Monday, June 12, 2006

What is Existence?

We all have an intuitive grasp of what it is for entities to exist. My parents exist whereas Santa doesn't, and all that. But what of abstract objects? When philosophers argue about whether numbers truly exist, what is in dispute here? Even ontological debates about material entities seem dubious: does there exist an individual entity which is a table, or are there merely particles arranged table-wise? What's the difference? These don't seem to be debates about how the world is. Everyone agrees that there is table-ish stuff in the world. They merely dispute how to count or describe it.

Of particular concern are too-easy arguments like the following:
(P) There are nine planets.
(C1) So, nine is the number of planets.
(C2) So, there is a number that is the number of planets
(C3) So, there exist numbers.

They start with some undisputed fact, and show that it trivially entails a (seemingly substantive) ontological conclusion. But surely that's cheating! Trivial entailments can't produce substantive new results. They merely serve to highlight what is already contained in the premise. But counting planets shouldn't commit us to the existence of numbers in any deep sense, should it? At least, if the above argument is sound, then it's a marvel that so many smart philosophers could make such a simple blunder. Ontology would be easy!

At this stage, many philosophers appeal to a distinction between kinds of existence claims -- I'll follow Cian Dorr in calling these "superficial" and "fundamental". The idea, then, is that the above argument is valid only if 'existence' is used in the same sense throughout. The Platonist conflates the two, invalidly jumping from premises about superficial existence to a conclusion about fundamental existence. We can all agree that numbers "exist" in the superficial sense that follows analytically from sentences like "there are nine planets". But that says nothing about fundamental existence, which is what philosophers (at least, ontologists) are interested in.

So what do these two senses of 'exist' really amount to? I think the "superficial" sense is tolerably clear. It concerns those claims we can arrive at through conceptual analysis, analytic entailments from commonsense truths, and so forth. In this sense, the existence of abstract objects is an entirely trivial matter. It's not to claim anything substantive about how the world is. Rather, claims like "there exist numbers" are analytic: true simply in virtue of meaning, without needing any input from the world. They're more semantic than metaphysical in nature, telling us only about language and not reality. (Of course, they might be combined with a worldly component to form synthetic claims, e.g. "there are nine planets".) Scientists can look into the empirical component of such claims, but there's nothing of interest here for philosophers.

What of "fundamental" existence? This seems harder to characterize. It is meant to involve a substantive claim about how reality is. As such, claims of fundamental existence are never merely analytic. The trivial argument given above has no place in "serious ontology". Instead, perhaps, we may use inference to the best explanation, or Quinean indispensibility arguments, to conclude that we should posit some class or other of abstract objects. I follow that much. My worry is this: what, exactly, are we "positing" here? ("The existence of numbers." "Um, okay, and that means...?")

To restate the problem: how would a world with numbers be any different from a world without them? I take it the answer must be that my question is ill-formed. There are not two such possibilities to compare. Whether numbers exist or not, they have this status necessarily, and there simply is no sense to be made of the alternative proposal. But then it's still hard to see what the ontologists are disputing. (Perhaps "which of us is speaking nonsense"?)

Here's something I found helpful: In last week's reading group, Brendan pointed out that when we're speaking in the superficial sense (i.e. all the time in everyday life), we have a limited concern for the ways in which what we say might not be literally true. We're only interested in a restricted class of "relevant alternatives". His example: when I say "The board is white", we would consider it relevant if this turned out to be false because the board is really black or blue, or perhaps if I was merely hallucinating the board in the first place. But we are not concerned about the possibility that the claim is strictly false because colours don't objectively exist, say, or because there exists no fundamental entity that is a "board", but merely atoms arranged board-wise!

What I take away from this is that, in communication, we seek to narrow down the list of (epistemically) possible worlds which are candidates for actuality. When I say "the board is white", this serves to knock out those possible worlds which lack white board-ish presences. Think of it this way: we are given the various possible worlds, and we have to sort them into an "in" pile and an "out" pile. We all know how to do this, or what kind of instructions "the board is white" is meant to convey here, even if we don't know exactly how to define or describe the contents of the possible worlds that have been given to us. In particular, we don't know whether those white-boardish presences should be described fundamentally as individual objects that are white. Perhaps they shouldn't -- perhaps such macroscopic commonsense terms do not make it into "the final analysis". But we can still identify which worlds they are meant to pick out. We can tell which worlds contain stuff that fills the whiteboard role.

