Schaffer, Sherlock and Shaddai¹

Abstract

I. INTRODUCTION

In his 2009 paper ‘On What Grounds What,’ Jonathan Schaffer defends the view that most of the controversial entities that ontologists debate exist. Numbers exist. Properties exist. Proper parts exist, and so on. Indeed, they exist in the same sense that electrons, elephants, and engines exist (because Schaffer only acknowledges one sense of ‘exist’).² Schaffer calls this view permissivism and he defends it by appealing to easy arguments for the existence of the entities in question. Here, for example, is Schaffer's easy argument for the existence of numbers:

• (1)

  a. There are prime numbers.

  b. Therefore, there are numbers.

According to Schaffer:

[(1a)] is a mathematical truism. It commands Moorean certainty, as being more credible than any philosopher's argument to the contrary. Any metaphysician who would deny it has ipso facto produced a reductio for her premises. And [(1b)] follows immediately, by a standard adjective-drop inference.

(Schaffer 2009, author's italics: 357)

Schaffer presents a few more easy arguments and offers a similar defence in each case: the premises command Moorean certainty and the inferences are trivially valid. This culminates in an easy argument for the existence of fictional characters and the surprising claim that there is an easy argument for the existence of God. Here is Schaffer's easy argument for the existence of fictional characters:

• (2)

  a. Arthur Conan Doyle created Sherlock Holmes.

  b. Therefore, Sherlock Holmes exists.

According to Schaffer, (2a) ‘is a literary fact, and [(2b)] follows, given that to create something is to make it exist’ (2009: 359). Here is what he says about God:

While I obviously cannot speak to every contemporary existence debate here, perhaps it will suffice to speak to one other debate that may stand in as a best case for a metaphysical existence question, namely the question of whether God exists. I think even this is a trivial yes (and I am an atheist). The atheistic view is that God is a fictional character.

(Schaffer 2009, author's italics: 359)

Schaffer doesn’t explicitly say that there is an easy argument for the existence of God, but it's clearly implied because the existence of an easy argument is the only reason he presents for believing that an existence question has a trivial answer. Presumably, Schaffer's easy argument for God goes something like this:

• (3) a.

  Either we discovered God or we created God (as Doyle created Holmes).

• b.

  If we discovered God, then God exists.

• c.

  If we created God (as Doyle created Holmes), then God exists (and God is a fictional character, just as Holmes is).³

• d.

  Therefore, God exists.

This much is clear: (3) only succeeds as an easy argument, if (2) does. Further, Schaffer isn’t telling us that there is an easy argument for the existence of God as a wayside curiosity. On the contrary, his defence of permissivism seems to depend on it. Schaffer doesn’t offer an explicit argument, but the following argument is implied in the passage quoted directly above:

• P1.

  If (3) is a sound easy argument, then there are sound easy arguments for most of the controversial entities that ontologists debate.

• P2.

  (3) is a sound easy argument.

• C1.

  There are sound easy arguments for most of the controversial entities that ontologists debate.

• C2.

  (Permissivism) Most of the controversial entities that ontologists debate exist.

Further, without this argument, Schaffer hasn’t given us a reason to believe permissivism. At best, he's given us a reason to believe in the existence of numbers, fictional characters, God, and a few other entities. No small achievement! But not permissivism.

P1 and P2 entail C1. And C1 entails C2. The only question, then, is whether the premises of this argument (P1 and P2) are true. On the face of it, P1 is plausible. If (3) is a sound easy argument, then we seem to have a recipe for generating sound easy arguments for the existence of most controversial entities: locate the references to God in (3) and replace them with references to some other controversial entity. For example:

• (4) a.

  Either we discovered numbers or we created numbers (as Doyle created Holmes).

• b.

  If we discovered numbers, then numbers exist.

• c.

  If we created numbers (as Doyle created Holmes), then numbers exist (and they are fictional entities, just as Holmes is).

• d.

  Therefore, numbers exist.⁴

What about P2? In this paper, I will assume (or suppose) that some easy arguments, including (1), can be defended in the way that Schaffer suggests. However, I will argue that (2) cannot be defended in this way—either its premise does not command Moorean certainty or it is not trivially valid. If this is correct, then (3) cannot be defended in this way either. I conclude that (3) is not an easy argument; hence, it is not a sound easy argument. So, P2 is false and Schaffer's argument for permissivism fails.

Business will proceed as follows. Section II is about Moorean certainty. Section III is about trivial validity. And Section IV is about Schaffer's easy argument for the existence of fictional characters.

II. MOOREAN CERTAINTY

According to Schaffer, the premises of an easy argument command ‘Moorean certainty, as being more credible than any philosopher's argument to the contrary’. The idea is this:

Moorean modesty: There is a class of beliefs, Moorean beliefs, that are prima facie reasonable, and philosophical arguments cannot feasibly undermine these beliefs.

Moorean certainty is the property that a Moorean belief has if Moorean modesty is true. In the literature, Moorean beliefs are often described as ‘commonsense’. Schaffer describes them as ‘truisms’ or ‘banalities’. These descriptions leave much to be desired. But we can use them, along with the examples that Schaffer provides, to extrapolate a set of indicators for being a Moorean belief. If a belief has most of these indicators, then that is evidence that it is a Moorean belief (à la Schaffer):

• i.

  The belief strikes us as highly obvious.

• ii.

  Almost everyone takes (or seems to take) the belief to be uncontroversially true, unless they are aware of the philosophical arguments that attempt to undermine the belief.

• iii.

  Someone who rejects the belief is rationally forced to concede that it is clearly correct, in some sense, even if it is literally false.

