Existence – Page 8 – Maverick Philosopher

Arguing with Brightly over Ficta

Earlier I wrote that the central problem in the philosophy of fiction is to find a solution to the following aporetic dyad:

1. There are no purely fictional items.

2. There are some purely fictional items.

The problem is that while the limbs of the dyad cannot both be true, there is reason to think that each is true.

David Brightly comments:

May I offer the following resolution of the paradox? I say that 'purely fictional' does not function as a concept term. Instead, it is ambiguous between two interpretations. On the one hand, it behaves like the pseudo-concept 'inexistent'. To say that Bone is a purely fictional alcoholic is to deny that Bone exists. [BV: Biconditionality seems too strong. If N is a purely fictional F, then N doesn't exist; but if N doesn't exist, it does not follow that N is purely fictional.] The same goes whatever name and concept term we substitute for 'Bone' and 'alcoholic'. This leads us to assert

1. There are no purely fictional items.

On the other hand, I say that 'fictional and 'purely fictional' appear to be concept terms because sentences like

Bone is a purely fictional alcoholic

arise via a surface transformation of

Purely fictionally, Bone is an alcoholic

and inherit their meaning and truth value. We can understand the latter as asserting that

Some work of fiction says that Bone is an alcoholic.

We take this as true, as evidenced by the work of Hamilton, and running the transformation in reverse gets us to

Bone is a purely fictional alcoholic.

Taking 'purely fictional alcoholic' as a predicate, which it superficially resembles, by Existential Generalisation we arrive at

There is some purely fictional alcoholic,

and hence to

2. There are some purely fictional items.

and apparent contradiction with (1).

The idea of a surface transformation may well appear controversial and ad hoc. But the phenomenon occurs with other pseudo-concept terms, notably 'possible'. We have

Bone is a possible alcoholic <—> Possibly, Bone is an alcoholic
Bone is a fictional alcoholic <—> Fictionally, Bone is an alcoholic.

On the left we have 'possible' and 'fictional' which look like concept terms but cannot be consistently interpreted as such. On the right we have sentential operators which introduce an element of semantic ascent which is not apparent on the left. It's precisely because 'possible' and 'fictional' involve hidden semantic ascent that they do not work as concept terms.

Response

I am afraid I don't quite understand what David is saying here despite having read it many times. This could be stupidity on my part. But I think we do need to explore his suggestion that there is an equivocation on 'purely fictional items.' Let me begin by listing what we know, or at least reasonably believe, about purely fictional characters.

First of all, we know that George Bone never existed: that follows from his being purely fictional.

Second, we know or at least reasonably believe that Bone is a character created by its author Patrick Hamilton, a character who figures in Hamilton's 1941 novel, Hangover Square. Just as the novel was created by Hamilton, so were the characters in it. Admittedly, this is not self-evident. One might maintain that there are all the fictional characters (and novels, stories, plays, legends, myths, etc.) there might have been and that the novelist or story teller or playwright just picks some of them out of Plato's topos ouranos or Meinong's realm of Aussersein. I find this 'telescope' conception rather less reasonable than the artifact conception according to which Bone and Co. are cultural artifacts of the creative activities of Hamilton and Co. Purely fictional characters are made up, not found or discovered. It is interesting to note that fingere in Latin means to mold, shape, form, while in Italian it means to feign, pretend, dissemble. That comports well with what fiction appears to be. Of course I am not arguing from the etymology of 'fiction.' But if you have etymology on your side, then so much the better.

Now there is a certain tension between the two points I have just made. On the one hand, Bone does not exist. On the other hand, Bone is not nothing. He is an artifact of Hamilton's creativity just as much as the novel itself is in which he figures. How can he not exist but also not be nothing? If he is not nothing, then he exists.

If Bone were to exist, he would be a human person, a concrete item. But there is no such concretum. On the other hand, Bone is not nothing: he is an artifact created by Hamilton over a period of time in the late '30s to early '40s. Since Bone cannot be a concrete artifact — else Hamilton would be God – Bone is an abstract artifact. Thus we avoid contradiction. Bone the concretum does not exist while Bone the abstract artifact does. This is one theory one might propose. (Cf. Kripke, van Inwagen, Thomasson, Reicher, et al.)

Note that this solution does not require the postulation of different modes of existence/being. But it does require that one 'countenance' (as Quine would say) abstract objects (in Quine's sense of 'abstract') in addition to concrete objects. It also requires the admission that some abstract objects are contingent and have a beginning in time. The theory avoids Meinongianism but is quasi-Platonic. London Ed needs a stiff drink long about now.

Now let's bring in a third datum. We know that there is a sense in which it is true that Bone is an alcoholic and false that he is a teetotaler. How do we reconcile the truth of 'Bone is an alcoholic' with the truth of 'Bone does not exist'? There is a problem here if we assume the plausible anti-Meinongian principle that, for any x, if x is F, then x exists. (Existence is a necessary condition of property-possession.) To solve the problem we might reach for a story operator. The following dyad is consistent:

3. According to the novel, Bone is an alcoholic

4. Bone does not exist.

From (3) one cannot validily move via the anti-Meinongian principle to 'Bone exists.' But if 'Bone is an alcoholic' is elliptical for (3), then 'Bone is a purely fictional character' is elliptical for

5. According to the novel, Bone is a purely fictional character.

But (5) is false. For according to the novel, Bone is a real man.

The point I am making is that 'Bone is a purely fictional character' is an external sentence, a sentence true in reality outside of any fictional context. By contrast, 'Bone is an alcoholic' is an internal sentence: it is true in the novel but not true in reality outside the novel. If it were true outside the novel, then given the anti-Meinongian principle that nothing can have properties without existing, Bone would exist — which is false.

I think Brightly and I can agree that a purely fictional man is not a man, and that a purely fictional alcoholic is not an alcoholic. And yet Bone is at least as real as the novel of which he is the main character. After all, there is the character Bone but no character, Son of Bone. In keeping with Brightly's notion that there is an equivocation on 'purely fictional item,' we could say the following. 'Bone' in the internal sentence 'Bone is an alcoholic' doesn't refer to anything, while 'Bone' in the external sentence 'Bone is a purely fictional character' refers to an abstract object.

We can then reconcile (1) and (2) by replacing the original dyad with

1* There are no purely fictional concreta

2* There are some purely fictional abstracta.

The abstract artifact theory allows us to accommodate our three datanic or near-datanic points. The first was that Bone does not exist. We accommodate it by saying that there is no concretum, Bone. The second was that Bone is a creature of a novelist's creativity. We accommodate that by saying that what Hamilton created was the abstract artifact, Bone*, which exists. Bone does not exist, but the abstract surrogate Bone* does. The third point was that there are truths about Bone that nevertheless do not entail his existence. We can accommodate this by saying that while Bone does not exemplify such properties as being human and being an alcoholic, he encodes them. (To employ terminology from Ed Zalta.) This requires a distinction between two different ways for an item to have a property.

I do not endorse the above solution. But I would like to hear why Brightly rejects it, if he does.

A Cartesian Argument Against Meinong

The following is excerpted from my "Does Existence Itself Exist? Transcendental Nihilism Meets the Paradigm Theory" in The Philosophy of Panayot Butchvarov: A Collegial Evaluation, ed. Larry Lee Blackman, The Edwin Mellen Press, 2005, pp. 57-73, excerpt pp. 67-68.

If anything can count as an established result in philosophy, it is the soundness of Descartes' famous cogito ergo sum 'argument.' Thus to the query, 'How do I know that I exist?', the Cartesian answer is that the very act of doubting that one exists proves that one indubitably exists. Now this may not amount to a proof that a substantial self, a res cogitans, exists; and this for the reason that one may doubt whether acts of thinking emanate from a metaphysical ego. But the cogito certainly does prove that something exists, even if this is only an act of thinking or a momentary bundle of acts of thinking. Thus I know with certainty that my present doubting is not a nonexistent object. But if Meinong were right, my present doubting could easily be a nonexistent object, indeed, a nonexistent object that actually has the property of being indubitably apparent to itself.

For on Meinongian principles, I could, for all I could claim to know, be a fictional character, one who cannot doubt his own existence. In that case, the inability to doubt one's own existence would not prove that one actually exists. This intolerable result certainly looks like a reductio ad absurdum of the Meinongian theory. If anything is clear, it is that I know, in the strictest sense of the word, that I am not a fictional character. My present doubting that I exist is an object that has the property of being indubitable, but cannot have this property without existing. It follows that there are objects whose actual possession of properties entails their existence. This implies the falsity of Meinong's principle of the independence of Sosein from Sein, and with it the view that existence is extrinsic to every object. Forced to choose between Descartes and Meinong, we ought to side with Descartes.

The Existent Round Square

One of Russell's objections to Meinong was that the denizens of Aussersein, i.e., beingless objects, are apt to infringe the Law of Non-Contradiction. Suppose a Meinongian subscribes to the following principle:

Unrestricted Satisfaction (US): Every definite description is such that some object satisfies it.

For any definite description we can concoct, there is a corresponding object or item, in many cases a beingless object or item. From (US) we infer that some object satisfies the definite description, 'the existent round square.' This object is existent, round, and square. So the existent round square exists, which is a contradiction. This is one Russell-type argument.

A similar argument can be made re: the golden mountain. By (US), not only is some object the golden mountain, some object is the existent golden mountain. This object is existent, golden, and a mountain. So the existent golden mountain exists, which is false, though not contradictory. This is a second Russell-type argument.

