Non-Existence: The Nuclear Option

1 Introduction

Noneism is the view that some things don’t exist. Since Quine’s essay “On What There Is,” the orthodox view concerning it in Anglo-philosophy has been as follows. Noneism is a view advocated by the Austrian philosopher Alexius Meinong (hence the usual name: Meinongianism). The view is highly counterintuitive and an historical aberration. After briefly flirting with the view, Russell showed how absurd it was, and it was completely demolished by Quine in his essay.

Except for the first sentence, the view is completely wrong on every point. That some things do not exist is a highly common-sense view – Sherlock Holmes, Atlantis, God (any one you don’t believe in), a constant motion machine, Newtonian space/time. Some version of the view has been standard in the history of Western logic. Russell never had Meinong’s view. He held that all objects have some form of being, existence or subsistence. Meinong held that some objects have no such form: They have Nichtsein. Finally, Russell and Quine’s arguments against the view are lame.^[1]

Perhaps unsurprisingly, then, we appear to be seeing the pendulum swing back from the Russell/Quine meontophobic aberration. And the Neo-noneists who have been pushing the pendulum have the advantage of being able to use all the techniques of contemporary logic – which they do.

There is really only one serious philosophical issue confronting noneism and that concerns the Characterisation Principle (CP). Suppose that you characterise an object in a certain way. Without the loss of generality, we can suppose that this is done with an indefinite description of some kind. I will use ε as an indefinite description operator. Then the naive version of the principle is to the effect that the object so characterised has its characterising properties:^[2]

• A x ( ε x A )

There are different ways in which contemporary noneists have addressed the problems.^[3] This essay is about one of them, advocated by Terry Parsons (1933–2017) and Richard Routley^[4] (1935–1996) – the two earliest figures in the “noneist revival.”^[5] The Parsons/Routley strategy with respect to the CP is to the effect that there is a distinction between two kinds of predicates/properties. Parsons calls them nuclear and non-nuclear.^[6] Routley calls them characterising and non-characterising. The claim is then that the CP holds when and only when the A in question contains only nuclear/characterising predicates. This is not my view of the correct account of the CP, and towards the end of the essay, I shall indicate what I take that to be. But this essay is about the Parsons/Routley view and its shortcomings.

A word on notation. In what follows, if will use S as the particular quantifier, some A is its mate, the universal quantifier, all. ∃ and ∀ are the existentially loaded quantifiers, some existent and all existent. So if E is the monadic existence predicate, ∃ x A is S x ( E x ∧ A ) , and ∀ x A is A x ( E x → A ) .

2 Some History

This is not the place to go into the details of the history of views about non-existence.^[7] But for reasons that will become clear later, I want to rehearse a little of it. In Medieval logic, noneism was completely standard due to the theory of ampliation. The notion of ampliation was articulated in slightly different ways by different people, though these differences do not matter here. At its core, the view was as follows. (It is nicely explained in Parsons’ excellent 2014 Articulating Medieval Logic.)

Consider the I form of Aristotelian syllogistic: some Ss are Ps. (Similar comments apply to the others.) According to standard theories of supposition, “some S s are P s” is true iff:

• a is a P , or b is a P , or …

• a will be [was] a P , or b will be [was] a P , or …

It might be thought that we may simply identify existence simpliciter with existence at some time, as the medievals did not. But they go further. They held, applying the notion of ampliation again, that “some S s can be P s” is true iff:

• a can be a P , or b can be a P , or …

A term put before the word ‘can’ … is ampliated to stand for possible things even if they do not and did not exist. Therefore the proposition ‘A golden mountain can be as large as Mont Ventoux’ is true.

William of Sherwood and other thirteenth-century figures speak quite unguardedly of terms ampliated to things that do not exist.^[9] And Paul of Venice states categorically:^[10]

The absence of the signification of a term from reality does not prevent the term’s suppositing for it.

The view was standardly extended to allow some verbs, notably intentional ones, an even broader ampliation: to objects of imagination. Thus, Marsilius of Inghen writes:^[11]

Ampliation is the supposition of a term … for its significates which are or were, for those which are or will be, for those which are or can be, or for those which are or can be imagined.