Another example: When I say that Santa Claus does not exist, I mean to reject those possible worlds which contain a certain qualitative character. This is the character we all associate with Santa: a red and white humanish presence usually located at the North Pole, which flies around the world delivering presents each Christmas Eve. I could draw a picture, if that'd help. ;-) Anyway, if you picture a possible world in your mind's eye, you can tell whether it contains the sorts of qualities I'm talking about here. (Or if you read a sufficiently thorough description in some idealized language.) It doesn't matter whether "Santa" is really just atoms arranged Santa-wise. So long as there's something(s) playing "the Santa role" in a world, then that counts as Santa "existing", for my purposes.

I welcome suggestions for how to express this notion more clearly, but hopefully you get the rough idea. (I feel like it's related to this post, but I can't say exactly how.) Substantive claims of superficial existence (say of concrete entities) serve to distinguish between various possible worlds. Fundamental existence claims are different. Ontologists don't discriminate between possibilities, telling us that world w1 is actual rather than w2. Rather, they fill out the possible worlds' contents, specifying what (exactly) we find in the given worlds w1 and w2.

If an ontologist says that Santa couldn't possibly exist because there are no composite objects but only arrangements of atoms, they haven't really said anything which narrows the space of possibilities. It's like Putnam's lesson from Twin Earth: the world we qualitatively imagine is still possible, it's just that we were misdescribing it. That watery presence shouldn't be called "water", and that Santa-Clausish presence shouldn't be called an individual.

Note that my analogy might be a little misleading, in that the ontologist isn't making a merely semantic claim about the meaning of our word "individual", or "exists". Rather, he's making a (purportedly) substantive claim about the contents of possible worlds. ("That Santa-ish presence is really not an individual entity! And there really are numbers -- and I'm talking about reality, not about our words!")

But we can grant that while recognizing my point that he's not really narrowing the possibilities in my sense. Since he's making claims about the necessary contents of possible worlds, if he's right then the alternative view doesn't invoke any genuine possibilities at all. It has the same kind of status as the "possibility" that there are finitely many prime numbers. This doesn't describe any coherent scenario -- it's just that not everyone realizes that.

Compositional nihilists don't really believe in a more restricted space of possible worlds than the rest of us, I take it. They simply dispute what those worlds contain. Pointing to a molecule of hydrogen gas in some possible world, they will deny that it is a third thing in addition to the two Hydrogen atoms that compose it. (Let's pretend that our so-called "atoms" really are indivisible.) They don't deny that this world (*points to a spot in the North-East of modal space*), that this world we're discussing is a possible one. They simply think we mistake its contents when we say it contains molecules as well as atoms.

I'm not convinced the difference between these views really is a substantive one though, since I can't see what the difference is. Sure, one philosopher says the two atoms compose a molecule, and the other denies this. But again, what is the content of this disagreement? What difference does it make whether we say there are three things here or just two? It seems to come down to the arbitrary matter of how you choose to count! So I'm skeptical that existence in this "fundamental" sense really amounts to much. Perhaps we should be pluralists about it, allowing that adopting different ontological frameworks might be useful for different philosophical purposes, but there's not really any deep fact of the matter. The important (even if "superficial"!) existence questions concern the differences between possibilites, and the empirical question of which one is actual.

(Though cf. Chalmers' more moderate view, which allows that there might be some determinate ontological truths, as well as some indetermine matters.)


  1. I'm not sure I follow this. Ted Sider argues that when, for instance, Lewis and van Inwagen argue over whether tables exist, they are using the same notion of existence, namely the one captured by an (appropriately) unrestricted quantifier. If they weren't, their dispute would be merely verbal - i.e. then there would be a case for deflationism about ontology. Is that what you're making here?

    Actually, I don't agree with Sider on this issue, but I'm not a deflationist either.

  2. Their dispute doesn't seem merely terminological, I agree: they do take themselves to be disputing the common issue of what fundamentally exists, as captured by the unrestricted existential quantifier. But I'm just not clear on what this dispute amounts to. I understand how quantifiers work in logic. But the application to reality seems less than straightforward. After all, quantification is defined against a domain of entities. So the more fundamental question concerns what entities there are in the absolute domain, i.e. what exists? (I don't see how appealing to quantifiers sheds any light on this question. That would seem to get things backward.)

    Now, my problem is that I don't understand what the different answers to this question are really claiming about the world. I can understand uses of the "superficial" sense, say when children dispute the existence of Santa Claus. No problems there: I can differentiate between the possible worlds endorsed by either side of the debate, as described in the main post. But ontological debates about "fundamental" existence are less comprehensible. Lewis says there are tables in the absolute domain, and van Inwagen denies this. Still I ask: what's the difference? They're clearly disagreeing with each other. But I just don't know what about! ("Whether tables exist." "Whether tables what?")

