In common usage, existence is the world we are aware of through our senses Senses are the physiological capacities within organisms that provide inputs for perception. The senses and their operation, classification, and theory are overlapping topics studied by a variety of fields, most notably neuroscience, cognitive psychology , and philosophy of perception. The nervous system has a specific sensory system or organ,, and that persists independently without them. In academic philosophy Philosophy is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. It is distinguished from other ways of addressing fundamental questions by its critical, generally systematic approach and its reliance on rational argument. The word "philosophy" comes from the the word has a more specialized meaning, being contrasted with essence In philosophy, essence is the attribute or set of attributes that make an object or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity. Essence is contrasted with accident: a property that the object or substance has contingently, without which the substance can still retain its identity. The, which specifies different forms of existence as well as different identity In philosophy, identity is whatever makes an entity definable and recognizable, in terms of possessing a set of qualities or characteristics that distinguish it from entities of a different type. Or, in layman's terms, identity is whatever makes something the same or different conditions for objects and properties. Philosophers investigate questions such as "What exists?" "How do we know?" "To what extent are the senses a reliable guide to existence?" "What is the meaning, if any, of assertions of the existence of categories Categorization is the process in which ideas and objects are recognized, differentiated and understood. Categorization implies that objects are grouped into categories, usually for some specific purpose. Ideally, a category illuminates a relationship between the subjects and objects of knowledge. Categorization is fundamental in language,, ideas In the most narrow sense, an idea is just whatever is before the mind when one thinks. Very often, ideas are construed as representational images; i.e. images of some object. In other contexts, ideas are taken to be concepts, although abstract concepts do not necessarily appear as images. Many philosophers consider ideas to be a fundamental, and abstractions Abstraction is a conceptual process by which higher, more abstract concepts are derived from the usage and classification of literal, "real," or "concrete" concepts?"

Ontology Ontology (from the Greek ὄν, genitive ὄντος: of being and -λογία, -logia: science, study, theory) is the philosophical study of the nature of being, existence or reality in general, as well as the basic categories of being and their relations. Traditionally listed as a part of the major branch of philosophy known as metaphysics, is the philosophical Philosophy is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. It is distinguished from other ways of addressing fundamental questions by its critical, generally systematic approach and its reliance on rational argument. The word "philosophy" comes from the study of the nature of being Being , is an English word used for conceptualizing subjective aspects fundamental to the self —related to and somewhat interchangeable with terms like "existence" and "living". In its objective usage —as in "a being," or "[a] human being" —it refers to a discrete life form that has properties of mind (, existence or reality Reality is the state of things as they actually exist, rather than as they may appear or may be thought to be. In its widest definition, reality includes everything that is and has being, whether or not it is observable or comprehensible in general, as well as of the basic categories of being In metaphysics , the different kinds or ways of being are called categories of being or simply categories. To investigate the categories of being is to determine the most fundamental and the broadest classes of entities. A distinction between such categories, in making the categories or applying them, is called an ontological distinction and their relations. Traditionally listed as a part of the major branch of philosophy known as metaphysics Metaphysics is a branch of philosophy that is not easily defined. It is concerned with explaining the fundamental nature of being and the world. Someone who studies metaphysics would be called either a metaphysicist or a metaphysician, ontology deals with questions concerning what entities An entity is something that has a distinct, separate existence, though it need not be a material existence. In particular, abstractions and legal fictions are usually regarded as entities. In general, there is also no presumption that an entity is animate. Entities are used in system developmental models that display communications and internal exist or can be said to exist, and how such entities can be grouped, related within a hierarchy A hierarchy (Greek: hierarchia , from hierarches, "leader of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above," "below," or "at the same level as" one another and with only one "neighbor" above and below each of, and subdivided according to similarities and differences.

