Existence is not a predicate
Thus spoke Kant, Russell, Frege or whomever they all were.
But what do you think? Feel free to justify your stance (that's the intent of this post).
I'll vote Nope for the time being. Here follows a brief justification.
Formally, where ? is a predicate (without unrestricted comprehension), x is a (bound) variable, and S is a set, existential quantification is properly written as
and this is a proposition, which may be true or false. In more ordinary language:
If the ? symbol could be ?, then you could already have x, except x does not exist, which seems wrong, since what was x in the first place then? If "exists" is a predicate which happens to be false for x, then it would seem that x is both present and absent. A fundamental demarcation among existing on paper, as it were, and also elsewhere, would have to be specified, but, more onerously, you'd have to contend with strange expressions, such as
which read as either nonsense or tautological.
Going by Quine, to exist is to be the value of a bound variable, which is x in the expression.
Thus, in general, existence is not a predicate, ? is not just another ?, though we may sometimes talk as if it were, and still make some sense.
But what do you think? Feel free to justify your stance (that's the intent of this post).
I'll vote Nope for the time being. Here follows a brief justification.
Formally, where ? is a predicate (without unrestricted comprehension), x is a (bound) variable, and S is a set, existential quantification is properly written as
- ?x?S [ ?x ]
and this is a proposition, which may be true or false. In more ordinary language:
- there exists an x in S so that ? holds for x
- e.g., there exists (?) a tree (x) in the forest (S), which is green (?)
- or just, there is (?) a round (?) apple (x) in the bowl of apples (S)
If the ? symbol could be ?, then you could already have x, except x does not exist, which seems wrong, since what was x in the first place then? If "exists" is a predicate which happens to be false for x, then it would seem that x is both present and absent. A fundamental demarcation among existing on paper, as it were, and also elsewhere, would have to be specified, but, more onerously, you'd have to contend with strange expressions, such as
- ¬?x?S [ ?x ]
- ?x?S [ ¬?x ]
- ?x?S [ ?x ]
- ¬?x?S [ ¬?x ]
which read as either nonsense or tautological.
Going by Quine, to exist is to be the value of a bound variable, which is x in the expression.
Thus, in general, existence is not a predicate, ? is not just another ?, though we may sometimes talk as if it were, and still make some sense.
Comments (65)
There does not exist a predicate (x) in language (S) which has the meaning, 'exists' (?).
I don't know, but there is a slight aroma of cutting off the branch one is standing on here... is it a rule that denies its own expression?
If you suppose that a fictional entity exists, then what would it take for it to be real?
It seems like fictional (not real) entities exist as their hypotheses (or definitions) alone.
@unenlightened, according to those pesky objectivists "existence exists", though I think Russell argued otherwise.
Does existence then not exist...? Maybe we should have a poll on that one as well.
How about this one? "There exists an apple in the bowl of apples, so that apple does not exist." :)
There are cases where "existence is a predicate" comes through as nonsense, which makes me think that (generally) "existence is not a predicate".
As far as I can tell, there isn't anything further that "to exist" can reduce to; existence is ground if you will.
Another angle:
We commonly characterize things by predication, quiddity — what those things are.
These are different propositions from merely existing though — that something exists.
By the way, is the King of France bald or not?
Russell and Whitehead:
I'm not the big logician, but I know that existence is tricksy. It can be readily proved that there is no greatest prime number. One supposes that one exists, and then shows there is a bigger one. But then that feels different from the question of whether or not there exists hair on someone's head. I feel like we can put restrictions of this sort on language for certain purposes, but for other purposes I might define existence as that which is immune to argument.
The principle of sufficient reason.
How come? As far as I see, the only reason why existence being a predicate or not was ever philosophically interesting was because people were interested in the ontological argument.
In my opinion, concepts are concepts and the things they signify are the things they signify. For example, a circle can be taken purely as a concept. A circle as a concept is not round, it doesn't have a radius, etc. - it's just a concept. However, that which the concept of the circle signifies does have a radius, is round, and can exist or not exist. We get confused because we don't have two different words to distinguish between the circle, and the concept of the circle so we equivocate. It's one thing for a concept to exist, and it's another for that which it signifies to exist.
Saying that something doesn't exist is more like saying that it cannot be found, it doesn't strip it of any particular quality, and I don't consider this a proper use of language anyway. If something truly didn't exist, then there would be nothing to talk about not existing.