And at least for some logicians, what can be imagined includes impossibilia too. Not all, though. Here is Buridan on the matter:^[12]

Every term which supposits, supposits for that which is or can be or will be or has been ; but … it is impossible that a chimera can be, or can have been or can come to be … [Hence] ‘A chimera is thinkable’ is false.

Note that a chimera is a standard Medieval example of an impossible object. It is not simply something which has parts of a lion, a goat, and a serpent, but something which has the essence of a lion, goat, and serpent, too. Since (according to Aristotle) a (primary) substance can have only one essence, this is impossible.

Some logicians, however, thought otherwise. Here is Paul of Venice again:^[13]

Although the significatum of the term ‘chimera’ does not and could not exist in reality, still the term ‘chimera’ supposits for something in the proposition ‘A chimera is thought of’, since it supposits for a chimera.

That disagreement notwithstanding, though, Medieval logicians were clearly noneists.

3 Parsons: Nuclear Properties

Let us now turn to Parson’s views concerning non-existent objects and his treatment of the CP. Let us start by being clear that no one can endorse the CP in full generality. It leads to triviality in a two-line argument. Let A be any statement. Consider the description ε x ( x = x ∧ A ) (or even just ε x A , if one does not care about vacuous quantification). Call this term t . Then the CP gives t = t ∧ A , from which A follows. A standard view (to be found in Hilbert’s use of the ε -operator) is to restrict the CP to those conditions which are satisfied by something existent (or in Russell’s case, a unique such thing):

• ∃ x A → A x ( ε x A )

Now to Parsons’ view. This was first indicated in a paper of 1974, “A Prolegomenon to Meinongian Semantics,” and then spelled out at length in his 1980 book Nonexistent Objects. (Page references to his work in what follows are to this.) Rather amazingly, given that much of Articulating Medieval Logic is concerned with using contemporary logical tools to perform the articulation, I find it striking that his approach to noneism does not so much as rate a mention in his chapter on ampliation. In fact, there is no mention of noneism, Meinong, or any contemporary noneist in the book.

Anyway, as already said, his treatment of the CP distinguishes between nuclear properties and non-nuclear properties. Let Σ be any set of nuclear properties, then there is a unique object, σ , such that the nuclear properties of σ are exactly the members of Σ (p. 19). If Σ = { P i : i ∈ I } , let us write σ as ε x Σ . (More accurately, it would be ε x A X N ( X N x ↔ X N ∈ Σ ) , where the second-order quantifiers range over nuclear properties.) Then if P is a nuclear property, P ε x Σ ↔ P ∈ Σ . This breaks the triviality argument, since P ε x Σ can be established only for predicates in Σ , which are nuclear.

The first and most obvious question about this solution is “What, exactly, are the nuclear properties?” And the first and most obvious problem for the solution is that Parsons does not answer the question. Indeed, he indicates that one may not be able to do so.^[15] He gives examples of each kind (p. 23). Nuclear: is blue, is tall, was kicked by Socrates. Extranuclear: exists, is possible, is worshipped by someone, is complete. But a bunch of examples doth not a theory make. He says (p. 24):

I find that I have … an intuitive ability [to distinguish between nuclear and non-nuclear properties], and that others pick it up quite readily.

But a gut-feeling gets us only so far and is likely to be no guide in any complex case, of which there are plenty, since every open sentence of a higher order modal logic is in play. Parsons himself points out (p. 24) that the property F such that:

• There is a set X of nuclear properties, not containing F , such that every object which has every member of X lacks F .

• There is a set X of nuclear properties such that every object which has every member of X has F .

My policy so far has been to classify a predicate as nuclear whenever it can be consistently classified in that way.

That policy, of course, makes the distinction entirely ad hoc, as well as undecidable.

For a decent theory, one needs a principled distinction between nuclear and non-nuclear properties. Without such a thing, the solution to the problem of the CP is, to put it kindly, only half done.^[16]

4 Intentionality and Relations

However, this is only the start of the problems. Another problem is as follows. A major application of noneism concerns intentional relations. If I characterise an object in some way, it would appear that I can bear such a relation to it. I may think of it, wonder whether it exists, admire it, be scared of it. And this is so, however I characterise it. It may exist, or it may not; it may be possible, or it may not; I may know which of these is the case, or I may not; and I may be mistaken about this matter, or I may not. In particular, the object may be characterised with non-nuclear predicates. For example, the characterisation might be ε x ( x is the first child of Jesus Christ and x exists). If Jesus had no children, this characterisation fails to refer to any object; so I cannot bear an intentional relation to it.

