Untangling Plato's Beard

I was asked by a commenter what motivates the thin theory of existence.  One motivation is 

. . . the old Platonic riddle of nonbeing. Nonbeing must in some sense be, otherwise what is it that there is not? This tangled doctrine might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor. (Willard Van Orman Quine, "On What There Is" in From a Logical Point of View, Harper Torchbook ed., 1963, pp. 1-2)

As I see it, here is how the paradox arises.

1) 'Pegasus does not exist' is true. Therefore:

2) The sentence in question has meaning. (Only meaningful sentences have a truth value.) 

3) If a sentence has meaning, then so do its (sentential and sub-sentential) parts. (Compositionality of meaning.) Therefore:

4) 'Pegasus' has meaning. Therefore:

5) Something is such that 'Pegasus' refers to it. ('Pegasus' is a proper name, and the meaning of a proper name is its referent, that to which it refers.) Therefore:

6) 'Pegasus' refers to something that exists. (Everything exists; there are no nonexistent objects; one cannot refer to what does not exist for it is not there to be referred to.) Therefore:

7) Pegasus must exist for it to be true that Pegasus does not exist.  Paradox!

None of the first four propositions is plausibly denied. To avoid the conclusion, we must deny either (5) or (6) and the assumptions that generate them. Now Quine is no Meinongian/Wymanian. Quine advocates a Russellian solution which amounts to rejecting (5) by rejecting the assumption that the meaning of a proper name is exhausted by its reference.  For Russell, ordinary proper names are definite descriptions in disguise. This allows them to have meaning or sense without reference.   Thus 'Pegasus' is elliptical for 'the winged horse of Greek mythology.'  This allows the following contextual paraphrase of 'Pegasus does not exist':

It is not the case that there exists an x such x is the winged horse of Greek mythology

which is free of paradox. What the paraphrase says is that the definite description which gives the sense of 'Pegasus' is not satisfied. Equivalently, it says that the concept winged horse of Greek mythology is not instantiated.   Thus the original sentence, which appeared to be about something that does not exist but which, if it existed, would be an animal, is really about about a description or concept which does exist and which is assuredly not an animal.

It is a brilliant solution, prima vista. It works for negative general existentials as well. 'Unicorns do not exist,' despite its surface grammar, cannot be about unicorns -- after all, there aren't any -- it is about the concept unicorn and predicates of it the property of not being instantiated.  Extending the analysis to affirmative general existentials, we can say that 'Horses exist,' for example, is not about horses -- after all, which horses would it be about? -- it is about the concept horse and predicates of it the property of being instantiated.  

What about singular affirmative existentials such as 'Harry exists'?  Quine maintains that, in a pinch, one can turn a name into a verb and say, with truth, 'Nothing pegasizes' thereby avoiding both Plato's Beard and Meinong's Jungle so as to enjoy, clean-shaven, the desert landscape bathed in lambent light.  So what's to stop us from saying 'Something Harry-sizes'?  (Quite a bit, actually, but I won't go into that in this post, having beaten it to death in numerous other entries. Briefly, there are no haecceity-concepts: there is no such concept Harry-ness that (i) can exist uninstantiated; (ii) if instantiated is instantiated by Harry and Harry alone in the actual world; (iii) is not instantiated by anything distinct from Harry in any possible world.)

Let us now pause to appreciate what the Russellian (or rather 'Fressellian') approach accomplishes in the eyes of its advocates. It untangles Plato's Beard. It avoids Meinong's jungle. It preserves the existence-nonexistence contrast by situating it at the second level, that of descriptions, concepts, propositional functions, properties, as the contrast between satisfaction-nonsatisfaction (for descriptions), instantiation-noninstantiation (for concepts and properties), and having a value-not having a value for propositional functions, or as Russell puts it, being sometimes true or the opposite.

What's more, it diagnoses the failure of certain versions of the ontological argument. Descartes' Meditation Five version has it that God exists because God has all perfections and existence is a perfection. But if Frege and Russell are right, existence is not even a property of God let alone a perfection of him inasmuch as '. . .exist(s)' has no legitimate use as a first-level predicate and can be be properly deployed only as a second-level predicate. (God is an individual.)

