The Relation Between Logic, Set Theory and Topos Theory as it Is Used by Alain Badiou

2015 ◽  
pp. 181-200 ◽  
Author(s):  
Régis Angot-Pellissier
Keyword(s):  
Set Theory ◽  
Topos Theory ◽  
Alain Badiou

scholarly journals NOVEL “ORANG-ORANG PROYEK”: SEJARAH ORDE BARU

TELAGA BAHASA ◽  
2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ramis Rauf
Keyword(s):  
Set Theory ◽  
Positive Relationship ◽  
New Order ◽  
The Novel ◽  
Literary Works ◽  
Alain Badiou ◽  
History Of ◽  
The Subject

This study wants to reveal the truth procedures in Ahmad Tohari's novel Orang-Orang Proyek, as a part of an event and a factor in the presence of a new subject. This research would answer the problem: how was the subjectification of Ahmad Tohari in Orang-Orang Proyek novel as truth procedures? This study used the set theory by Alain Badiou. The set theory explained that within a set there were members of "Existing" or Being and events as "Plural" members.  The results proved that the subjectivity between Tohari and New Order events produced literary works: Orang-Orang Proyek. This happened because there was a positive relationship between the author and the event as well as on the naming of the event. Not only as of the subject but also do a fidelity to what he believed to be a truth. The truth procedures or the void—originating from the New Order event—was in the history of the making of a bridge in a village in Java island, Indonesia during the New Order period that filled with corruption, collusion, and nepotism. Tohari then embodied it in his novel. By the presences of the novel, we could know the category of Tohari's presentation as a new subject such as faithful, reactive, and obscure.

scholarly journals Fuzzy Set Theory and Topos Theory

1986 ◽  
Vol 29 (4) ◽  
pp. 501-508 ◽  
Author(s):  
Michael Barr
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Topos Theory

AbstractThe relation between the categories of Fuzzy Sets and that of Sheaves is explored and the precise connection between them is explicated. In particular, it is shown that if the notion of fuzzy sets is further fuzzified by making equality (as well as membership) fuzzy, the resultant categories are indeed toposes.

scholarly journals A Brief Introduction to Algebraic Set Theory

2008 ◽  
Vol 14 (3) ◽  
pp. 281-298 ◽  
Author(s):  
Steve Awodey
Keyword(s):  
Set Theory ◽  
Algebraic Models ◽  
Topos Theory ◽  
Algebraic Set ◽  
Logical Constraints ◽  
Models Of Set Theory

AbstractThis brief article is intended to introduce the reader to the field of algebraic set theory, in which models of set theory of a new and fascinating kind are determined algebraically. The method is quite robust, applying to various classical, intuitionistic, and constructive set theories. Under this scheme some familiar set theoretic properties are related to algebraic ones, while others result from logical constraints. Conventional elementary set theories are complete with respect to algebraic models, which arise in a variety of ways, such as topologically, type-theoretically, and through variation. Many previous results from topos theory involving realizability, permutation, and sheaf models of set theory are subsumed, and the prospects for further such unification seem bright.

Hegel’s Leaps and the Historicist Theory of Knowledge

2015 ◽  
Author(s):  
Nathan Coombs
Keyword(s):  
Set Theory ◽  
Marxist Theory ◽  
Theory Of Knowledge ◽  
Close Reading ◽  
Technological Determinism ◽  
Revolutionary Change ◽  
Science Of Logic ◽  
Irrational Numbers ◽  
Alain Badiou ◽  
Quantitative Properties

This chapter locates the roots of the Marxist theory of revolutionary change in G.W.F. Hegel’s philosophy. In the well-known formula, cumulative changes in quantitative properties give rise to a qualitative leap into the future. However, the chapter argues that the idea rests on shaky ontological foundations. Through a close reading of the Science of Logic, it is shown that Hegel’s idea of leaps relies on excising irrational numbers. To make his dialectical transitions work, Hegel has to dialecticise the mathematical infinite and ignore scientific epistemological breaks from the classical period onwards. This compares unfavourably to Alain Badiou, who makes Georg Cantor’s breakthrough with transfinite set theory the lynchpin for his discontinuous philosophy of events. The final section argues that Hegel’s notion of quantity to quality leaps is also complicit with the reformism and technological determinism promoted by key thinkers of Second International Marxism.

scholarly journals Lawvere–Tierney sheaves in Algebraic Set Theory

2009 ◽  
Vol 74 (3) ◽  
pp. 861-890 ◽  
Author(s):  
S. Awodey ◽  
N. Gambino ◽  
P. L. Lumsdaine ◽  
M. A. Warren
Keyword(s):  
Set Theory ◽  
Topos Theory ◽  
Algebraic Set

AbstractWe present a solution to the problem of denning a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

scholarly journals Beyond Recognition: Badiou’s Mathematics of Bodily Incorporation

2020 ◽  
Vol 41 (2) ◽  
Author(s):  
Norman Madarasz
Keyword(s):  
Set Theory ◽  
Category Theory ◽  
Alain Badiou ◽  
General Logic ◽  
Phenomenological Methodology ◽  
The Absolute ◽  
The One

In Being and Event, Alain Badiou disconnects the infinite from the One and the Absolute, thus recasting the basis from which to craft a new theory of generic subject, the existence of which is demonstrated through set theory. In Logics of Worlds, Badiou turns his attention to the modes by which this subject appears in a world. It does so by being incorporated as a subjectivizable body, a body of truth. As opposed to Being and Event, the demonstration of this argument takes shape according to two distinct levels, that of a “calculated phenomenology” and that of a formalism in which category theory provides a general logic, the combination of which delineates an “onto-logic”. In this essay, we trace Badiou’s derivation of the notion of body of truth and evaluate the innovative phenomenological methodology applied to explain its association with a world.