Parsons accepts that his account of non-existent objects cannot help with the issue of how to understand intentional relations apparently directed to objects (p. 48), and admits that he does not know how to address it. He suggests that in such contexts some kind of Fregean solution might work (p. 47). The term in question refers to its sense, not its reference. But this will not do, since we quantify into such contexts. We can say correctly:

• I am thinking of Russell and he was a great philosopher. So I am thinking of someone who was a great philosopher.

A second problem concerns nuclear relations. Consider married. Let e be Elizabeth Windsor, and consider ε x ( x married e ). Write this term as p . Then the CP gives: p married e . So Elizabeth was married – which indeed she was. p was Philip Mountbatten. Now let b be Eliza von Brabant, and consider ε x ( x married b ). Write this term as l . Then the CP gives: l married b . So Eliza was married. Perhaps that’s okay. l was Lohengrin.

This does assume that things said to be true in fiction (in this case Wagner’s Lohengrin) may be literally true – and not just true-in-the-fiction – as Parsons does.^[17] And such accounts of fiction give rise to all sorts of problems. In Doyle’s fictions the detective Sherlock Holmes lived in 221B Baker St. But in reality no detective ever lived in 221B Baker St. So we appear to have a contradiction here. Moreover, fictions can be internally inconsistent. In Sylvan’s Box,^[18] Nick (Griffin) finds a box which was empty and had something in it. So the box was both empty and not empty.

I shall not pursue this matter further here. A decent discussion of Parson’s account of fiction, and the notion of fictional truth in general, would take us off at a tangent. The most serious problem about relations arises when they relate an existent object to a non-existent object. Let f be Pope Francis, and let ε x ( x married f ). Write this term as Mrs. Bergoglio, m . Then the CP gives: m married f . So Francis was married. That is, of course, false. Or consider ε x ( x is a town such that x is south of Sydney and Brisbane is south of x ). Call this Routleyville. Then by the CP, Routleyville is south of Sydney and Brisbane is south of Routleyville. So by the transitivity of is south of, Brisbane is south of Sydney (which it is not).

Parson’s solution is to deploy the notion of plugging-up a relation (p. 59 f). Given any term, t , relation x R y can be “plugged up” in two different ways, one for each argument, giving the monadic predicates, x [ R t ] , of x , and [ t R ] y , of y . t 1 [ R t 2 ] and [ t 1 R ] t 2 are equivalent if both t 1 and t 2 exist; and t 1 R t 2 means that [ t 1 R ] t 2 ∧ t 1 [ R t 2 ] (p. 60).

Then it is true that Mrs Bergoglio [married Francis], but not that [Mrs Bergoglio married] Francis. So one cannot infer that Francis was married. Similarly, Routleyville [is south of Sydney], and [Brisbane is South of] Routleyville. But the other of each pair does not hold, and we do not have that the plain south of relation obtains. So transitivity cannot be applied.

An obvious problem with Parsons’ strategy is that it diagnoses a three-way ambiguity in natural language concerning statements of the form “ a married (is south of) b ,” for which there is no independent linguistic evidence.^[19]

But worse, chunking a relation into two monadic predicates destroys its integrity. A relation is relational, and as is well known, a binary relation, x R y , cannot be reduced to two monadic predicates, P 1 x ∧ P 2 y . There are no non-relational statements about the length of x and the length of y , the conjunction of which is logically equivalent to “ x is longer than y .”^[20]

The failure of reducing a binary predicate to two monadic predicates is, in fact, noted by Parsons himself (p. 168 f). Let t be (Terry) Parsons (who was of average height); let h be Hercule Poirot (who was short); and let T be is taller than. Then it would appear that t T h . But it is not the case that t [ T h ] since an existent object cannot have a nuclear property that involves a non-existent object. And it is not the case that [ t T ] h , since the Agatha Christie stories say nothing about Parsons.

