When we say something exists, what do we mean by X? Specifically, my question is about whether there's something more primitive than saying something exists.

In mathematics, existence is asserted by means of the existential quantifier. And the definition of the existential quantifier can be established by set axioms, like so:


Then again, the element symbol ∈ turns up which lacks any further definition.

More precisely, I'd like to investigate what the concept of existence of something (be it matter or information) means.

I'm not asking for a merely reductionist account where an apple exists because the molecules in the apple exist. I'm asking how existence works once we're at the level of the fundamental existing things (whether those be electrons or something else).

That is, at some point it seems to me we are reliant upon our intuitive notions and have to build up on them.

What sort of philosophical positions are common about the nature of existence on this level? How can it be explained?

  • related: philosophy.stackexchange.com/questions/27964/…
    – Dave
    Jun 28, 2016 at 20:19
  • 1
    Without additional constraints (what problem are you trying to solve? What are you reading for which this is an important question? What have you already tried in order to answer the question? etc.) this question is too broad/unclear.
    – Dave
    Jun 28, 2016 at 20:24
  • I'd say it belongs to ontology which is a branch of metaphysics.
    – Zetaman
    Jun 29, 2016 at 8:10
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    By the way, why is there no MathJax on the philosophy community?
    – Zetaman
    Jun 29, 2016 at 8:10
  • When philosophers talk about existence they generally use the term Being. See Sartre's Being and Nothingness, Heidegger's Being and Time, Hegel's first book of Science of Logic. Sorry am not more helpful. With respect to mathematics look up the account of mathematics called Intuitionism by L.E.J. Brouwer (you happily even mention "intuitive notions") which asserts that mathematics is a human construction that rests on conceptual primitives that are non-mathematical - See Lakoff and Nuñez Where Mathematics Comes From for a contemporary cognitive science/linguistics account.
    – igravious
    Jun 29, 2016 at 8:25

5 Answers 5


This may not be exactly an answer, but it is too long for a comment.

We say things like:

  • Black swans exist.
  • Ghosts do not exist.
  • Finland exists.
  • God exists.
  • God does not exist.
  • My belief in God exists.
  • Emerging properties do exist.
  • Honesty doesn't exist (anymore).

If someone tells us that black swanns don't exist, we will usually tell them that they can be easily found in zoologics, or show them a picture of black swanns. If someone tells us that Finland does not exist, we may show them a map, or a travel agency's fares for travels to Helsinki. Is someone doubts the existence of emerging properties, we might point to the fact that while a plane can fly, no separate piece of a plane can. Or that while Boris Johnson is for Brexit, the cells on his liver, toe, or even brain, do not know anything about the issue.

We would, in fewer words, propose a "verificationist" approach to the subject: "you think X doesn't exist? Here is an instance of X: a black swan, a post card just coming from Finland, the emerging property of Mr. Johnson's support for Brexit."

Things get more complicated if someone tells us that ghosts or unicorns do exist. A verificationist approach seems insufficient, because we would have to search for either ghosts or unicorns in the whole universe. "Proving" in a verificationist way that there are no unicorns in the Isle of Man may be not too difficult, but our interlocutor may argue that "perhaps they exist in Alpha Centauri system, who knows". The obvious retort is that the burden of proof lies on the person making such claim. But this is not a very good answer; the person may well tell us that "I am not making any claim at all, except the very limited one that you cannot prove that unicorns do not exist in Alpha Centauri, or, indeed, in any place that you cannot directly inspect." A better line of argument is to show that unicorns are material impossibilities: horses have evolved in certain ways, that preclude the existence of horned horses; and the evolution of horses in other planets is even more impossible, for the natural history of another planet is necessarily different from Earth's own natural history.

But things get complicated again if we allow the interlocutor to move the goal posts (for instance, if he points us to a rhynoceros, and tells us "here, the unicorn; I told you it existed". Of course, the rhynoceros is not a horned horse, and the definition of unicorn requires exactly this). This is relevant for the discussion of the existence of God, for one of the argumentative tactics of theists is to get their interlocutors into admitting that they cannot prove that some "superior" entity doesn't exist (that is what the traditional arguments for the existence of God do), and then trying to confuse us into a quite different idea - that this "superior" entity, a) created the world, b) is omnipotent, c) is omniscient, and d) is benevolent towards humans (or even more, maintains a "personal relationship" with some or even all humans). The goal post is moved; while the theist originally intends to make us believe in a being with all the properties from a) to d), he then gets us to admit that we cannot prove the inexistence of a being that has at most the property a). The proper response, of course, is that property d) is incompatible with property b), or at least with properties b) and c) combined.

