Second-order theories

Second-order theories are often seen as the orthodox position. They understand existence as a second-order property rather than a first-order property.^[24] For instance, the Empire State Building is an individual object and being 443.2 meters tall is a first-order property of it. Being instantiated is a property of being 443.2 meters tall and therefore a second-order property. According to second-order theories, to talk about existence is to talk about which properties have instances.^[25] For example, this view states that the sentence "God exists" does not claim that God has the property of existing. Instead, it means "Godhood is instantiated".^[2]

A key motivation of second-order theories is that existence is in important ways different from regular properties like being a building and being 443.2 meters tall: regular properties express what an object is like but existence does not.^[26] According to this view, existence is more fundamental than regular properties since, without it, objects cannot instantiate any properties.^[27]

Second-order theorists usually hold that quantifiers rather than predicates express existence.^[28] Quantifiers are terms that talk about the quantity of objects that have certain properties. Existential quantifiers express that there is at least one object. Examples are expressions like "some" and "there exists", as in "some cows eat grass" and "there exists an even prime number".^[29] In this regard, existence is closely related to counting since to claim that something exists is to claim that the corresponding concept has one or more instances.^[30]

Second-order views imply that a sentence like "egg-laying mammals exist" is misleading since the word "exist" is used as a predicate in them. They hold instead that their true logical form is better expressed in reformulations like "there exist entities that are egg-laying mammals". This way, existence has the role of a quantifier while egg-laying mammals is the predicate. Quantifier constructions can also be used to express negative existential statements. For instance, the sentence "talking tigers do not exist" can be expressed as "it is not the case that there exist talking tigers".^[31]

Bertrand Russell proposed his theory of descriptions to dissolve paradoxes surrounding negative existential statements.

Many ontologists accept that second-order theories provide a correct analysis of many types of existential sentences. However, it is controversial whether it is correct for all cases.^[32] One difficulty is caused by so-called negative singular existentials. Negative singular existentials are statements that deny that a particular object exists. An example is the sentence "Ronald McDonald does not exist". Singular terms, like Ronald McDonald, seem to refer to individuals. This poses a difficulty since negative singular existentials deny that this individual exists. This makes it unclear how the singular term can refer to the individual in the first place. One influential solution to this problem was proposed by Bertrand Russell. He holds that singular terms do not directly refer to individuals but are instead descriptions of individuals. Positive singular existentials affirm that an object matching the descriptions exists while negative singular existentials deny that an object matching the descriptions exists. According to this view, the sentence "Ronald McDonald does not exist" expresses the idea that "it is not the case that there is a unique happy hamburger clown".^[33]

First-order theories

First-order theories claim that existence is a property of individuals. They are less widely accepted than second-order theories but also have some influential proponents. There are two types of first-order theories. According to Meinongianism, existence is a property of some but not all entities. This view implies that there are nonexistent entities. According to universalism, existence is a universal property instantiated by every entity.^[34]

Meinongianism

According to Alexius Meinong, there are some entities that do not exist.

Meinongianism is a view about existence defended by Meinong and his followers. Its main claim is that there are some entities that do not exist. This means that objecthood is independent of existence. Proposed examples of nonexistent objects are merely possible objects, like flying pigs, as well as fictional and mythical objects, like Sherlock Holmes and Zeus. According to this view, these objects are real and have being even though they do not exist.^[35] Meinong states that there is an object for any combination of properties. For example, there is an object that only has the single property of being a singer without any additional properties. This means that neither the attribute of wearing a dress nor the absence of it applies to this object. Meinong also includes impossible objects, like round squares.^[36]

Meinongians state that sentences describing what Sherlock Holmes and Zeus are like refer to nonexisting objects. They are true or false depending on whether these objects have the properties ascribed to them.^[37] For instance, the sentence "Pegasus has wings" is true because having wings is a property of Pegasus, even though Pegasus lacks the property of existing.^[38]