Epistemology Epistemology or theory of knowledge is the branch of philosophy concerned with the nature and scope (limitations) of knowledge. It addresses the questions: studies criteria of truth, defining "primary truths" inherently accepted in the investigation of knowledge. The first is existence. It is inherent in every analysis. Its self-evident In epistemology , a self-evident proposition is one that is known to be true by understanding its meaning without proof, a priori The terms a priori and a posteriori ("subsequent to") are used in philosophy (epistemology) to distinguish two types of knowledge, justifications or arguments. A priori knowledge or justification is independent of experience (for example 'All bachelors are unmarried'); a posteriori knowledge or justification is dependent on experience or nature cannot be consistently doubted, since a person objecting to existence according to some standard of proof must implicitly accept the standard's existence as a premise.^[1]

Materialism In philosophy, the theory of materialism holds that the only thing that exists is matter; that all things are composed of material and all phenomena are the result of material interactions. In other words, matter is the only substance. As a theory, materialism is a form of physicalism and belongs to the class of monist ontology. As such, it is holds that the only thing that exists is matter Matter is a general term for the substance of which all physical objects are made. Typically, this includes atoms and other particles which have mass. However in practice there is no single correct scientific meaning; each field uses the term in different and often incompatible ways. A common way of defining matter is as anything that has mass and, that all things are composed of material, and all phenomena (including consciousness Consciousness is variously defined as subjective experience, or awareness, or wakefulness, or the executive control system of the mind. It is an umbrella term that may refer to a variety of mental phenomena. Although humans realize what everyday experiences are, consciousness refuses to be defined, philosophers note :) are the result of material interactions. In other words, matter is the only substance. Supernaturalism The term supernatural or supranatural pertains to being above or beyond what one holds to be natural. In the case of one who has strong scientific and atheist beliefs, the supernatural is anything unexplainable by natural law or phenomena. While one who holds mystical or heavenly beliefs may have no conception of supernatural phenomena, he or she, on the other hand, holds that other things exist (or may exist) in addition.

Life Life is a characteristic that distinguishes objects that have signaling and self-sustaining processes (biology) from those that do not, either because such functions have ceased (death), or else because they lack such functions and are classified as inanimate is a characteristic that distinguishes objects Object is a technical term used in epistemology, a branch of philosophy concerning itself with the study of knowing. Aristotle had said, "All men by nature desire to know." René Descartes expanded this knowing into the grounds of certainty with cogito ergo sum, typically translated as "I think therefore I am." The thinker that have self-sustaining biological processes A biological process is a process of a living organism. Biological processes are made up of any number of chemical reactions or other events that results in a transformation that exist from those that do not^[2][3] —either because such functions have ceased (death Death is the termination of the biological functions that define a living organism. The word refers both to a particular process and to the condition that results thereby. The nature of the latter has been for millennia a central concern of the world's religious traditions and of philosophical enquiry. Belief in some kind of afterlife or rebirth), or else because they lack such functions and are classified as "inanimate".^[4]

Etymology

The word "existence" comes from the Latin Latin or sometimes Roman is an Italic language originally spoken in Latium and Ancient Rome. Although often considered a dead language, in view of the fact that it has no native, fluent speakers, Latin continues to be taught in schools and has been, and currently is, used in the process of new word production in modern languages from many word existere meaning "to appear," "to arise," "to become," or "to be," but literally, it means "to stand out" (ex- being the Latin prefix for "out" added to the Latin verb stare, meaning "to stand").

Formal languages

Formal languages A formal language is a set of words, i.e. finite strings of letters, symbols, or tokens. The set from which these letters are taken is called the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar ; accordingly, words that belong to a formal language are sometimes called well-formed words ( are entirely syntactic In linguistics, syntax is the study of the principles and rules for constructing sentences in natural languages in nature but may be given semantics Semantics is the study of meaning, usually in language. The word "semantics" itself denotes a range of ideas, from the popular to the highly technical. It is often used in ordinary language to denote a problem of understanding that comes down to word selection or connotation. This problem of understanding has been the subject of many that give meaning to language elements. Formal languages are applied in logic Logic is the study of reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies. It is one kind of critical thinking. In philosophy, the study of logic because they have procedural formulas that can be interpreted as expressing logical truth Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature. A logical truth is a statement which is true and remains true under all reinterpretations of its components other than its logical constants. It is a type of analytic statement. A formal language interpretation is the assignment of meanings to its symbols and formulas. Existence in formal languages is defined by the principles and rules for constructing sentences In the field of linguistics, a sentence is an expression in natural language, often defined to indicate a grammatical and lexical unit consisting of one or more words that represent distinct concepts. A sentence can include words grouped meaningfully to express a statement, question, exclamation, request or command.

In naive set theory Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics. The informal content of this naive set theory supports both the aspects of mathematical sets familiar in discrete mathematics , and the everyday usage of set theory concepts in most contemporary mathematics, the empty set In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size is zero. Some axiomatic set theories assure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced. Many possible properties of sets are trivially true for the empty set is a primitive notion because to assert that it exists is an implicit axiom In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other truths in the axiom of empty set.

In mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions, an identity element In mathematics, an identity element is a special type of element of a set with respect to a binary operation on that set. It leaves other elements unchanged when combined with them. This is used for groups and related concepts leaves existing elements unchanged when combined with them. It is a special type of element of a set A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Although it was invented at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In with respect to a binary operation In mathematics, a binary operation is a calculation involving two operands, in other words, an operation whose arity is two. Examples include the familiar arithmetic operations of addition, subtraction, multiplication and division and is applied in groups In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity and invertibility. While these are familiar from.

In Zeroth Order Logic, existence is either true or false and can represented by the (1,0) binary group. First-order logic First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic. First-order logic is distinguished from propositional logic by its use of quantifiers; each is a formal logic used in mathematics, philosophy, linguistics, and computer science. First-order logic requires at least one additional rule of inference to obtain completeness. It is distinguished by applying quantifiers Quantification has several distinct senses. In mathematics and empirical science, it is the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method, such that each interpretation of first-order logic includes a domain of discourse The domain of discourse, sometimes called the universe of discourse, logical discourse, or simply discourse, is an analytic tool used in deductive logic, especially predicate logic. It indicates the relevant set of entities that are being dealt with by quantifiers over which the quantifiers range. Logical connectives In logic, a logical connective is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the compound sentence produced has a truth value dependent on the respective truth values of the original sentences are applied to restrict the domain of discourse to fulfill a given predicate.

In mathematical logic Mathematical logic is a subfield of mathematics with close connections to computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the existence is a quantifier, the "existential quantifier In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. It is denoted by the logical operator symbol ∃ , which is called the existential quantifier. Existential quantification is distinct from universal quantification ("for all"), which asserts that the", symbolized by ∃, a backwards capital E. To symbolize "Four leaf clovers exist", mathematicians would first define predicates, P(x) = "x is a clover" and Q(x) = "x has four leaves", and then form the well-formed formula In the formal languages used in mathematical logic and computer science, a well-formed formula or simply formula is an idea, abstraction or concept which is expressed using the symbols and formation rules (also called the formal grammar) of a particular formal language. To say that a string of symbols is a wff with respect to a given formal (∃x)(P(x) and Q(x)). While ∃ can mean "for some", to contrast in symbolic logic, the "universal quantifier In predicate logic, universal quantification formalizes the notion that something is true for everything, or every relevant thing. The resulting statement is a universally quantified statement, and we have universally quantified over the predicate. In symbolic logic, the universal quantifier (typically , ∀, a turned a) is the symbol used to" (typically, ∀) is the symbol used to denote universal quantification, and is often informally read as "given any" or "for all". These statements may be applied in an existence proof or existence theorem.

In the philosophy of mathematics The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists. When one assumes that an object does not exist and derives a contradiction from that assumption, one still has not found the object and therefore not proved its existence, according to constructivists. A mathematical singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.

Second-order logic is more expressive than first-order logic and it is possible to write formal sentences that quantify "the domain is finite" for existence, which is theoretically impossible in first order logic. In ordinary language, such second-order forms use either grammatical plurals or terms such as “set of” or “group of”.

The study of quantification in natural languages is much more difficult than the corresponding problem for formal languages. This comes in part from the fact that the grammatical structure of natural language sentences may conceal the logical structure. Moreover, mathematical conventions strictly specify the range of validity for formal language quantifiers; for natural language, specifying the range of validity requires dealing with non-trivial semantic problems.

In classical logic, the logical connective is a symbol or word used to connect two or more sentences in a grammatically valid way, such that the compound sentence produced has a truth value ("existence") dependent on the original sentences' truth values. A truth table can be used to tell whether a propositional expression is true for all legitimate input values, that is, logically valid. When the input truth values are exclusively preserved in the output, they persistently exist.

• In truth-preserving validity, the interpretation under which all variables are assigned a truth value of 'true' produces a truth value of 'true'.

• In a false-preserving validity, the interpretation under which all variables are assigned a truth value of ‘false’ produces a truth value of ‘false'.^[5]

Preservation properties	Logical connective sentences
True and/or false preserving:	Logical conjunction (AND, ) • Logical disjunction (OR, )
True preserving only:	Tautology ( ) • Biconditional (XNOR, ) • Implication (if then, ) • Converse implication (then if, )
False preserving only:	Contradiction ( ) • Exclusive disjunction (XOR, ) • Nonimplication ( ) • Converse nonimplication ( )
Non-preserving:	Proposition • Negation ( ) • Alternative denial (NAND, ) • Joint denial (NOR, )

Non-preserving sentences subjectively exist, without preserving validity. Preserving sentences objectively exist within the logical validity of logical connective sentences.