In thinking that existence is a predicate, we immediately wish to predicate anything said to exist or not exist, and this leads to confusion in my view. It exists, therefore it has the qualities of being material, or occupying space and time. Or it doesn't exist, this must mean that it is lacks those and such qualities -- but then can it really be said that we're in possession of a such a powerful predicate, so that we know that universal quality for existence, and know that it must be present in every single thing that exists in all realms and modes, and possible worlds? All scales and possibilities?
Predicating something with "existence" simply imports our metaphysical presuppositions in my view, rather than actually zones in the very quality that grants something existence. My view is both cool because something that truly doesn't exist isn't there at all in the first place to not exist, and resting on distinction it's far more phenomenological, which I take to be both more grounded in experience, and humble in its reach.
?x?S[¬?x]
The universal quantifier does not require existence. This statement says that for every member of S, it doesn't exist. Since there are no members of S, we can assign any attribute we want.
The only case where the above statement makes sense of course is when S is the empty set. If it had members, it would be false. And it works for the empty set because, again, the universal quantifier does not require existence.
I do not believe the existential (or universal) quantifiers may stand alone. Rather there must be a unary predicate P so that you can write ?xP(x).
If you have a reference illustrating a use of a standalone quantifier like ?x I would appreciate a link or specific reference.
An expression such as ¬?x is meaningless, as is ?x?S[¬?x]. That's just not a well-formed formula in predicate logic.
If the general form of the existential quantifier is ?xP(x) then in your example you are saying that ¬?x may be a predicate. So you are assuming the thing you are trying to prove. In fact ¬?x is not a predicate.
How about if you wanted to state that a set contains at least one member? The only sensible way to write it is ?x?S. That is a case of a standalone quantifier. That isn't to say anything about it being a predicate, but it could be extended for that case.
Next, how would you state that a set is empty in predicate logic?
At least one absolute being is absolutely necessity for the laws, of universe to be necessary if not, everything could be otherwise. Kant's refutation of the ontological argument ended dogmatic metaphysics.
?x?S (x ? S)
That would be the formal way, since x ? S is a predicate.
Quoting Joseph
Technically that is a convenient abuse of notation. Everyone writes it that way, everyone knows what it means. But it's not actually correct if one is being precise.
Quoting Joseph
No. Besides, it has a completely different form than your earlier example of writing ?x without any predicate at all. You are giving two completely different examples. ?x by itself is is meaningless. ?x?S is technically wrong but everyone understands that it's a shorthand for ?x(x?S).
Quoting Joseph
¬?x(x?S).
Hmmm. To me science makes more sense the other way around, where you have some idea what your domain is -- and you might get that wrong and have to change it -- and the question is either "What in my domain has the properties my effect needs it to?" or "Does anything in my domain have such-and-such a property?"
The formalism was developed for mathematics, where you always specify the domain. Science has no choice but to follow suit. What are you going to do? look everywhere? at everything?
I think that may be the wrong approach. It's a little like saying, "There does not exist a predicate (x) in language (S) which has the meaning, 'and' (?)."
Existence is not a predicate because it is something else, namely a quantifier. It's just a matter of getting it in the right logical bucket.
But "is a fiction" is a predicate, yet fictional things don't exist.
I wonder if perhaps there's conflation between the existential quantifier in logic and "existence" as an ordinary language term.
Is "to be a predicate" a predicate? I suppose so, but haven't figured out whether that's problematic.
Quoting Agustino
Philosophy and forums? In my own case, also looking for (in)consistencies among different things, e.g. ? and quiddity (old post).
Quoting Michael
In this case, any such meanings (including hypothetical) already exemplifies existence. Seems in some ways, existence is auto-presupposed.
Anyway, using existence as a predicate can sometimes lead to nonsense, and other times make sense. So, ? is not just another ?, except sometimes it is?
I haven't figured it out either, but if it's problematic, it's logic that has a problem, not existence. If existence declares that particles are waves or whatever quantum weirdness you care to mention, logic will just have get it's act together about it. It might just be the usual problem of ordinary language being its own meta-language.
Quoting Michael
Fictional things don't exist, but fictions do.
This is where the problem is then. If, from the perspective of what is logical, to exist is simply to be the subject of a predicate, then logic isn't consistent with what we normal mean when we say "exists". This is why logic and epistemology must be based in a good ontology, not vise versa. If we turn this around, and try to base an ontology in what logic makes of existence, we are headed into problems.
'a exists', has 'a' as its subject and 'exists' as its predicate.
But, exists is not a primary predicate.