One key motivation of Meinongianism is to explain how negative singular existentials, like "Ronald McDonald does not exist", can be true. Meinongians accept the idea that singular terms, like "Ronald McDonald" refer to individuals. For them, a negative singular existential is true if the individual it refers to does not exist.^[39]

Meinongianism has important implications for how to understand quantification. According to an influential view defended by Willard Van Orman Quine, the domain of quantification is restricted to existing objects. This view implies that quantifiers carry ontological commitments about what exists and what does not exist. Meinongianism differs from this view by holding that the widest domain of quantification includes both existing and nonexisting objects.^[20]

Some aspects of Meinongianism are controversial and have received substantial criticism. According to one objection, one cannot distinguish between being an object and being an existing object.^[38] A closely related criticism rests on the idea that objects cannot have properties if they do not exist.^[38] A further objection is that Meinongianism leads to an "overpopulated universe" since there is an object corresponding to any combination of properties.^[20] A more specific criticism rejects the idea that there are incomplete and impossible objects.^[40]

Singular and general

One distinction is between singular and general existence. Singular existence is the existence of individual entities. For example, the sentence "Angela Merkel exists" expresses the existence of one particular person. General existence pertains to general concepts, properties, or universals. For instance, the sentence "politicians exist" states that the general term "politician" has instances without referring to any one politician in particular.^[46]

Singular and general existence are closely related to each other and some philosophers have tried to explain one as a special case of the other. For example, Frege held that general existence is more basic. One argument in favor of this position is that general existence can be expressed in terms of singular existence. For instance, the sentence "Angela Merkel exists" can be expressed as "entities exist that are identical to Angela Merkel", where the expression "being identical to Angela Merkel" is understood as a general term. A different position is defended by Quine, who gives primacy to singular existence.^[47] A related question is whether there can be general existence without singular existence. According to philosophers like Henry S. Leonard, a property only has general existence if there is at least one actual object that instantiates it. A different view, defended by Nicholas Rescher, holds that properties can even exist if they have no actual instances, like the property of being a unicorn.^[48]

This question has a long philosophical tradition in relation to the existence of universals. Platonists claim that universals have general existence as Platonic forms independently of the particulars that instantiate them. According to this view, the universal of redness exists independent of whether there are any red objects.^[49] Aristotelianism also accepts that universals exist. However, it holds that their existence depends on particulars that instantiate them and that they are unable to exist by themselves. According to this view, a universal that has no instances in the spacio-temporal world does not exist.^[50] Nominalists claim that only particulars have existence and deny that universals exist.^[51]

Concrete and abstract

Another influential distinction in ontology is between concrete and abstract objects. Many concrete objects are encountered in regular everyday life, like rocks, plants, and other people. They exist in space and time and influence each other: they have causal powers and are affected by other concrete objects. Abstract objects exist outside space and time and lack causal powers. Examples of abstract objects are numbers, sets, and types.^[52] The distinction between concrete and abstract objects is sometimes treated as the most general division of being.^[53]

There is wide agreement that concrete objects exist but opinions are divided in regard to abstract objects. Realists accept the idea that abstract objects have independent existence.^[54] Some of them claim that abstract objects have the same mode of existence as concrete objects while others maintain that they exist but in a different way.^[55] Antirealists state that abstract objects do not exist. This is often combined with the view that existence requires a location in space and time or the ability to causally interact.^[56]

Fictional objects, like dragons and centaurs, are closely related to abstract objects and pose similar problems. However, the two terms are not identical. For example, the expression "the integer between two and three" refers to a fictional abstract object while the expression "integer between two and four" refers to a non-fictional abstract object. In a similar sense, there are also concrete fictional objects besides abstract fictional objects, like the winged horse of Bellerophon.^[57]

Possible, contingent, and necessary

A further distinction is between merely possible, contingent, and necessary existence.^[58] An entity has necessary existence if it must exist or could not fail to exist. Entities that exist but could fail to exist are contingent. Merely possible entities are entities that do not exist but could exist.^[59]

Avicenna and Thomas Aquinas argued that God has necessary existence.