5 Routley and the CP

Let us now move on to Routley. The earliest published work by him on the issue is a paper of 1966, “Some Things do not Exist.” He wrote a long paper “Exploring Meinong’s Jungle” in 1967, which was circulated but never appeared in print.^[21] The material from the paper was finally incorporated as part of chapter 1 of Routley’s mammoth Exploring Meinong’s Jungle and Beyond, which appeared in the same year as Parsons’ Nonexistent Objects. This book was virtually unobtainable for many years, but has now appeared in a four-volume edition.^[22] The original chapter 1 comprises volume 1, Exploring Meinong’s Jungle and Beyond.^[23]

Parsons clearly had a copy of the 1967 paper, since he acknowledges it in the introduction to Nonexistent Objects (p. xii). For his part, Routley had a copy of the manuscript of Parsons’ book, since it is referenced as a 1978 typescript in Exploring Meinong’s Jungle and Beyond (p. 492) and referred to several times in the book. Whether Terry and Richard ever met to discuss their views, I do not know. But each was clearly well aware of, and influenced by, the work of the other.

Routley’s version of noneism is simpler and more straightforward than Parsons’. He takes every term to refer to an object, either existent or non-existent. And most straightforwardly, the logic can be classical logic, where the quantifiers are simply not existentially loaded. However, Routley’s treatment of the CP is essentially the same as Parsons’.^[24] In particular, the CP holds only for those A ( x ) which are characterising. Unsurprisingly, it has similar problems.^[25]

First, Routley is able to define what a characterising predicate is, no more than Parsons. He discusses the matter, but in the end is able to do no better than give a list of examples, similar to those of Parsons, though more extensive. Characterising predicates include (p. 346 ff):

• simple descriptive predicates (e.g., is dry, is dusty, is a triangle, is a horse, runs, sits)

• predicate negations, conjunctions, and disjunctions of these

• descriptive relational predicates, R ( x , a 1 , … , a n ) , where the x place is extensional and the a s are names or descriptions which contain no non-characterising predicates.

• ontic status predicates (e.g., exists, is possible),

• evaluative predicates (e.g., is good, is beautiful),

• theoretical predicates (e.g., is complete),

• logical predicates (e.g., =, ∈ ),

• intentional predicates (e.g., is thought of, is believed in).

Routley’s account of the distinction is, then, no more theoretically adequate than Parsons’.

6 Intentionality and Relations Again

Let us turn to the other problems that Parsons’ account faces. The first of these was that agents can bear intentional relations to an object, however characterised. Routley is better off than Parsons here, since every characterisation, ε x A , refers to an object. But there is still a problem. Because of the failure of the CP in general, the object may not have the properties it is characterised as having. But as Routley is well aware, the object must have the properties it is characterised as having in some sense, or we would not know what we are talking about.^[26] So suppose that A x is “ x is Atlantis” and “Ex is x exists.” Then suppose that I am thinking of (or seeking, or imagining) ε x ( A x ∧ E x ) . It would appear that I am thinking of (or seeking, or imagining) something that is indeed an existent Atlantis.

As far as I have been able to determine, the problem is not explicitly addressed in Exploring Meinong’s Jungle. There is a move that could be made, however. Routley countenances the predicate modifier s , to be read as “presents itself as” (p. 352 ff).^[27] So it could be that when I am thinking of ε x ( A x ∧ E x ) , I am really thinking of ε x ( A x ∧ s ( E ) x ) . So the object of my thought does not exist, but it presents itself to me as existing. But that cannot be right. Various archaeologists and explorers have searched for an Atlantis they believed to exist, ε x ( A x ∧ E x ) . But they were not seeking something that merely presented itself as existing – which they might have found in a hologram. So they could not have been seeking ε x ( A x ∧ s ( E ) x ) . That is a quite different object of intention. Perhaps it was for this reason that, as Griffin puts it,^[28] Routley had nothing to do with the approach.

In the end, then, the problem is just as much one for Routley, as it is for Parsons.