Are these arguments compelling refutations of Meinong's signature thesis? Here is one way one might try to evade the Russellian objections, a way similar to one Meinong himself treads. Make a distinction between nuclear properties and extranuclear properties. (See Terence Parsons, Nonexistent Objects, Yale UP, 1980, p. 42) Nuclear properties are those that are included in an object's Sosein (so-being, what-being, quiddity). Extranuclear properties are those that are not so included. The distinction can be made with respect to existence. There is nuclear existence and extranuclear existence. 'Existent' picks out nuclear existence while 'exists' picks out extranuclear existence.

This distinction blocks the inference from 'The existent round square is existent, round, and square' to the 'The existent round square exists.' Similarly in the golden mountain case. You will be forgiven for finding this distinction between nuclear and extranuclear existence bogus. It looks to be nothing more than an ad hoc theory-saving move.

But there may be a better Meinongian response. The Russellian arguments assume an Unrestricted Characterization Principle:

UCP: An object exemplifies each of the properties referenced in the definite description it satisfies.

From (US) we get the object, the existent golden mountain, and the object, the existent round square. But without (UCP) one cannot move to the claim that the existent golden mountain exists or to the claim that the existent round square exists.

A Meinongian can therefore defeat the Russellian arguments by substituting a restricted characterization principle for (UCP). And he can do this without distinguishing between nuclear and extranuclear existence.

The Grand Central Conundrum in the Philosophy of Fiction

As I see it, the central problem in the philosophy of fiction is to find a solution to the following aporetic dyad:

1. There are no purely fictional items.

2. There are some purely fictional items.

The problem is that while the limbs of the dyad cannot both be true, there is reason to think that each is true.

(1) looks to be an analytic truth: by definition, what is purely fictional is not, i.e., does not exist. George Harvey Bone, the main character in Patrick Hamilton's 1941 booze novel Hangover Square, does not now and never did exist. He is not a real alcoholic like his creator, Patrick Hamilton, who was a real alcoholic. What is true is that

3. Bone is a purely fictional alcoholic.

That (3) is true is clear from the fact that if a student wrote on a test that Bone was a teetotaler, his answer would be marked wrong. But if (3) is true, then, given that nothing can satisfy a predicate unless it exists, it follows that

4. Bone exists

and, given the validity of Existential Generalization, it follows that

5. There is a purely fictional alcoholic.

But if (5) is true, then so is (2).

It should now be spectacularly obvious what the problem is. There are two propositions, each the logical contradictory of the other, which implies that they cannot both be true, and yet we have excellent reason to think that both are true.

Now what are all the possible ways of solving this problem? I need a list. London Ed et al. can help me construct it. Right now all I want is a list, a complete list if possible, not arguments for or against any item on the list. Not all of the following are serious contenders, but I am aiming at completeness.

A. Dialetheism. Accept dialetheism, which amounts to the claim that there are true contradictions and that the Law of Non-Contradiction (LNC) is false.

B. Paraphrasticism. Reject (2) by attempting to show that sentences such as (3) can be paraphrased in such a way that the apparent reference to ficta is eliminated. For example, one might offer the following paraphrase of (3): 'Hamilton wrote a story implying that here is an alcoholic named Bone.' The paraphrastic approach works only if every reference to a fictional item, whether it be a person or place or event or fiction, can be paraphrased away. (As Kripke and others have noted, there are fictional fictions, fictional plays for example, such as a fictional play referenced within a play.)

C. Logic Reform. Reject Existential Generalization (off load existence from the particular quantifier) and reject the anti-Meinongian principle that nothing can satisfy a predicate (or exemplify a property) unless it exists. One could then block the inference from (3) to (2).

D. Ontology Reform. Reject (1) by arguing that fictional items, without prejudice to their being purely fictional, do exist. Saul Kripke, for example, maintains that a fictional character is an abstract entity that "exists in virtue of more concrete activities of telling stories, writing plays, writing novels, and so on . . . the same way that a nation is an abstract entity which exists in virtue of concrete relations between people." (Reference and Existence: The John Locke Lectures, Oxford UP, 2013, p. 73.) Or one might hold that fictional items are abstract items that exist necessarily like numbers.

E. Dissolutionism. Somehow argue that the problem as posed above is a pseudoproblem that doesn't need solving but dissolving. One might perhaps argue that one or the other of the dyad's limbs has not even a prima facie claim on our acceptance.

F. Neitherism. Reject both limbs. Strategy (A) rejects LNC. This strategy rejects the Law of Excluded Middle. (Not promising, but I'm aiming for completeness.)

G. Mysterianism. Accept both limbs but deny that they are mutually contradictory. Maintain that our cognitive limitations make it either presently or permanently impossible for us to understand how the limbs can be both true and non-contradictory. "They are both true; reality is non-contradictory; but it is a mystery how!"

H. Buddhism. Reject the tetralemma: neither (1) nor (2), nor both, nor neither.

I. Hegelianism. Propose a grand synthesis in which thesis (1) and antithesis (2) are aufgehoben, simultaneously cancelled and preserved. (I have no idea what this would look like — again, I want a complete list of options.)

First question: Have I covered all the bases? Or are there solution strategies that cannot be brought under one of the above heads? If you think there are, tell me what you think they are. But don't mention something that is subsumable under one of (A)-(I).

Second question (for London Ed): under which head would you book your solution? Do you favor the paraphrastic approach sketched in (B) or not? Or maybe Ed thinks that the problem as I have formulated it is a pseudoproblem (option (E)).

Be a good sport, Ed, play along and answer my questions.

London Paraphrastics Questioned

To block the inference from

1. Frodo is a hobbit

2. There are hobbits

we can invoke story operators and substitute for (1)

1*. In the Tolkien story, Frodo is a hobbit.

From (1*) one cannot validly infer (2). So far, so good. But what about the true

3. Frodo is a purely fictional character

given that the following is plainly false:

3*. In the Tolkien story, Frodo is a purely fictional character. (?)

How do we block the inference from (3) to

4. There are purely fictional characters. (?)

At this juncture, London Ed makes a paraphrastic move:

Note that 'fiction' just means what is contrived, or made up, or invented. To say that Frodo 'is' a fictional character is simply to say that he is made up, which itself no more than saying that someone (Tolkien) made him up.

Indeed, that is what 'fiction' means, 'pure fiction' leastways. 'Fiction' is from the Latin fingere. So Ed would paraphrase (3) as

3P. Someone (Tolkien) made up (created, invented, contrived) Frodo.

Now if the paraphrase is adequate, then (3) does not commit us ontologically to anything beyond Tolkien. It does not commit us to the existence of fictional characters. Ed wants to avoid views like that of van Inwagen according to which purely fictional items exist. It is worth noting that Ed agrees with van Inwagen about the univocity of 'is' and 'exists.' There are no modes of existence/being for either of them. And for both the one sense of 'is'/'exists' is supplied adequately and completely by the existential quantifier of modern predicate logic. Both are thin theorists when it comes to existence.

But is (3P) an adequate paraphrase of (3)?

I don't think so. If Tolkien made up Frodo, but Frodo does not exist, then what did Tolkien create? A mere modification of his own consciousness? No. He created a character that outlasted him and that cannot be identified with any part of Tolkien's body or mind. Tolkien ceased to exist in 1973. But no one will say that the character Frodo simply vanished in 1973. When Tolkien ceased to exist, his mental contents ceased to exist. But when the writer ceased to exist, Frodo did not stop being a quite definite fictional character. So Frodo cannot be identified with any mental content of Tolkien. Nor could Frodo be said to be an adverbial modification of one of Tolkien's acts of thinking.

I grant that Frodo is an artifact. He came into being by the creative acts of Tolkien and is dependent on Tolkien for his coming into being, and perhaps even tied to Tolkien for his very identity: essentiality of origin for ficta. Frodo is also dependent on the continuing existence of physical copies of LOTR. Frodo is an artifact that came into being and can pass out of being. This makes Frodo a contingent artifact. What's more, Frodo is not merely a content in Tolkien's mind: he can be thought about and understood and referred to by many different minds. So Frodo has a curious status: he is in one way dependent and in another independent.

Now I claim that if one admits that there are different modes of being/existence, one can make sense of this. Fictional characters have a dependent mode of being, but they are, nonetheless, items in their own right. They obviously don't exist in the way a fiction writer exists. But it would be false to say that they don't exist at all. After all, Frodo cannot be identified with a mental content of Tolkien.

So while it is true that someone made up Frodo, as Ed rightly insists, that does not suffice to show that Frodo does not exist.

Ed's paraphrase is inadequate. And so he is stuck with the problem of blocking the inference from (3) to (4).

……………………

UPDATE (7/31). I said above, "Frodo is also dependent on the continuing existence of physical copies of LOTR." That's not quite right. If all the copies of LOTR were destroyed tomorrow, Frodo would continue on as a cultural artifact in the oral tradition for as long as that tradition was maintained. But once that tradition petered out, it would be all over for Frodo if there were no physical copies of LOTR (electronic or otherwise) or writings about LOTR on hand. The dependence of abstract cultural artifacts on human beings, their practices and memories, is not easy to understand. We are in the realm of Hegel's objektiver Geist.

London Ed on Peter van Inwagen on Fiction

Comments by BV in blue.

Inwagen gives persuasive arguments that there is only one sort of existential quantifier, that we cannot quantify over ‘things’ that are in some sense ‘beyond being’, and that ‘exists’ means the same as ‘is’ or ‘has being’. No review of his work would be complete without a careful discussion of these arguments, but as I agree with them, I will not discuss them here.