Objectivity in referring requires a definition of truth. According to metaphysical objectivists, an object may truthfully be said to have this or that attribute, as in the statement "This object exists," whereas the statement "This object is true" or "false" is meaningless. Thus, only propositions have truth values.

In the philosophy of language and metaphysics, an existential commitment is necessary to make a proposition where the existence of one thing is presupposed or implied by asserting the existence of another.

Intuitionistic logic, or constructive logic, is a symbolic logic system that preserves justification, rather than truth, across transformations yielding derived propositions. From a practical view point, the motivation for applying intuitionistic logic, is that it has the existence property, making it suitable for other forms of mathematical constructivism. The existence property is fundamental to understanding in what sense proofs can be considered to have content: the essence of the discussion of existence theorems. A strict formalist does not require meaning or content as sufficient for existence.

Calculus is intuitively constructed with infinitesimal small objects that approach non-existence in their limits. l'Hôpital's rule can evaluate indeterminate forms having non-existing solutions where the derivative limit of the function may exist. Application (or repeated application) of the rule often converts an indeterminate form to a determinate form, allowing easy evaluation of the limit.

The fundamental theorem of calculus specifies the existence between the two central operations of calculus: differentiation and integration. Calculus is the study of change and area, (in the same way that geometry is the study of shape and algebra is the study of operations) and their application to solving equations. This subject constitutes a significant part of modern mathematics. Calculus is applied in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired.

Calculus has two major branches, differential calculus (change) and integral calculus (area), which are related by the fundamental theorem of calculus. The first part of the theorem, sometimes called the first fundamental theorem of calculus, shows that an indefinite integration^[6] can be reversed by a differentiation. The first part is important because it guarantees the existence of antiderivatives for continuous functions.^[7]

In summary: for a derivative to exist for a function ƒ it is necessary for the function ƒ to be continuous, but continuity alone is not sufficient. When an antiderivative g exists, there are infinitely many antiderivatives for ƒ, validity is obtained by adding a necessary and arbitrary existing constant C to g (which is lost in differentiation). Also, g antiderivatives of ƒ always exist when ƒ is continuous. An antiderivative can only be made definite over a valid interval range (a,b) to resolve the C constant. In simple language this says, area integrals exist over a valid range. Differentiation removes existing constants.

In calculus, the definition of a critical point is extended to include points where the derivative does not exist. This is important to optimization problems of local maxima and minima of where the function does exist. A critical point is either a stationary point or a point where the derivative is not defined. In simple language, this says that extrema values exist in calculus where there is no change.

In probability, an event only exists within a sample space. The probability is the ratio of the event to the sample space, which gives a frequency for the event existence in the sample space. Bayesian probability, assigns probabilities to any statement and can be constructed to represent a subjective degree of belief in a statement, given the existing evidence.

In philosophy, an objective fact means a truth that remains true everywhere, independently of human thought or feelings, as existence implies. To be termed scientific, a method of inquiry must be based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning.^[8] Philosophy of science looks at the underpinning logic of the scientific method, at what separates science from non-science, and the ethic that is implicit in science. There are basic assumptions derived from philosophy that form the base of the scientific method - namely, that reality is both objective and consistent, that humans have the capacity to perceive reality accurately, and that rational explanations exist for elements of the real world. These assumptions from methodological naturalism form the basis on which science is grounded. Logical Positivist, empiricist, falsificationist, and other theories have claimed to give a definitive account of the logic of science, but each has in turn been criticized.

An unobservable (also called impalpable) is an entity whose existence, nature, properties, qualities or relations are not directly observable by man. In philosophy of science typical examples of "unobservables" are atomic particles, the force of gravity, causation and beliefs or desires.

An object of the mind is an object that exists in the imagination, but only appears in the real world through an abstract representation (a model, picture, writing, etc.). Some such objects are mathematical abstractions, literary concepts, or fictional scenarios.

