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Towards Non-Being by Graham Priest
Graham Priest presents a ground-breaking account of the semantics of intentional language--verbs such as "believes," "fears," "seeks," or "imagines." Towards Non-Being proceeds in terms of objects that may be either existent or non-existent, at worlds that may be either possible or impossible. The book will be of central interest to anyone who is concerned with intentionality in the philosophy of mind or philosophy of language, the metaphysics of existence and identity, the philosophy of fiction, the philosophy of mathematics, or cognitive representation in AI.
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First published January 1, 2005
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April 21, 2012
Intentionality is a hot topic in the philosophy of language, philosophy of mind, and metaphysics. Intentionality is basically "a mental state whereby it is 'directed towards' an object of some kind." (5), though Priest himself admits that it is much more difficult than this. This work is a clever defense of noneism, the view that one can have meaningful intentional states directed towards non-existent (even impossible!) objects. The form of the book is broken down into two parts: the first is a development for the semantics of intentionality, the second is a defense of noneism. Needless to say, the first half is extremely technical, but it is nothing that anyone familiar with first-order logic as well as some modal logic can't work through. In the rest of the review, I will give a brief summary of some of the details (avoiding the technical as much as possible) as well as raise a few objections to the project.
Priest introduces noneism in an intuitive way. We assume that since different things exist in different worlds, the domain D of the set of worlds C will be different for the actual world, @∈C, and any worlds w, w'. This is the anti-noneist position. A noneist takes the domain D to be the same over the set of worlds C. Thus, there are some worlds where something exists and some worlds where that same thing does not. Existence would have to operate as a predicate, E, and therefore a noneist formulation in the first-order language will have to include such a predicate.
Because of this, Priest abandons the typical existential quantifiers because the temptation to include the existence predicate when reading the quantifier is too strong. When typical existential quantifiers are used, they are existentially loaded. To say, 'Something which is x is A', is to say Gx(Ex & Ax) (G is the best html analogue I can think of to represent Priests operator. It is not to be confused with the G operator in temporal logic.). To say 'Everything which is x is A' is to say, Ux(Ex & Ax).
Priest separates himself from other Meinongians by claiming that he does not permit a realm of 'subsistence' in his ontology. All objects which are not spatiotemporally located are non-existent.
It would here be helpful to note that Priest's intentional semantics rely heavily on possible world semantics. He is not afraid to introduce a new realm of worlds to account for certain novelties in intentional attitudes. For example, to deal with certain paradoxes of conditionals, Priest introduces impossible worlds I. Likewise, since intentional verbs are not the type of things which are closed under entailment, Priest introduces open worlds. For some formula tψA, if A is true, then ψ should necessarily obtain as well. An example illustrates this: I desire to eat my cake, if I eat my cake it will no longer exist, I desire that my cake no longer exist. But surely I don't. All I want is to eat it! To correct this, we are asked to accept open worlds O. An open world is a world such that entailment is not closed. So the totality of worlds W includes <O, I, C, P, @>. Just as conditionals behave arbitrarily in impossible worlds, so do all formulas in open worlds.
Following this, Priest uses open worlds to solve the hooded man paradox, talk about intentional predicates, and then discuss the characterization principle (CP). CP is a controversial principle which allows any characteristic, property or conjunction of properties to form some arbitrary object. Thus, for any property or conjunction of properties A(x), we can characterize an object cA and be guaranteed A(cA). From this it seems we can prove the existence of any arbitrary object. So let A(x) be any property and let B be A(x) & Ex (where E is the existence predicate), applying CP to B we get the characterization cB, where A(cB) & E(cB). So Gx(Ax & Ex). This is clearly unacceptable.
Priest believes we can get around this by saying that A(x) is any condition, and thus any condition or set of conditions may hold in some other world, though not in the actual world. So the object A(cA) is true of some world. The conditions will be different as represented by individuals.
Now we may not have some object cA in the actual world, so it will not be the case that @ ||-+ A(cA), but given some agent a and intentional operator φ in the form '... represents... as holding [in the matter at hand]' where 'cA is a rigid designator, we will have @ ||-+ aφA(cA). In this way, we can apparently accept CP in full generality.