The problem I want to discuss is with his main thesis. He aims to explain what he calls ‘fictional discourse’, namely discourse like “There are characters in some 19th-century novels who are presented with a greater wealth of physical detail than is any character in any 18th-century novel." Such sentences are true, according to him, but when we translate them into quantifier-variable idiom, we have to use the existential quantifier which, on his view, is equivalent to ‘exists’. This seems to imply that fictional characters like Tom Sawyer and Mr Pickwick exist. Inwagen bites the bullet, and argues that they do exist. They are abstract objects, which exist in exactly the way that numbers exist. So when we say, in a work of literary criticism, that “Mrs Gamp is a character in a novel”, the proper name ‘Mrs Gamp’ refers to an abstract or ‘theoretical’ entity.

BV: I don't think Ed is representing van Inwagen correctly here. Numbers cannot come into being, but it is plausible to hold that fictional characters do. So while fictional characters, for van Inwagen, are abstract entities, he remains noncommittal on the question whether they are abstract artifacts in the way that chess could be thought of as a abstract artifact, or instead abstract non-artifacts like numbers and cognate platonica. See the last paragraph of "Existence, Ontological Commitment, and Fictional Entities."

This leads to the following problem. Inwagen argues that when a sentence like “Tom Sawyer was a boy who grew up along the banks of the Mississippi River in the 1840s” appears in a work of fiction, it is not true. Indeed, it is not even false, since it does not make an assertion at all (Existence, Ontological Commitment, and Fictional Entities, p.148, footnote 15). But when it appears in a work of literary criticism, as ‘literary discourse’, it is true. But if it is true, it seems to imply that there was some individual who is [in] the extension of the property expressed by ‘boy who grew up along the banks of the Mississippi River in the 1840s’, and yet there was no such individual.

Inwagen resolves the problem as follows. Tom Sawyer the fictional character exists, but he does not have the property ‘boy who grew up along the banks of the Mississippi River in the 1840s’. Nor does Mrs. Gamp have properties such as being old, being fat and so on. He concedes that this sounds odd (Creatures of Fiction, p. 304-5), but he argues there is something rather like it in a familiar philosophical doctrine, namely Descartes’ thesis that a person such as Jones is an immaterial substance, and so cannot have properties like ‘being tangible’, ‘weighing 220 lbs’ and so on, but only properties appropriate to immaterial objects, such as ‘thinking about Vienna’, ‘being free from pain’ and so on. Descartes says that Jones bears a relation to the properties on the former list that is not the relation of ‘having’ or ‘exemplifying’ but, rather, the relation of “animating a body” that has or exemplifies the property. We say that Jones is about six feet tall, but we should really say ‘animates a body that is six feet tall’: “what looks like predication in ordinary speech is not always predication”.

Thus when we say that Tom Sawyer is the main character in a well-known book of the same name, we are saying something that is true because the copula ‘is’ signifies the relation of having or exemplifying. But if we say, in literary discourse, that Tom is a boy, or that he is a resident of Mississippi, it is true because the copula signifies a quite different relation, which Inwagen calls ‘holding’.

BV: This is an accurate summary of van Inwagen's position as I understand it.

Problems

Bill has already identified some problems with Inwagen’s thesis. For example, he says that when I think of Mrs Gamp, I think of a woman. But according to Inwagen, I am thinking of an abstract or theoretical entity, and no theoretical entity has gender.

I shall not discuss these (although I broadly agree with them), but will mention some further ones.

1. Plot summaries. I discussed plot summaries in a comment to Bill’s post. We have a clear notion of what counts as a ‘correct’ summary. E.g. “Tom Sawyer lives with his Aunt Polly and his half-brother Sid” is correct, “Tom Sawyer lives with his Aunt Polly and his sisters Lizzie, Jane, Kitty, Lydia and Mary” is clearly not. But this notion of ‘correctness’ is close enough to the notion of truth that Inwagen’s theory needs to deal with it. If we assimilate it to Inwagen’s notion of truth in ‘literary discourse’, i.e. if we regard a statement in a plot summary as of the same kind as “Mrs Gamp is a character in a novel”, then we have the problem that plot summaries are written ‘in universe’, and that the names of the characters refer to the characters as characters, and not as abstract theoretical entities. But if we assimilate plot summaries to condensed versions of the original literary work, we have the problem of how they can be ‘correct’ at all. It is fundamental to Inwagen’s account that sentences in a work of fiction do not make assertions at all, and so cannot admit of truth or falsity – or correctness or incorrectness.

BV: Ed's point here seems to be that van Inwagen cannot account for the correctness of plot summaries. It is clear that some summaries are correct or accurate and that some are not. Now a summary of a piece of fiction is either itself a piece of (severely condensed) fiction, in which case it contains sentences that are, on van Inwagen's theory, neither true nor false, or it is not a piece of fiction but a piece of writing containing true sentences about the content of the fictional work being summarized. This disjunction appears to be a dilemma. For on the first disjunct, it is hard to see how a plot summary could be correct or true. But the second disjunct is also unacceptable. For suppose the summary contains the sentence 'Mrs Gamp is a fat old lady.' Then 'Mrs Gamp' in this sentence takes an abstract existent as its referent, an existent that does not HAVE but HOLDs the properties of being fat, being old, and being a lady, when the novel is not about abstract objects at all, but is about concrete objects one of which HAS, but does not HOLD, the properties of being fat, old and a lady.

A very astute criticism that may in the end hit the mark. I don't know.

Suppose I write a three-sentence novella:

It was a dark and rainy night. Shaky Jake, life-long insomniac, awakened from his dogmatic slumbers by the rythm of the rain, and deciding he needed a nightcap, grabbed his flashlight and his raincoat and headed for the Glass Crutch bar and grill, a local watering hole a half a mile from his house. Bellying up to the bar, he said to the 'tender: "One scotch, one bourbon, one beer."

A correct plot summary: An insomniac awakened by the rain goes to a bar for a drink.

An incorrect summary: A philosopher in La Mirada, California, dreaming about the ontological argument, is awakened when an earthquake causes a copy of David Hume's A Treatise of Human Nature to fall on his head.

Ed's question is how the first summary can be correct and the second incorrect if fictional sentences 'in universe' as Ed writes, lack truth-values. I am not convinced that there is a problem here. For a summary to be correct it doesn't have to be true of anything; it merely has to reproduce in condensed form the sense of the the piece of fiction summarized. I can take in the sense of a sentence without knowing whether it is true or false. A summary merely boils down the sense of the original.

2. ‘Sincere’ fiction. Not all fiction is ‘insincere’, i.e. knowingly made up. What if a sincere but deluded person writes a long account about characters (angels, spirits etc) and events which were ‘revealed’ to him in a vision? Contra Inwagen, his claims are assertions, and are capable of truth or falsity.

BV: But is this a case of literary fiction? The delusive account is fictional in that it is false, but that might be different use of 'fictional.' Why can't van Inwagen insist that literary fiction is by definition 'insincere' in Ed's sense?

3. Story-relative reference. Any serious account of fiction needs to deal with the way that names in fiction (and empty names generally) are able to identify or individuate within the story by telling the reader which character is being talked about. Inwagen needs to explain how such story-relative reference works, for his theory does not address it. He also has the problem that ‘literary discourse’ also seems to use story-relative reference. Consider the story (A) “A man called Gerald and a boy called Steve were standing by fountain. Steve had a drink”, and the statement (B) “In the second sentence the proper name ‘Steve’ identifies Steve." Statement (B) is true, and so is ‘literary discourse’, according to Inwagen, and so ‘Steve’ in (B) identifies an abstract object. But it clearly ‘refers back’ to the ‘Steve’ in (A). How can a term referring to an abstract object also refer back to a character in a story, when the character is not an abstract object?

BV: Van Inwagen might respond by saying that in (B) ''Steve' identifies Steve only in the sense that 'Steve' in the second sentence has 'Steve' in the first sentence as antecedent. So there is no (extralinguistic) reference at all, and 'Steve' in (B) does not pick out an abstract object.

Note the ambiguity of 'Ed signed his book.' It could mean that Ed signed Ed's book. Or it could mean that Ed signed a book belonging to someone distinct from Ed. (Suppose, while pointing at Tom, I say to Peter, "Ed signed his book.") In the first case, 'his' exercises no (extralinguistic) reference. In the second case it does.

4. The problem is worse in the case of names whose emptiness is in doubt. Suppose I make a reference statement: “Luke 1 v5 refers to Zachary, a high priest at the temple”. Like many characters in the New Testament, we are not certain whether Zachary existed or not. If he did exist, the name in my reference statement refers to him. If not, according to Inwagen, it refers to an abstract object. How can the semantics of the sentence be so utterly different without my knowing? For I don’t know whether Zachary existed or not, and so I don’t know what the semantics of the reference statement is. But surely I do.

BV: I don't think van Inwagen will have any trouble with this objection. Suppose we don't know whether Zachary existed or not. Our not knowing this is not the same as our not knowing whether he is nonfictional or fictional. For we know that the NT is not a work of fiction — assuming that, necessarily, every work of fiction involves pretence on the part of its author or authors. If we agree that the NT is not a work of fiction and it turns out that Zachary never existed, then van Inwagen can say that no one had all the properties ascribed to Zachary. His theory does not require him to say that 'Zachary' refers to an abstract object.

5. What about statements where we say what the author says? For example “Dickens says that Mrs Gamp is fat”. Inwagen would classify this as literary discourse, but if so, the token of ‘Mrs Gamp’ refers to an abstract object. But Dickens is surely not saying that an abstract object is fat?

