The final blow to the property view of existence is dealt by the so-called ontological argument for the existence of God. The argument, whose original version is due to St Anselm, can be presented as follows. Let us define God as a being than which nothing greater can be conceived. As you should recall, underlying the property view is the assumption that to each description there corresponds an object which can be either existent or non-existent. Suppose that the object which corresponds to the above description is a non-existent entity (i.e. that God does not exist). In that case it can be argued that a greater being can be conceived, namely God that possesses the property of existence. Hence we have a contradiction, since the object which was to satisfy the description ("the greatest conceivable being") in fact does not satisfy it. The cause of the contradiction was the assumption that God does not exist, thus we conclude that God has to exist.
Analogously we could argue that there exists the greatest imaginable island, or any other object for that matter. It is even possible to eliminate the controversial assumption that existence is greater than non-existence. We could simply define the following concept: God who possesses the property of existence. By the same reasoning we can show that the assumption that the referent of this description is a non-existent object leads to a contradiction. But it cannot be so easy to prove the existence of God or any other object you could think of. The culprit was the assumption that each description has a referent - existent or non-existent. If we abandon it, the argument can't even get off the ground, since we cannot argue that it is possible to conceive a greater being than non-existent God. There is no non-existent God, hence we cannot compare it with anything else.
The quantifier view of existence deals with the problem easily. If God existed, it would be the greatest being conceivable, but if God does not exist, there is simply no object in the whole universe than which nothing greater can be conceived (it is not true that for some x, x is God). In a similar way, Kant stressed that existence is not a property whose absence can be detrimental to the greatness of an object. Kant's view should not be interpreted as implying that an existing coin does not differ from a non-existent one. Rather, a non-existent coin is not an object at all, so "it" cannot differ from anything. If we formulate a description of an object, adding to its definitional characteristic that it should exist does not make the description more informative.
Required reading:
B. Garrett, "The Ontological Argument", in What is this thing called metaphysics?, pp. 4-7
Tuesday, October 27, 2009
Thursday, October 22, 2009
Existence part II. Quantifiers
The conception of non-existent objects creates more problems than it solves. But there is an alternative approach. We can insist that all objects are existent and still solve the semantic problem of negative existential statements. One such solution is based on the observation that "existence" is a second-order notion, i.e. it applies not to things but to concepts. The sentence "Vulcan does not exist" is in fact about the concept of "Vulcan", and it states that the concept is empty (and not that it does not exist - obviously we have to assume that concepts exist).
Another solution is as follows. When we state that Vulcan does not exist, we in fact talk not about (non-existent) Vulcan, but about all objects in our universe - and we say that there is no Vulcan among them. Hence the sentence can be understood as being equivalent to "No object is Vulcan", which clearly does not carry the presupposition that Vulcan is an object. Using the definition of the term "Vulcan" we can express the same thought in an even more straightforward fashion as "No planet is closer to the Sun than Mercury", which leaves no trace of suggestion that it is some non-existent object that we talk about.
According to the quantifier conception of existence, all existential statements have to be reformulated in order to reveal their genuine logical structure, different from their surface grammar. The sentence "Elephants exist" does not attribute the property of existence to elephants, but rather speaks in a general fashion about all objects in the universe, claiming that some of them are elephants. Thus the literal form of the sentence should be "There is an x such that x is an elephant", where expression "there is" is known as the existential quantifier, "x" is a variable that can take any value from the domain of all objects, and "is an elephant" is a predicate. The formalization of the statement "Vulcan does not exist" leads to either "It is not the case that there is an x such that x is Vulcan" or, equivalently "For all x, x is not Vulcan" ("for all" is another quantifier, called universal).
It has to be stressed that the expression "x is Vulcan" is to be understood as consisting of the predicate "is Vulcan", and not as being equivalent to the identity statement x = Vulcan. In logic you can apply the identity symbol only to variables and terms called "proper names", of which it is assumed that they represent exactly one object. "Vulcan" cannot be interpreted as a proper name, since there is no object that is represented by that name. Generally, no empty name can be interpreted as a proper name, but only as a predicate.
One consequence of the quantifier view of existence is that certain expressions in natural language become "ontologically committing" (this notion was introduced by Willard V.O. Quine). For instance, the use of the word "some" indicates that we have to accept the existence of certain objects. If I say "Some thoughts of philosopher A are hard to understand", my utterance should be literally interpreted as "There is an x such that x is a thought of philosopher A and x is hard to understand", which implies that there are objects which are thoughts. In order to avoid unwanted ontological commitments, we can try to paraphrase our statements so that they no longer imply the existence of dubious entities.