Most entities encountered in ordinary experience, like telephones, sticks, and flowers, have contingent existence.^[60] It is an open question whether any entities have necessary existence. According to one view, all concrete objects have contingent existence while all abstract objects have necessary existence.^[61] According to some theorists, one or several necessary beings are required as the explanatory foundation of the cosmos. For instance, philosophers like Avicenna and Thomas Aquinas follow this idea and claim that God has necessary existence.^[62]

There are many academic debates about whether there are merely possible objects. According to actualism, only actual entities have being. This includes both contingent and necessary entities. But it excludes merely possible entities.^[63] This view is rejected by possibilists, who state that there are also merely possible objects besides actual objects.^[64] For example, David Lewis argues that possible objects exist in the same way as actual objects. According to him, possible objects exist in possible worlds while actual objects exist in the actual world. Lewis holds that the only difference between possible worlds and the actual world is the location of the speaker: the term "actual" refers to the world of the speaker, similar to how the terms "here" and "now" refer to the spatial and temporal location of the speaker.^[2]

Physical and mental

A further distinction is between entities that exist on a physical level in contrast to mental entities.^[65] Physical entities include objects of regular perception, like stones, trees, and human bodies as well as entities discussed in modern physics, like electrons and protons. Physical entities can be observed and measured. They possess mass and a location in space and time.^[66] Mental entities belong to the realm of the mind, like perceptions, experiences of pleasure and pain as well as beliefs, desires, and emotions. They are primarily associated with conscious experiences but also include unconscious states, like unconscious beliefs, desires, and memories.^[67]

The ontological status of physical and mental entities is a frequent topic in metaphysics and philosophy of mind. According to materialists, only physical entities exist on the most fundamental level. Materialists usually explain mental entities in terms of physical processes, for example, as brain states or as patterns of neural activation. Idealists reject this view and state that mind is the ultimate foundation of existence. They hold that physical entities have a derivative form of existence, for instance, that they are mental representations or products of consciousness. Dualists believe that both physical and mental entities exist on the most fundamental level. They state that they are connected to one another in various ways but that one cannot be reduced to the other.^[68]

Western philosophy

Western philosophy originated with the Presocratic philosophers, who explored the foundational principles of all existence. Some, like Thales and Heraclitus, suggested that concrete principles, like water or fire, are the root of existence. This position was opposed by Anaximander, who held that the source must lie in an abstract principle beyond the world of human perception.^[84]

Plato argued that different types of entities have different degrees of existence. He held that shadows and images exist in a weaker sense than regular material objects. He claimed that the unchangeable Platonic forms have the highest type of existence. He saw material objects as imperfect and impermanent copies of Platonic forms.^[85]

Aristotle held that different types of entities have different modes of existence.

While Aristotle accepted Plato's idea that forms are different from matter, he challenged the idea that forms have a higher type of existence. Instead, he held that forms cannot exist without matter.^[86] Aristotle further claimed that different entities have different modes of existence. For example, he distinguished between substances and their accidents and between potentiality and actuality.^[87]

Neoplatonists, like Plotinus, suggested that reality has a hierarchical structure. They held that a transcendent entity called "the One" or "the Good" is responsible for all existence. From it emerges the intellect, which in turn gives rise to the soul and the material world.^[88]

Anselm of Canterbury is known for his formulation of the ontological argument aiming to prove the existence of God.