Historical conceptions

In the western tradition of philosophy, the first comprehensive treatments of the subject are from Plato's Phaedo, Republic, and Statesman and Aristotle's Metaphysics, though earlier fragmentary writing exists. Aristotle developed a complicated theory of being, according to which only individual things, called substances fully have being, but other things such as relations, quantity, time and place (called the categories) have a derivative kind of being, dependent on individual things. In Aristotle's Metaphysics, there are four causes of existence or change in nature: the material cause, the formal cause, the efficient cause, and the final cause.

The Neo-Platonists and some early Christian philosophers argued about whether existence had any reality except in the mind of God. Some taught that existence was a snare and a delusion, that the world, the flesh, and the devil existed only to tempt weak humankind away from God.

The medieval philosopher Thomas Aquinas, perhaps following the Islamic philosopher Avicenna, argued that God is pure being, and that in God essence and existence are the same. At about the same time, the nominalist philosopher William of Ockham, argued, in Book I of his Summa Totius Logicae (Treatise on all Logic, written some time before 1327) that Categories are not a form of Being in their own right, but derivative on the existence of individuals.

Early modern philosophy

The early modern treatment of the subject derives from Antoine Arnauld and Pierre Nicole's Logic, or 'The Art of Thinking', better known as the Port-Royal Logic, first published in 1662. Arnauld thought that a proposition or judgment, consists of taking two different ideas and either putting them together or rejecting them:

After conceiving things by our ideas, we compare these ideas and, finding that some belong together and others do not, we unite or separate them. This is called affirming or denying, and in general judging. This judgment is also called a proposition, and it is easy to see that it must have two terms. One term, of which one affirms or denies something, is called the subject; the other term, which is affirmed or denied, is called the attribute or Praedicatum.

—Antoine Arnauld, The Art of Thinking (Port-Royal Logic),(1662) (translated J. Buroker 1996), Logic, II.3, page 82

The two terms are joined by the verb "is" (or "is not", if the predicate is denied of the subject). Thus every proposition has three components: the two terms, and the "copula" that connects or separates them. Even when the proposition has only two words, the three terms are still there. For example "God loves humanity", really means "God is a lover of humanity", "God exists" means "God is a thing".

This theory of judgment dominated logic for centuries, but it has some obvious difficulties: it only considers proposition of the form "All A are B.", a form logicians call universal. It does not allow propositions of the form "Some A are B.", a form logicians call existential. If neither A nor B includes the idea of existence, then "some A are B" simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that "triangle" contains the idea "three angles equal to two right angles", then "A exists" is automatically true, and we have an ontological proof of A's existence. (Indeed Arnauld's contemporary Descartes famously argued so, regarding the concept "God" (discourse 4, Meditation 5)). Arnauld's theory was current until the middle of the nineteenth century.

David Hume argued that the claim that a thing exists, when added to our notion of a thing, does not add anything to the concept. For example, if we form a complete notion of Moses, and superadd to that notion the claim that Moses existed, we are not adding anything to the notion of Moses.

Kant also argued that existence is not a "real" predicate, but gave no explanation of how this is possible, indeed his famous discussion of the subject is merely a restatement of Arnauld's doctrine that in the proposition "God is omnipotent", the verb "is" signifies the joining or separating of two concepts such as "God" and "omnipotence".^{[original research?]}

Schopenhauer claimed that “everything that exists for knowledge, and hence the whole of this world, is only object in relation to the subject, perception of the perceiver, in a word, representation.”^[9] According to him there can be "No object without subject" because "everything objective is already conditioned as such in manifold ways by the knowing subject with the forms of its knowing, and presupposes these forms…."^[10].

Predicative nature

John Stuart Mill (and also Kant's pupil Herbart) argued that the predicative nature of existence was proved by sentences like "A centaur is a poetic fiction" ^[11] or "A greatest number is impossible" (Herbart).^[12] Franz Brentano challenged this, so also (as is better known) did Frege. Brentano argued that we can join the concept represented by a noun phrase "an A" to the concept represented by an adjective "B" to give the concept represented by the noun phrase "a B-A". For example, we can join "a man" to "wise" to give "a wise man". But the noun phrase "a wise man" is not a sentence, whereas "some man is wise" is a sentence. Hence the copula must do more than merely join or separate concepts. Furthermore, adding "exists" to "a wise man", to give the complete sentence "a wise man exists" has the same effect as joining "some man" to "wise" using the copula. So the copula has the same effect as "exists". Brentano argued that every categorical proposition can be translated into an existential one without change in meaning and that the "exists" and "does not exist" of the existential proposition take the place of the copula. He showed this by the following examples:

The categorical proposition "Some man is sick", has the same meaning as the existential proposition "A sick man exists" or "There is a sick man".

