Existence means, literally, "standing out" or "appearing". The dominant view of twentieth-century and contemporary Anglo-American philosophy is that existence is what is asserted by statements of first-order logic of the form "for some x, Fx". This agrees with the simple and commonsensical view that, in uttering "There is a bridge across the Thames at Hammersmith", or "A bridge crosses the Thames at Hammersmith", one asserts the existence of a bridge across the Thames at Hammersmith. The word "existence", in this view, is a simple way of describing the logical form of an ordinary "subject-predicate" sentence.
Unfortunately, this simplistic view is vulnerable to a number of philosophical objections, and the problem of existence is one which still exercises the minds of contemporary philosophers. This article is a brief overview of those problems, of the solutions which certain philosophers have offered, and suggestions for further reading.
The problems of existence.
The first problem is that, on the simple view above, any sentence of apparently subject-predicate form "S is P" must assert the existence of an entity satisfying "S" and "P". Thus any noun phrase whatsoever that is the subject or predicate of a true sentence of this form, must be presumed to denote something. This leads to the question of what is denoted in sentences containing abstract noun phrases, such as "goodness is a virtue", "blindness can be overcome", "the number 9 is the sum of 6 and 3" and so on. Are goodness, blindness, virtue etc. objects in the sense that chairs, tables and houses are objects?
Worse, a sentence like "existence is not a predicate" is apparently of subject predicate form, thus "existence" must be presumed to denote something. Thus "signifies existence", cannot simply be a way of describing the logical form of ordinary subject-predicate sentence. The sentence "a bridge crosses the Thames at Hammersmith" cannot just be about a bridge, the Thames, and Hammersmith. It must be about "existence" as well.
This question has divided philosophers into two classes: realists, who assert the existence of objects corresponding to abstract concepts, and nominalists, who deny the existence of such things. The subject of what things exist corresponding to grammatical categories of noun phrase is known as ontology.
The nominalist approach to the question is to argue that certain noun phrases can be "eliminated" by rewriting a sentence in a form that has the same meaning, but which 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 so-called analytic school of philosophy.
Realists, however, turn this argument on its head, 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".
The second problem is that both a singular sentence like "Pegasus flies" and its negation seem to imply the existence of a subject. If "Pegasus flies" is true, then something (namely Pegasus) flies. So if the sentence is true, "Pegasus" has a referent. But if the sentence is false, its negation is true. But the negation of "Pegasus flies" is "it is not the case that Pegasus flies". If this is true, then something (namely Pegasus) does not fly, and so "Pegasus" still has a referent. Whether "Pegasus flies" is true or not, "Pegasus" has a referent, and so "Pegasus" has a referent. But common sense suggests that "Pegasus" does not have a referent.
Modern approaches to the problem of existence.
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 Peter Strawson, and (some have argued) even earlier by Gottlob Frege, a proper name strictly has no meaning when there is no object to which it refers. This view is sometimes justified by 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. To adapt an argument of Strawson's, someone who points to an apparently empty space, uttering "that's a fine red one" communicates nothing to someone who cannot see or understand what he is pointing to. Variants of the Direct reference view have been proposed by Saul Kripke, Gareth Evans, Scott Soames and others.
According to the "two sense" view of existence, existential statements fall into two classes.
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, Venus the planet, New York) that have existence in the narrow sense, and those (like Sherlock Holmes, Venus the goddess, Minas Tirith) that do not.
Supporters of this view (which derives from Alexius Meinong) include Terence Parsons and Edward Zalta.
The difficulty with this view is (a) that common sense suggests that there are no such things as fictional characters, places, (b) there is no strong evidence for two kinds of existential sentence as used in ordinary language.
Earlier views on existence.
The first comprehensive treatment of the subject was by Aristotle in the metaphysics. He 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 (See the article on ontology for a detailed discussion). The medieval philosopher Thomas Aquinas, perhaps following the Persian 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) the Categories are not a form of Being in their own right, but derivative on the existence of individuals.
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.
Arnauld thought that a proposition or judgment, consists of taking two different ideas and either putting them together or rejecting them:
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. It has the obvious difficulty, noted above, that a proposition of the form "Some A is B" is not necessarily existential. If neither A nor B includes the idea of existence, then "some A is B" simply joins 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. (Indeed Arnauld's contemporary Descartes famously argued so, regarding the concept "God" (discourse 4, Meditation 5).
The theory was current until the middle of the nineteenth century. 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".
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" (Mill) or "A greatest number is impossible" (Herbart). 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:
Frege developed a similar view (thought later) in his great work The Foundations of Arithmetic, as did Charles Peirce. The Frege-Brentano view is the basis of the dominant position in modern Anglo-American philosophy that existence asserted by the existential quantifier. (As expressed by Quine's slogan "To be is to be the value of a variable).
European views of existence.
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. See the article on Existentialism for further detail.
Quotations about existence.