Last, but not least, the Fressellian analysis consigns entire libraries of school metaphysics to he flames, the books in which drone on endlessly about Being and Existence and the distinctio realis, and the analogia entis, and ipsum esse subsistens, ad nauseam.  Swept aside are all the hoary and endlessly protracted debates about the relation of essence and existence in individuals: is it a real distinction, and what could that mean? Is it a formal distinction, and what could that mean? Etc. On the Frege-Russell approach there simply is no existence of individuals.

And now you know why the thin theory is called 'thin.' It could also be called 'shallow' in that it eliminates existence as a deep and mysterious topic.  The thin theory disposes of existence as a metaphysical topic, reducing it to a merely logical topic.  As Quine famously says in an essay other than the one cited above, "Existence is what existential quantification expresses."  Thus 'Cats exist' says no more and no less than 'For some x, x is a cat.'  You will note that the analysans makes no mention of existence. It features only the word 'cat' and some logical machinery. Existence drops out as a metaphysical topic.

Of course, I don't accept the thin theory; but as you can see, I appreciate what motivates it in the minds of its adherents.

Comments

[David Gudeman]

Bill, you write, "Briefly, there are no haecceity-concepts: there is no such concept Harry-ness that (i) can exist uninstantiated; (ii) if instantiated is instantiated by Harry and Harry alone in the actual world; (iii) is not instantiated by anything distinct from Harry in any possible world.)"

You have referred to this argument many times, but it has always struck me as weak because as a thin theorist, I have no use for haecceity concepts. You did argue here for why thin theorists need these concepts: https://maverickphilosopher.blogspot.com/2004/12/. You say this: "It follows that my existence cannot be identified with the being-instantiated of this property [a descriptive property]. For if anything is clear, it is that my existence is bound up with my identity: my existence is essential to me..."

This looks a lot like begging the question. Why would a thin theorist agree that your existence is bound up with your identity? Quite the opposite: I would say that "my existence" is an odd turn of phrase with no clear meaning--rather like "my numerousness". In order for that argument even to get off the ground, one must already agree that existence of a thing is something that the thing has.

I noticed the same sort of problem in your previous post on the topic, but didn't comment on it at the time. In the course of finding circularity in the thin theory, you said, "does Tom exist because some concept C is instantiated, or is C instantiated because Tom exists?", but to a thin theorist, "Tom exists" just means that there is a Tom, and "C is instantiated" just means that there is a C, so if C is the concept associated with the name "Tom", then that question can be translated to "is there a Tom because there is a Tom, or is there a Tom because there is a Tom?"

Again, you seem to be begging the question against the thin theorist by assuming that there is a difference between Tom existing and the concept of Tom being instantiated.

As far as I can see, the thin theory accounts for all of the normal-language and mathematical uses of the word "exists" and only fails on uses of the word that presuppose a thick theory of existence.

[José Guilherme]

If I could ask you a comment on this problem…

So… as you have said multiple times in contrast to the thin-theory of existence where there isn’t the existence of individuals, such that we can’t say of a concrete particular thing that he exists, we have a thick-theory of existence. Now, I believe that in the system that you presented in “A Paradigm Theory of Existence” surely we can maintain that a particular thing exists, but even more important we have an answer to the question “what is existence?”. In that metaphysical system the answer, I believe, is “existence is the (external) unifier of the ontological constituents of the (particular) being”. Now those constituents are the bare particular and the universals. So, in your system an ordinary particular (say, my cat “Kenshin”) it’s a thick particular and that really is a concrete state-of-affairs.

My question is what are the consequences of this conception to the issue of causation. For instance, some authors (E.J. Lowe in “Free Agency, Causation and Action Explanation” for instance) maintain that the engines of chance in the world are substances, not events. The conclusions that we arrive in this question would be, I believe, decisive to the way that we engage other philosophical problems, for instance the problem of free will, for instance.