In medieval philosophy, Anselm of Canterbury formulated the influential ontological argument. This argument aims to deduce the existence of God from the concept of God. Anselm defined God as the greatest conceivable being. He reasoned that an entity that did not exist outside his mind would not be the greatest conceivable being. This led him to the conclusion that God exists.^[89]

Thomas Aquinas distinguished between the essence of a thing and its existence. According to him, the essence of a thing constitutes its fundamental nature. He argued that it is possible to understand what an object is and grasp its essence even if one does not know whether this object exists. He concluded from this observation that existence is not part of the qualities of an object and should instead be understood as a separate property.^[21] Aquinas also considered the problem of creation from nothing. He claimed that only God has the power to truly bring new entities into existence. These ideas later inspired Gottfried Wilhelm Leibniz's theory of creation. He held that to create is to confer actual existence to possible objects.^[90]

Both David Hume and Immanuel Kant rejected the idea that existence is a property. According to Hume, objects are bundles of qualities. He held that existence is not a property since there is no impression of existence besides the bundled qualities.^[91] Kant came to a similar conclusion in his criticism of the ontological argument. According to him, this proof fails because one cannot deduce from the definition of a concept whether entities described by this concept exist. He held that existence does not add anything to the concept of the object, it only indicates that this concept is instantiated.^[92]

Franz Brentano defended the idea that all judgments are existential judgments.

Franz Brentano agreed with Kant's criticism and his claim that existence is not a real predicate. He used this idea to develop his theory of judgments. According to him, all judgments are existential judgments: they either affirm or deny the existence of something. He stated that judgments like "some zebras are striped" have the logical form "there is a striped zebra" while judgments like "all zebras are striped" have the logical form "there is not a non-striped zebra".^[93]

Gottlob Frege and Bertrand Russell aimed to refine the idea of what it means that existence is not a regular property. They distinguished between regular first-order properties of individuals and second-order properties of other properties. According to this view, to talk about existence is to talk about the second-order property of being instantiated. For instance, to deny that dinosaurs exist means that the property of being a dinosaur does not have the property of being instantiated.^[94] According to Russell, the fundamental form of predication happens by applying a predicate to the proper name of an individual. An example of this type of atomic proposition is "Laika is a dog". Russell held that talk of existence in the form of sentences like "dogs exist" is less fundamental since it means that there is an individual to which this predicate applies without naming this individual.^[95]

Willard Van Orman Quine followed Frege and Russell in accepting that existence is a second-order property. He drew a close link between existence and the role of quantification in formal logic.^[96] He applied this idea to scientific theories and stated that a scientific theory is committed to the existence of an entity if the theory quantifies over this entity. For example, if a theory in biology claims that "there are populations with genetic diversity" then this theory has an ontological commitment to the existence of populations with genetic diversity.^[97]

Despite the influence of second-order theories, this view was not universally accepted. Alexius Meinong rejected it and claimed that existence is a property of individuals and that not all individuals have this property. This led him to the thesis that there is a difference between being and existence: all individuals have being but only some of them also exist. This implies that there are some things that do not exist, like merely possible objects and impossible objects.^[98]

Eastern philosophy

Adi Shankara taught that only the divine exists on the most fundamental level and that the impression of a multiplicity of different entities is an illusion.

Many schools of thought in Eastern philosophy discuss the problem of existence and its implications. For instance, the ancient Hindu school of Samkhya developed a metaphysical dualism. According to this view, there are two types of existence: pure consciousness (Purusha) and matter (Prakriti). Samkhya explains the manifestation of the universe as the interaction between these two principles.^[99] A different approach was developed by Adi Shankara in his school of Advaita Vedanta. He defended a metaphysical monism by claiming that the divine (Brahman) is the ultimate reality and the only existent. According to this view, the impression that there is a universe consisting of many distinct entities is an illusion (Maya).^[100] The essential features of ultimate reality are described as Sat Chit Ananda, meaning existence, consciousness, and bliss.^[101]

A central doctrine in Buddhist philosophy is called the three marks of existence. The three marks are aniccā (impermanence), anattā (absence of a permanent self), and dukkha (suffering). Aniccā is the doctrine that all of existence is subject to change. This means everything transforms at some point and nothing lasts forever. Anattā expresses a similar state in relation to persons. It is the claim that people do not have a permanent identity or a separate self. Ignorance about aniccā and anattā is seen as the main cause of dukkha by leading people to form attachments that cause suffering.^[102]

Laozi saw the dao as a fundamental principle that constitutes the root of all existence.

