Remarks on existence - what it is not
and what it might be

Draft preliminary remarks dated 08/06/07 - 10/09/07

1. What kind of existence?

The word "existence" is used in various ways. For example, mathematicians might use it to refer to the sorts of things that are to be found in a particular domain or range. Thus π and √2 don't exist in the domain of natural numbers, but they do exist in the domain of real numbers; there exist no prime numbers between 23 and 29; between any 2 points in a Euclidean space there exists a third point; there exists an integral solution to the equation 2x² - 6x = 0 (see this article from the University of Toronto). So, in the mathematical realm, assertions or denials of existence are invariably relative to some concept or specific context.

Sometimes expressions containing a denial of existence are used to refer to inconsistent combinations of words or scientifically impossible states of affairs. For example, one might say "Round squares do not exist", meaning that the phrase "round squares" is self-contradictory. Or: "Weightless elephants don't exist (on the Earth's surface)" because massive objects at rest in a gravitational field necessarily have weight. This usage is in my opinion suspect, because you would not ordinarily use "exists" in positive expressions of similar type, i.e. to denote tautology or necessity. Thus, you would not say "squares with 4 corners exist", meaning that it is part of the definition of squares that they have 4 corners, or "Heavy elephants exist", meaning that elephants (at rest on the Earth's surface) necessarily have weight. These kinds of expression stand in contrast to matter-of-fact denials such as “Nuclear powered motorbikes don’t exist” or “Sparrows don’t exist in Perth” or “Dinosaurs no longer exist”, which are paralleled by positive expressions that make good sense ( “Petrol powered motorbikes exist” etc).

In the following notes our discussion will be mainly about existence in the sense in which physical objects and people exist - what you might think of as real things. Most things in this category are, well, unmistakably in it, but there are many things that seem to be on the fringe of existence - for example sub-atomic phenomena and various other "scientific" entities. And some things that we often say are "real" may exist in a different sense to which ordinary objects exist, or perhaps they don't exist at all - for example human minds, perceptions and experiences, the European Union, the current price of tomatoes, the horizon, the vacancy for the post of Senior Lecturer in the Department of Ngadjunmaia Studies. We shall be concerned almost entirely with the central, "common or garden" variety of existence or "reality", the prevailing view that there's a universe of objects and events existing in space and time, that these objects and events can (at least in principle) be experienced, but that they exist independently of one's experiencing them and mostly possess a degree of stability, forming a kind of permanent, though changing, physical environment to which we humans can relate. This kind of existence is sometimes thought of rather subjectively, as a continuum of personal experiences or possible experiences, and sometimes rather objectively, as things and events in the outside world. We shall try to remain as "objective" as possible, but the truth is that whatever we know about the world, we know (only?) through experience.

In this world view, time is of the essence. A feature of existence is that whatever exists does so for a finite length of time. Here, I am not sure what "whatever" means - perhaps anything that conserves sufficient recognisabilty or utility to answer to a name. Another feature is that from the human perspective the present time ("now") has a special existential significance, while the future is so uncertain that we cannot now say that it exists, nor do we know how many possible futures there are. Here, I am not sure what "now" means - at the very least, a short period of time leading up to the present moment (or a very recent moment) and long enough for me to finish what I was thinking and saying! One thing is clear - this notion of time is eminently experiential, and to the extent that we must confront it we keep one foot in the subjective camp, so to speak.

2. The concept of existence

The first important thing we are going to have to say about existence is immediately controversial. Existence is a concept. At least, we are going to treat it this way, because there is no alternative. We can only consider existence as an idea, because ideas are all we have to work with. (This might seem to be keeping both feet in the "subjective" camp, but in fact it has little to do with the subjective/objective distinction referred to above. It's more like an outer shell that encloses just about everything we can usefully say about existence.)

In saying that existence is a concept, however, I imply no more than that existence is conceptual - that we must have some kind of concept of existence. And this is not to say very much at all, as almost everything falls into this category. A tree is conceptual, but this is not the same as saying a tree is a concept. The problem is that some philosophers apparently won't even allow that existence is conceptual - they won't admit that we can have any idea of existence at all. Existence, for them, is precisely something that is not conceptual, not meaningful, the absolute antithesis of thought, something that "goes on" even in the complete absence of thought. And this precludes them from saying anything at all about existence (except for a few logical frivolities about how we use the word). Existence is relegated to a no-man's land, a little black box whose contents are impossible to see. Indeed, existence becomes more or less indistinguishable from nothing!