He then reviews identity and descriptions and finishes the first part of the book with a sturdy intentional semantics.
The second half is certainly the more philosophical. It is able to piggy-back off of the semantics established in the previous half. Here, Priest overviews Quine's objections to Meinongianism and claims that they are all unfounded. He reviews fictional objects, abstract objects and paradoxes of multiple denotation.
It is here where the bulk of my criticism comes in. I will permit that Priest wants a well founded and established first-order language of intentionality before he moves onto the more philosophical issues concerning noneism, but I'm not sure that this is the best approach. First, because noneism is so deeply dependent upon world semantics, we should be sure that talk about worlds truly captures our intentional intuitions. It is not my belief that it does. Intentionality is first a phenomenological character. It is the minds direction towards an object or state of affairs. As such, a proper account should begin with the phenomenological character of intentionality.
First, the claim that intentional verbs are open to entailment has too many counter-examples to seem as obviously true as Priest maintains. If I promise you a penny and you are using that penny to throw off of the Empire State Building, I am not necessarily promising you a penny to throw off of the Empire State Building. Hence, it is open to entailment. But if I promise to give you a penny now and I promise that whatever object I now give you is such that you may throw it off of the Empire State Building, then I promise to give you a penny that you may throw off of the Empire State Building. This argument is closed under entailment. So using Priest's formula where P is the promise, Q is a penny, G is to give, y is you, and T is 'throw off the Empire State Building:
aPGx(Qx & aGx)
aPUx(aGx → yTx)
∴ aPGx(Qx & aGx & yTx)
The same can be said of intentional states involving belief and knowledge. Here, it may be best to analyze intentionality as direction of fit like Searle. It is my belief that Searle's taxonomy of direction of fit and direction of causation illustrate just when intentional states are open to entailment and when they are closed. There is no appeal to open worlds, and I think we should take this to be a virtue.
Given Priest's format, he approaches the philosophical issues using the semantics which are founded on world-talk. So, for example, when arguing about fictional objects one can ask "Are non-existent objects in fictions created by their authors?"
In one sense, this is absurd. To create seems to imply to bring into existence, but then we would not be talking about a non-existent object. Even saying that if the author didn't exist, the fictional object wouldn't either. But in those other worlds, say where Conan Doyle never wrote Sherlock Holmes, Holmes wouldn't exist just as Holmes doesn't exist in the actual world. This may be true, so perhaps we should drop the existential assumption and ask, if Doyle never wrote about Sherlock Holmes would something be Holmes (Gx x=h)? The answer again would be yes, Holmes is self-identical in such a world just as he is in the actual world.
Priest claims that Doyle did not determine Holmes's status, but instead was the first to imagine him, or have a certain intentional relation to his characterization. When Doyle imagined him, he had a wide array of possible world referents, though the imagined Holmes by Doyle was one in particular. As the stories get more intricate, more characterizations narrow the set of worlds, but Holmes is not then a different referent after each characterization.
But I do not share Priest's intuition on this at all, nor I suppose do most folk. It seems at first plainly false that Doyle did not create Sherlock Holmes. When one imagines a fictional object, one brings into existence an intentional state towards a particular characterization. This would effectively bring about an incomplete world which becomes more and more complete. Others who imagine a slightly more specific (or characterized) world which contradicts that of some other will be creating a further non-existent entity not identical to, but related to the original non-existent object.
Maybe one can set up a distinction between those non-existent objects which have intentionality by an agent towards them and those that do not. Those that have such intentionality are necessarily self-identical and characterized. Perhaps those that aren't are non-existent in a way that they are literally empty and there is no distinction between them. Of course, this may be the very type of distinction Priest is denying in his noneist framework, but it is my sense that that is just too bad for his framework.