The general problem, and here I think I am agreeing with Bill, is that the semantics of proper names as used in fiction (or ‘sincere’ fiction) doesn’t seem to be enormously different from the semantics of the same names as used in ‘literary discourse’. Yet, according to Inwagen, the difference is as enormous as it gets.

Do Purely Fictional Items Exist? On Van Inwagen’s Theory of Ficta

A character in a novel is an example of a purely fictional item provided that the character is wholly 'made up' by the novelist. Paul Morphy, for example, is a character in Francis Parkinson Keyes' historical novel, The Chess Players but he is also a real-life 19th century New Orleans chess prodigy. So Paul Morphy, while figuring in a piece of fiction, is not a purely fictional item like Captain Ahab or Sancho Panza or Frodo.

Earlier I said that it is a datum that Frodo, a purely fictional item, does not exist. Saying that it is a datum, I implied that it is not something that can be reasonably questioned, that it is a 'Moorean fact.' After all, most of us know that Frodo is a purely fictional character, and it is obvious — isn't it? — that what is purely fictional does not exist. Whatever is purely fictional does not exist looks to be an analytic proposition, one that merely unpacks the sense of 'purely fictional.'

But then after I uploaded my entry I remembered something that van Inwagen says in his essay Existence, Ontological Commitment, and Fictional Entities (in Existence: Essays in Ontology, CUP 2014, p. 105):

The lesson I mean to convey by these examples is that the nonexistence of [Sherlock] Holmes is not an ontological datum; the ontological datum is that we can use the sentence 'Sherlock Holmes does not exist' to say something true.

I think this sentence would make more sense if van Inwagen had 'linguistic datum' for the second occurrence of 'ontological datum.' If the nonexistence of Holmes is a datum, then it is an ontological datum; but the fact that we can use the sentence in question to say something true is a linguistic datum.

In any case, PvI is saying the opposite of what I was saying earlier. I was saying something that implies that the nonexistence of Holmes is an ontological datum in virtue of his being a purely fictional entity whereas PvI is saying in effect that Holmes exists and that his existence is consistent with his being purely fictional. One man's datum is another man's (false) theory!

To sort this out, we need to understand PvI's approach to ficta.

Van Inwagen's Theory of Fictional Entities

We first note that van Inwagen holds to the univocity of 'exists' and 'is.' The ontological counterpart of this semantic thesis is that there are no modes of being/existence. He also has no truck with Meinongian Aussersein. Bear in mind that Aussersein is not a mode of being. And bear in mind that the doctrine of Aussersein is not the same as, and goes far beyond, the thesis that there is a weak mode of being had by the fictional Mrs. Gamp and her ilk. The thesis of Aussersein is that

M. Some items are such that they have no being whatsoever.

For van Inwagen, (M) is self-contradictory. He thinks that it entails that something is not identical with itself, which, if the entailment went through, would amount to a reductio ad absurdum of (M). (95) Now I have argued that van Inwagen is wrong to find (M) self-contradictory. But let's assume that he is right. Then it would follow, in conjunction with the univocity thesis, that everything exists and indeed in the same sense of 'exists.' And what sense is that? The sense supplied by the existential quantifier of standard modern predicate logic. Van Inwagen is thoroughly Quinean about existence. There is nothing more to existence than what existential quantification expresses. I call this a dogma of analysis. Fo an attempt at refutation, see my "Existence: Two Dogmas of Analysis" in Neo-Aristotelian Perspectives in Metaphysics, eds. Novotny and Novak, Routledge, 2014, pp. 45-75.

Now consider the sentence

1. Tom Sawyer is a character in a novel by Mark Twain.

By van Inwagen's lights, when (1) is translated into the quantifier-variable idiom it can be seen to imply that Tom Sawyer exists. I won't repeat van Inwagen's tedious rigmarole, but the idea is simple enough: (1) is plainly true; (1) cannot be supplied with an ontologically noncommittal paraphrase; and (1) ontologically commits us to the existence of the fictional character, Tom Sawyer. This is plausible and let's assume for present purposes that it is right: we accept (1) as true, and this acceptance commits us to the existence of a referent for 'Tom Sawyer.' Tom Sawyer exists! The same goes for all pure ficta. They all exist! They exist in the same sense that you and I do. Indeed, they actually exist: they are not mere possibilia. (What I just said is, strictly, pleonastic; but pleonasm is but a peccadillo when precision is at a premium.)

But now we have a problem, or at least van Inwagen does. While we are ontologically committed to the existence of purely fictional characters by our use and acceptance of true sentences such as (1), we must also somehow accommodate everyone's firm conviction that purely fictional characters do not exist. How?

When we say that Sherlock Holmes does not exist, we can be taken to express the proposition that "No one has all the properties the fictional character Sherlock Holmes holds . . . ." (105, emphasis added) There are properties that fictional characters HAVE and those that they HOLD. Among the properties that fictional characters HAVE are such logical properties as existence and self-identity, and such literary properties as being a character in a novel, being introduced in chapter 6, being modelled on Sancho Panza, etc. Among the properties fictional characters HOLD are properties like being human, being fat, having high blood pressure, being a resident of Hannibal, Missouri, and being a pipe-smoking detective.

What van Inwagen is doing is making a distinction between two modes of property-possession. A fictional item can possess a property by having it, i.e., exemplifying it, in which case the corresponding sentence expresses an actual predication. For example, a use of 'Tom Sawyer was created by Mark Twain' is an actual predication. A fictional item can also possess a property by holding it. For example, 'Tom Sawyer was a boy who grew up along the banks of Mississippi River in the 1840s' is not an actual predication but a sentence that expresses the relation of HOLDING that obtains between the fictional entity and the property expressed by 'was a boy who grew up, etc.'

With this distinction, van Inwagen can defang the apparent contradiction: Tom Sawyer exists & Tom Sawyer does not exist. The second limb can be taken to express the proposition that no one exemplifies or HAS the properties HELD by the existing item, Tom Sawyer.

To put it in my own way, what van Inwagen is maintaining is that there really is an entity named by 'Tom Sawyer' and that it possesses (my word) properties. It exemplifies some of these properties, the "high-category properties," but contains (my word) the others but is not qualified (my word) by them. Thus Mrs Gamp contains the property of being fat, but she does not exemplify this property. Analogy (mine): The set {fatness} is not fat: it holds the property but does not have (exemplify) it.

For van Inwagen, creatures of fiction exist and obey the laws of logic, including the Law of Excluded Middle. So they are not incomplete objects. On a Meinongian approach, Tom Sawyer is an incomplete nonexistent object. For van Inwagen, he is a complete existent object. Now although I am not aware of a passage where van Inwagen explicitly states that purely fictional entities are abstract objects, this seems clearly to be entailed by what he does say. For Tom Sawyer exists, and indeed actually exists — he is not a merely possible being — but he does not interact causally with anything else in the actual world. He does not exist here below in the land of concreta, but up yonder in Plato land. So if abstract entities are those that are causally inert, Tom Sawyer is an abstract object. That is consistent with what van Inwagen does explicity say, namely, that "creatures of fiction" are "theoretical entities of [literary] criticism." (Ontology, Identity, and Modality, p. 53.)

Some Questions about/Objections to van Inwagen's Theory

1. The theory implies that Sherlock Holmes exists, and exists as robustly as I do. That he exists follows from there being truths about him. That he exists as robustly as I do follows from the rejection of Meinongian nonentities and the rejection of modes of being/existence (and also of degrees of being/existence). But when I think about Sherlock I seem to myself to be thinking about something that does not exist. For I know that Sherlock is a purely fictional item, and I know that such items do not exist. If I am asked to describe the object of my thinking, I must describe it as nonexistent, for that is how it appears. So what should we say? Should we say that when I think of Sherlock, unbeknownst to myself, I am thinking of an existing abstract object? Or should we say that there are two objects, the one I am thinking of, which is nonexistent, and the existent abstract object?

Either way there is trouble. Surely I am the final authority as to what I am thinking of. It is part of the phenomenology of the situation that when I think about a detective that I know to be purely fictional I am thinking about an item that is given as nonexistent. But then the existing abstract object is not the same as the object I am thinking of. Van Inwagen's abstract surrogate exists; the object I am think of does not exist; ergo, they are not the same object.

On the other hand, if there are two objects, and it is van Inwagen's surrogate object that I am really thinking of when I think of Sherlock, then I am always in error when I think of pure ficta. I appear to myself to be thinking about nonexistent concreta when in reality I am thinking about existent abstracta.

2. When I think of Sherlock, I think of a man, and when I think of Mrs Gamp, I think of a woman. But no abstract object has sex organs. So either I am not thinking of what I appear to be thinking of, and a systematic error infects my thinking of pure ficta, or I am thinking of what I appear to be thinking of, namely, a man or a woman, in which case I am not thinking of an abstract existent.

3. When I think of Mrs Gamp as fat, I think of her as exemplifying the property of being fat, not as holding the property or containing it or encoding (Zalta) it. But then I cannot be thinking about an existent abstract object, for no such object is (predicatively) fat.

According to the Meinongian, when one think about Mrs Gamp, one thinks about a fat woman who does not exist. According to van Inwagen, when one thinks about Mrs Gamp, one thinks about an existing abstract object that is (predicatively) neither a woman not fat. Pick your poison!

I say neither theory is acceptable.

A Possible Objection to My Critique

"In the articles you cite, van Inwagen doesn't address our thinking about fictional items. He is not doing descriptive psychology or phenomenology; his approach is linguistic. He argues that fictional discourse — discourse about fictional items — commits us ontologically to fictional entities. He then tries to square this commitment with our acceptance of such sentences as 'Sherlock Holmes does not exist.' Your objections, however, are phenomenologically based. So it is not clear that your objections hit their target.