So, could we say that in your metaphysical system we really can’t have the distinction between event-causation and agent-causation? Or could we say that that distinction still exists since in in any thick-particular there is an integrity and unity between its ontological constituents and that makes it possible to distinguish between an thick-particular as a cause and an event as a cause?

Any comment would be greatly appreciated. Thank you so much,

José Guilherme

[Dominik Kowalski]

David, now you have to really explain to me where you are supposed to have avoided haeccities. If you say the concept Tom being instantiated is equivalent to Tom existing, then that just means that there is indeed a universal Tomness, which just is a haeccity. And to say that this is begging the question is to not see that this is a reductio ad absurdum against that position.

[David Gudeman]

Dominik, I searched for an argument where Bill argued that haeccities are needed for the thin theory and only found the one. I explained why that argument does not work, but if you have another one, I'd love to hear it or get a pointer to it.

All a thin theory requires (I claim) is that the speakers share some concept of Tom. It may be as simple as "the guy Barbara is always referring to as Tom". The question of whether Tom exists is then nothing more than the question as to whether Barbara is making things up. If Tom is someone you know, then your concept of Tom may be much more complex, but whatever it is, there is someone who satisfies your concept, so Tom exists. The concept doesn't have to get at Tom's essence (whatever that is) or be invariant over all possible worlds.

This goes to the fact that another advantage of the thin theory is that it is neutral with respect to ontology. Because it doesn't require a true essence of an object for that object to exist. The thin theory is consistent with idealism and transcendental idealism, whereas the thick theory, is (it seems to me) only compatible with realism.

[Dominik Kowalski]

David, I'd answer that I think you are misrepresenting the argument. The question proposed by Bill is whether Tom is the instantiation of a specific concept Tomness. Or if Tom as an individual can't be identified with the instantiation of a specific concept. If it's the former, then we need haeccities. If I were to take your translation st face value that would be what we would end up with, because you already identify Tom with a specific concept here.

If you don't want to say that however, then you should outline what "Tom" as an individual means on your ontology. I don't believe you want to go the crazy route and eliminate the individual here altogether. It's obvious that "Tom" refers to something real. But what exactly is that? Admittedly here is a weak point of when it comes to outlining my views in detail, so I'd appreciate Bill's comments here, but roughly I'd say that Tom is the particular instantiation of the properties being linked to existence where the properties particular. It isn't perfect, far from it, but it faces the issue head on. If you however claim that for a thin theorist "Tom exists" just means "There is a Tom" and "C is instantiated" just means that there is a C, then I don't see how the question has been answered. The way I see it in your translation into

"is there a Tom because there is a Tom, or is there a Tom because there is a Tom?"

you are equivocating on the meaning of Tom here, because that translation is incapable of addressing the question of ontological priority I take Bills question to have raised. On Lemma 1 there seems to be a reductive approach, the individual just is the instantiation of a particular universal that just makes the individual. A haeccity. On Lemma 2 however there seems to be a holistic approach, because whatever Tom is exactly referring to, it can't be the instantiation of a particular concept, for that would give rise to a vicious circle.

In short, "Tom exists" is a statement that has meaning. But in virtue of what? To say because that there is a Tom is to give no answer. To give reference to a specific property or concept, even in the verb-sense that Bill quoted Quine as proposing, is to accept haeccities.

But it seems to me, as to your last answer, that you are quite willing to eliminate any real meaning in the statement "Tom exists". In fact, to refer to the last sentence in your paragraph, there may be no sense even to be made of the referent "Tom" at all on your view. But that is a reductio. It doesn't solve the problem Bill raised, it cuts off before it could even arise.

Now I hope I haven't told complete nonsense. If it is then I leave it to the blogger in chief to set me straight.

[Dominik Kowalski]

David, I'd answer that I think you are misrepresenting the argument. The question proposed by Bill is whether Tom is the instantiation of a specific concept Tomness. Or if Tom as an individual can't be identified with the instantiation of a specific concept. If it's the former, then we need haeccities. If I were to take your translation st face value that would be what we would end up with, because you already identify Tom with a specific concept here.