(Ga & (a exists)) <-> Ga, ie. (a exists) does not add information to Ga.
If we define (a exists) as ?F(Fa), and
(G exists) as ?xGx.
1. |-. Ga -> ?F(Fa). |-. Ga -> (a exists).
2. |-. Ga -> ?x(Gx). |-. Ga -> (G exists).
3. |-. Ga -> ?F?x(Fx). |-. Ga -> ((Ga) exists).
(x exists) <-> ?F(Fx).
(x exists) <-> ?y(x=y).
(x exists) <-> x=x.
(x exists) <-> ((~F)x <-> ~(Fx)).
For one thing, classical theism is in jeopardy. To claim that God can be proven or believed to exist, despite not knowing his essence, becomes a nonsensical distinction if existence isn't a predicate.
For "Ga" to be a wff, doesn't a have to be an object in your domain of discourse?
What sense can be made of asserting "Ga" if you don't already know that a exists?
The whole conundrum seems a bit nonsensical to me. Nothing can be "proven" to exist. You can't even "prove" other minds exist. Classical theism does not claim to "prove" God in the sense of showing that it is irrational and illogical not to believe in God. Rather classical theism tries to give a defence of the faith which means to give very compelling reasons for believing in God, not a deductive and bullet proof argument. The premises of Aquinas' arguments can be denied for example. They are certainly sensible propositions that many people would be inclined to acknowledge, but one can still do the mental gymnastics required to deny them.
That's nothing but an argument from authority. I asked you to use your head and give me an actual reason. Philosophers of the past may have thought it is important to debate whether existence is a property or not (because they were interested in the ontological argument) but maybe they were bothering to address unimportant and sterile matters to begin with (and later philosophers like Russell merely picked up on such sterility without questioning it). Maybe they were asking the wrong questions, and discussing dead ends. So just because philosophers have thought it important to discuss it, doesn't mean it really is important. So again, why is it important? Why should I care about resolving this issue? How will it change anything?
What's a proof then? A proof to me is undeniable evidence that something is the case. Such cannot be given in the case of God.
I can prove the Theorem of Pythagoras within a certain system undeniably. But I cannot undeniably prove the existence of God.
"For "Ga" to be a wff, doesn't a have to be an object in your domain of discourse?"
Vulcan rotates.
Pegasus flies.
Santa wears a red suit.
Etc. are false WFF where the subject terms do not exist.
"What sense can be made of asserting "Ga" if you don't already know that a exists?"
Pegasus exists, is a sensible wff that is false.
There are no true propositions that have non-referring names or non-referring descriptions as their subject.
Not helpful.
Russell would take all of these as false, but not as predicating anything of Vulcan or Pegasus or Santa.
How do you predicate, truly or falsely, of an object that does not exist in your domain of discourse?
Quoting Owen
And its logical form is what?
Quoting Owen
But on your view, "Pegasus does not exist" should be true, shouldn't it?
'Exists is not a predicate'
since 'exists' is grammatically a predicate and 'existence' is not.
It seems odd to say that a grammatical predicate is not a predicate. We must mean a different sort of predicate. I think we mean a logical predicate, so that the statement, at the expense of making it longer, becomes:
'Exists is a grammatical predicate but not a logical predicate.'
The way I make sense of this is to observe that when we say 'Santa Claus does not exist' what we actually mean is 'No being that ever lived had the key properties ascribed to Santa Claus'. Then in this sentence, the logical predicate is IsSantaClausLike, which means 'has all the key properties ascribed to the legendary Santa Claus' and it is formally rendered as something like:
for all x, for all t, (Alive(x,t) --> NOT IsSantaClausLike(x))
Yeah that's Russell's solution, to take the name as an abbreviated description.
I think we also want a way to talk about fiction (hypothesis, supposition, etc) "in world." So there are two answers, say, to "Does Santa fly in a helicopter?" One is "No, because he doesn't exist," but another is "No, it's a sleigh pulled by flying reindeer." Both have their use.
When you tell people things, the actual physical exactitude of representation is entirely irrelevant, but the significance and effect of your experiences, and the events that transpired is what is remembered, and sought. None of which is any less real or true when represented with words, stones, stick figures, or bunny rabbits.
All that you do when you make that distinction is tell me that you're confusing some representations for the true true, and holding them as fundamentally different than others. You're a fanboy of a particular kind of story, is all.
I'm not sure anyone wrote up a concise grammar for their syntax in general, but that'd be interesting to take a look at (feel free to point me in their direction if you know any).