The picture above legitimizes some of Priest and Quine's intuitions. Quine wonders how such non-existent objects can be identical, if they can be, and if so, when they are. As long as an incomplete characterization exists, an answer of identity between the possible bald man and the possible fat man in the doorway will have no determinate answer. It also seems to be more economical than having so many possible worlds where one discovers, or refers to one of the objects when one imagines them.
A further issue which may illuminate this more: if I tell a fiction about some fictional object with particular characteristics and someone in the actual world satisfies all of these, the fiction must be about them since it is (unbeknownst to me) the actual world which I have an intentional attitude towards. But this isn't true since it was intended as fiction. As an author, I would deny this and claim that it is simply a coincidence. Priest asserts that what would be going on when one represents a fiction is that they represent that thing such that it is not actual. So they have an intentional attitude Φ' where it is non-actual rather that Φ which represents the object as actual. So aΦ'A, a represents A as holding non-actually.
But isn't this just further evidence against fictions being possible worlds? Couldn't we say that when Kafka wrote The Metamorphoses, he intendeds that Gregor Samsa be taken as represented non-actually? To Priest, there is a possible world with a Gregor Samsa which fits Kafka's characterization perfectly, but wouldn't Kafka just say that this is just a coincidence and that he intended it to be a fiction? Wouldn't that come to mean that we intend something very different from a possible world when we conceive of a fiction? And if so, what is this? Wouldn't all such object have the same status then? So any intentional state towards some non-actual fictional object will be of the form aΦ'A?
Another issue involves abstract objects which are supposed to be further objects, like fictional ones, which do not exist. Mathematical objects and worlds seem to be just those things. Meinong gave these objects a special status (subsistence) but Priest thinks that since they do not exist spatiotemporally, they are just as non-existent as fictional objects. There is a difference for the noneist between fictional and abstract objects. A fictional object could exist in some possible world, but abstract objects don't seem to be the type that could have existed actually. Priest suggests that if an abstract object existed, it could not causally interact with us, whereas if a fictional object existed, it could causally interact with us.
Priest claims that worlds are not necessarily abstract objects. One can causally interact with them and their properties had they existed. But wouldn't it be better and more intuitive to say that had the actual world been some other possible way, one could causally interact with it? If we understand our causal relationship with these worlds in this way, don't we simply interact with fictional objects and not the world that houses them? Isn't the 'world' such that one could never have a causal interaction with it? There is something paradoxical about talking about worlds in the manner Priest wishes us to as well. If we say, "Had the possible world been actual, we could causally interact with it." But if it were actual, this would be the actual world and all other woulds would be possible, impossible or open. Thus, one can only causally interact with the actual world and never any other world. It makes more sense to say that the objects of those worlds could be actual in the actual world. Thus, we can say that they are fictional and not abstract. But one cannot do this with worlds.
Priest then goes over five objections to his noneist account so far. One of which is that noneism is just platonism in disguise. The idea goes, a noneist claims that non-existent objects are objects, just ones which do not exist, and existent objects are just objects that do exist, while the platonist claims that abstract objects exist and actual objects are just concrete objects. But what is the difference between these? It seems to only be a difference of terminology. Priest thinks that since this view assumes platonism and noneism are symmetrical, there is no reason to claim that platonists aren't just noneists in disguise. He contends such an objection is simply question begging.
But next he draws a distinction between a platonist and a noneist. A noneist accepts CP in an unrestricted form, while a platonist does not necessarily do so. But this difference is just the sort of thing which establishes an asymmetry allowing noneism to be reduced to a form of platonism without platonism being reduced to noneism. A platonist can, but need not, accept CP in its unrestricted form. So the objection still holds since Noneism can be classified as a sub-class of platonism.
Priest mentions a paraconsistent plentitudinous platonist who appears to hold a view very much like a noneist one. Such a platonist, Priest contends, claims that these objects exist at all worlds (some transcendent platonic heaven) where a noneist claims that these non-existent objects are at various possible worlds. But is there a strict difference between these views? I do not believe there is. A noneist claims that these objects are at some worlds from any world. Thus, they are non-existent objects from the perspective of all worlds. If there isn't a legitimate difference, Priest has not offered a reason to think otherwise.
