What is existence? What is it for something – the Moon, let us say, for example, or the Eiffel Tower – to actually exist? This is not the kind of question that comes up in specific disciplines (such as planetary astronomy, e.g., or Parisian town planning), but one might have expected it to be exactly the sort of question that falls within the province of philosophy. Yet remarkably, if one looks at the entry on ‘existence’ in the Stanford Encyclopedia of Philosophy (widely respected for its authoritative entries on all the main topics in philosophy), one finds this question conspicuous, like the curious incident of the dog in the night-time, for its absence. One looks in vain to find it addressed.Footnote ¹

True, there is in the article just mentioned much informative discussion of Frege and Russell and quantificational logic, and the idea of existence as a second-order property, so that ‘foxes exist’ comes out as the claim that the concept fox is instantiated and is symbolised using the existential quantifier as ‘∃x (x is a fox)’. And the same article contains in its bibliography a reference to a well-known article by W. V. O. Quine, very much in the tradition of Russell, which states that ‘to be assumed as an entity is, purely and simply, to be reckoned as the value of a variable’.Footnote ² But invoking formal logic does nothing to distinguish things that really, actually exist from those that do not (or to distinguish concepts that are really instantiated from those that are not). Russell was notable for insisting that logic should have a ‘robust sense of reality’, and that logic ‘should no more admit unicorns than zoology does’Footnote ³; yet while philosophers may of course make such a stipulation if they choose, so far as the formal structure of predicate logic goes, there is no reason why the concept unicorn cannot be the value of the variable F in the function Fx just as well as the concept fox. So the celebrated work of Russell and Quine on logic and language seems to get us no nearer to addressing the question of what it is actually to exist.Footnote ⁴

Our Stanford article also lucidly expounds the view of Alexius Meinong that allows non-existent objects (such as the golden mountain) to be genuine subjects of predication, a view that the article then proceeds to criticise (in the tradition of Russell) for its ‘metaphysical abundance’. But the debates about fictional objects, from Meinong and Russell through to Quine and beyond, fascinating though they might be for those interested in the development of twentieth-century philosophical logic, in the end only skirt round our original question. They presuppose that we have a clear intuitive grasp of the difference between really actually existing and being fictitious or imaginary, but they do not attempt to explicate what the difference might actually consist in.

At this point, someone might object that actually existing is such an intuitively clear and obvious notion that no philosophical theory is needed to explicate it. Let us go back to the case of the Eiffel Tower. Off you go to Paris, follow the directions on your map, and there it is, right in front of you. Or alternatively, let us think about what it would be for it not to exist. You might go back to your hotel for the night, return in the morning, and find that the Eiffel Tower is gone. Perhaps a team of engineers, assisted by robots, has worked all night to dismantle it and take the pieces away; but however it happened, it is not there any more.

So perhaps actually existing amounts to a very basic and simple notion, that of being there. This seems to be part of what the philosopher Brian Davies has in mind when he discusses how Thomas Aquinas employs the notion of esse or existence. The notion, argues Davies, is actually a ‘rather straightforward one’:

Unlike the deflationary approaches of Russell and Quine, which treat existence as a matter to be dealt with simply by deploying the appropriate symbolic apparatus, what we now have instead is a way of putting things that has the advantage of focusing on the real world and that directly addresses the difference between existing and not existing.

It is striking that the way this difference is captured by Davies involves the use of demonstrative or indexical terms – words that point (such as ‘there’) or involve reference to the speaker or investigator (‘natural scientists exploring our environment’). Actual existence, in short, seems to be explicated in terms of being there in front of me or being investigated, or investigable, by us. Footnote ⁶ Someone might possibly infer from this that actual existence is a notion that involves an implicit reference not just to an object being there but also to a conscious subject apprehending it.Footnote ⁷ Thus, we find the twentieth-century British philosopher Michael Dummett observing that ‘we can make no clear sense of there being a world that is not apprehended by any mind’.Footnote ⁸

This kind of remark puts us in mind of Bishop Berkeley’s famous thesis that esse est percipi – to exist is to be perceived.Footnote ⁹ But many have felt (plausibly, I think) that Berkeley’s thesis diverges too far from our ordinary common-sense understanding of these matters. For while my perceiving the Eiffel Tower is an obvious consequence of its being there in front of me, its being perceived by me or others does not seem to capture what its actually existing consists in. For if I and all conscious beings were suddenly eliminated, this would surely not mean that the Eiffel Tower ceased to exist. Intuitively, one wants to say that if every conscious being on the planet dropped down dead, the Eiffel Tower would still be there (though, of course, there would be no one to recognise it, describe it, or call it the Eiffel Tower).