In computing there are analogies to be found in comprehensions.
Quoting unenlightened
Yep.
That's the crux of the pseudo problem expressed by "existence is not a predicate".
I think it might be helpful to distinguish the issue of whether existence is a predicate, with the issue of how philosophers handle fiction. That latter in itself is a huge topic.
If I say, "Ahab is the cabin boy of the Pequod," that statement is false. Yet Ahab does not exist, he's a fictional character. And someone could write fan fiction in which Ahab is the cabin boy, or the whale, or Gregory Peck. ("He tasks me. He heaps me!")
Now analyzing the truth values of statements about fictional characters is a deep business, but it's not really the same question as whether existence is a predicate.
After all, "Ahab is captain of the Pequod" is a shorthand for: "In Melville's novel Moby Dick, Ahab is captain of the Pequod." That statement is true, and there is no ambiguity or confusion. So perhaps one way out of the fiction dilemma is to fully qualify all statements. "Kirk is captain of the Enterprise in the original Star Trek tv show."
But all of this discussion of the truth values of statements about fictional entities, are red herrings (IMO) in the discussion of whether existence is a predicate.
Every discussion about existence ends up being a discussion about negative existentials!
But I agree. And I stand by what I said earlier:
Quoting Srap Tasmaner
Frege makes the point that "The king's coach was pulled by four horses" has a very different logical structure from "The king's coach was pulled by black horses." That's the right place to start, in my opinion.
Sorry, I was never warned of this message, and just accidentally saw it now.
Because I don't think we need undeniable evidence (proof) of God to believe. Rather I, along with Pascal, take it that there is enough light for those who want to believe to believe, and enough darkness for those who don't want to believe, not to believe. Christianity does talk, in the end, about a Hidden God.
If someone says, "Hobbits exist," in order for the statement to be meaningful it would have to be about something, but what could the statement be about? It can't be about Hobbits since there are none. Thus it's about the concept of Hobbits. Thus, existence isn't something individuals possess - instead it's a way of talking about concepts of individuals.
Something seems awry here. The concept of Hobbits exists. Hobbits don't exist (at least not outside of the fictional media depicting them).
Under your theory, how could we coherently express the proposition that some X does not exist? If we can talk sensibly about X and whether or not it exists, I think it's safe to say that the concept of X exists (and is at least partially understood by the interlocutors). However, it would then be a contradiction in terms to state that X does not exist. Therefore, anything and everything which can be subsumed under some sensible concept can be said to exist!
I think Sam was saying that talk of existence is really talk of whether a concept is instantiated. I don't see how saying that a concept isn't instantiated is a contradiction.
You get a contradiction if you treat existence as a predicate, because you can only predicate of objects in your domain of discourse.
Another important point, is that we must be able to explain the meaning of a proposition, including the subject, apart from knowing whether they're true or false. We also know that statements about hobbits are meaningful apart from knowing whether they are true or false. How is this possible? It possible because we understand the concept, and the only thing we know exists is the concept, not the subject. It can only make sense if the statement is about the concept, and not about the subject.
Moreover, we can coherently talk about the proposition that some X exists, or does not exist, because we are asking whether or not the concept X has an instance in reality. There is no inherent contradiction in the argument. Other philosophers who believed this were Kant and Russell, one being a theist, and the latter an atheist.
Quoting Sam26
And what do you mean when you say that the concept is not instantiated, has no instances? (I deliberately emphasized the verb "to be" in these phrases.) Well, it means that there are no such things, that they do not exist. Oh, wait...
That's roughly along the lines of how I use the words.
Say, Superman exists, but just isn't real.
Quoting Owen
Right.
(Y) I'll go with that.
In brief, something like:
Yes, absolutely. But this
Quoting jorndoe
is confusing for everyone.
Quoting SophistiCat
If your point is that this is not an explanation of existence -- the ineffable there-ness of stuff -- I don't think it was intended to be. Neither, really, is "To be is to be the value of a bound variable," which comes to the same thing. Or saying the copula is sortal-hungry, which also comes to the same thing.
But it does clarify the logical form of existence statements and cut off the weirdness of saying "Superman is an object that has the property of not existing." If instead you say, "The concept of Superman has the property of having no instances," at least you haven't tried to predicate of an object that in the same breath you say doesn't exist. (And people get hinky about this and say things like, before it was built the Empire State Building did exist "as an idea".)