Some critics point out that the quantifier view of existence commits us to the truth of the statement "Everything exist", which is clearly absurd. While it is true that this is a consequence of the quantifier view, it is by no means absurd. "Everything exists" means "For all x, x exists", and if we accept the quantifier interpretation of existence this statement has to be interpreted as "For all x there is a y such that x = y", which states a trivial truth that everything is identical with something. Instead of saying that not everything exists (which is self-contradictory on any interpretation that eliminates non-existent objects) we should better express our intuition in the statement "Some concepts are empty (non-referring)".
Further reading:
B. Garrett, "What is existence?" in What is this thing called metaphysics?
Another solution is as follows. When we state that Vulcan does not exist, we in fact talk not about (non-existent) Vulcan, but about all objects in our universe - and we say that there is no Vulcan among them. Hence the sentence can be understood as being equivalent to "No object is Vulcan", which clearly does not carry the presupposition that Vulcan is an object. Using the definition of the term "Vulcan" we can express the same thought in an even more straightforward fashion as "No planet is closer to the Sun than Mercury", which leaves no trace of suggestion that it is some non-existent object that we talk about.
According to the quantifier conception of existence, all existential statements have to be reformulated in order to reveal their genuine logical structure, different from their surface grammar. The sentence "Elephants exist" does not attribute the property of existence to elephants, but rather speaks in a general fashion about all objects in the universe, claiming that some of them are elephants. Thus the literal form of the sentence should be "There is an x such that x is an elephant", where expression "there is" is known as the existential quantifier, "x" is a variable that can take any value from the domain of all objects, and "is an elephant" is a predicate. The formalization of the statement "Vulcan does not exist" leads to either "It is not the case that there is an x such that x is Vulcan" or, equivalently "For all x, x is not Vulcan" ("for all" is another quantifier, called universal).
It has to be stressed that the expression "x is Vulcan" is to be understood as consisting of the predicate "is Vulcan", and not as being equivalent to the identity statement x = Vulcan. In logic you can apply the identity symbol only to variables and terms called "proper names", of which it is assumed that they represent exactly one object. "Vulcan" cannot be interpreted as a proper name, since there is no object that is represented by that name. Generally, no empty name can be interpreted as a proper name, but only as a predicate.
One consequence of the quantifier view of existence is that certain expressions in natural language become "ontologically committing" (this notion was introduced by Willard V.O. Quine). For instance, the use of the word "some" indicates that we have to accept the existence of certain objects. If I say "Some thoughts of philosopher A are hard to understand", my utterance should be literally interpreted as "There is an x such that x is a thought of philosopher A and x is hard to understand", which implies that there are objects which are thoughts. In order to avoid unwanted ontological commitments, we can try to paraphrase our statements so that they no longer imply the existence of dubious entities.
Some critics point out that the quantifier view of existence commits us to the truth of the statement "Everything exist", which is clearly absurd. While it is true that this is a consequence of the quantifier view, it is by no means absurd. "Everything exists" means "For all x, x exists", and if we accept the quantifier interpretation of existence this statement has to be interpreted as "For all x there is a y such that x = y", which states a trivial truth that everything is identical with something. Instead of saying that not everything exists (which is self-contradictory on any interpretation that eliminates non-existent objects) we should better express our intuition in the statement "Some concepts are empty (non-referring)".
Further reading:
B. Garrett, "What is existence?" in What is this thing called metaphysics?
Tuesday, October 13, 2009
Existence part I. Non-existent objects
Existence is one of the most fundamental notions of metaphysics. Hence it may be advisable to start our course with a precise definition of this term. Unfortunately this task is not so easy to complete, and some even claim that the term "exist" is primitive and cannot be defined. Others come up with fancy and long-winded definitions of existence that explain nothing. Here, instead of providing a direct definition, we will focus on the way the term "exist" functions in philosophical language and its logical connections with other, closely related terms.
Let us begin with a seemingly straightforward observation: apparently we should agree that not everything exists. We can give numerous examples of fictional objects (objects that don't exist): dwarfs, fairies, centaurs, Santa Claus. But the list is not limited to mythological creatures. In science we often discover that something does not exist, for instance aether or Vulcan (hypothetical planet located inside the orbit of Mercury). In math we can rigorously prove that the greatest prime number does not exist.