Anyway, what we seem to be discussing is a property independent of the person, or people, talking about it. If black swans exist, they exist whether or not I believe in them, see them, like them, and whether I am looking at them, awake, aware of their "existence", or even alive. This independence we use to call, rightly or - more probably - wrongly, "objectivity". Existence is "objective". Which brings up the issue of

  • My belief in God exists.

While we can verify that black swans exist, or conclude that unicorns must not exist because their existence would contradict what we know about the structure of the universe, or that God doesn't exist because its description is self-contradictory, a sentence that refers to the psyche of an individual is much problematic. The faithful in question could be lying, or could have not given enough thought to the issue of God to really hold a significant faith - and we may not have any actual means to confirm or dismiss the claim. Besides, this seems to in some way break the idea that existence is "objective". Whether someone's faith in God exists or not, that certainly depends, at least partially, on that person and her beliefs - and we can't demonstrate that such existence is self-contradictory; while the belief in itself can be absurd, people do often believe in impossible things. In that sence, it would seem that the beliefs of a person - be them religious or not - do not "exist" in the same way that Finland exists. We can perhaps assert that certain symptoms of the existence of the belief exist, and that they may indicate the existence of the belief (whenever John is going to cross the street, he looks both sides first, which indicates that he may believe that cars exist and are dangerous) - but is that the same thing?

This lack of objectivity is, of course, part of the problem with

  • Honesty doesn't exist.

Here the person uttering the sentence is admiting to being dishonest (which brings the question, why would we believe what they are telling us, but that is a digression). But is that person being honest about her own dishonesty, and how can they assess the existence of honesty in other people? This brings on a very interesting issue: that of statements that imply the impossibility of any verification. Any person that tries to answer to this with a sentence by asserting their own honesty will probably be told that this in fact "proves" the inexistence of honesty, as their answer is itself one more instance of lying.

Similarly, the assertion of the existence of invisible green pixies: "of course you cannot see them; as I told you, they are invisible".


Meinongians and other "relative modal realists" imagine there is something more basic than existing, that being 'modally existing'.

The most basic mode is the alethic or indicative mode, the 'is' mode. What exists, exists.

The next layer of modality is the potential, the 'could' mode: Everything that exists must potentially exist, and not the other way around. This is the mode in which mathematics is conducted most of the time. Whatever can exist, mathematically, does.

Another kind of sub-existence that may be even more basic is the state of being held as a fiction. Whether or not it is even potentially realizable, it may be possible to hold the idea of its possibility in one's imagination. This is the natural subjunctive (or conditional), the 'would' mode. Objects whose existence is an open conjecture in mathematics exist in this mode.

Below that lies the state of what could be wanted, whether or not it might be clear enough to imagine as a fiction. Wishes for states other than reality often fall in this modality. We would like contradictory things that are bothering us not to conflict, but we cannot see how that might happen. This is the optative, the 'should' mode. Laws and other moral concerns often operate in this mode. Idealized rules exist, whether or not they can be followed, and whether or not one can even work out in one's imagination what the effects would be. Mathematics models this mode in proof theory by means of paraconsistency, where arguments can conduct or conserve truth, even though they are not true.

Finally, at least grammatically, there are statements that we can construct that describe states independent of their status relative to reality -- 'Colorless green ideas sleep furiously.' This may be the most basic kind of sub-existence, the intensional mode. This is the construct of all possible hypothetical conditions that can be potentially expressed. Mathematical logic sometimes entertains this kind of thing in contexts like "Nonstandard" logic -- imagining the set of all well-formed formulas in any algebra and the collections they would define, considering the different empty sets all as independent objects according to their intension (hence the name). Lewis Carroll and people on psilocybin sometimes live there.