In response I would say that no adequate theory of fictional discourse or fictional objects can abstract away from the first-person point of view of one who thinks about fictional objects. Such linguistic reference as we find in a sentence such as (1) above is parasitic upon intentional or thinking reference. But this is a very large and a very hairy theme of its own. See The Primacy of the Intentional Over the Linguistic.

Thinking About Frodo

Let me attack yesterday's puzzle from a different angle. The puzzle in one sentence: we think about things that do not exist; but how is this possible given that they do not exist?

Here is the problem set forth as an aporetic hexad:

1. When I think about Frodo, as I am doing right now, I am thinking about, precisely, Frodo: not about some semantic or epistemic intermediary or surrogate or representative. I am thinking about a concrete, albeit nonexistent, item. I am not thinking about an idea in my mind, or a mental image, or any mental content; nor am I thinking about an abstract entity of any kind such as a property; nor am I thinking of a word or a phrase or anything linguistic.

2. Thinking about (thinking of) is a relation the relata of which are a subject who thinks and an object thought of. Thinking is triadic: ego-cogito-cogitatum.

3. Every relation is such that if it obtains, then all its relata exist/are.

4. There are no different modes of existence/being. This is the ontological counterpart of the semantic thesis of the univocity of 'exists' and 'is' and cognates.

5. To exist is to exist extramentally and extralinguistically, where the minds in question are finite.

6. Frodo, a purely fictional item, does not exist.

The limbs of the hexad are individually plausible but jointly inconsistent. To solve the problem we must reject one of the limbs. But which one? (6) is a datum, and (5) is an unproblematic definition. So the the candidates for rejection are (1)-(4). I'll take these in reverse order.

Deny (4): There are two modes of being, esse reale and esse intentionale. When we say, with truth, that Frodo does not exist, we mean that he lacks esse reale. But we can still think about him in a manner to satisfy (1)-(3) since he has merely intentional being.

Deny (3): Twardowski-Meinong-Grossmann Solution. There are items that have no being at all, and there are genuine relations that connect existents such as minds to beingless items in the realm of Aussersein.

Deny (2): Thinking-of is not relational, whether or not the obtaining of a relation requires that all its relata exist. This can be developed in different ways. Adverbial theories, Brentano's theory, Butchvarov's theory.

Deny (1): One way to deny (1) is via abstract artifactualism. A number of philosophers, including van Inwagen, have been putting forth some version of this view. The idea is that purely fictional items such as Frodo are created by the authors of works of fiction in which they figure. They are a peculiar species of abstract object since they come into being, unlike 'standard' abstract objects. They exist, but they are abstract. Meinong, by contrast, held that they are concrete but do not exist or have any being at all. Here is a paper that defends artifactualism against some objections by Sainsbury.

Now, gentlemen, pick your poison! Which limb will you deny? I claim, though this is but a promissory note, that no theory works and that the problem, though genuine, is insoluble.

London Ed on Reference to What is Not

Two weeks in Greece passed both quickly and slowly. No access to internet or phone, much walking (on a lonely hillside I found a deserted monastery built on the ruins of a 6th century pagan temple) and much thinking. In particular, thinking about the 'Meinongian' thesis that there are objects that do not exist, and that 'there are Fs' can be understood in a 'wide' or unrestricted sense, so that nonexistent entities are to be included [in the ] domain of quantification and discourse, but also in a 'narrow' sense, including only existing objects.

You implictly defend this view often, but explicitly here: "the crux of the matter is whether there are different ways of existing, or different modes of existence. I say there are …". Here is a brief critique of this view. Consider:

(1) Tom is thinking of Frodo

(2) There is no such thing as Frodo

I think we both agree that both of these propositions* are true. If so, what are we to make of the following argument?

BV: Yes. We can call them data sentences. They record Moorean facts.

(3) Proposition (1) is of the form 'aRb', where a = 'Tom', R = 'is thinking of' and b = 'Frodo'

BV: Permit me a quibble. You don't want to say that a = 'Tom,' you want to say that 'a' is a placeholder for 'Tom.' Likewise for the other terms. It seems to me that you are making two very minor mistakes. One is use-mention confusion; the other is confusing a placeholder with an abbreviation. Sorry to be such a pedant!

I would add that if we distinguish between grammatical and logical form, then proposition (1) is of the grammatical form, aRb. It is at least conceivable that the deep logical form of (1) be something else. Brentano, no slouch of a philosopher, would read (1) as nonrelational, as having the form of 'Tom is a Frodo-thinker.' An adverbialist would take (1) as having the form of 'Tom is thinking Frodo-ly.'

(4) The truth of a proposition of the form 'aRb' always implies the truth of 'for some x, x = b and aRx', and hence the truth of 'for some x, x = b.'

BV: Agreed if you insert 'logical' right before 'form' in (4).

(5) [Interpreting (4)] If Tom is thinking of Frodo then there is such a thing as Frodo.

(6) [from (5) and (1), modus ponens] There is such a thing as Frodo.

(7) [(6) and (2)] Contradiction.

BV: For this reductio ad absurdum to be formally valid, you need an auxiliary premise to the effect that 'For some x, x = b' asserts the existence of b. In other words, you must read the particular quantifier 'For some x, ___ x ___' as an existential quantifier, where an existential quantifier expresses existence, where existence is real, i.e., mind-independent, existence. It is at least a question whether existence can be reduced to someness!

We might attempt to resolve the contradiction as follows. We should read (6) as asserting existence in some wide or unrestricted quantification sense, as follows:

(6A) There is such a thing[w] as Frodo

where 'thing[w]' ranges over all kinds of things, existent and non-existent. Likewise, we should read (2) as asserting existence in some narrow or restricted quantification sense, as follows:

(2A) There is no such thing[n] as Frodo

where 'thing[n]' ranges only over real or existing things. Where there is ambiguity, there is no real contradiction. To assert that Frodo is a thing in the wide sense does not contradict the assertion that he is not a thing in the narrow sense.

BV: I have been toying with a solution something like this, except that it is not strictly Meinongian. For Meinong, items like Frodo have no being whatsoever. That is his famous doctrine of Aussersein. I have been toying with the idea that they have being all right, but merely intentional being, esse intentionale as opposed to esse reale, where these are two different modes of being/existence. Lukas Novak, who shares with me the idea that thinking is genuinely relational, denies that it is impossible to refer to what has no being. See Lukas Novak on Reference to What is Not. It looks like I am fighting a war on two fronts, the London front and the Prague front.

My objection is as follows.

BV: Your objection, I take it, is to a solution along the lines I sketched.

Consider:

(8) Tom thinks that there is such a thing as Frodo, but he is wrong

The conjunct 'but he is wrong' is a negation, and in order to be a negation, what it negates must have the same sense as what is asserted (inside the belief context). Having the same sense includes the terms having the same range, and so the range of the term 'thing' as it occurs in the assertion must be identical to the range of the same term as it occurs (although elided) in the negation. I.e. (8) can be expanded into

(8A) Tom thinks that there is such a thing[x] as Frodo, but it is not the case that there is such a thing[x] as Frodo

where 'x' indicates sameness of range. I.e. if the range in the assertion is narrow, it is so in the negation, and likewise if it is wide. Thus the range of the term 'thing' is irrelevant.

BV: Now you've lost me completely. There is clearly a difference between (1) — Tom is thinking of Frodo — and 'Tom thinks that there is such a thing as Frodo.' I don't understand why you shifted to the latter sentence. To think about x is not to think that there is such a thing as x, nor is it to think that there is not such a thing as x. It is just to think about x.

At this point in the dialectic I don't know what you are up to. From previous discussions, your aim was to pin a certain exportation fallacy on me, the fallacy of moving from

Tom is thinking of Frodo

There exists an x such that x = Frodo & Tom is thinking of x.

That is clearly a non sequitur; I recognize it as such, and I don't commit it. If Tom is thinking of Frodo, then Tom is thinking of something; but it doesn't follow that this thing exists. On Meinong's theory, Tom is thinking of a beingless item. On my theory, he is thinking of an item that has esse intentionale but not esse reale. On Meinong's theory, intentionality is a relation, but the object relatum has no being at all. On my theory, is a relation, but the object relatum has merely intentional being.

Yet the form of 'Tom thinks that there is such a thing as Frodo' is also 'aRb', where a is 'Tom', b is 'Frodo', and R is 'thinks that there is such a thing as'. If premiss (4) above were true, then from (8) we could derive 'there is such a thing such that Tom thinks that there is such a thing as it', which would mean Tom was right, rather than wrong.

My solution to the problem, as I have argued before, is to reject premiss (4). 'Tom is thinking of Frodo' has the grammatical form 'aRb', but that is not its logical form. Clearly its logical form includes an internal quantifier, i.e. a quantifier that is included inside the belief operator, but cannot be legitimately exported outside.

BV: Now I think I see what you are up to. You take

(1) Tom is thinking of Frodo

to have the logical form of

(9) Tom is thinking that Frodo exists.

And then your point is that (9) does not entail

(10) Frodo exists.

I agree that the inferential move from (9) to (10) is invalid. But I think it is a mistake that (1) can be replaced by (9). Suppose I am thinking of something. It might be London's Trafalgar Square or Boston's Scollay Square. The former exists (last time I checked) but the latter no longer exists. Clearly I can have either thought without the additional thought that the square in question exists or does not exist. To think about something is not eo ipso to think that the thing in question exists — or to think that it does not exist.

Perhaps I have misunderstood you.

___________________
*Proposition: (def) a sentence capable of truth or falsity, and so not a question, a command or a prayer.

