Round square copula
Encyclopedia
The "Round square copula" is a common example of the Dual Copula Strategy used in reference to the problem of nonexistent objects as well as their relation to problems in modern Philosophy of language
. The issue arose, most notably, between the theories of Alexius Meinong
, Bertrand Russell
- Gilbert Ryle
playing a minor part as well in the eventual dismissal of Meinong's object theory (see Meinong's 1904 book, Theory of Objects).
By borrowing Edward Zalta's notational method (Fb stands for b exemplifies the property of being F; bF stands for b encodes the property of being F), and using a revised version of Meinongian object theory which makes use of a dual copula distinction (MOTdc), we can say that the object called "the round square" encodes the property of being round, the property of being square, all properties implied by these, and no others. But it is true that there are also infinitely many properties being exemplified by an object called the round square (and, really, any object) - e.g. the property of not being a computer, and the property of not being a pyramid. Note that this strategy has forced "is" to abandon its predicative use, and now functions abstractly.
When one now analyzes the round square copula using the MOTdc, one will find that it now avoids the three common paradoxes: (1) The violoation of the law of contradiction, (2) The paradox of claiming the property of existence without actually existing, and (3) producing counterintuitive consequences. Firstly, the MOTdc shows that the round square does not exemplify the property of being round, but the property of being round and square. Thus, there is no subsequent contradiction. Secondly, it avoids the conflict of existence/non-existence by claiming non-physical existence: by the MOTdc, it can only be said that the round square simply does not exemplify the property of occupying a region in space. Finally, the MOTdc avoids counterintuitive consequences (like a 'thing' having the property of nonexistence) by stressing that the round square copula can be said merely to encode the property of being round and square, not actually exemplifying it. Thus, logically, it does not belong to any set or class.
In the end, what the MOTdc really does is created a kind of object: a nonexistent object that is very different from the objects we might normally think of. Occasionally, references to this notion, while obscure, may be called "Meinongian objects."
First is the "Other worlds" strategy. Similar to the ideas explained with Possible worlds
theory, this strategy employs considering that logical principles and the law of contradiction have limits, but without assuming that everything is true. Enumerated and championed by Graham Priest
, who was heavily influenced by Richard Routley, this strategy forms the notion of "noneism
." In short, assuming there exist infinite possible and impossible worlds, objects are freed from necessarily existing in all worlds, but instead may exist in impossible worlds (where the law of contradiction does not apply, for example) and not in the actual world. Unfortunately, accepting this strategy entails accepting the host of problems that come with it, such as the ontological status of impossible worlds.
Secondly, there is the strategy of nuclear-extranuclear properties. According to Meinong, it is possible to distinguish the natural
(nuclear) properties of an object, from its external (extranuclear) properties. Terence Parsons
identifies four types of extranuclear properties: ontological, modal
, intentional, technical
- however, philosophers dispute Parson's claims in number and kind. Additionally, Meinong states that nuclear properties are either constitutive or consecutive, meaning properties that are either explicitly contained or implied/included in a description of the object. Essentially the strategy denies the possibility for objects to have only one property, and instead they may have only one nuclear property. Meinong himself, however, found this solution to be inadequate in several ways and its inclusion only served to muddle the definition of an object.
Philosophy of language
Philosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for analytic philosophers is concerned with four central problems: the nature of meaning, language use, language cognition, and the relationship between language...
. The issue arose, most notably, between the theories of Alexius Meinong
Alexius Meinong
Alexius Meinong was an Austrian philosopher, a realist known for his unique ontology...
, Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
- Gilbert Ryle
Gilbert Ryle
Gilbert Ryle , was a British philosopher, a representative of the generation of British ordinary language philosophers that shared Wittgenstein's approach to philosophical problems, and is principally known for his critique of Cartesian dualism, for which he coined the phrase "the ghost in the...
playing a minor part as well in the eventual dismissal of Meinong's object theory (see Meinong's 1904 book, Theory of Objects).
Round Square Theory
The strategy employed is the Dual Copula Strategy, which is used to make a distinction between relations of properties and individuals. It entails creating a sentence that isn't supposed to make sense by forcing the term "is" into ambiguous meaning.By borrowing Edward Zalta's notational method (Fb stands for b exemplifies the property of being F; bF stands for b encodes the property of being F), and using a revised version of Meinongian object theory which makes use of a dual copula distinction (MOTdc), we can say that the object called "the round square" encodes the property of being round, the property of being square, all properties implied by these, and no others. But it is true that there are also infinitely many properties being exemplified by an object called the round square (and, really, any object) - e.g. the property of not being a computer, and the property of not being a pyramid. Note that this strategy has forced "is" to abandon its predicative use, and now functions abstractly.