But there is a logical problem here. Let us consider the sentence "Vulcan does not exist". What is this sentence about? If, as its grammatical structure suggests, it is a sentence about Vulcan, then we have a contradiction here, because Vulcan has to exist in order for the sentence to be true. One way out of trouble is to divorce the notion of an object from the concept of existence. The initial sentence is about a particular object - Vulcan, that is - but this object does not have to exist. In fact Vulcan is a nonexistent object. We have arrived at a metaphysical conception according to which the set of all objects splits into two parts: existing and non-existing ones. The word "exist" is no longer synonymous with "there is" (there is Santa Claus, but he doesn't exist). Existence becomes a property of only some objects. The main proponent of this theory is the Austrian philosopher Alexius Meinong.
The conception of non-existent objects encounters serious difficulties. Some of them are listed below.
1. What is the extent of the domain of non-existent objects? It turns out that this domain has to be pretty large, vastly outnumbering the domain of existing things. To each description must correspond an object - in the majority of cases a non-existent one. Let's consider for instance the following description: "an x-foot high golden mountain". For each real number x there is a different non-existent object that satisfies this description, so we have easily created a continuum of non-existent objects. Morever, some of the non-existent objects are contradictory: compare a square circle. But this means that we have to accept a pair of contradictory statement: "the square circle is a circle" and "the square circle is not a circle".
2. Non-existent objects are incomplete. Vulcan can only be said to possess two properties: being a planet, and being closer to the Sun than any other planet (this is a relational property). But Vulcan is indeterminate with respect to any other properties that typically characterize planets: its mass, density, period of revolution, period of rotation, etc. Consequently, non-existent objects do not admit unambiguous criteria of identity and distinctness. It is impossible even in principle to decide whether Vulcan whose diameter equals 10000 km is identical with or distinct from the Vulcan whose period of revolution around its axis equals 20 hours.
3. Non-existent objects do not admit answers to the "How many?" questions. How many Vulcans are there? What if we define Vulcan as the only planet that orbits the Sun closer than Mercury? Then it looks like it is a definitional property of Vulcan that there is only one Vulcan, but on the other hand we can have two incompatible descriptions "The unique Vulcan whose diameter equals 1000 km" and "The unique Vulcan whose diameter equals 2000 km". Both non-existent referents of these descriptions obviously satisfy the definition of Vulcan simpliciter. If there are two unique non-existent Vulcans, we have a contradiction.
4. In what sense do non-existent object possess their properties? Vulcan is said to be an object that possesses the property of being a planet and the (relational) property of being closer to the Sun than any other planet, including Mercury. But if Vucan is literally located inside the orbit of Mercury, then it should be possible to see it there. Moreover, it should gravitationally affect Mercury and any other planet. But this is absurd. No non-existent object can gravitationally interact with existent ones. Some reply to this objection that non-existent Vulcan possesses its properties in a different sense than existent objects. But when we defined the concept of Vulcan, we wanted it to denote an object that literally possesses its definitional properties. So non-existent Vulcan understood in that way cannot be claimed to be a referent of our description.
5. If we admit non-existent objects, all laws of nature become literally false. The statement "All metals conduct electricity" is falsified by non-existent metals that do not conduct electricity. One possible solution: to limit the quantifiers in the laws of nature to existent objects only. But in that case we lose an ability to distinguish between laws and accidental generalizations.
Required reading:
Brian Garrett, "Non-existent objects", in What is this thing called metaphysics?, pp.27-31.
Let us begin with a seemingly straightforward observation: apparently we should agree that not everything exists. We can give numerous examples of fictional objects (objects that don't exist): dwarfs, fairies, centaurs, Santa Claus. But the list is not limited to mythological creatures. In science we often discover that something does not exist, for instance aether or Vulcan (hypothetical planet located inside the orbit of Mercury). In math we can rigorously prove that the greatest prime number does not exist.
But there is a logical problem here. Let us consider the sentence "Vulcan does not exist". What is this sentence about? If, as its grammatical structure suggests, it is a sentence about Vulcan, then we have a contradiction here, because Vulcan has to exist in order for the sentence to be true. One way out of trouble is to divorce the notion of an object from the concept of existence. The initial sentence is about a particular object - Vulcan, that is - but this object does not have to exist. In fact Vulcan is a nonexistent object. We have arrived at a metaphysical conception according to which the set of all objects splits into two parts: existing and non-existing ones. The word "exist" is no longer synonymous with "there is" (there is Santa Claus, but he doesn't exist). Existence becomes a property of only some objects. The main proponent of this theory is the Austrian philosopher Alexius Meinong.