Divine Simplicity, the Formal Distinction, and the Real Distinction

If I understand Duns Scotus on the divine simplicity, his view in one sentence is that the divine attributes are really identical in God but formally distinct. (Cf. Richard Cross, Duns Scotus on God, Ashgate 2005, p. 111) I can understand this if I can understand the formal distinction (distinctio formalis) and how it differs from the real distinction (distinctio realis). This will be the cynosure of my interest in this post.

There appear to be two ways of construing 'real distinction.' On the first construal, the real distinction is plainly different from the formal distinction. On a second construal, it is not so clear what the difference is. I have no worked-out view. In this entry I am merely trying to understand the difference between these two sorts of distinction and how they bear upon the divine simplicity, though I will not say anything more about the latter in this installment.

First Construal of 'Real Distinction'

On the first construal, the real distinction is to be understood in terms of separability. But 'separable' has several senses. Here are my definitions of the relevant senses. I am not trying to exposit Thomas or any scholastic. I am merely trying to get to the truth of the matter.

D1. Individuals x, y are mutually separable =_df it is broadly logically possible that x exist without y, and y exist without x.

Example. The separability of my eyeglasses and my head is mutual: each can (in a number of different senses of 'can' including the broadly logical sense) exist without the other. This distinction is called real because it has a basis in extramental and extralinguistic reality. It is not a merely verbal distinction like that between 'eyeglasses' and 'spectacles.'

D2. Properties F, G are mutually separable =_df it is broadly logically possible that F be instantiated by x without G being instantiated by x, and vice versa.

Example. Socrates is both seated and speaking. But he is possibly such as to be the one without the other, and the other without the one. He can sit without speaking, and speak without sitting. The properties of being seated and speaking, though co-instantiated by Socrates, are mutually separable. Of course, this does not imply that these properties can exist uninstantiated.

D3. Individuals x, y are unilaterally separable =_df it is broadly logically possible that one of the pair x, y exist without the other, but not the other without the one.

Example. A (primary) substance S and one of its accidents A. Both are individuals, unrepeatables. But while A cannot exist without S, S can exist without A. Second example. Consider a fetus prior to viability. It is not an accident of the mother, but a substance in its own right. Yet it cannot exist apart from the mother, while the mother can exist apart from it. So what we seem to have here are two individuals that are unilaterally separable.

D4. Properties F, G are unilaterally separable =_df it is broadly logically possible that one of the pair F, G be instantiated by x without the other being instantiated, but not the other without the one.

Example. Suppose Socrates is on his feet, running. His being on his feet and his running are unilaterally separable in that he can be on his feet wthout running, but he cannot be running without being on his feet.

D5. Items (whether individuals or properties) I, J are weakly separable =_df I, J are either mutually separable or unilaterally separable.

On the first construal of 'real distinction,' it comes to this:

D6. Items (whether individuals or properties), I, J are really distinct =_df I, J are weakly separable.

My impression is that when Scotists speak of the real distinction they mean something identical to or very close to my (D6). Real distinctness is weak separability. Two items, whether individuals or properties, are really distinct if and only if they are either mutually separable or unilaterally separable. According to Alan B. Wolter ("The Formal Distinction" in John Duns Scotus, 1265-1965, eds. Ryan and Bonansea, CUA Press, 1965, pp. 45-60),

In the works of Aquinas, for example, the term ['real distinction'] seems to have two basically different meanings, only one of which corresponds to the usage of Scotus, Ockham, or Suarez. For the latter, the real distinction is that which exists between individuals, be they substances or some individual accident or property. It invariably implies the possibility of separating one really distinct thing from another to the extent that one of the two at least may exist apart from the other. (p. 46)

Second Construal of 'Real Distinction'

On a Thomist view, my essence and my existence are not really distinct on the first construal of 'real distinction' because they are mutually inseparable: neither can be without the other. This strikes me as entirely reasonable. My individual essence is nothing without existence, and there are no cases of pure existence. I am not now and never have been an existence-less essence, nor a bit of essence-less existence. And yet Thomists refer to the distinction between (indvidual) essence and existence in finite concrete individuals as a real distinction. So 'real distinction' must have a second basic meaning, one that does not require that really distinct items be either mutually or unilaterally separable. What is this second basic meaning? And how does it differ from the Scotistic formal distinction?

Seeking an answer to the first question, I turn to Feser's manual where, on p. 74, we read:

But separability is not the only mark of a real distinction. Another is contrariety of the concepts under which things fall . . . . For example, being material and being immaterial obviously exclude one another, so that there must be a real distinction between a material thing and an immaterial thing. A third mark sometimes suggested is efficient causality . . . .

In this passage, Feser seems to be saying that there is one disinction called the real distinction, but that it has more than one mark. He does not appear to be maintaining that 'real distinction' has two different meanings, one that requires separability and another that does not. On the next page, however, Feser makes a distinction between a "real physical distinction" and a "real metaphysical distinction" where the former requires separability but the latter does not. He goes on to say that for Scotus and Suarez a necessary condition of any real distinction in created things is that the items distinguished be separable: "a distinction is real only when it entails separability." (75)

The Formal Distinction

I asked: "What is the second basic meaning of 'real distinction'?" The answer I glean from Feser is that the second meaning is real metaphysical distinction, a distinction that does not require separability. Now for my second question: How does this real metaphysical distinction differ from the formal distinction? According to Cross, "the formal distinction is the kind of distinction that obtains between (inseparable) properties on the assumption that nominalism about properties is false." (108) Feser describes it as a third and intermediate kind of disinction that is neither logical nor real. (75) Both what Cross and Feser say comport well with my understanding of the formal distinction.

Consider the distinction between a man's animality and his rationality. They are clearly distinct because there are animals that are not rational, and there are rational beings that are not animals. It is also clear that the distinction is not purely logical: the distinction is not generated by our thinking or speaking, but has a basis in extramental and extralinguistic reality. Is it then a real distinction? Not if such a distinction entails separability. For it is not broadly logically possible that the rationality of Socrates exist without his animality, or his animality without his rationality. Anything that is both animal and rational is essentially both animal and rational. (Whereas it is not the case that anything that is both sitting and speaking is essentially both sitting and speaking.) So the Scotist, for whom the reality of a real distinction entails separability, says that what we have here is a formal distinction, a distinction between two 'formalities,' animality and rationality, that are really inseparable but formally distinct.

My second question, again, is this: How does the real metaphysical distinction differ from the formal distinction? In both cases, the distinction is not purely logical, i.e., a mere distinctio rationis. So in both cases the distinction has a basis in reality. Further, in both cases there is no separability of the terms of the distinction. Socrates cannot be rational without being an animal, and he cannot be an animal without being rational. Similarly, he cannot exist without having an essence, and he cannot have an essence without existing.

So what is the difference between the real metaphysical distinction (that Feser distinguishes from the real physical distinction) and the formal distinction? If I understand Feser, his view is that the formal distinction collapses into the virtual distinction, which is a logical distinction, hence not a real distinction, whereas the real metaphysical distinction is a real distinction despite its not requiring separability. But what is the virtual distinction?

The Virtual Distinction

Feser tells us that a logical distinction is virtual "when it has some foundation in reality." (73) A virtual distinction is a logical distinction that is more than a merely verbal distinction. He gives the example of a man's nature which, despite its being one thing, can be viewed under two aspects, the aspect of rationality and the aspect of animality. The distinction between the two aspects is not real but virtual. The virtual distinction thus appears to be identical to the formal distinction.

Accordingly, the difference between the real metaphysical distinction and the formal distinction is that the first is real despite its not entailing separability while the second is logical despite having a foundation in reality. I hope I will be forgiven for not discerning a genuine difference between these two kinds of distinction. Feser suggests that the difference may only be a matter of emphasis, with the Thomist emphasizing the logical side of the virtual/formal distinction and the Scotist emphasizing the real side. (76)

Should we then irenically conclude that the metaphysical real distinction of the Thomists (or, to be cautious, of Feser the Thomist) is the same as the formal distinction of (some of) the Scotists?

Essence and Existence Again

I am afraid that matters are much messier. Suppose you agree that essence and existence in Socrates are neither mutually nor unilaterally separable. Suppose you also agree that Socrates is a contingent being: he exists (speaking tenselessly) but there is no broadly logical necessity that he exist. The second supposition implies that Socates does not exist just by virtue of his essence: his existence does not follow from his nature. Nor is his existence identical to his essence or nature, as it is in the ontologically simple God. So they must be distinct in reality. But — and here comes trouble — this real distinction in Socrates as between his essence and his existence cannot be a distinction between inseparable aspects. Animality and rationality are inseparable aspects of Socrates' nature; but essence and existence cannot be inseparable aspects of him. If they were inseparable, then Socrates would exist by his every nature or essence. This seems to imply that the metaphysical real distinction is not the same as the formal distinction. For the metaphysical real distinction between essence and existence requires separability of essence and existence in creatures.

Aporetic Conclusion

It looks like we are in a pickle. We got to the conclusion that the real metaphysical distinction is the same as the formal distinction. But now we see that they cannot be the same. Some may not 'relish' it, but the 'pickle' can be savored as an aporetic polyad:

1. Socrates is a metaphysically contingent being.

2. Metaphysical contingency entails weak separability (as defined above) of essence and existence.

3. Nothing is such that its essence and existence are weakly separable.

The triad is logically inconsistent.

Solution by (1)-denial. One cannot of course maintain that Socrates is metaphysically necessary. But one could deny the presupposition upon which (1) rests, namely, the constituent-ontological assumption that Socrates is compounded of essence and existence. On a relation ontology, essence-existence composition makes no sense.