scholarly journals A New Hope for the Symbolic, for the Subject

2020 ◽  
Vol 41 (2) ◽  
Author(s):  
Norma M. Hussey
Keyword(s):  
Set Theory ◽  
Present Moment ◽  
Alain Badiou ◽  
Mathematical Ontology ◽  
The Subject

This paper is perhaps an impressionistic response to accounts of the extraordinary set-theoretical activity being undertaken by W. Hugh Woodin (mathematician) and colleagues in the present moment, in the context of the mathematical ontology proposed and elaborated by Alain Badiou (philosopher). The argument presented is that the prevailing and sustained incoherence of the mathematical ontology (i.e. set theory) underscores a contemporary deficit of humanity’s symbolic organization which, in turn, yields confusion and conflict in terms of subjective orientation. But a new axiom (conjectured as yet) promises to realize a coherent set theory, i.e. stable, consistent and complete. This remarkable (and completely unexpected) development offers hope for the pursuit of a modern (i.e. non-hierarchical) symbolic, and a consequent resolution of the general subjective disorientation.

Structuralism

2009 ◽  
Author(s):  
Geoffrey Hellman
Keyword(s):  
Modal Logic ◽  
Set Theory ◽  
Model Theory ◽  
Second Order ◽  
Mathematical Framework ◽  
Topos Theory ◽  
Mathematical Structuralism

The main types of mathematical structuralism that have been proposed and developed to the point of permitting systematic and instructive comparison are four: structuralism based on model theory, carried out formally in set theory (e.g., first- or second-order Zermelo–Fraenkel set theory), referred to as STS (for set-theoretic structuralism); the approach of philosophers such as Shapiro and Resnik of taking structures to be sui generis universals, patterns, or structures in an ante rem sense (explained in this article), referred to as SGS (for sui generis structuralism); an approach based on category and topos theory, proposed as an alternative to set theory as an overarching mathematical framework, referred to as CTS (for category-theoretic structuralism); and a kind of eliminative, quasi-nominalist structuralism employing modal logic, referred to as MS (for modal-structuralism). This article takes these up in turn, guided by few questions, with the aim of understanding their relative merits and the choices they present.

Alain Badiou’s New Constructivism and Universalism

2018 ◽  
Author(s):  
Antonio Calcagno
Keyword(s):  
World War Ii ◽  
Set Theory ◽  
Political Power ◽  
New Order ◽  
Human Beings ◽  
World War ◽  
Alain Badiou ◽  
Form Part ◽  
Human Reality ◽  
French Theory

French philosopher Alain Badiou (b. 1937) is one of the more important European thinkers to emerge after May 1968. His work may be read as a response to the structuralism, post-structuralism, existentialism, and postmodern thought characteristic of post-World War II French theory. Through the use of set theory, he argues that our understanding of reality is largely determined by major, world shifting events in politics, mathematics/science, aesthetics/poetry, and love. A Maoist, he maintains that true changes in human reality require decisive interventions that create a new sense of temporality, subjectivity, and order. Events radically change the order of an existing world and create new worlds. For example, the Russian or French revolutions brought an end to absolutist monarchies and the rule that were specific to them. A new order and form of political power were introduced by the ascendant regimes. The sense of who and what human beings living under such regimes were changed from that of subject to citizen. The idea of subjects being absolutely ruled and determined by divine monarchs only responsible to God and themselves would no longer be possible as a legitimate form of political rule. The contents and relations constitutive of a world come to be structured by the event, though the worlds regimented by an event are never identical to the event itself. The event always lies outside, though it conditions, the sets of relations and contents that express it. His work is often read in conjunction with and in opposition to the philosopher Jacques Rancière. Both thinkers form part of what is seen as the new constructivism and universalism.

Alain Badiou and Education

2020 ◽  
Author(s):  
Torill Strand
Keyword(s):  
Set Theory ◽  
Academic Discipline ◽  
German Idealism ◽  
The State ◽  
History Of Philosophy ◽  
Alain Badiou ◽  
French Philosophy ◽  
Radical Innovations ◽  
Philosophical System ◽  
History Of

The French philosopher Alain Badiou (1937–) is one of the most significant philosophers of our time, well known for his meticulous work on rethinking, renewing, and thereby strengthening philosophy as an academic discipline. In short, his philosophy seeks to reveal and make sense of the potential of radical innovations in, or transformations of, any given situation. Although he has not written extensively on education, the pedagogical theme is vital, constitutive, and ongoing throughout his work. Badiou is an outspoken critic of the analytic and postmodern schools of thought, as he strongly promotes the virtue of curiosity, and prospects of “an education by truths.” “Truths” are not to be confused with matters of knowledge or opinion. Truths are existential, ongoing, and open-ended ontological operations that do not belong to any epistemic category. An education by such truths operates through a subtraction from the state of the situation and proposes a different direction regarding the true life. According to Badiou, the task of philosophy is to think these truths as processes that emerge from and pursue gradually transformations of particular situations. Overall, the structure of Badiou’s philosophical system demonstrates an extraordinary ontological style as it concurrently stands in relation to, and breaks off from, the history of contemporary French philosophy, German Idealism, and Greek antiquity. His system, which is of vast complexity, is based on mathematical set theory, consisting of a series of determinate negations of the history of philosophy, and also created by the histories of what Badiou terms philosophy’s conditions: science, art, politics, and love.

Sign in / Sign up

Export Citation Format

Share Document