The second of Parsons’ problems concerned the vexed issue of relations. Routley’s discussion of the matter (p. 348 ff.) is tangled and somewhat inconclusive.^[29] He considers several responses to the problem of existent objects being married to non-existent ones, but in the end says that the most robust solution is to reject the “passive transformation.”^[30] It is true, for example, that Mrs Bergoglio married Francis, but not true that Francis was married to Mrs Bergoglio, and so that Francis was married.^[31] But this will not do, since the passive transformation is irrelevant.^[32] We can just consider ε x (Francis married x ). Call this Mrs Bergoglio II. Then by the CP, Francis married Mrs Bergoglio II, and so was married.^[33]

In any case, this move will not address the problem with the transitivity of is south of. Routley does not discuss this problem explicitly,^[34] though in §21 he draws a distinction between entire and reduced relations as follows (p. 350):

Entire relations are those which to put it roughly, satisfy the full range of classically expected logical relations and inferences. For example, if due south of is entire then it will be (at least in all ordinary terrestrial contexts) transitive, asymmetric and irreflexive, it will permit passive conversions, and also replacement of each relatum by extensional identicals. By contrast, reduced relations satisfy only a reduced class of these features.

Perhaps this suggests that is south of is a reduced relation, and so the inference from transitivity fails. However, this is not a solution for the problem, just a name for it. It says no more than that transitivity fails. It does not provide an explanation of why it does. We are left totally in the dark as to why the relation is reduced, how to reason with reduced relations, when one can appeal to standard properties, etc.^[35]

Routley, then, gives a satisfactory solution to the relational problem no more than does Parsons.

7 Properties of Non-existent Objects

Before I conclude the story, let us return to Medieval logic. According to the Medievals, what properties does a non-existent object have?

If an object exists, its properties are, in principle, straightforward. The Pope (Francis) has the property living in Rome, being able to speak Latin, etc. But what of non-existent objects? Take an object that does not exist, but will (let us suppose), the Antichrist. According to the Bible, the Antichrist is a liar, and denies that Jesus is Christ.^[36] But the sentence “The Antichrist is a liar” is (currently) false, since the subject of the sentence fails to refer to an existent object, something it would have to do to satisfy the predicate “is a liar.” But it will be true in the future, when the Antichrist exists. The Antichrist, then, has the properties we take him(?) to have at a future time. Similarly, Socrates does not have the property of living in Athens. (No searching in Athens would find him there.) But in 400 BCE, he did have that property.

What of a merely possible object, such as my third child? It is not difficult to see what the analogue of the temporal view is, if one is entitled to invoke possible worlds. These are not standard fare in Medieval logic – or rather, it was fairly standard to reduce necessity to omni-temporality. However, it certainly appears that, drawing on theological considerations, Duns Scotus made a clean break with this tradition, and gave an account of possibility in what we might now think of as possible worlds. As one commentator says of Scotus’ modal theory:^[37]

Its starting point is the domain of possibility, considered as consisting of all possible individuals, their possible properties, and their mutual relations. Because the possible properties of individuals can be mutually exclusive, and because possibilities are treated as something which are compatible with existence, individuals must be considered simultaneously as members of several different combinations of possibilities. The domain of all possible states of affairs it therefore structured into “possible worlds” on the basis of compatibility relations. If possible beings, which occur in several possible states of affairs at the same time, also belong to the actual world, they have the predicate of existence.

And at least implicitly given such an account, an object possibly has a property iff it has it at some “possible world.”

This matter aside, in contemporary possible-world semantics, there is one actual world, and there are scenarios that realise non-actual states of affairs, for example, one in which the United States lost the war of Independence and is still a British colony. The mathematics of such things is now well understood, though their metaphysical status is still a matter of dispute.^[38] Provided that we may invoke such things, they can play exactly the same role with respect to merely possible objects that the past and the future play with respect to past and future objects. Thus, Vulcan does not actually have the property of being the closest planet to the Sun, but it does in those worlds where the nineteenth century astronomers got it right. Or consider my third child. Call them Dana. Dana does not actually have the property of being my third child. No searching in the registry of births and deaths of any country would find them. However, Dana does have the property of being my third child in a world where I had a relationship which engendered my first two children, and then resulted in Dana as well. To give another example: Sherlock Holmes does not have the property of living at 221B Baker St in this world, but he does have that property in the worlds which realise the Conan Doyle stories.