There are a few other issues I have with his noneism, but I will not go into them for the sake of space. As it stands, the second half of the book leaves much to be desired. That being said, the first half seems entirely solid. But how can this be? My contention is that his semantics in a worlds framework is sound, but that the philosophical difficulties which abound his noneism result directly from these semantics. I think this should be a good indication that world semantics just do not capture intentionality as it is phenomenologically. Before we begin to discuss the objects we are directed towards, we must deal with the mental.
Although I find the general approach contentious, there are certainly many philosophical gems here, and it should not be overlooked by anyone who is interested in intentionality and the metaphysics of non-being.
Priest introduces noneism in an intuitive way. We assume that since different things exist in different worlds, the domain D of the set of worlds C will be different for the actual world, @∈C, and any worlds w, w'. This is the anti-noneist position. A noneist takes the domain D to be the same over the set of worlds C. Thus, there are some worlds where something exists and some worlds where that same thing does not. Existence would have to operate as a predicate, E, and therefore a noneist formulation in the first-order language will have to include such a predicate.
Because of this, Priest abandons the typical existential quantifiers because the temptation to include the existence predicate when reading the quantifier is too strong. When typical existential quantifiers are used, they are existentially loaded. To say, 'Something which is x is A', is to say Gx(Ex & Ax) (G is the best html analogue I can think of to represent Priests operator. It is not to be confused with the G operator in temporal logic.). To say 'Everything which is x is A' is to say, Ux(Ex & Ax).
Priest separates himself from other Meinongians by claiming that he does not permit a realm of 'subsistence' in his ontology. All objects which are not spatiotemporally located are non-existent.
It would here be helpful to note that Priest's intentional semantics rely heavily on possible world semantics. He is not afraid to introduce a new realm of worlds to account for certain novelties in intentional attitudes. For example, to deal with certain paradoxes of conditionals, Priest introduces impossible worlds I. Likewise, since intentional verbs are not the type of things which are closed under entailment, Priest introduces open worlds. For some formula tψA, if A is true, then ψ should necessarily obtain as well. An example illustrates this: I desire to eat my cake, if I eat my cake it will no longer exist, I desire that my cake no longer exist. But surely I don't. All I want is to eat it! To correct this, we are asked to accept open worlds O. An open world is a world such that entailment is not closed. So the totality of worlds W includes <O, I, C, P, @>. Just as conditionals behave arbitrarily in impossible worlds, so do all formulas in open worlds.
Following this, Priest uses open worlds to solve the hooded man paradox, talk about intentional predicates, and then discuss the characterization principle (CP). CP is a controversial principle which allows any characteristic, property or conjunction of properties to form some arbitrary object. Thus, for any property or conjunction of properties A(x), we can characterize an object cA and be guaranteed A(cA). From this it seems we can prove the existence of any arbitrary object. So let A(x) be any property and let B be A(x) & Ex (where E is the existence predicate), applying CP to B we get the characterization cB, where A(cB) & E(cB). So Gx(Ax & Ex). This is clearly unacceptable.
Priest believes we can get around this by saying that A(x) is any condition, and thus any condition or set of conditions may hold in some other world, though not in the actual world. So the object A(cA) is true of some world. The conditions will be different as represented by individuals.
Now we may not have some object cA in the actual world, so it will not be the case that @ ||-+ A(cA), but given some agent a and intentional operator φ in the form '... represents... as holding [in the matter at hand]' where 'cA is a rigid designator, we will have @ ||-+ aφA(cA). In this way, we can apparently accept CP in full generality.
He then reviews identity and descriptions and finishes the first part of the book with a sturdy intentional semantics.
The second half is certainly the more philosophical. It is able to piggy-back off of the semantics established in the previous half. Here, Priest overviews Quine's objections to Meinongianism and claims that they are all unfounded. He reviews fictional objects, abstract objects and paradoxes of multiple denotation.