The categorical proposition "No stone is living" has the same meaning as the existential proposition "A living stone does not exist" or "there is no living stone".

The categorical proposition "All men are mortal" has the same meaning as the existential proposition "An immortal man does not exist" or "there is no immortal man".

The categorical proposition "Some man is not learned" has the same meaning as the existential proposition "A non-learned man exists" or "there is a non-learned man".

Frege developed a similar view (though later) in his great work The Foundations of Arithmetic, as did Charles Sanders Peirce (but Peirce held that the possible and the real are not limited to the actually, individually existent). The Frege-Brentano view is the basis of the dominant position in modern Anglo-American philosophy: that existence is asserted by the existential quantifier (as expressed by Quine's slogan "To be is to be the value of a variable." — On What There Is, 1948).^[13]

Semantics

In mathematical logic, there are two quantifiers, "some" and "all", though as Brentano (1838–1917) pointed out, we can make do with just one quantifier and negation. The first of these quantifiers, "some" is also expressed as "there exists". Thus, in the sentence "There exists a man," the term "man" is asserted to be part of existence. But we can also assert, "There exists a triangle." Is a "triangle" — an abstract idea — part of existence in the same way that a "man" — a physical body — is part of existence? Do abstractions such as goodness, blindness, and virtue exist in the same sense that chairs, tables, and houses exist? What categories, or kinds of thing can be the subject or the predicate of a proposition?

Worse, does "existence" exist?^[14]

In some statements, existence is implied without being mentioned. The statement "A bridge crosses the Thames at Hammersmith." cannot just be about a bridge, the Thames, and Hammersmith. It must be about "existence" as well. On the other hand, the statement "A bridge crosses the Styx at Limbo," has the same form, but while in the first case we understand a real bridge in the real world made of stone or brick, what "existence" would mean in the second case is less clear.

The nominalist approach is to argue that certain noun phrases can be "eliminated" by rewriting a sentence in a form that has the same meaning, but does not contain the noun phrase. Thus Ockham argued that "Socrates has wisdom," which apparently asserts the existence of a reference for "wisdom," can be rewritten as "Socrates is wise," which contains only the referring phrase "Socrates." This method became widely accepted in the twentieth century by the analytic school of philosophy.

However, this argument may be inverted by realists in arguing that since the sentence "Socrates is wise" can be rewritten as "Socrates has wisdom," this proves the existence of a hidden referent for "wise."

A further problem is that human beings seem to process information about fictional characters in much the same way that they process information about real people. For example, in the 2008 United States presidential election, a politician and actor named Fred Thompson ran for the Republican Party nomination. In polls, potential voters identified Fred Thompson as a "law and order" candidate. Thompson plays a fictional character on the television series Law and Order. Doubtless the people who make the comment are aware that Law and Order is fiction, but at some level, they process fiction as if it were fact^{[dubious – discuss][citation needed]}. Another example of this is the common experience of actresses who play the villain in a soap opera being accosted in public as if they are to blame for the actions of the character they play.

A scientist might make a clear distinction about objects that exist, and assert that all objects that exist are made up of either matter or energy. But in the layperson's worldview, existence includes real, fictional, and even contradictory objects. Thus if we reason from the statement Pegasus flies to the statement Pegasus exists, we are not asserting that Pegasus is made up of atoms, but rather that Pegasus exists in a particular worldview, the worldview of classical myth. When a mathematicians reasons from the statement "ABC is a triangle" to the statement "triangles exist", she is not asserting that triangles are made up of atoms but rather that triangles exist within a particular mathematical model.

Modern approaches

According to Bertrand Russell's Theory of Descriptions, the negation operator in a singular sentence takes wide and narrow scope: we distinguish between "some S is not P" (where negation takes "narrow scope") and "it is not the case that 'some S is P'" (where negation takes "wide scope"). The problem with this view is that there appears to be no such scope distinction in the case of proper names. The sentences "Socrates is not bald" and "it is not the case that Socrates is bald" both appear to have the same meaning, and they both appear to assert or presuppose the existence of someone (Socrates) who is not bald, so that negation takes narrow scope.