(And you don't even need to predicate of concepts: "Nothing has the property of being Superman" is a reasonable natural language equivalent to "¬?xFx".)
You know all that though, so what was your point?
ADDED: That sounds belligerent, but was meant to sound puzzled.
I think I have a better idea of what you're driving at. A couple of questions/points: what does it then mean to say that a concept exists? That the concept of the concept is instantiated (presumably in one or more minds, or at least in one or more products of minds such as novels, etc., or wherever it is that concepts inhere)?
Secondly, in yoking existence to concepts, it would seem to imply that nothing exists which is unconceptualized. If the existence of X simply means that the concept of X is realized in at least one concrete instance, then the notion of existence is meaningless without reference to concepts. However, concepts require minds, do they not? Did that mean that nothing "existed" prior to the advent of minds which were capable of realizing concepts?
The existence of X is not dependent upon the existence of the concept. Thus, things can exist apart from us referring to them as part of a language. However, we want to know whether it is true or false, to say that hobbits exists in reality, as opposed to being part of a fictional work.
I'm not simply yoking existence to concepts, but yoking existence to whether or not that concept has an instance in reality. This doesn't mean that existence is dependent upon the concepts, but talking about existence is dependent upon the concepts. So obviously things could exist apart from minds.
Hm. Seems reasonably clear to me.
For something to be real, it have to exist.
For something to exist, it doesn't have to be real. Like Superman or other imaginary things.
Do you have a simpler understanding or use of the words?
I just don't want to say that Superman exists one way in fiction and another way outside it. The fiction exists in our world. Superman doesn't, not even "as" something.
If you want to say he exists here "as an idea", then as an idea of what? As an idea of an object, namely himself. So Superman is the idea of Superman, and that's an infinite regress.
We need a nice way to talk about fictional objects, but this is headed in the wrong direction, I'd say.
P(x) iff ?x(x=x)
P(x) is true if and only if x exists. (x exists iff it equals with itself)
Semantical existence can't be modelled imo. We need an ontology as a naive metatheory for that.
No, you are right, I think I got carried away.
Quoting Meta
So x exists iff there exists x (?x) such that it is equal to itself? The last bit seems unnecessary, but otherwise you have a perfect tautology.
The last part is necessary for the formula to be well-formed.
And yes, it is a tautology, but it expresses existence. Any other tautologies would be sufficent.
If the predicate expressing existence isn't a tautology then it does not characterize existence.
I think the point could be to show that if we want to define a predicate P(x) in a formal language that means x exists then our only option is to make P a tautology.
I actually do believe that concepts inhere in minds (or at least their products), and all else that follows from that: I'm not sure where else they would inhere.
The good folks at the comic con told me my best bet is getting written into a comic book, and that's it.
How disappointing. :)
, I'd say we auto-presuppose that anything that exists is self-identical.
We sort of have to; trying the contrary leads no where.
Concepts come to life in language, and language is made up of rules that happen between and amongst people. For me it's a confusion to think that concepts exist in minds, concepts only have existence in terms of how we use words in statements; and this happens in the practice of following the rules of language. So concepts get their life in terms of how we act, but this is quite separate from the idea that concepts exist in a mind.
To illustrate this point, let's say that I create a concept that doesn't exist, call it samigga, what would it mean to say that the concept exists in my mind? Is there some thing in your mind that has existence apart from how the concept is used? Note though, that if a new word is created, it gets its life how? It gets its life, thus its existence, as we use it with others, and as it's gradually accepted by others into a language.
Logic is like music theory. First we make music, and then we theorise about harmony and dissonance and so on. So first we talk, and then we theorise about the logic of language. Which means, I think, that logic cannot tells how to talk, any more than music theory can tell us how to make music. It may be convenient for the purposes of logic to say:
But it is well to remember that this is just another song about Doh being a deer, a female deer. Existence is prior to to talk, and talk is prior to logic.
Relativity!!
Being unmarried is not a predicate of everyone. However it is for a bachellor.
In the same way existence is only predicate to itself.
Existence is what exists.
What exists is existence.
Does an apple exist, then?
it neither exists nor doesn't exist. That's the implications of relativity.
The apple can be said to exist if the conditions are so that there is an apple. an apple can be said not to exist if the conditions are so that there is not an apple.
Phenomena is interdependent causation, therefore for phenomena it is not accurate saying it has existece as a predicate. But it is also innacurate saying it has not existence as a predicate.
Only the metaphenomenological can have the predicate of existing. In other words just existence itself and its attributes.