But if we say that the Eiffel Tower is still actually there in a world suddenly devoid of perceivers, then (someone might respond) it is still at least capable of being perceived; it still could be perceived were there anyone around to perceive it. This kind of thought may have led John Stuart Mill to define physical objects as ‘permanent possibilities of sensation’. Mill acknowledged that we have an idea of matter, or a material object, as something that ‘exists when we are not thinking of it; which existed before we had ever thought, and would exist if we were annihilated’.Footnote ¹⁰ But he immediately went on to suggest that its continuing to exist in such circumstances simply amounts to the possibility of its being perceived: ‘though I have ceased to see it … I believe that when I again place myself in the circumstances in which I had those sensations … I shall again have them; and further, that there is no intervening moment at which this would not have been the case’.Footnote ¹¹

Mill is thus led to the theory known as ‘phenomenalism’, whose essence is the view that the notion of material objects existing in the ‘external world’ is ultimately to be analysed in terms of the more basic category of conscious sensation: we must, according to Mill, reject the idea of matter as something ‘intrinsically distinct’ from sensation.Footnote ¹² It would take us too far round to examine the intricacies of Mill’s theory here, but for present purposes, all that needs to be noted is that such a view gets us no nearer to an account of what actual existence amounts to. What does it mean to say that the piece of paper on my study table actually exists? According to Mill, it means that there is a permanent possibility of certain sensations occurring. But what does this mean? That certain conscious experiences would actually occur and would actually exist. So, the theory presupposes the notion of actual existence but does not explicate it.

Let us try another tack. In what he says about our conception of an object as something that would exist ‘if we were annihilated’, Mill seems to be trying to grapple with our intuitive or common-sense idea that the actual existence of something means that it is there anyway – there 24 hours a day, so to speak, irrespective of whether anyone is perceiving it, or indeed irrespective of whether there are any perceivers at all. How might we explicate this idea of an item’s ‘being there anyway’ so as to avoid any reference to actual or hypothetical perceivers? One answer that suggests itself is that even if there were no perceivers, the item in question would still continue to interact with inanimate objects in the vicinity. So, on this view, for an item to actually exist is for it to play a causal role in relation to other objects.

To see how this might work, let us go back to our other opening example, that of the Moon. We want to say that the Moon would be there anyway, circling the Earth, even if all life on Earth were eliminated. In that imaginary (but sadly all too possible) scenario, the Moon’s surface would still be illuminated by the sun’s rays in the characteristic pattern of phases during the course of each month; the Moon’s gravitational pull would still govern the tides; the Moon’s mass would continue to affect the relative positions of the Earth and other planets, and so on. So perhaps the actual existence of an object can be defined in terms of its being a nexus of causal powers – to be such as to be capable of affecting and being affected by other objects.

This suggestion seems initially promising, but it is by no means clear that it enables us to distinguish actual from merely possible or imagined objects. The causal powers attributed to the planet Vulcan posited as a result of Urbain Le Verrier’s prediction in 1859, included the power, in virtue of its mass, to produce certain observed aberrations in the orbit of the planet Mercury. But there was only one problem: Vulcan did not actually exist. Astronomers searched in vain for such a planet, and Vulcan, along with all its causal properties, turned out to be fictitious. Le Verrier’s predictions impeccably followed the logic of Newton’s laws, but the world these predictions described was not the actually existing world, and the anomalies in Mercury’s orbit had to await Einstein’s theory of the curvature of space-time for an explanation.

Following the progress in understanding gravity arising from Einstein’s theory of general relativity, there was, in the event, no need to incorporate Vulcan into the description of the solar system – indeed, as things turned out, it could not possibly be so incorporated. This, in turn, prompts a fresh suggestion about actual existence (at least in the domain of natural science), namely that the real existence of an object might be explicated in terms of its being able to be fitted or incorporated into a system of physics. More specifically, for something to actually exist or to be real, on this view, is simply for it to be locatable within a given spatio-temporal framework. This was more or less the suggestion put forward by the philosopher Rudolph Carnap, writing in the middle of the twentieth century:

This suggestion, as it stands, could be interpreted either in a subjectivist way or in an objectivist way. On the first, subjectivist, interpretation, the way Carnap phrases his criterion, in terms of ‘recognition according to the rules of the framework’, means that it is up to us (the scientists) whether to bestow the title of actual existence upon a given item, depending on the criteria we decide upon as entitling something to qualify for incorporation within our chosen framework. But the problem with defining actual existence in this way is that it seems, so to speak, to put the cart before the horse. Real, actual existence (one is strongly inclined to think) is not something that can be bestowed or withheld by human fiat. On the contrary, it seems evident that we need to tailor our criteria for incorporation into our chosen framework in such a way as to be responsive to whether something actually exists, not the other way round: we must not make something’s actual existence depend on how we shape our criteria.