The conception of non-existent objects encounters serious difficulties. Some of them are listed below.
1. What is the extent of the domain of non-existent objects? It turns out that this domain has to be pretty large, vastly outnumbering the domain of existing things. To each description must correspond an object - in the majority of cases a non-existent one. Let's consider for instance the following description: "an x-foot high golden mountain". For each real number x there is a different non-existent object that satisfies this description, so we have easily created a continuum of non-existent objects. Morever, some of the non-existent objects are contradictory: compare a square circle. But this means that we have to accept a pair of contradictory statement: "the square circle is a circle" and "the square circle is not a circle".
2. Non-existent objects are incomplete. Vulcan can only be said to possess two properties: being a planet, and being closer to the Sun than any other planet (this is a relational property). But Vulcan is indeterminate with respect to any other properties that typically characterize planets: its mass, density, period of revolution, period of rotation, etc. Consequently, non-existent objects do not admit unambiguous criteria of identity and distinctness. It is impossible even in principle to decide whether Vulcan whose diameter equals 10000 km is identical with or distinct from the Vulcan whose period of revolution around its axis equals 20 hours.
3. Non-existent objects do not admit answers to the "How many?" questions. How many Vulcans are there? What if we define Vulcan as the only planet that orbits the Sun closer than Mercury? Then it looks like it is a definitional property of Vulcan that there is only one Vulcan, but on the other hand we can have two incompatible descriptions "The unique Vulcan whose diameter equals 1000 km" and "The unique Vulcan whose diameter equals 2000 km". Both non-existent referents of these descriptions obviously satisfy the definition of Vulcan simpliciter. If there are two unique non-existent Vulcans, we have a contradiction.
4. In what sense do non-existent object possess their properties? Vulcan is said to be an object that possesses the property of being a planet and the (relational) property of being closer to the Sun than any other planet, including Mercury. But if Vucan is literally located inside the orbit of Mercury, then it should be possible to see it there. Moreover, it should gravitationally affect Mercury and any other planet. But this is absurd. No non-existent object can gravitationally interact with existent ones. Some reply to this objection that non-existent Vulcan possesses its properties in a different sense than existent objects. But when we defined the concept of Vulcan, we wanted it to denote an object that literally possesses its definitional properties. So non-existent Vulcan understood in that way cannot be claimed to be a referent of our description.
5. If we admit non-existent objects, all laws of nature become literally false. The statement "All metals conduct electricity" is falsified by non-existent metals that do not conduct electricity. One possible solution: to limit the quantifiers in the laws of nature to existent objects only. But in that case we lose an ability to distinguish between laws and accidental generalizations.
Required reading:
Brian Garrett, "Non-existent objects", in What is this thing called metaphysics?, pp.27-31.
Thursday, October 8, 2009
Introductory remarks
Philosophy is traditionally divided into metaphysics (ontology), epistemology (the study of knowledge) and axiology the study of values (ethics + aesthetics). Metaphysics is variously characterized as a study of reality itself, of what exists, of being. It is the study of reality as opposed to appearances.
The word “metaphysics” derives from the Greek “ta meta ta physica” (literally "what comes after physics"), which was the title of one of Aristotle’s treatises that followed the one devoted to physics. Aristotle never used this term. However, he used the term “first philosophy” and he explained it twofold.
First: as a knowledge of first causes. The central notion of Aristotle's first philosophy was God, or the Unmoved Mover.
Second: as the study of ‘being qua being” (being as such). This is a universal science that considers all the objects that there are. It also deals with very general notions that apply to all beings: identity, similarity, difference. Moreover, it delineates general classes of being, called categories.
Metaphysics is concerned with what is required for something to exist: the nature of things. One of the central questions of metaphysics is: what kinds of things are there? Are there any types of things other than ordinary physical objects? For instance properties: things that physical objects have in common. Do they exist, or is the talk about properties merely metaphorical?
Examples of categories of objects that are analyzed by ontology are: concretes, abstracts, universals, particulars, sets, numbers, events, minds.
An important part of metaphysics is an analysis of the fundamental structure of the material world. The fundamental categories with the help of which we describe the physical world are the categories of time, space, and causation. Philosophy of time forms a central part of modern metaphysics. It considers, among others, the following questions: Is the passing of time real or illusory? Do past and future events exist? Is time an independent substance, or does it depend ontically on the material world? In considering these and other metaphysical questions about the nature of time we should takie into account the advancements of modern science, in particular physics. Especially the development of the special and general theories of relativity had a significant impact on the modern metaphysics of time.
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