Solution by (2)-denial. One could try to show that contingency has an explanation that does not require weak separability of essence and existence.

Solution by (3)-denial. One could argue that the individual essence of Socrates can be wthout being exemplified along the lines of Plantinga's haecceity properties.

Each of these putative solutions brings trouble of its own.

Book Notice: Elmar J. Kremer, Analysis of Existing: Barry Miller’s Approach to God

I recall a remark by Hans-Georg Gadamer in his Philosophische Lehrjahre to the effect that the harvest years of a scholar come late. That was certainly true in the case of the Australian philosopher Barry Miller (1923-2006). His philosophical career culminated in a burst of productivity. In roughly the last decade of his long life he published a trilogy in philosophical theology: From Existence to God (1992), A Most Unlikely God (1996), and The Fullness of Being (2002). I reviewed the first two in the journals and made substantial comments on a manuscript version of the third. Miller kindly acknowledged my help at the end of the preface of the 2002 book. So I was pleased to be of some small service on Miller's behalf by refereeing Kremer's manuscript for Oxford UP and supplying the blurb below when it was accepted by Bloomsbury.

Reviews of Analysis of Existing

“Barry Miller’s philosophical theology clearly shows how a philosopher can think rigorously about God without caving into fashionable and facile refutations of theism. In this study of his writings, Elmar Kremer provides an exemplary account of his sophisticated arguments while discussing their value and cogently defending them against a number of objections. Kremer’s welcome book is both a fine introduction to Miller and a significant contribution to philosophy of religion.” – Brian Davies, Professor of Philosophy, Fordham University, USA,

“Barry Miller was a brilliant philosophical theologian with an original argument for, and development of, the Thomist idea of God as the entity whose essence is existence. Unfortunately Miller's ideas have not been given the attention they deserve. In part this is because he made few concessions to the reader. In this book Elmar J. Kremer provides the 'clear, well-developed exposition' that Miller's ideas deserve. I recommended it highly to all interested in metaphysics, philosophy of religion, or theology.” – Peter Forrest, Retired Professor of Philosophy, University of New England, Australia,

“Barry Miller's penetrating work in philosophical theology has not received the attention it deserves. It is therefore with pleasure that I recommend the first book-length treatment of Miller's work, Elmar J. Kremer's Analysis of Existing: Barry Miller's Approach to God.” – William F. Vallicella, Retired Professor of Philosophy, USA,

“Kremer's book consists of philosophically acute, painstaking scholarship. It is a very fine introduction to Miller’s highly original work on the metaphysics of theism.” – Bruce Langtry, Senior Fellow in Philosophy, The University of Melbourne, Australia,

What Exists Exists

Reflecting on the seeming tautology, 'What exists exists,' Jacques Maritain writes,

This is no tautology, it implies an entire metaphysics. What is posited outside its causes exercises an activity, an energy which is existence itself. To exist is to maintain oneself and to be maintained outside nothingness; esse is an act, a perfection, indeed the final perfection, a splendid flower in which objects affirm themselves. (A Preface to Metaphysics, Sheed and Ward, 1939, pp. 93-94)

This is the sort of writing, florid and French, that drives analytic philosophers crazy and moves them to mockery. But I think Maritain is here expressing an important insight. Let me see if I can explain it with as little reliance as possible on Maritain's Thomistic machinery.

1. A tautology is a logical truth, a truth true in virtue of its logical form alone. Now it certainly does seem that 'What exists exists' is true in virtue of its logical form alone. Write it like this: For any x, if x exists, then x exists. By Universal Instantiation, we get if a exists, then a exists, which is of the form, if p then p, which is equivalent to p or not-p, which is the Law of Excluded Middle.

2. On the other hand, it has been clear for a long time that 'exist(s)' is no ordinary predicate. To say of an item that it exists is not to characterize it or classify it. Existence is not a classificatory concept. It doesn't partition neutral items into two classes, the existent ones and the nonexistent ones. Pace Meinong, there are no nonexistent items. And existence certainly does not partition existing items into two classes, the existing and the nonexisting. When I say of a thing that it exists I am saying that it is not nothing. I am not saying that it is F or G, but that it is. I am pointing to its sheer being or existence.

3. The same goes for 'What exists, exists.' Although it can be used to express a tautology, it can also be used non-tautologically. Used non-tautologically, it does not say that that-which-exists is that-which-exists; it says that that-which-exists exists. In other words, it does not say, tautologically, that beings are beings; it says, non-tautologically, that beings are.

4. Somewhere in The Enneads Plotinus writes, "It is by the One that all being are beings." But there would be no need to drag The One into the picture if 'all beings are beings' is a tautology. Tautologies do not need truth-makers. Plotinus' point, of course, is that it is by the One that all beings are. They are in virtue of the One; their Being derives from the One. Whether or not that it true, we understand what is being said and we understand that 'all beings are being' is not a tautology.

5. Metaphysics targets the existence of that-which-exists, the Being of beings, the esse of entia, das Sein des Seienden. Thus metaphysics presupposes a difference between existence and the existent. But existence is "odious to the logician" as George Santayana once observed. (Scepticism and Animal Faith, Dover, 1955, p. 48, orig. publ. 1923.) And so the logician will try to knock the wind out of the metaphysical sails by trying to accommodate the difference between existence and what exists in some such aseptic fashion as the following:

x exists =_df for some y, y = x.

Accordingly, existence is identity-with-something-or-other. 'Exists' as a load-bearing predicate gets replaced by some purely logical machinery: the particular quantifer, a bound variable, the identity sign, and a free variable. Existence for the logician is a 'thin' topic. Thin to the point of being anorexic. It is just logical bones bare of metaphysical meat.

6. Well, why not be a thin theorist? I have written a lot on this topic, so now I will be very brief. While it is of course true that everything that exists is identical to something, namely, itself, this presupposes that the things in question exist in a sense that cannot be captured by the above definition. Another way of putting the point is that the above definition is circular. For it amounts to

x exists =_df for some y that exists, y = x.

If I want to know what it is for something to exist, I learn nothing by being told that it is identical to something that exists, although that is of course true.

7. Getting back to Maritain, he is right as against the thin theorists: existence is a metaphysically weighty topic. 'What exists exists' can be given a non-tautological reading. But on the thin theory, it could only amount to the tautological 'What is identical to something is identical to something.' But whether existence is a perfection, or indeed the final perfection, or rather the opposite, as Santayana and Sartre would maintain, is a further question.

8. Unfortunately, no resolute thin theorist will be persuaded by anything I or anyone says to abandon his theory. All my dialectic can do is lead the reader to a point where he either gets it or he doesn't, where he either sees it, or he doesn't. You can lead a horse to water, but you can't make him drink.

It's a bit like arguments over religion. If you think that religion is nothing but a tissue of childish superstitions, will I ever be able to convince you otherwise? No. For it is not a matter of analytical intelligence, but of insight, or rather, in your case a lack of insight.

The Stromboli Puzzle Revisited

Here is a little puzzle I call the Stromboli Puzzle. An earlier post on this topic was defective. So I return to the topic. The puzzle brings out some of the issues surrounding existence. Consider the following argument.

Stromboli exists.
Stromboli is an island volcano.
Ergo
An island volcano exists.

This is a sound argument: the premises are true and the reasoning is correct. It looks to be an instance of Existential Generalization. How can it fail to be valid? But how can it be valid given the equivocation on 'exists'? 'Exists' in the conclusion is a second-level predicate while 'exists' in the initial premise is a first-level predicate. Although Equivocation is standardly classified as an informal fallacy, it induces a formal fallacy. An equivocation on a term in a syllogism induces the dreaded quaternio terminorum, which is a formal fallacy. Thus the above argument appears invalid because it falls afoul of the Four Term Fallacy.

Objection 1. "The argument is valid without the first premise, and as you yourself have pointed out, a valid argument cannot be made invalid by adding a premise. So the argument is valid. What's your problem?"

Reply 1. The argument without the first premise is not valid. For if the singular term in the argument has no existing referent, then the argument is a non sequitur. If 'Stromboli' has no referent at all, or has only a nonexisting Meinongian referent, then Existential Generalization could not be performed, given, as Quine says, that "Existence is what existential quantification expresses."

Objection 2: "The first premise is redundant because we presuppose that the domain of quantification is a domain of existents."

Reply 2: Well, then, if that is what you presuppose, then you can state your presupposition by writing, 'Stromboli exists.' Either the argument without the first premise is an enthymeme or it is invalid. If it is an enthymeme, then we need the first premise to make it valid. If it is invalid, then it is invalid.

Therefore, we are stuck with the problem of explaining how the original argument is valid, which it surely is.

My answer is that the original argument is an enthymeme an unstated premise of which links the first- and second-level uses of 'exist(s)' and thus presupposes the admissibility of the first-level uses. Thus we get:

A first-level concept F exists (is instantiated) iff it is instantiated by an individual that exists in the first-level way.
Stromboli is an individual that exists in the first-level way.
Stromboli is an island volcano.
Ergo
The concept island volcano exists (is instantiated).
Ergo
And island volcano exists.

Now what does this rigmarole show? It shows that Frege and Russell were wrong. It shows that unless we admit as logically kosher first-level uses of 'exist(s)' and cognates, a simple and obviously valid argument like the the one with which we started cannot be made sense of.

'Exists(s)' is an admissible predicate of individuals, and existence belongs to individuals: it cannot be reduced to, or eliminated in favor of, instantiation. This has important consequences for metaphysics.