Well, perhaps they confuse thought with imagination. For consider this: if existence were not conceptual, we would be unable to tell what exists and what doesn't. We would never be able to distinguish fact from fantasy. You can imagine, say, owning a million dollars (small change these days). But there's a lot of difference between an imaginary million dollars and a real million dollars. You can do lots of things with a real million that you can't with an imagined million. Of course, you can also imagine yourself doing lots of things with a million dollars. But no matter how creative your imagination, if you can't tell the difference between what you imagine and what actually exists, then there's probably something vitally wrong with your mind. It could lead to all sorts of trouble - I mean, real trouble! In fact it does!

This point might become clearer if you consider the difference between an actual and an imaginary bash on the head, or an actual and an imaginary loss of an arm and a leg in a road accident.

Yet some philosophers appear to have denied this fundamental distinction. For example Kant said (words to the effect of): "Do I have a different conception in my mind when I am thinking of a 100 real thalers (coins) than when I am thinking of 100 imaginary thalers? In both cases I merely have an idea of 100 thalers. Existence doesn't add to my idea of what exists." (NB: This is taken out of context and might mean something different to what it seems to mean. In particular, as suggested above, the word "imaginary" is a bit suspect. Kant might be talking about imagining some particular, existent 100 thalers, in which case you can't "add on" existence. But you can in that case subtract it.)

However, our ability to distinguish really existing things from mere fantasy is by no means foolproof. Under the influence of hallucinatory drugs, for example, we could lose that ability, believing in the physical existence of phenomena that are really “only in the mind”. Idealists are apt to make hay of this irregularity, insisting that all the knowledge we can ever have of reality is of the same nature as hallucinations. I think their point can only be taken so far, and very much doubt that the possibility of hallucination and illusion have much relevance for the concept of existence. After all, we can also tell when people are hallucinating and when they are not - including ourselves, given time. If this were not so, the words hallucination and illusion would presumably be redundant.

While some philosophers might allow that existence is a concept, still they would argue that it is not a predicate. They mean, essentially, that it is not a property of anything. For example, when you say "The ball is red" or "The ball is rolling", "is red" and "is rolling" are grammatical predicates, and red and rolling are properties of the ball. But if you say "The ball exists" or "Balls exist" you are not really saying anything about the ball or balls in general. You are not describing anything. Furthermore, if exists is forced into certain predicate roles, the resultant expression often seems pointless - as in "All balls exist", "This ball exists" or "Some balls don't exist". So the prevailing view is that exists is not a predicate because it tells you nothing about anything, and it doesn't always behave as a predicate should. There's a lot of sense in this, but perhaps not quite as much as is sometimes implied - it often depends on context. What's wrong with "Some honey-eating bears don't exist, e.g. Winnie-the-Pooh"? And if we're ruling out exists as a predicate, must we also rule out (for example) extinct, absent, and current?

Sensible or not, the idea that exists can't be a predicate is built in to the standard modern theory and symbolism of logic. It is this theory which, for the last century, has been the chief impediment to progress in one of philosophy's most important quests: the search for the meaning of "existence". The main problem seems to be that the theory has led to a rather too general, ingrained acceptance of the classical roles of logical concepts such as individuals, names, negation and quantification. Thus the prevaling view of logic-minded philosophers is that existence is what is asserted by statements of the form "for some x, Fx". This is mischievously evasive, a striking example of cart before horse and a painful reminder of the abject poverty of logicism. Indeed few philosophers in the analytic/empiricist tradition have given the topic much thought, other than to examine the ways we use the words exists and existence. As with their theories of truth, much of this analysis seems to be aimed at avoiding paradox, and usually yields some cunning terminology and constructions, but entirely at the expense of meaning. It has been left largely to existentialists themselves to ponder the question in terms which, on the face of it, look full of importance, but unfortunately their background is predominantly one of metaphysical nonsense, so their discussions tend to lack not only logic but meaning too. Moreover their concern has been directed toward aspects of human existence rather than to the basic notion of physical reality.