    What does the inclusion or exclusion of composite objects (or numbers, etc.) from the absolute domain really say about the world?

    (Maybe I'm a deflationist. Mostly I'm confused.)

  3. The ultimate problem is conflating existence and reality. A consequence of the nominalist tendencies within philosophy.

  4. Very interesting, Richard. I've often thought we tend to give too much credit to the existential operator in existence matters simply because it's called 'existential'. Really, the existential operator is more of a positing operator; its closest translation is more like, "It is posited that..." and there are a number of different reasons you might posit something, besides trying to identify something as existing or fundamentally existing, or whatever is at stake in this sort of dispute.

  5. Richard,
    sounds deflationist to me. It also sounds convincing, because I dont know what it means either and see no hint of potential for it being explained in a satisfactory manner (as opposed to a "backwards" one).

  6. Hi Richard,

    Is it possible that the debate you refer to is really over some form of Platonic essentialism? I.e., could Lewis be claiming that tables exist as distinct objects regardless of their material composition, whereas van Inwagen is saying that tables are ontologically reducible to the atoms that compose them and have no existence independently of those atoms?

  7. This is a slightly irrelevant comment, but what the heck.

    I think that I agree with Clarke when he says “The ultimate problem is conflating existence and reality”, although I may misunderstand that statement. I disagree with Richard’s suggestion that ontologists “merely” dispute how to count and how to describe things like tables, because I do not think there is any “merely” about it; in fact, I think, that according to one very reasonable sense of “metaphysics”, metaphysics is essentially the study of what is the best way to organise our descriptions of the world. This is where my putative agreement with Clarke comes in, because I think that the matter of determining whether or not some thing “exists” (fundamentally or not) is just one of the many matters that might concern a person who is interested in the study of “what is real”, which I take to be a much richer concept than the concept of a “existence”, and which encompasses all of those matters that concern a person who wants to come up with a well-organised description of their world. This conception of metaphysics gives a different view of why certain notions qualify as metaphysical notions, while others do not, and also of the things we should consider when we try to decide whether or not a certain metaphysical notion is a good one or not. For example, I would say that the statement “the world is like a cave and a sun (etcetera)” qualifies as a metaphysical statement, because it organises a wide range of views about the world (about knowledge, morality, etc.) into a single summarising account. Also, I would say that the reason we might regard atoms as “real”, and tables as “unreal”, is because we have an organising conception (physics) which is able to describe everything of interest in terms of atoms, and it does not need tables. Also, whether or not the universals debate qualifies as a metaphysical debate depends upon one’s metaphysical beliefs: for a person whose world is fully and elegantly described in terms of atoms, for example, the debate over the existence or otherwise of universals is of general, rather than metaphysical, interest. If this turns metaphysics into a subjective and aesthetic sort of pursuit, then I think that is all to the good if we want our metaphysical systems to deliver on their claim to describe the “fundamental nature of reality.” I can’t say whether or not this conception of metaphysics is better overall than the orthodox one, but I think it is better to recognise it than not to do so.

  8. Clark, could you elaborate on how you see the difference between existence and reality? (Do you think there are real non-existents, or unreal existants, or what?)

    Ebonmuse, debates over essentialism might be another target for deflation, but I think that's an independent question from the mereological one (i.e. whether parts compose new wholes). For instance, one could accept both mereological universalism (the sum or "fusion" of any objects is a new object) and strict essentialism (an object could not have any different parts and still exist as one and the same object).

  9. Richard I was thinking along Peircean terms. Reality is that which is true independent of any one person thinking about it. Existence is what acts. The distinction is important since Peirce is a Scholastic realist. That is he allows for real universals. But clearly these don't exist as occurent entities.

    I might put some quotes up at my blog tomorrow as several discussions I'm in make reference to this distinction.

  10. Sounds interesting... does that mean that existence entails causal powers (being "what acts"), so that claiming abstract objects exist would be self-contradictory?

  11. Let's say we point red laser of some kind to a wall... There will be small red dot on the wall.
    Does that dot exist or not?
    It is hard to say that it doesn't exist, as we are looking at it, we can move it etc... In a superficial existence way, we can imagine worlds in which it exist and worlds in which it doesn't.
    But if we frame it using existential quantifier, we could say, that there aren't things in the world, which are spotlights. In such way it doesn't exist.

    Maybe we could compare it with distances between things? When we look at two things, we can say... obviously there is some distance between them, but there aren't any things in the world which are distances also. Distance would be function of two existing things, but not a thing.

