Mathematical object
A mathematical object is an abstract object arising in mathematics. The concept is studied in philosophy of mathematics.
In mathematical practice, an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs. Commonly encountered mathematical objects include numbers, permutations, partitions, matrices, sets, functions, and relations. Geometry as a branch of mathematics has such objects as hexagons, points, lines, triangles, circles, spheres, polyhedra, topological spaces and manifolds. Another branch—algebra—has groups, rings, fields, group-theoretic lattices, and order-theoretic lattices. Categories are simultaneously homes to mathematical objects and mathematical objects in their own right. In proof theory, proofs and theorems are also mathematical objects.
The ontological status of mathematical objects has been the subject of much investigation and debate by philosophers of mathematics.
Cantorian framework
Goal
A goal is a desired result that a person or a system envisions, plans and commits to achieve: a personal or organizational desired end-point in some sort of assumed development. Many people endeavor to reach goals within a finite time by setting deadlines.
It is roughly similar to purpose or aim, the anticipated result which guides reaction, or an end, which is an object, either a physical object or an abstract object, that has intrinsic value.
Goal setting
Goal setting may involve establishing specific, measurable, achievable, relevant, and time-bounded (SMART) objectives, but not all researchers agree that these SMART criteria are necessary.
Research on goal setting by Edwin A. Locke and his colleagues suggests that goal setting can serve as an effective tool for making progress when it ensures that group members have a clear awareness of what each person must do to achieve a shared objective. On a personal level, the process of setting goals allows individuals to specify and then work toward their own objectives (such as financial or career-based goals). Goal-setting comprises a major component of personal development and management.
Object (philosophy)
An object is a technical term in modern philosophy often used in contrast to the term subject. A subject is an observer and an object is a thing observed. For modern philosophers like Descartes, consciousness is a state of cognition that includes the subject—which can never be doubted as only it can be the one who doubts–—and some object(s) that may be considered as not having real or full existence or value independent of the subject who observes it. Metaphysical frameworks also differ in whether they consider objects exist independently of their properties and, if so, in what way.
The pragmatist Charles S. Peirce defines the broad notion of an object as anything that we can think or talk about. In a general sense it is any entity: the pyramids, Alpha Centauri, the number seven, a disbelief in predestination or the fear of cats. In a strict sense it refers to any definite being.
A related notion is objecthood. Objecthood is the state of being an object. One approach to defining it is in terms of objects' properties and relations. Descriptions of all bodies, minds, and persons must be in terms of their properties and relations. The philosophical question of the nature of objecthood concerns how objects are related to their properties and relations. For example, it seems that the only way to describe an apple is by describing its properties and how it is related to other things. Its properties may include its redness, its size and its composition, while its relations may include "on the table", "in the room" and "being bigger than other apples".
Defiance (play)
Defiance is a play by American playwright John Patrick Shanley. It ran Off-Broadway in 2006.
Background
Defiance is the second of three plays of a planned trilogy. Shanley explained that the trilogy "... 'explores specifics of my life story as it overlaps with major changes in the social fabric of this country'..." Shanley had military duty at Camp Lejeune from 1970 to 1972.
Shanley commented about the play that "In short, Doubt turned into Defiance, which is my second play about American hierarchy".
Plot overview
The play concerns a colonel who promotes a black officer solely based on race. The black officer finds out that the colonel has had a brief affair with a private's wife, and is torn between his desire to go unnoticed and his realization that he must do the right thing.
Productions
The play premiered Off-Broadway at the Manhattan Theatre Club's City Center Stage I on February 9 (in previews), 2006. Directed by Doug Hughes, the cast featured Stephen Lang, Chris Chalk, Margaret Colin and Chris Bauer. The play closed on June 4, 2006. It received a Henry Hewes Design Award nomination for Costumes design by Catherine Zuber.
Defiance (season 3)
The third and final season of the American science fiction television series Defiance premiered on Syfy on June 12, 2015, concluded on August 28, 2015, and consisted a total of 13 episodes. The show stars Grant Bowler, Julie Benz, Stephanie Leonidas, Tony Curran, Jaime Murray, Graham Greene, Jesse Rath, Anna Hopkins and Nichole Galicia.
The series is produced by Universal Cable Productions, in transmedia collaboration with Trion Worlds, who have released an MMORPG video game of the same name which is tied in to the series.
Cast
Main
^1 Greene is only credited for the episodes he appears in.
^2 Galicia was promoted to series regular, starting with "History Rhymes". She was previously credited as a guest in the first two episodes.
Defiance (TV series)
Defiance is an American science fiction television series developed by Rockne S. O'Bannon, Kevin Murphy, and Michael Taylor. The series is produced by Universal Cable Productions, in transmedia collaboration with Trion Worlds, who have released an MMORPG video game of the same name that is tied in to the series.
The show takes place in the future on a radically transformed Earth containing new species, some having arrived from space, many others the result of contamination by Votan terraforming technology, which has transformed native flora and fauna in unforeseen ways. As the series opens, Joshua Nolan (Grant Bowler) works as the local sheriff, or Lawkeeper, for the town of Defiance, a community where humans and intelligent extraterrestrial species coexist. The show follows Nolan, his adopted alien daughter Irisa (Stephanie Leonidas), and the town's new mayor, Amanda Rosewater (Julie Benz).
The series is broadcast in the United States on the cable channel Syfy and in various international markets. It premiered on April 15, 2013, in the United States and that same week in most countries that picked up the series.Defiance was renewed for a 13 episode third season on September 25, 2014, which premiered on June 12, 2015. On October 16, 2015, the show was cancelled by Syfy after three seasons.
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