This suggests that it is more satisfactory to construe Carnap’s pronouncement about real existence in an objectivist sense. On this construal, what bears the determining weight in his account of what it means to be a real thing or event is not the role of human conventions or decisions, but rather the question of whether a given item does in fact occupy a certain spatio-temporal position. So, in our Moon example, the Moon has a determinable place in relation to the other bodies in the solar system and has a temporal history in relation to the development of the solar system, and it is this notion of fitting in with the rest of the spatio-temporal system, on Carnap’s account, that constitutes what we mean by its being real and actual.

What seems intuitively to support this account of existence is the fact that real objects like the Moon can be assigned a set of spatio-temporal coordinates, whereas non-existent or imaginary objects like Vulcan and Father Christmas cannot. But there is a problem for this account, namely, that even if we were to concede that having a set of spatio-temporal coordinates is a necessary condition for something’s actual existence, it cannot be sufficient.

To see this, we need to consider what is involved in the notion of a set of spatio-temporal coordinates. Since the early modern period, when Descartes developed his mathematical physics, the idea of mathematically defined or ‘Cartesian’ coordinates has been a basic tool of science. There are various ways of representing these, arithmetical, geometrical, and algebraical, and as mathematical physics has become more complex, so the representations have become more intricate, to the point where in place of the traditional three spatial dimensions plus the temporal axis, there are current versions of string theory that require up to 10 or even more dimensions. But the crucial point here is that irrespective of which system of coordinates we employ, there will always necessarily be a gap between the mathematical representation or formula that is employed and the question of whether or not we are dealing, in any given case, with something that really, actually exists.

The underlying moral here can be generalised and applied to the cosmos as a whole: no matter how detailed or elaborate a given mathematical model of the cosmos may be, all that that mathematical model consists of will be abstract representations (variables, operators, functions, or whatever logical or mathematical apparatus is employed within the theory), and there will always be a gap between the resulting theoretical description of the cosmos and the conclusion that the cosmos actually exists.

If this is right, then no invoking of a scientific or mathematical ‘framework’ of the kind suggested by Carnap can provide a satisfactory account of what is meant by actual existence. Indeed, it begins to look as if the notion of actual existence somehow eludes the reach of scientific theorising. This is a conclusion that many contemporary cosmologists have seemed very reluctant to accept. In his best-selling A Brief History of Time, the prize-winning physicist Stephen Hawking looked forward to a complete, all-inclusive set of scientific equations that would explain everything in the universe, and indeed the very existence of the universe itself:

The last italicised sentence is somewhat awkwardly phrased,Footnote ¹⁵ but what it seems to suggest is that a sufficiently powerful theory could somehow jump the unbridgeable gap between an abstract mathematical representation of the cosmos and the conclusion that the cosmos actually exists. Subsequently, however, reflection on Kurt Gödel’s famous incompleteness proof led Hawking to recant. In a more sober assessment. He acknowledged that we can never be ‘angels who view the universe from the outside’, but instead that both we and our models are ‘part of the universe we are describing’. He concluded that one might therefore expect any scientific theory produced by human beings to be ‘either inconsistent, or incomplete’. So, in place of his earlier ambition ‘to know the mind of God’ (by which ironically deployed phrase he meant to provide a complete naturalistic theory of the existence of the cosmos), Hawking later wrote that he was glad to have changed his mind: ‘I’m now glad that our search for understanding will never come to an end’.Footnote ¹⁶

One further attempt to approach the problem of actual existence from a scientific perspective is suggested by proponents of a ‘multiverse’ cosmology who argue that the actual existence of the cosmos in which we find ourselves arises from its being but one among a large, perhaps infinite, number of universes that exist. (Some go on to argue that supposing ours is but one of many universes serves to counter the apparent improbability of the constants of our own universe being fine-tuned for life.)Footnote ¹⁷ But even if it is accepted that there are good reasons for positing the existence of a multiverse (something that many scientists and philosophers dispute), this would not obviate the need to give an account of what makes such a multiverse real and actual, as opposed to a mere hypothetical construct.