Another indication that existence is a concept - that it has some kind of meaning - is the fact that it can be usefully included in definitions. For example, you could define Mauritius and Reunion as existent Indian Ocean islands or David Copperfield as an existent magician, as opposed to defining Lilliput and Blefuscu as fictional Indian Ocean islands and Gandalf as a fictional magician. You can sometimes adequately distinguish two similarly named entities from one another purely in terms of their existential status, for example the fictional (Dickensian) David Copperfield and the living (magician) David Copperfield. I'm inclined to think you can even include existence in general descriptions: you could say "All existing sheep eat grass" (implying that nobody has ever come across a sheep that doesn't eat grass, but that it is not part of the definition of sheep that they must eat grass) as opposed to "All sheep are herbivorous animals" (implying that, whether or not there are sheep, it is part of the definition of sheep that they are hebivorous animals). However, it is very doubtful whether "grass eating" could be included as part of a definition of "existent sheep". On the other hand, it is also doubtful whether one could have a taxonomical definition of sheep if there were no real sheep. More on this later.

In fiction, of course, anything goes. The novelist can say things like "Mythical unicorns are shy animals, but real unicorns are exceedingly tame and will readily accept your gherkin sandwiches" with complete impunity. As we shall discover, the philosopher's situation in trying to pin down existence is little different from that of the novelist. An obvious, but important, point is that defining something as existential cannot guarantee its existence. Indeed no amount of talk can ever prove or guarantee the existence of anything. (Yet how much time have philosophers and theologians wasted trying to do just this!)

At the beginning of this section, we considered some examples of existential statements in mathematics, observing that most of them confine existence to a defined range, domain or context. To say that π exists in the domain of real numbers is really saying no more than that π is a real number ¹, and this seems to be much like saying that the Sphynx is a monument or the Eucalyptus is a kind of tree. By analogy, one might wonder whether saying that the Sphynx "exists in reality" is saying no more than that it is a certain kind of thing (a "real" thing), as opposed to other kinds of thing such as mythical things or hallucinations. I shall later argue against this view.

My chief contention is that quantification confounds many different concepts, of which existence is one, and this has led some people to believe that various concepts are the same, or necessarily connected, when really they are very different or only contingently connected. On top of this, there are a number of other general concepts that are not normally handled by quantification at all, but which probably could be, and which have an “existence-like” flavour but are not the same as existence.

First I will list all these concepts (all the ones I can think of, anyway) and then I will attempt to make my case as briefly as possible by giving examples of their application to illustrate how they differ from existence. During the course of this exercise I will also try to get the message across that much of the confusion stems from a widespread but primitive obsession with drawing a sharp distinction between sense and reference (intension and extension, connotation and denotation), which in the context of the real world has very little justification. Unfortunately this dichotomy now forms the nucleus of standard logic and set theory, the new testament of analytic philosophy, resulting in the perpetuation of a religion-like mindset from one generation to the next.

Here is the list of logical concepts which are, or can be, confounded with real existence:

1. Positive number (singularity, finite number)

2. Regular (“distributive”) uses of some

3. “Aboutness” – being the logical subject of a statement

4. “Competence” – other kinds of presupposition/currency /adequacy/groundedness

5. Antecedence in connexive or restricted implications

6. Membership of a set

7. Being the referent of a proper name

8. Instantiation, exemplification

9. Individuation, particularisation

10. Specificity/particularity – “referential” v “attributive”

11. Quantity/extent (non-numerical – mass terms)

12. Extension

13. “Accommodation” – context/collection/external relation

14. Analytic generality/”intrinsicality”

15. Being the value of a variable

16. Whatever can have a property

17. Other kinds of “existence” – relative “existence”, meaningfulness, consistency, definition, hypothesis, fiction

18. Probability

My contention is that existence is not identical with any of the following.