It is here where the bulk of my criticism comes in. I will permit that Priest wants a well founded and established first-order language of intentionality before he moves onto the more philosophical issues concerning noneism, but I'm not sure that this is the best approach. First, because noneism is so deeply dependent upon world semantics, we should be sure that talk about worlds truly captures our intentional intuitions. It is not my belief that it does. Intentionality is first a phenomenological character. It is the minds direction towards an object or state of affairs. As such, a proper account should begin with the phenomenological character of intentionality.
First, the claim that intentional verbs are open to entailment has too many counter-examples to seem as obviously true as Priest maintains. If I promise you a penny and you are using that penny to throw off of the Empire State Building, I am not necessarily promising you a penny to throw off of the Empire State Building. Hence, it is open to entailment. But if I promise to give you a penny now and I promise that whatever object I now give you is such that you may throw it off of the Empire State Building, then I promise to give you a penny that you may throw off of the Empire State Building. This argument is closed under entailment. So using Priest's formula where P is the promise, Q is a penny, G is to give, y is you, and T is 'throw off the Empire State Building:
aPGx(Qx & aGx)
aPUx(aGx → yTx)
∴ aPGx(Qx & aGx & yTx)
The same can be said of intentional states involving belief and knowledge. Here, it may be best to analyze intentionality as direction of fit like Searle. It is my belief that Searle's taxonomy of direction of fit and direction of causation illustrate just when intentional states are open to entailment and when they are closed. There is no appeal to open worlds, and I think we should take this to be a virtue.
Given Priest's format, he approaches the philosophical issues using the semantics which are founded on world-talk. So, for example, when arguing about fictional objects one can ask "Are non-existent objects in fictions created by their authors?"
In one sense, this is absurd. To create seems to imply to bring into existence, but then we would not be talking about a non-existent object. Even saying that if the author didn't exist, the fictional object wouldn't either. But in those other worlds, say where Conan Doyle never wrote Sherlock Holmes, Holmes wouldn't exist just as Holmes doesn't exist in the actual world. This may be true, so perhaps we should drop the existential assumption and ask, if Doyle never wrote about Sherlock Holmes would something be Holmes (Gx x=h)? The answer again would be yes, Holmes is self-identical in such a world just as he is in the actual world.
Priest claims that Doyle did not determine Holmes's status, but instead was the first to imagine him, or have a certain intentional relation to his characterization. When Doyle imagined him, he had a wide array of possible world referents, though the imagined Holmes by Doyle was one in particular. As the stories get more intricate, more characterizations narrow the set of worlds, but Holmes is not then a different referent after each characterization.
But I do not share Priest's intuition on this at all, nor I suppose do most folk. It seems at first plainly false that Doyle did not create Sherlock Holmes. When one imagines a fictional object, one brings into existence an intentional state towards a particular characterization. This would effectively bring about an incomplete world which becomes more and more complete. Others who imagine a slightly more specific (or characterized) world which contradicts that of some other will be creating a further non-existent entity not identical to, but related to the original non-existent object.
Maybe one can set up a distinction between those non-existent objects which have intentionality by an agent towards them and those that do not. Those that have such intentionality are necessarily self-identical and characterized. Perhaps those that aren't are non-existent in a way that they are literally empty and there is no distinction between them. Of course, this may be the very type of distinction Priest is denying in his noneist framework, but it is my sense that that is just too bad for his framework.
The picture above legitimizes some of Priest and Quine's intuitions. Quine wonders how such non-existent objects can be identical, if they can be, and if so, when they are. As long as an incomplete characterization exists, an answer of identity between the possible bald man and the possible fat man in the doorway will have no determinate answer. It also seems to be more economical than having so many possible worlds where one discovers, or refers to one of the objects when one imagines them.
A further issue which may illuminate this more: if I tell a fiction about some fictional object with particular characteristics and someone in the actual world satisfies all of these, the fiction must be about them since it is (unbeknownst to me) the actual world which I have an intentional attitude towards. But this isn't true since it was intended as fiction. As an author, I would deny this and claim that it is simply a coincidence. Priest asserts that what would be going on when one represents a fiction is that they represent that thing such that it is not actual. So they have an intentional attitude Φ' where it is non-actual rather that Φ which represents the object as actual. So aΦ'A, a represents A as holding non-actually.
