Related Research Articles
Existence is the state of being real or participating in reality. The terms "being", "reality", and "actuality" are often used as close synonyms. Existence contrasts with nonexistence, nothingness, and nonbeing. A common distinction is between the existence of an entity and its essence, which refers to the entity's nature or essential qualities.
In mathematical logic, Russell's paradox is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901. Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. The paradox had already been discovered independently in 1899 by the German mathematician Ernst Zermelo. However, Zermelo did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other academics at the University of Göttingen. At the end of the 1890s, Georg Cantor – considered the founder of modern set theory – had already realized that his theory would lead to a contradiction, as he told Hilbert and Richard Dedekind by letter.
Friedrich Ludwig Gottlob Frege was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever.
Analytic philosophy is a broad movement or tradition within philosophy focused on analysis, which has been dominant within Western philosophy and especially anglophone philosophy since the latter half of the 20th century. The proliferation of analysis in philosophy began around the turn of the 20th century in the contemporary era in Germany, Austria, the United Kingdom, the United States, Canada, Australia, New Zealand, and Scandinavia.
Alexius Meinong Ritter von Handschuchsheim was an Austrian philosopher, a realist known for his unique ontology. He also made contributions to philosophy of mind and theory of value.
In set theory, several ways have been proposed to construct the natural numbers. These include the representation via von Neumann ordinals, commonly employed in axiomatic set theory, and a system based on equinumerosity that was proposed by Gottlob Frege and by Bertrand Russell.
Richard Sylvan was a New Zealand–born philosopher, logician, and environmentalist.
In logic and philosophy, a property is a characteristic of an object; a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties. A property, however, differs from individual objects in that it may be instantiated, and often in more than one object. It differs from the logical/mathematical concept of class by not having any concept of extensionality, and from the philosophical concept of class in that a property is considered to be distinct from the objects which possess it. Understanding how different individual entities can in some sense have some of the same properties is the basis of the problem of universals.
In metaphysics, the distinction between abstract and concrete refers to a divide between two types of entities. Many philosophers hold that this difference has fundamental metaphysical significance. Examples of concrete objects include plants, human beings and planets while things like numbers, sets and propositions are abstract objects. There is no general consensus as to what the characteristic marks of concreteness and abstractness are. Popular suggestions include defining the distinction in terms of the difference between (1) existence inside or outside space-time, (2) having causes and effects or not, (3) having contingent or necessary existence, (4) being particular or universal and (5) belonging to either the physical or the mental realm or to neither. Despite this diversity of views, there is broad agreement concerning most objects as to whether they are abstract or concrete. So under most interpretations, all these views would agree that, for example, plants are concrete objects while numbers are abstract objects.
Philosophical realism – usually not treated as a position of its own but as a stance towards other subject matters – is the view that a certain kind of thing has mind-independent existence, i.e. that it exists even in the absence of any mind perceiving it or that its existence is not just a mere appearance in the eye of the beholder. This includes a number of positions within epistemology and metaphysics which express that a given thing instead exists independently of knowledge, thought, or understanding. This can apply to items such as the physical world, the past and future, other minds, and the self, though may also apply less directly to things such as universals, mathematical truths, moral truths, and thought itself. However, realism may also include various positions which instead reject metaphysical treatments of reality entirely.
A free logic is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free logics may also allow models that have an empty domain. A free logic with the latter property is an inclusive logic.
Ernst Mally was an Austrian analytic philosopher, initially affiliated with Alexius Meinong's Graz School of object theory. Mally was one of the founders of deontic logic and is mainly known for his contributions in that field of research. In metaphysics, he is known for introducing a distinction between two kinds of predication, better known as the dual predication approach.
Edward Nouri Zalta is an American philosopher who is a senior research scholar at the Center for the Study of Language and Information at Stanford University. He received his BA from Rice University in 1975 and his PhD from the University of Massachusetts Amherst in 1981, both in philosophy. Zalta has taught courses at Stanford University, Rice University, the University of Salzburg, and the University of Auckland. Zalta is also the Principal Editor of the Stanford Encyclopedia of Philosophy.
In metaphysics and ontology, Austrian philosopher Alexius Meinong advanced nonexistent objects in the 19th and 20th centuries within a "theory of objects". He was interested in intentional states which are directed at nonexistent objects. Starting with the "principle of intentionality", mental phenomena are intentionally directed towards an object. People may imagine, desire or fear something that does not exist. Other philosophers concluded that intentionality is not a real relation and therefore does not require the existence of an object, while Meinong concluded there is an object for every mental state whatsoever—if not an existent then at least a nonexistent one.
Noneism, also known as modal Meinongianism, is a theory in logic and metaphysics. It holds that some things do not exist. It was first coined by Richard Routley in 1980 and appropriated again in 2005 by Graham Priest.
Héctor-Neri Castañeda was a Guatemalan-American philosopher and founder of the journal Noûs.
William Joseph Rapaport is a North American philosopher who is an Associate Professor Emeritus of the University at Buffalo.
In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess." According to formalism, the truths expressed in logic and mathematics are not about numbers, sets, or triangles or any other coextensive subject matter — in fact, they aren't "about" anything at all. Rather, mathematical statements are syntactic forms whose shapes and locations have no meaning unless they are given an interpretation. In contrast to mathematical realism, logicism, or intuitionism, formalism's contours are less defined due to broad approaches that can be categorized as formalist.
Meinong's jungle is the name given by Richard Routley (1980) to the repository of non-existent objects in the ontology of Alexius Meinong.
The Meinongian argument is a type of ontological argument or an "a priori argument" that seeks to prove the existence of God. This is through an assertion that there is "a distinction between different categories of existence." The premise of the ontological argument is based on Alexius Meinong's works. Some scholars also associate it with St. Anselm's ontological argument.
References
- Edward N. Zalta, Abstract Objects: An Introduction to Axiomatic Metaphysics, Dordrecht: D. Reidel, 1983.
- Edward N. Zalta, Intensional Logic and the Metaphysics of Intentionality, Cambridge, MA: The MIT Press/Bradford Books, 1988.
- Edward N. Zalta, Principia Metaphysica, Center for the Study of Language and Information, Stanford University, February 10, 1999.
- Daniel Kirchner, Christoph Benzmüller, Edward N. Zalta, "Mechanizing Principia Logico-Metaphysica in Functional Type Theory", Review of Symbolic Logic13(1) (March 2020): 206–18.
- Edward N. Zalta, Principia Logico-Metaphysica, Center for the Study of Language and Information, Stanford University, February 6, 2024.