The theory of descriptions has generally fallen into disrepute, though there have been recent attempts to revive it by Stephen Neale and Frank Jackson. According to the direct-reference view, an early version of which was originally proposed by Bertrand Russell, and perhaps earlier by Gottlob Frege, a proper name strictly has no meaning when there is no object to which it refers. This view relies on the argument that the semantic function of a proper name is to tell us which object bears the name, and thus to identify some object. But no object can be identified if none exists. Thus, a proper name must have a bearer if it is to be meaningful.

Existence in the wide and narrow senses

According to the "two sense" view of existence, which derives from Alexius Meinong, existential statements fall into two classes.

1. Those asserting existence in a wide sense. These are typically of the form "N is P" for singular N, or "some S is P".
2. Those asserting existence in a narrow sense. These are typically of the form "N exists" or "S's exist".

The problem is then evaded as follows. "Pegasus flies" implies existence in the wide sense, for it implies that something flies. But it does not imply existence in the narrow sense, for we deny existence in this sense by saying that Pegasus does not exist. In effect, the world of all things divides, on this view, into those (like Socrates, the planet Venus, and New York City) that have existence in the narrow sense, and those (like Sherlock Holmes, the goddess Venus, and Minas Tirith) that do not.

However, common sense suggests the non-existence of such things as fictional characters or places.

European views

Influenced by the views of Brentano's pupil Alexius Meinong, and by Edmund Husserl, Germanophone and Francophone philosophy took a different direction regarding the question of existence. Existentialism has been a major strand of continental philosophy in the twentieth century.

Anti-realist arguments

Anti-realism is the view of idealists who are skeptics about the physical world, maintaining either: 1) that nothing exists outside the mind, or 2) that we would have no access to a mind-independent reality even if it may exist. Realists, in contrast, hold that perceptions or sense data are caused by mind-independent objects. An "anti-realist" who denies that other minds exist (i. e., a solipsist) is different from an "anti-realist" who claims that there is no fact of the matter as to whether or not there are unobservable other minds (i. e., a logical behaviorist).

Dharmic "middle way" view

The Indian philosopher Nagarjuna (c. 150 - 250 CE) largely advanced existence concepts and founded the Madhyamaka school of Mahāyāna Buddhism.

The philosophical meaning of the Sanskrit word 'Satya' is "unchangeable", "that which has no distortion", "that which is beyond distinctions of time, space, and person", "that which pervades the universe in all its constancy".

The two truths doctrine differentiates between two levels of 'truth' (Sanskrit: satya) in Buddhist discourse, a "relative", or commonsense truth and an "ultimate" or absolute spiritual truth. It holds that truth exists in conventional and ultimate forms, and that both forms are co-existent and non-dual.

In eastern philosophy, Anicca (Sanskrit anitya) or "impermanence" describes existence. It refers to the fact that all conditioned things (sankhara) are in a constant state of flux. In reality there is no thing that ultimately ceases to exist; only the appearance of a thing ceases as it changes from one form to another. Imagine a leaf that falls to the ground and decomposes. While the appearance and relative existence of the leaf ceases, the components that formed the leaf become particulate material that goes on to form new plants. Buddhism teaches a middle way, avoiding the extreme views of eternalism and nihilism.^[15] The middle way recognizes there are vast differences between the way things are perceived to exist and way things really exist. The differences are reconciled in the concept of Shunyata by addressing the existing object's served purpose for the subject's identity in being. What exists is in non-existence, because the subject changes.

Trailokya elaborates on three kinds of existence, that of desire, form, and formlessness in which there are karmic rebirths. Taken further to the Trikaya doctrine, it describes how the Buddha exists. In this philosophy, it is accepted that the Buddha exists in more than one absolute way.

The Twelve Links of Conditioned Existence describe the empirical study of the cause and effect relationships in the analysis of phenomena arising to existence, according to dependent origination principles. This is applied for the Buddha's purpose to reduce the existence of suffering.