A central idea in many schools of Chinese philosophy, like Laozi's Daoism, is that a fundamental principle known as dao is the source of all existence. The term is often translated as "the Way" and is understood as a cosmic force that governs the natural order of the world. One position in Chinese metaphysics holds that dao is itself a form of being while another contends that it is non-being that gives rise to being.^[103]

The concept of existence played a central role in Arabic-Persian philosophy. Avicenna and Al-Ghazali discussed the relation between existence and essence. According to them, the essence of an entity is prior to its existence. The additional step of instantiating the essence is required for the entity to come into existence. Mulla Sadra rejected this priority of essence over existence. He argued that essence is only a concept used by the mind to grasp existence. Existence, by contrast, encompasses the whole of reality, according to his view.^[104]

Formal logic

Formal logic studies which arguments are deductively valid.^[105] First-order logic is the most commonly used system of formal logic. In it, existence is expressed using the existential quantifier (${\displaystyle \exists }$). For example, the formula ${\displaystyle \exists xHorse(x)}$ can be used to state that horses exist. The variable x ranges over all elements in the domain of quantification and the existential quantifier expresses that at least one element in this domain is a horse. In first-order logic, all singular terms, like names, refer to objects in the domain and imply that the object exists. Because of this, one can deduce that ${\displaystyle \exists xHonest(x)}$ (someone is honest) from ${\displaystyle Honest(Bill)}$ (Bill is honest).^[106]

Many logical systems that are based on first-order logic also follow this idea. Free logic is an exception. It allows there to be empty names that do not refer to any object in the domain.^[107] One motivation for this modification is that reasoning is not limited to regular objects but can also be applied to fictional objects.^[108] In free logic, for instance, one can express that Pegasus is a flying horse using the formula ${\displaystyle Flyinghorse(Pegasus)}$. One consequence of this modification is that one cannot infer from this type of statement that something exists. This means that the inference from ${\displaystyle Flyinghorse(Pegasus)}$ to ${\displaystyle \exists xFlyinghorse(x)}$ is invalid in free logic even though it would be valid in first-order logic. Free logic uses an additional existence predicate (${\displaystyle E!}$) to express that a singular term refers to an existing object. For example, the formula ${\displaystyle E!(Homer)}$ can be used to express that Homer exists while the formula ${\displaystyle \lnot E!(Pegasus)}$ states that Pegasus does not exist.^[109]

Epistemology, philosophy of mind, and philosophy of language

The disciplines of epistemology, philosophy of mind, and philosophy of language aim to understand the nature of knowledge, mind, and language.^[110] A key issue in these fields is the problem of reference. This problem concerns the question of how mental or linguistic representations can refer to existing objects. Examples of such representations are beliefs, thoughts, perceptions, words, and sentences. For instance, in the sentence "Barack Obama is a Democrat", the name "Barack Obama" refers to a particular individual. In relation to perception, the problem of reference concerns the question of whether or to what extent perceptual impressions bring the perceiver in contact with reality by presenting existing objects rather than illusions.^[111]

Closely related to the problem of reference is the relation between truth and existence. Representations can be true or false. According to truthmaker theory, true representations require a truthmaker. A truthmaker of a representation is the entity whose existence is responsible for the fact that the representation is true. For example, the sentence "kangaroos live in Australia" is true because there are kangaroos in Australia: the existence of these kangaroos is the truthmaker of the sentence. Truthmaker theory states that there is a close relation between truth and existence: there exists a truthmaker for every true representation.^[112]

Existentialism

Existentialism is a school of thought that explores the nature of human existence. One of its key ideas is that existence precedes essence. This claim expresses the notion that existence is more basic than essence and that the nature and purpose of human beings are not pregiven but develop in the process of living. According to this view, humans are thrown into a world that lacks preexistent intrinsic meaning. They have to determine for themselves what their purpose is and what meaning their life should have. Existentialists use this idea to focus on the role of freedom and responsibility in actively shaping one's life.^[113]

Notes

Citations

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