What of impossible objects, of the kind that, as we saw, at least some Medieval logicians endorsed? Again, I know of no Medieval texts which discuss the matter, but the extrapolation of the view concerning possible objects is obvious. We just have to suppose that the menagerie of worlds comprises both possible and impossible worlds. Impossible worlds are worlds that realise impossible scenarios, such as there being a greatest prime number; and an impossible object is one which has the properties in question only at an impossible world. Impossible worlds are perhaps more exotic in contemporary logic than possible worlds. However, their mathematics is just as straightforward as that of possible worlds,^[39] and whatever the reasons for invoking possible worlds, these hold just as much for impossible worlds.^[40] The view of those Medievals who were prepared to invoke impossible objects can, therefore, be happily accommodated by employing such worlds.

The view that I have described is essentially the account of the CP I endorsed when I became a noneist^[41] (though the Medieval precedents were unknown to me then). Every characterisation, ε x A , refers to an object. If S x A holds at the actual world, then A x ( ε x A ) holds at the actual world. But if it does not hold at the actual world, it holds at some world or other, either possible or impossible. For example, if ε x A is a purely fictitious object, described in the fiction as satisfying A , then it holds in those worlds that realise the fiction. In other words, the CP holds universally, though maybe not at the place (world) you might first have thought of.

And with this, all the problems associated with trying to restrict the CP to nuclear or characterising conditions disappear. There is no need to define characterising predicates, because one does not need to appeal to the notion. Every characterisation refers to an object which has its characterising properties, at least a some world. Francis was married to Mrs Bergoglio – and so married – but not at this world. And it is some other world (maybe an impossible one?) at which Brisbane is south of Routleyville and so Sydney.

8 Routley’s Later Thoughts

This is not the place to pursue my version of noneism any further. I have said what I said partly to connect the view explicitly with Medieval logic and partly to finish the story about Routley.

I don’t think that Routley was ever entirely satisfied with his presentation of noneism in Meinong’s Jungle, and especially with his treatment of the CP. Shortly before he died he published a paper “Re-Exploring Item Theory: Object-Theory Liberalized and Simplified but Comprehensivized,” which, as the name suggests, reviews the views of Meinong’s Jungle and explores ways to improve them.

The main liberalisation is an attempt to make room for a completely unrestricted CP. The strategy invoked appeals to a metaphor – no formal details are given – of a city centre and suburbs (or sometimes a capital region and provinces). The old version of the CP – no new clarification of the notion of a characterising condition is provided – holds at the centre. But every characterisation holds in some suburb. What holds in the city centre is (actually) true; what holds in a suburb may not be.

This is clearly a move in the general direction that I was to take in Towards Non-Being, though I was not aware of the paper until much later. For the city centre, take the actual world; for the suburbs, take other worlds, and one is pretty close. Indeed, Routley does sometimes speak of worlds in this connection. The parallel is not, however, exact. For a start, he still maintains that if a condition is composed of nuclear predicates, the instance of the CP is true. (So, for example, the golden mountain is golden, Pegasus is indeed a winged horse.) Moreover, he holds that suburbs other than the centre may be actual. The thought that there can be a plurality of actual worlds was further explored in Routley’s posthumously published Transcendental Metaphysics.

For my part, I take it that there is only one actual world. For better or for worse, this is it. Also, once one can accommodate a completely unrestricted CP in the way that I have indicated, it is not clear why one should worry about or employ the notion of a nuclear predicate at all. Since Richard died four years before I came up with my approach to the CP, I never had the pleasure of finding out what his response would have been. Maybe there is a close possible world in which he would have agreed. Maybe not.

9 Conclusion

The story I have told is an historical narrative which weaves together many elements, held together by the characters involved: Terry Parsons, Richard Routley/Sylvan, and myself. However, the topic of central concern has been the CP, and the problems of formulating it in terms of nuclear/characterising properties, as do Parsons and Routley.

Clearly, I have been critical of both Parsons and Routley in this regard. This should not be taken to imply that I think ill of their work. I do not. Quite the contrary. These were the two philosophers who had the courage to endorse a view that was widely taken to be absurd and so to lead us back from the benighted days of Russell/Quine orthodoxy. That is a singular and admirable achievement.^[42]