If you don't want to say that however, then you should outline what "Tom" as an individual means on your ontology. I don't believe you want to go the crazy route and eliminate the individual here altogether. It's obvious that "Tom" refers to something real. But what exactly is that? Admittedly here is a weak point of when it comes to outlining my views in detail, so I'd appreciate Bill's comments here, but roughly I'd say that Tom is the particular instantiation of the properties being linked to existence. It isn't perfect, but it faces the issue head on. If you however claim that for a thin theorist "Tom exists" just means "There is a Tom" and "C is instantiated" just means that there is a C, then I don't see how the question has been answered. The way I see it in your translation into

"is there a Tom because there is a Tom, or is there a Tom because there is a Tom?"

you are equivocating on the meaning of Tom here, because that translation is incapable of addressing the question of ontological priority I take Bills question to have raised. On Lemma 1 there seems to be a reductive approach, the individual just is the instantiation of a particular universal that just makes the individual. A haeccity. On Lemma 2 however there seems to be a holistic approach, because whatever Tom is exactly referring to, it can't be the instantiation of a particular concept, for that would give rise to a vicious circle. It has to be the whole, not an identifiable part.

Now you seem however to be quite willing to eliminate any sense to the statement "Tom exists". In fact, I take your last sentence in the second paragraph to go even further, namely that on your view there needn't be anything that designates "Tom", an external referent is sufficient. If however there is nothing about the individual that can be said to be responsible for the individuation, then the conclusion must be that there are no individuals. That indeed seems to be a solution for the question Bill raised, but only because there is a cut off before it could even arise. But at what a price!

So in short, if we take "Tom" as referring to something real (the external reference by Barbara in your example as insufficient for real individuation), then Bills question seems to come up again. And the need for haeccities on the thin theory this would stand undefeated.

I actually already suspected that without admitting of haeccities, the thin theorist must eliminate the reality of individuals altogether, perhaps following the naturalist in eliminating it in favor of spatiotemporal relations. But I won't investigate that idea any further now, it already took me long enough to write this up. While I hope I didn't write complete nonsense here, I'd ask the blogger-in-chief to set me straight if I went completely off the rails here.

[BV]

José Guilherme,

You are posing a very difficult question, one that I do not address in my book. A central problem in my book was to explain how existence could belong to concrete individuals. I found that I could answer the question to my satisfaction if I assayed ordinary individuals as thick particulars in Armstrong's sense and thus as states of affairs. But then how explain alterational change? But this problem is off-topic and cannot be set forth here with the care it deserves.

[BV]

Dominik writes,

>>David, now you have to really explain to me where you are supposed to have avoided haeccities. If you say the concept Tom being instantiated is equivalent to Tom existing, then that just means that there is indeed a universal Tomness, which just is a haeccity. And to say that this is begging the question is to not see that this is a reductio ad absurdum against that position.<<

You shouldn't refer to an haecceity concept as a universal. A universal is a repeatable, either a one-in-many or a one-over-many. Universals, by definition, are multiply instantiable. But no haecceity is multiply instantiable. Ergo, no haecceity is a universal.

[BV]

Dominik writes,

>>The question proposed by Bill is whether Tom is the instantiation of a specific concept Tomness. Or if Tom as an individual can't be identified with the instantiation of a specific concept.<<

Genus-species-individual. So it is best to refer to an haecceity concept as an individual concept. But I know what you mean.

The question is this: Can the existence of Tom be identified with the being-instantiated of an haecceity concept? I say No for two reasons. First there are no such concepts. I argue that elsewhere, and it is off-topic here. Gudeman seized upon my parenthetical remark and ignored the whole point of my post whcih was to explain to Frank one of the motivations of the thin theory.

The second reason is that, if if there were haecceity concepts, one would move in an explanatory circle if one identified the existence of Tom with the being-instantiated of an haecceity concept or ANY concept. If a first-level concept is instantiated, it is instantiated by an individual (which of course is not concept). This individual must exist. One cannot therefore account for the (singular) existence of an individual in terms of the being-instantiated of a concept without presupposing precisely what it is you are trying to account for, namely the existence of an individual.

[José Guilherme]

Ok!

Thanks a lot for your comment.

José