The extreme form of modal realism asserts that everything expressible in the intensional mode has some limited existence. Other forms cut off the relevance of sub-existential states at one of the layers above.


From Heideggers Being & Time:

But we call many things existent (seiend) and in different senses.

Being is found in whatness and thisness, reality, and the objective presence of things, subsistence, validity and existence and in the 'there is'.

Now this might seem a little circular, in that we've mentioned 'existent' in terms of 'existence'; but H points out that to stall a process of reasoning by calling it reasoning circular

is an argument that is always raised in the area of investigation of principles and are always sterile when weighing concrete ways of investigating.

For H, existence isn't a matter of deduction, mathematical or otherwise:

It is not a matter of grounding by deduction but of laying bare and exhibiting the ground

This is not a million miles away from Descartes 'clear and distinct ideas'; and nor is it a million miles away from your 'building on intuitive ideas'. H goes on to say:

Here it becomes evident that the ancient interpretaion of the being of beings is orientated towards the world or nature, in the broadest sense, and that it indeed gains it's understanding of being from 'time'. The outward evidence of this - but of course obnly outward - is the determination of the meaning of being as ousia or paroussia, which ontologically or temporally means presence. Beings are grasped in their being as 'presence', that is to say that they are understood in a definite mode of time - the present.

H does in this book, reflect in passing, on the foundational crises of the physical sciences; it might have interested him that Penrose in a centenary volume celebrating Einsteins achievements calls GR a theory of 'chronometry' rather than of length ie Spinozan extension.

But its not this kind of Being that interests Heidegger, he writes:

So when we designate this entity with the term Dasein we are not expressing its whatness, as if it was a table, a tree, or house - but its Being.

So also not an electron, nor a planet, or a universe. There are classes of being - but no single genus of being; which is exactly what the first quote alludes to.

  • "that they are understood in a definite mode of time - the present."; what does understood mean in this context? Is he asserting an ontologically Idealist Position? Jul 3, 2016 at 23:27
  • @user2278997: no; he's a phenomenologist. The sentence seems straight-forwrd enough. Jul 3, 2016 at 23:56
  • "Understood" in the usual sense (perceived), will result in the statement: something exists only if it's understood, which is what ontological Idealism is about. Jul 4, 2016 at 0:21
  • its in the usual sense, that you will find in any dictionary; ie in conventional language. the word understood here is not being used in a technical sense. Jul 4, 2016 at 0:33
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    @user2268997: The sentence does not say that something exists by virtue of being grasped/understood/perceived, but that grasping/understanding/perceiving requires the presence of a being and therefore the mode of time in which being is grasped/understood/perceived (passive!) has to be the present.
    – Philip Klöcking
    Jul 4, 2016 at 3:59

The mode of being of a non-living object is referred to as being extant. To be extant means it has been observed (or deduced) by an existing, sentient observer. The difference between extantness and existence is called the ontological difference. Extantess is a two-way process. Without the observer the unobserved 'thing' has no concept, no definition. Nevertheless, all unobserved things can be deemed to be extant under the group of 'unobserved things' - which we can safely say there are.

it is

I am

Despite sharing the same verb, to exist, the subjective existence of a living person is of a different order from that of an observed thing. That's where the mystery begins.


Judging by your update, you are concerned with extantness. So consider the existence of a tachyon. The concept of a tachyon has been established as a seemingly possible thing. However, no one has found one yet so it 'is' still just a mere concept. One might suppose that if tachyons exist but no people had ever existed the tachonys would continue to exist. However, there would be no concept of tachyon - no discrimination of one part of reality from another - so how could a 'tachyon' exist? Thus objective existence (extantness) is the interaction between observer and object.


We say that something exists based on our ability to interact with it, experience it's effects etc. Unicorns are said to not exist (on earth) because we haven't found any and we have looked around enough that we should have found them if they were here (they're pretty big). We can't see air but we don't need to, we feel and measure it's effects Gravitational fields, magnetic fields etc basically the same. Other peoples consciousness is just inferred from behavior. Existence is just a word we use when we have certain types of experiences. Worrying about "actual" existence, if that means outside of experience in principle, can't go anywhere, there's nothing to base it on.

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