Notes

1. ^ Dolhenty, Jonathan. "Part Thirteen:The Criterion of Truth". The Problem of Knowledge: A brief introduction to epistemology. http://www.radicalacademy.com/epistom.htm. Retrieved 2007-10-31.
2. ^ Koshland Jr, Daniel E. (March 22, 2002). "The Seven Pillars of Life". Science 295. (5563): 2215–2216. doi:10.1126/science.1068489. http://www.sciencemag.org/cgi/content/full/295/5563/2215. Retrieved 2009-05-25.
3. ^ The American Heritage Dictionary of the English Language, 4th edition, published by Houghton Mifflin Company, via Answers.com:
   • "The property or quality that distinguishes living organisms from dead organisms and inanimate matter, manifested in functions such as metabolism, growth, reproduction, and response to stimuli or adaptation to the environment originating from within the organism."
   • "The characteristic state or condition of a living organism."
4. ^ Definition of inanimate. WordNet Search by Princeton University.
5. ^ R. L. Simpson, "Essentials of symbolic logic",Taylor & Francis,1998
6. ^ More exactly, the theorem deals with definite integration with variable upper limit and arbitrarily selected lower limit. This particular kind of definite integration allows us to compute one of the infinitely many antiderivatives of a function (except for those without a zero). Hence, it is almost equivalent to indefinite integration, defined by most authors as an operation that yields any one of the possible antiderivatives of a function, including those without a zero.
7. ^ Spivak, Michael (1980), Calculus (2nd ed.), Houstan, Texas: Publish or Perish Inc.
8. ^ "[4] Rules for the study of natural philosophy", Newton 1999, pp. 794-6, from the General Scholium, which follows Book 3, The System of the World.
9. ^ The World as Will and Representation, vol. I, § 1
10. ^ The World as Will and Representation, vol. I, § 7
11. ^ John Stuart Mill, A System of Logic, 1843 I. iv. 1.page 124
12. ^ Uberweg (System of Logic) §68
13. ^ On What There Is - in Review of Metaphysics (1948). Reprinted in W.V.O. Quine, From a Logical Point of View (Harvard University Press, 1953)
14. ^ To exist is to have a specific relation to existence - a relation, by the way, which existence itself does not have. Bertrand Russell - The Principles of Mathematics - New York, W. W. Norton & Company, 1903, second edition 1937 pages 449-450.
15. ^ The Buddhist Publication Society. "The Three Basic Facts of Existence". http://www.accesstoinsight.org/lib/authors/various/wheel186.html. Retrieved 2009-07-14. "(ref.1) Change or impermanence is the essential characteristic of all phenomenal existence. We cannot say of anything, animate or inanimate, organic or inorganic, "this is lasting"; for even while we are saying this, it would be undergoing change. All is fleeting; the beauty of flowers, the bird's melody, the bee's hum, and a sunset's glory."

See also

• Cogito ergo sum
• Conservation law
• Cosmogony
• Cosmological argument
• Existence of God
• Existence precedes essence
• Existence proof
• Existentialism
• Gödel's ontological proof
• Identity and change
• Meaning of life
• Performative contradiction
• Right to exist
• Solipsism
• Three marks of existence

References

• Antoine Arnauld and Pierre Nicole 'Logic', or The Art of Thinking, (known as the Port-Royal Logic), translated J. Buroker, Cambridge 1996
• Mill, J.S., A System of Logic, 8th edition 1908
• Loux, M., Ockham's Theory Of Terms (translation of book I of the Summa Logicae c-1327).

Further reading

• Plato, The Republic, translated by Desmond Lee, Penguin Classics, 2003, ISBN 0-14-044914-0, ISBN 978-0-14-044914-3
• Aristotle, The Metaphysics, translated by Hugh Lawson-Tancred, Penguin Classics, 1999, ISBN 0-14-044619-2, ISBN 978-0-14-044619-7
• Heraclitus, Fragments, James Hilton, forward, Brooks Hexton, translator, Penguin Classics, 2003, ISBN 0-14-243765-4, ISBN 978-0-14-243765-0.
• The Meaning of Life, Terry Eagleton, Oxford University Press, 2007, ISBN 0-19-921070-5 ISBN 978-0-19-921070-1
• The Story of Philosophy, Bryan Magee, Dorling Kindersley Lond. 1998, ISBN 0-7513-0590-1
• What is Existence?, C.J.F. Williams, Oxford University Press, 1981

External links

• "Existence" article by Barry Miller in the Stanford Encyclopedia of Philosophy, 2002-05-24
• Existence. Definitions from leading philosophers
• Existence - A matter of interpretation.

Categories: Ontology | Concepts in metaphysics | Philosophy of life

See Also:

• Existentialism: Encyclopedia
• Existence of God: Encyclopedia
• Atheist Existentialism: Encyclopedia
• Agnostic Existentialism: Encyclopedia
• Christian Existentialism: Encyclopedia

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