1. Positive number

The expression (∃x)Fx, generally read as “For some x, x has F” or “Something F’s”, can be interpreted either as “There exists something with the property F” or as “At least one x has the property F”, both versions being considered perfectly legitimate and effectively identical. The first interpretation is associated with a number of problems concerning existential import and ontological commitment, while the second interpretation is central to attempts to derive numbers and arithmetic, if not the whole of mathematics, from logical concepts alone. However, in common parlance the two interpretations certainly do not mean the same and neither one implies the other.

Not everything that exists is denumerable. Water and air, for example, undoubtedly exist, but cannot be counted. Conversely, one can imagine denumerable collections that don’t exist. Snow White’s dwarfs are seven in number but don’t exist. At least one kind of bird (the Phoenix) is born from the ashes of its parent’s funeral, but no such creature exists in reality. The sentence “One heliotrophoid crystal would be enough to power three spacewinders” does not imply that either heliotroph crystals or spacewinders exist.

If a concept is signified by the number zero, this might be taken to imply that nothing of that sort exists. But this would be to accredit the number zero with a kind of significance that it actually lacks, as it cannot stand in contrast to any number that does imply existence. One might as well argue that negative numbers imply negative existence. The number zero is not necessarily connected with the negation operation in e.g. “Flamingoes are not blue”, “Hobbits do not exist” and (the allegedly illformed statement) “The Golden Mountain does not exist” (see below).

Besides, the notion of existence in the abstract world of mathematics is one thing, in the real world quite another. In particular, the temporality of real existence creates some serious complications.

2. Regular (“distributive”) uses of some – overlapping concepts

In common parlance some has no necessary connection with existence. As a pronoun its primary use is to refer to an indefinite part of a whole (collection, quantity or extent, named or described). Thus “Some Hobbits live in holes” means precisely “Either all Hobbits live in holes or some Hobbits live in holes and some don’t” and “Some water is salty” means precisely “Either all water is salty or some water is salty and some is not”. The logic of this usage, which could be called distribution as opposed to quantification, is captured by Euler circles (disjoint, overlapping and contained areas), not by Venn diagrams or classical quantifiers. Accordingly “All bugweed stinks” entails “Some bugweed stinks”, both these propositions are existentially uncommitted but, if some kind of existence is presupposed, both have the same existential status.

The relation between the distributive usage of some and number is that, if the class comprises denumerable members (individuals), some implies at least one, and if the class comprises subclasses, some implies at least one subclass. (Note that in “Some species of wasp have red stripes” it’s the wasps that have the stripes, not the species, whether or not there exist any wasps of that species. What this really says is “Some wasps have red stripes and all those wasps belong to certain species”.)

In summary, formulae of classical logic such as (∃x)(Fx & Gx) confound the idea of overlapping (or intersecting or conjoined) classes or concepts with that of existence, but in fact the two ideas are quite distinct.

3. “Aboutness” – being the logical subject of a statement (subjectivity)

Classical logic confounds existence with “subjectivity”, that is, with being the logical subject of a statement. In my view, however, the subject of a statement differs logically from the predicate only in that it is what the sentence is about. To be more exact, in statements of subject/predicate form, whatever the subject term stands for is what the statement is about. (In fact I am strongly of the opinion that whatever the subject means is what the statement is about:  subjects and predicates are essentially the same sort of thing, only their roles differ.)

Aboutness is a simple concept. The subject of a statement that is unambiguously in subject/predicate form is the extra-argumental part of the statement. Any argument applied to the statement affects only the predicate (as it relates to the subject). For example, the negation of “Tom Brown drives a Jaguar” is “It is not true that Tom Brown drives a Jaguar” and this is equivalent to “Tom Brown does not drive a Jaguar”. It is not equivalent to “Somebody other than Tom Brown drives a Jaguar” or “Nobody drives a Jaguar”. These would be appropriate arguments only if the statement was not about Tom Brown, i.e. “Tom Brown” was not a logical subject.

Some simple statements in grammatical subject/predicate form might be considered to have two logical subjects and (more commonly) some to have none. Thus “Tom hit Mary” is about both Tom and Mary if either “No, it was Bill who hit Mary” or “No, it was Flo whom Tom hit” are acceptable rebuffs. On the other hand, “A bell is ringing” has no explicit logical subject:  it is about an unspecified present situation and is therefore wholly “predicative” or descriptive. The proper denial of this statement is “It is not the case that a bell is ringing” (or very loosely “No bell is ringing” or “Nothing is ringing”) and not “A bell is not ringing”. Of course “The bell is ringing” is entirely different as it is presumably about some particular bell.