But isn't this just further evidence against fictions being possible worlds? Couldn't we say that when Kafka wrote The Metamorphoses, he intendeds that Gregor Samsa be taken as represented non-actually? To Priest, there is a possible world with a Gregor Samsa which fits Kafka's characterization perfectly, but wouldn't Kafka just say that this is just a coincidence and that he intended it to be a fiction? Wouldn't that come to mean that we intend something very different from a possible world when we conceive of a fiction? And if so, what is this? Wouldn't all such object have the same status then? So any intentional state towards some non-actual fictional object will be of the form aΦ'A?
Another issue involves abstract objects which are supposed to be further objects, like fictional ones, which do not exist. Mathematical objects and worlds seem to be just those things. Meinong gave these objects a special status (subsistence) but Priest thinks that since they do not exist spatiotemporally, they are just as non-existent as fictional objects. There is a difference for the noneist between fictional and abstract objects. A fictional object could exist in some possible world, but abstract objects don't seem to be the type that could have existed actually. Priest suggests that if an abstract object existed, it could not causally interact with us, whereas if a fictional object existed, it could causally interact with us.
Priest claims that worlds are not necessarily abstract objects. One can causally interact with them and their properties had they existed. But wouldn't it be better and more intuitive to say that had the actual world been some other possible way, one could causally interact with it? If we understand our causal relationship with these worlds in this way, don't we simply interact with fictional objects and not the world that houses them? Isn't the 'world' such that one could never have a causal interaction with it? There is something paradoxical about talking about worlds in the manner Priest wishes us to as well. If we say, "Had the possible world been actual, we could causally interact with it." But if it were actual, this would be the actual world and all other woulds would be possible, impossible or open. Thus, one can only causally interact with the actual world and never any other world. It makes more sense to say that the objects of those worlds could be actual in the actual world. Thus, we can say that they are fictional and not abstract. But one cannot do this with worlds.
Priest then goes over five objections to his noneist account so far. One of which is that noneism is just platonism in disguise. The idea goes, a noneist claims that non-existent objects are objects, just ones which do not exist, and existent objects are just objects that do exist, while the platonist claims that abstract objects exist and actual objects are just concrete objects. But what is the difference between these? It seems to only be a difference of terminology. Priest thinks that since this view assumes platonism and noneism are symmetrical, there is no reason to claim that platonists aren't just noneists in disguise. He contends such an objection is simply question begging.
But next he draws a distinction between a platonist and a noneist. A noneist accepts CP in an unrestricted form, while a platonist does not necessarily do so. But this difference is just the sort of thing which establishes an asymmetry allowing noneism to be reduced to a form of platonism without platonism being reduced to noneism. A platonist can, but need not, accept CP in its unrestricted form. So the objection still holds since Noneism can be classified as a sub-class of platonism.
Priest mentions a paraconsistent plentitudinous platonist who appears to hold a view very much like a noneist one. Such a platonist, Priest contends, claims that these objects exist at all worlds (some transcendent platonic heaven) where a noneist claims that these non-existent objects are at various possible worlds. But is there a strict difference between these views? I do not believe there is. A noneist claims that these objects are at some worlds from any world. Thus, they are non-existent objects from the perspective of all worlds. If there isn't a legitimate difference, Priest has not offered a reason to think otherwise.
There are a few other issues I have with his noneism, but I will not go into them for the sake of space. As it stands, the second half of the book leaves much to be desired. That being said, the first half seems entirely solid. But how can this be? My contention is that his semantics in a worlds framework is sound, but that the philosophical difficulties which abound his noneism result directly from these semantics. I think this should be a good indication that world semantics just do not capture intentionality as it is phenomenologically. Before we begin to discuss the objects we are directed towards, we must deal with the mental.
Although I find the general approach contentious, there are certainly many philosophical gems here, and it should not be overlooked by anyone who is interested in intentionality and the metaphysics of non-being.
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