    Maybe we could conclude that the distinction is that things exist by themselves, while relations exist just as consequence of existence of things. Seems that case of spotlights is similar, they can be said that they exist (in superficial way), but they exist just as grounded in existence of something else (laser, wall, observer with specific cognitive apparatus).

  12. Yeah, that's a helpful idea: the search for 'fundamental existence' is then the search for a minimal "supervenience base", or class of facts (perhaps "PQTI" - see Chalmers & Jackson [PDF]) from which all other facts can be inferred. That's a notion which makes plenty of sense. Yet it doesn't seem to be what ontologists have in mind when they debate these things. I don't think anyone denies that the table supervenes on its microphysical constituents, for example. Yet some still want to say that it really does exist as an entity distinct from its constituent parts. (As previously lamented, I don't really know what they mean by this. I hope they do.) The minimal entailment account would also seem to exclude "superficially necessary" abstract objects like numbers and propositions, which can be inferred a priori from nothing at all. Many ontologists wouldn't like that. So I suspect they'd want to say that you're pointing to a different kind of "fundamentality" from the one they have in mind.

  13. "Supervenience base" or "scrutability base"? Perhaps I should've said the latter. Thought it probably comes to much the same in the end, since metaphysical necessity (for supervenience) and epistemic apriority (for scrutability) plausibly coincide for the cases we're interested in here.

  14. Thye reason that some people say that things like numbers exists is the following Quinian point: The things that exist are the things that science tells us exist, like your mother, or trees, or electrons. But sometimes in orter to do science we have to make statements like "There is a function from X to Y." or "There is a Point X in the universe" . . . And so whenever real science needs to say something like "There is. . ." they are making a claim about what exists. If Science tells us that numbers or functions or points exist, then many argue that therefore it does.

    A good chunk of the work showing that things like numbers do not exist show how we can do science without numbers.

  15. Richard, I think one could argue abstract entities act. Peirce doesn't do that. At least not in a normal sense. But the distinction is a subtle one and wrapped up in his notion of signs.

    Interestingly Peirce has a very clear discussion of all this wrapped up in a discussion of Berkeley. In it he ends up distinguishing his realism from idealism (typified by Berkeley). Pragmatic realism is sort of a middle ground between realism as traditional materialism and then idealism (especially German idealism). Unfortunately this isn't always noted and so the pragmatists are often misunderstood: even by people sympathetic to them such as neo-pragmatists like Rorty or Putnam.

  16. This paper by Cathy Legg on universals and realism might be of interest as well, even for those not taken by Peirce. In it she argues that existence and reality aren't co-extensive and that the distinction between semantic and ontological is blurry.

  17. Richard, if you don't mind this tangential question...
    Why would ontologists argue that numbers exist? What Karl said doesn't sound like convincing argument.
    And to say "There is nine planets in Solar system" can be changed to numerical quantifier, i.e. "there are nine x, such as that x is planet in Solar system".
    I would understand arguing that numbers have objective meaning, and propositions about numbers objective truth, but why say that they exist, what would that mean? Surely not that they exist qua numbers? E.g. number 9 exists qua 9?

  18. I wonder if this matter is entirely a matter for philosophy. I am not committed to accepting that philosophy can answer questions regarding what a planet is or as to how many planets there may be and the question as to what numbers do or do not exist seems to me to belong to mathematics. I am inclined to say the question of what does is does not exist is simply not a question for philosophy, but what of the existence of other subjects? Suppose I were a proponent of thingology, the study of this and that, how would I show that my subject exists?

  19. Whether the number nine exists is not a mathematical question. Mathematicians presuppose the number system, and inquire into its internal relations. (So they might inquire into the 'superficial' existence question whether there is a number with such-and-such properties: e.g. a largest prime. But this is very different from asking the philosophical question whether any numbers exist at all. Compare Carnap on the distinction between 'internal' and 'external' questions.)

  20. I suggest that the author of the article on what is existence tell readers in just 20 words or less what is existence: simple, plain, clear, common words.

    Like this: [Existence is] anything at all that men can discourse on and understand.

    10 words.

    Better phrase the question what is existence this way:

    What is a thing?

    Then you can go into telling readers that a thing can exist even if man were not around, and it can be a thing that is a thought in man's mind represented by a word.

    So, for man in relation to the universe there are two kinds of things, things that exist even were man not existing, and things which are thoughts in man's mind that have corresponding things outside man's thoughts, or don't have.

    Then you can continue to explain things that exist were man not existing at all, and things in man's thoughts, etc.



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