Ostensible subjects and predicates clearly do not always have unambiguous subject and predicate status. Furthermore both subjects and predicates often change their roles during the course of a narrative or argument.

Now, in the context of classical logic it is often said that one of the salient characteristics of a logical subject is that the existence of what it refers to is presupposed. Thus “Tom Brown drives a Jaguar” presupposes the existence of a certain person named Tom Brown and “John’s children are asleep” presupposes not only that there exists (or once existed) somebody named John but that he has some children, i.e. that John’s children also exist. So if Tom Brown doesn’t exist and John has no children these statements are neither true nor false but simply fall by the wayside - a condition that can befall many kinds of statement for various reasons and which I call "incompetence" (see #4).

An alternative way of handling “John’s children are asleep” is to reformulate the statement so that the existence of the subject’s referent is explicitly asserted, thus:  “John has children and they are all asleep”. Under this formulation (which originated with Russel’s theory of definite descriptions) if John has no children the statement is false. This approach clearly takes away from “John’s children” what seems to me to be the critical feature of a subject term – that it is extra-argumental. So whatever merits the formulation may possess, it has the great weakness of destroying the subject/predicate structure, and therefore will not be considered here.

However, the reason for the definite descriptions approach is just that those who believe that the subject of a statement must be existential find difficulty with statements such as “The Golden Mountain does not exist” (which appears to them to be self-contradictory) and “The King of France is bald” (which appears to them to presume the existence of a monarch who in reality does not exist}. But I doubt that there’s any good reason for encumbering the subject with “existence”, whether real or of some other kind, so their worries seem to be needless. Clearly, aboutness or subjectivity, as I have defined it, is conceptually different from existential import, especially if the latter is understood as the function of denoting an object in the real world.

In fact, the very existence of sentences having non-existential subjects, yet which are nonetheless perfectly meaningful, is evidence enough that subject terms, whether names or descriptions, do not denote in this sense at all (a view which receives some support from examination of the structure of certain Indo-European languages which lack much of the apparatus for denotation found in English and the modern Romantic languages). And while a logical subject might sometimes fail to sustain a competent statement (one which is true or false), this is because it is meaningless or its meaning is inadequate or inappropriate in the current context. Such failure might or might not be associated with non-existence in the real world (see #4).

Subject terms are often proper names, as in “Tom Brown drives a Jaguar” and “Gollum lives in a dark, damp place”, and seem to create a host of problems – in the minds of many, anyway. The theory of proper names is indeed in a total muddle, with some utterly incredible ideas floating around (e.g. Kripke, Burge). Whether or not they are subjects, proper names are often assumed to denote existing individuals (so some would say Gollum doesn't count as a proper name). I will discuss this dubious supposition below (#7) and possibly at some later date in a separate article.

Then again, subject terms can be general. Both "This rabbit eats lettuce" and "A rabbit normally eats lettuce" would be subject/predicate statements in most contexts, and there is no reason to assume that they are existentially different from one another. "Trucks are noisy" is about trucks, "Hobbits live in holes" is about Hobbits and “Smokeless cigars are good for the lungs” is about smokeless cigars, regardless of considerations of existential import. By the same token there's no reason to suppose that singular terms can't be predicates. If "The best restaurant in town is the Rising Sun" is about best restaurants then that is the subject and the Rising Sun is predicate.

A final example: “Ill health is depressing”. Although (in keeping with Gilbert Ryle’s opinion) this should probably be rephrased as “Whoever is ill is depressed”, nonetheless it holds up as a subject/predicate statement. The point of the translation is obvious (ill health is not an existing object but an attribute predicated of people) but when formalised as (x)(Ix ⇒ Dx) the subject/predicate format is lost. At the same time the non-correspondence of the subject of the original expression (ill health) with the denotation of the translated version (people) becomes immediately clear. This gives weight to my contention that logical subjects need not be existential or denoting.