When one now analyzes the round square copula using the MOTdc, one will find that it now avoids the three common paradoxes: (1) The violoation of the law of contradiction, (2) The paradox of claiming the property of existence without actually existing, and (3) producing counterintuitive consequences. Firstly, the MOTdc shows that the round square does not exemplify the property of being round, but the property of being round and square. Thus, there is no subsequent contradiction. Secondly, it avoids the conflict of existence/non-existence by claiming non-physical existence: by the MOTdc, it can only be said that the round square simply does not exemplify the property of occupying a region in space. Finally, the MOTdc avoids counterintuitive consequences (like a 'thing' having the property of nonexistence) by stressing that the round square copula can be said merely to encode the property of being round and square, not actually exemplifying it. Thus, logically, it does not belong to any set or class.
In the end, what the MOTdc really does is created a kind of object: a nonexistent object that is very different from the objects we might normally think of. Occasionally, references to this notion, while obscure, may be called "Meinongian objects."
Criticism and other strategies
Making use of the notion of "non-physically existent" objects is highly controversial in philosophy, and created the buzz for many articles and books on the subject during the first half of the 20th century. There are other strategies for avoiding the problems of Meinong's theories, but they suffer from serious problems as well.The "other worlds" strategy
- For the main page on this topic, see Other worlds strategy.
First is the "Other worlds" strategy. Similar to the ideas explained with Possible worlds
Possible Worlds
Possible Worlds may refer to:* Possible worlds, a concept in philosophy* Possible Worlds , by John Mighton** Possible Worlds , by Robert Lepage, based on the Mighton play* Possible Worlds , by Peter Porter...
theory, this strategy employs considering that logical principles and the law of contradiction have limits, but without assuming that everything is true. Enumerated and championed by Graham Priest
Graham Priest
Graham Priest is Boyce Gibson Professor of Philosophy at the University of Melbourne and Distinguished Professor of Philosophy at the CUNY Graduate Center, as well as a regular visitor at St. Andrews University. Priest is a fellow in residence at Ormond College. He was educated at the University...
, who was heavily influenced by Richard Routley, this strategy forms the notion of "noneism
Noneism
Noneism is a theory in logic and metaphysics first coined by Richard Routley and appropriated again in 2005 by Graham Priest. It holds that there are some things that do not exist. That is, we can quantify over non-existent things using the particular quantifier...
." In short, assuming there exist infinite possible and impossible worlds, objects are freed from necessarily existing in all worlds, but instead may exist in impossible worlds (where the law of contradiction does not apply, for example) and not in the actual world. Unfortunately, accepting this strategy entails accepting the host of problems that come with it, such as the ontological status of impossible worlds.
The "nuclear-extranuclear" strategy
- For the main page on this topic, see Nuclear-extranuclear strategy.
Secondly, there is the strategy of nuclear-extranuclear properties. According to Meinong, it is possible to distinguish the natural
Nature (philosophy)
Nature is a concept with two major sets of inter-related meanings, referring on the one hand to the things which are natural, or subject to the normal working of "laws of nature", or on the other hand to the essential properties and causes of those things to be what they naturally are, or in other...
(nuclear) properties of an object, from its external (extranuclear) properties. Terence Parsons
Terence Parsons
Terence Parsons is an American contemporary philosopher of the analytic tradition. Parsons is also a Professor at UCLA in its Department of Philosophy....
identifies four types of extranuclear properties: ontological, modal
Modal
Modal may refer to:* Modal , a textile made from spun Beechwood cellulose fiber* Modal analysis, the study of the dynamic properties of structures under vibrational excitation...
, intentional, technical
Technical
Technical may refer to:*Technical , a fighting vehicle based on a pickup truck*Technical analysis, a discipline for forecasting the future direction of prices through the study of past market data*Technical drawing, also known as drafting...
- however, philosophers dispute Parson's claims in number and kind. Additionally, Meinong states that nuclear properties are either constitutive or consecutive, meaning properties that are either explicitly contained or implied/included in a description of the object. Essentially the strategy denies the possibility for objects to have only one property, and instead they may have only one nuclear property. Meinong himself, however, found this solution to be inadequate in several ways and its inclusion only served to muddle the definition of an object.
See also
- Philosophy of languagePhilosophy of languagePhilosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for analytic philosophers is concerned with four central problems: the nature of meaning, language use, language cognition, and the relationship between language...
- Set theorySet theorySet theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
- Edward Zalta
- List of paradoxes
- On DenotingOn Denoting"On Denoting", written by Bertrand Russell, is one of the most significant and influential philosophical essays of the 20th century. It was published in the philosophy journal Mind in 1905; then reprinted, in both a special 2005 anniversary issue of the same journal and in Russell's Logic and...
- IntentionalityIntentionalityThe term intentionality was introduced by Jeremy Bentham as a principle of utility in his doctrine of consciousness for the purpose of distinguishing acts that are intentional and acts that are not...
- OntologyOntologyOntology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...
- Philosophical realismPhilosophical realismContemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....