is that if there is an inner model with a Woodin cardinal, then the solid core is a fine-structural extender model.


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