For more on the topic of existence see my "Existence: Two Dogmas of Analysis," in Neo-Aristotelian Perspectives in Metaphysics, Routledge 2014, forthcoming.

On Conceiving that God does not Exist

In a recent post you write:

The Humean reasoning in defense of (3) rests on the assumption that conceivability entails possibility. To turn aside this reasoning one must reject this assumption. One could then maintain that the conceivability by us of the nonexistence of God is consistent with the necessity of God's existence.

I’m not convinced this is right. Conceivability has a close analogue with perception. If it seems to S that p, then S is prima facie justified in believing that (actually) p. So consider cases of perceptual seemings. Care must be taken to distinguish two forms of negative seemings:

1. It does not seem that p.
2. It seems that ~p.

Clearly, (1) is not properly a seeming at all; it is denying an episode of seeming altogether. If I assert (1), me and a rock are on epistemic par with respect to it seeming to us that p. (2) also faces an obvious problem: how could ~p, a lack or the absence or negation of something, appear to me at all? Photons do not bounce off of lacks. There are ways around this, but for now I just want to register the distinction between (1) and (2) and the prima facie difficulties with them that do not attend to positive seemings.

BV: Excellent so far, but I have one quibble. Suppose I walk into a coffee house expecting to encounter Pierre. But Pierre is not there; he is 'conspicuous by his absence' as we say. There is a sense in which I perceive his absence, literally and visually, despite the fact that absences are not known to deflect photons. I see the coffee house and the people in it and I see that not one of them is identical to Pierre. So it is at least arguable that I literally see, not Pierre, but Pierre's absence.

Be this as it may. You are quite right to highlight the operator shift as between (1) and (2).

So now consider conceivability. The analogue: If it is conceivable to S that p, then S is prima facie justified in believing that possibly p. Now for our two negative conceivablility claims:

1’. It is not conceivable that p.
2’. It is conceivable that ~p.

Again, (1’) is trivial; it is (2’) we’re interested in. Does (2’) provide prima facie evidence for possibly ~p? It depends. What we do when we try to conceive of something is imagine "in our mind’s eye" a scenario—i.e., a possible world—in which p is the case. So really (2’) translates:

2’’. I can conceive of a possible world in which ~p.

BV: Permit me a second quibble. Although 'conceive' and 'imagine' are often used, even by philosophers, interchangeably, I suggest we not conflate them. I can conceive a chliagon, but I cannot imagine one, i.e., I cannot form a mental image of a thousand-sided figure. We can conceive the unimaginable. But I think we also can imagine the inconceivable. If you have a really good imagination, you can form the mental image of an Escher drawing even though what you are imagining is inconceivable, i.e., not thinkable without contradiction.

More importantly, we should avoid bringing possible worlds into the discussion. For one thing, how do you know that possibilities come in world-sized packages? Possible worlds are maximal objects. How do you know there are any? It also seems question-begging to read (2') as (2'') inasmuch as the latter smuggles in the notion of possibility.

Given that the whole question is whether conceivability either entails or supplies nondemonstrative evidence for possibility, one cannot help oneself to the notion of possibility in explication of (2'). For example, I am now seated, but it is conceivable that I am not now seated: I can think this state of affairs witout contradiction. The question, however, is how I move from conceivability to possibility. How do I know that it is possible that I not be seated now?

It is obvious, I hope, that one cannot just stipulate that 'possible' means 'conceivable.'

(2'') seems innocent enough, but whether it gives us prima facie evidence for possibly ~p will depend on what p is; in particular, whether p is contingent or necessary. Consider:

3. There is a possible world in which there are no chipmunks.
4. There is a possible world in which there are no numbers.

(3) seems totally innocent. I can conceive of worlds in which chipmunks exist and others in which they don’t.

BV: It seems you are just begging the question. You are assuming that it is possible that there be no chipmunks. The question is how you know that. By conceiving that there are no chipmunks?

(4), on the other hand, is suspect. This is because numbers, unlike chipmunks, if they exist at all exist necessarily; that is, if numbers do not exist in one world they do not exist in any. Thus, what (4) really says is

(4*) There is no possible world in which there are numbers.

BV: (4) and (4*) don't say the same thing; I grant you, however, that the first entails the second.

With its conceivability counterpart being

(4’) I cannot conceive of a possible world in which there are numbers.

which looks a lot like the above illicit negative seemings: negations or absences of an object of conceivability. But my not conceiving of something doesn't entail anything! But suppose we waive that problem, and instead interpret (4’) as a positive conceiving:

(4’’) It is conceivable to me that numbers are impossible

The problem now is that (4’’) is no longer a modest claim that warrants prima facie justification. In fact, (4*) has a degree of boldness that invites further inquiry: presumably there is some obvious reason—a contradiction, category mistake, indelible opacity—etc. apparent to me that has led me to think numbers are impossible. But if that’s so, then surely my critic will want to know what exactly I’m privy to that he isn’t.

Mutatis mutandis in the case of God qua necessary being.

Thoughts?

BV: You lost me during that last stretch of argumentation. I am not sure you appreciate the difficulty. It can be expressed as the following reductio ad absurdum:

a. Conceivability entails possibility. (assumption for reductio)

b. It is conceivable that God not exist. (factual premise)

c. It is conceivable that God exist. (factual premise)

d. God is a necessary being. (true by Anselmian definition)

Ergo

e. It is possible that God not exist and it is possible that God exist. (a, b, c)

Ergo

f. God is a contingent being. (e)

Ergo

g. God is a necessary being & God is a contingent being. (d, f, contradiction)

Ergo

~a. It is not the case that conceivability entails possibility.

Is short, as John the Commenter has already pointed out, it seems that the Anselmian theist ought to reject conceivability-implies-possibility.

A Being-Knowledge Antilogism

An antilogism is an inconsistent triad: a set of three propositions that cannot all be true. The most interesting antilogisms are those in which the constitutent propositions are each of them plausible. If they are not merely plausible but self-evident or undeniable, then we are in the presence of an aporia in the strict sense. (From the Greek a-poros, no way.) Aporiai are intellectual impasses, or, to change the metaphor, intellectual knots that we cannot untie. Here is a candidate:

1. Being is independent of knowledge: what is or is the case is not made so by anyone's knowledge of it.

2. Knowledge is knowledge of being: we cannot know what is not or what is not the case.

3. Knowledge requires an internally available criterion or justification.

Each of the limbs of this aporetic triad is exceedingly plausible if not self-evident.

Ad (1). If a thing exists, its existence is not dependent on someone's knowledge of it. It is rather the other around: knowledge of thing presupposes the logically antecedent existence of the thing. And if a proposition is true, it not true because someone knows it. It is the other way around: the proposition's being true is a logically antecedent condition of anyone's knowing it.

Ad (2). 'Knows' is a verb of success: what one knows cannot be nonexistent or false. There is no false knowledge. What one 'knows' that ain't so, as the saying goes, one does not know. Necessarily, if S knows x, then x exists; necessarily, if S knows that p, then p is true. The necessity is broadly logical.

Ad (3). If I believe that p, p a proposition, and p happens to be true, it does not follow that I know that p. There is more to knowledge than true belief. If I believe that Jack is at home, and he is, it does not follow that I know that he is. Justification is needed, and this must be internalist rather than externalist. If I see a cat, it does not follow that I know a cat exists or that the cat I see exists. For I might be dreaming or I might be a brain in a vat. There are dreams so vivid that one literally sees (not imagines, or anything else) what does not exist. If I know a cat just in virtue of seeing one, then I need justification, and this justification must be available to me internally, in a way that does not beg the question by presupposing that there exist things external to my consciousness. Note that 'I see a cat' and 'No cat exists' express logically consistent propositions. They both can (logically) be true. For in the epistemologically primary sense of 'see,' seeing is not existence-entailing. In its epistemologically primary sense, 'see' is not a verb of success in the way 'know' is. 'False knowledge' is a contradictio in adiecto; 'nonexistent visual object' is not.

The limbs of our antilogism, then, are highly plausible and for some of us undeniable. Speaking autobiographically, I find each of the propositions irresistable. But I think most philosophers today would reject (3) by rejecting internalist as opposed to externalist justification.

The propositions cannot all be true. Any two, taken together, entails the negation of the remaining one. Thus, corresponding to this one antilogism, there are three valid syllogisms. That is true in general: every antilogism* sires three valid syllogisms.

The first takes us from (1) & (2) to ~(3). If what exists is independent of knowledge, and knowledge is of what exists, then it is not the case that knowledge requires an internally available criterion.

The second syllogism takes us from (1) & (3) to ~(2). If being is independent of knowledge, and knowledge requires a purely internal criterion, then being is inaccessible to knowledge: what we know are not things themselves, but things as they appear to us. To solve the antilogism by rejecting (2) would put us in the vicinity of Kant's epistemology according to which there are things in themselves but we know only phenomena.

The third syllogism takes us from (2) & (3) to ~(1). If knowledge is of what exists, and knowledge is knowledge only if justified internally, then being is not independent of knowledge, and we arrive at a form of idealism.

Is our antilogism insoluble? In one sense, no aporetic polyad is insoluble: just deny one of the limbs. In the above case, one could deny (3). To justify that denial one would have to work out an externalist theory of epistemic justification. An aporetically inclined philosopher, however, will expect that the resulting theory will give rise to aporetic polyads of its own.

And so we descend into a labyrinth from which there is no exit except perhaps by a confession of the infirmity of reason, a humble admission of the incapacity of the discursive intellect to solve problems that it inevitably and naturally poses to itself.

______________

*The term and the theory was introduced by Christine Ladd-Franklin.