(1a) has most of these indicators. It clearly has (i) and (iii), although it presumably doesn’t have (ii)—many people, in many parts of the world, don’t know what a prime number is. For the sake of a more vivid example, consider the following argument:

• (5) a.

  1 + 1 = 2.

• b.

  Therefore, there is a number, n, such that n + 1 = 2.

• c.

  Therefore, there is a number.

Arguably, (5a) has all the indicators of a Moorean belief. The belief that 1 + 1 = 2 strikes us as highly obvious. Further, almost everyone, with the exception of a few philosophers, takes (or seems to take) this belief to be uncontroversially true. Finally, this belief is clearly correct, in some sense, even if it is literally false. It is clearly correct, in some sense, that 1 + 1 = 2, and incorrect that 1 + 1 = 1, or 3, or 110. After all, in non-philosophical contexts, we are rationally permitted to use the premise that 1 + 1 = 2 as a basis for belief or action and rationally forbidden to use the premise that 1 + 1 = 1, or 3, or 110.

III. TRIVIAL VALIDITY

According to Schaffer, the inferences in an easy argument are trivially valid. I will analyse this as follows: an inference is trivially valid iff it is trivial that the inference is valid. What do ‘trivial’ and ‘valid’ mean in this context?

I start with the meaning of ‘trivial’. There are at least three interpretations of ‘trivial’ in this context. On the first interpretation, it is trivial that an inference is valid iff the inference is valid and it is highly intuitive that the inference is valid. On the second interpretation, it is trivial that an inference is valid iff the inference is valid and we can draw this inference simply by exercising our basic reasoning capacities, which are analogous to our basic perceptual capacities. On the third interpretation, it is trivial that an inference is valid iff the inference is valid and we cannot seriously question its validity.

Note that each interpretation has the form: An inference is trivially valid iff it is valid and satisfies a second condition. I assume that when Schaffer defends easy arguments as trivially valid, he is saying that the fact that an inference satisfies the second condition (if it does) is a (more or less) decisive reason to believe that it satisfies the first condition, namely, that it's valid. Of course, you could object that this gives us a reason, but not a decisive reason, or that it doesn’t give us a reason at all. However, in this paper, I grant Schaffer that this is a good defence of at least some easy arguments.

Further, Schaffer can be read as adopting the first or third interpretation, but not the second (because he doesn’t offer the sort of evidence from empirical psychology needed to establish trivial validity on the second interpretation). So, these are the interpretations that I will focus on in the next section. Since each interpretation states two conditions that must be satisfied for an inference to be trivially valid and we have granted that the second condition is evidence for the first, the issue is this: Given an easy argument, is it highly intuitive that its inferences are valid or that we cannot seriously question their validity?

I turn to the meaning of ‘valid’. There are at least two interpretations of ‘valid’ in this context. On the first interpretation, an inference is valid iff it is formally valid. That is, it is necessarily truth preserving—if the premises are true, then the conclusion must be true—in virtue of its logical form. On the second interpretation, an inference is valid iff it is analytically valid in a metaphysical sense.⁵ That is, it is necessarily truth preserving in virtue of semantic facts.⁶

On the face of it, Schaffer is talking about analytic validity, not formal validity. According to Schaffer, the inference from ‘Doyle created Holmes’ to ‘Holmes exists’ is valid. Presumably, Schaffer is saying that this inference is necessarily truth preserving in virtue of certain semantic facts, including facts about the meaning of the word ‘create’, not that it's formally valid.

However, if Schaffer adopts the first interpretation of ‘trivial’ then he's also saying that the validity of certain inferences is intuitive. As I understand it, analytic validity is a technical notion—one way of making our ordinary notion of validity more precise. Further, I assume that if Schaffer counts intuitions about validity as evidence for validity, then the relevant intuitions are about validity in an ordinary, non-technical sense. So, in what follows, I will interpret ‘valid’ as ‘analytically valid’ except in the expression ‘it is intuitive that the inference from p to q is valid’, which I will interpret as ‘it's intuitive that the truth of p guarantees the truth of q’. (If you think that this doesn’t capture our ordinary notion of validity, then feel free to substitute your own gloss.)

IV. FICTIONAL CHARACTERS

According to Schaffer, (2) is a sound easy argument for the existence of fictional characters. But strictly speaking, (2) is not an argument for the existence of fictional characters at all; it's an argument for the existence of Sherlock Holmes. This is easily remedied:

• (6) a.

  Arthur Conan Doyle created the fictional character Sherlock Holmes.

• b.

  Therefore, the fictional character Sherlock Holmes exists.

• c.

  Therefore, a fictional character exists.

By Schaffer's standards, (6a) is a good candidate for being a Moorean belief. (6a) is plausibly described as a truism or banality. It strikes us as highly obvious. And it's clearly correct, in some sense, that Doyle created the fictional character Holmes, and didn’t create the fictional character Dr Frankenstein. However, there may still be many people around the world who have not heard of Doyle or his books. So, it's not obvious that almost everyone takes, or seems to take, (6a) to be true. But everyone is familiar with at least one obviously fictional character (or object), so everyone has a premise that they could put in place of (6a).⁷

(6) consists of two inferences: the inference from (6a) to (6b) and the inference from (6b) to (6c). However, I will argue that the inference from (6a) to (6b) is not trivially valid.⁸ This leaves it open whether the second inference is trivially valid or not. I think that it isn’t, but I won’t pursue that in this paper.

Consider the inference from (6a) to (6b). Taking heed of the remarks in Section III, there are two questions to ask. First, is it highly intuitive that the inference from (6a) to (6b) is valid? Second, is the validity of this inference a matter that we cannot seriously question? I will take these questions in turn. According to Schaffer, ‘to create something is to make it exist’. I assume that Schaffer is making a semantic claim: ‘x created y’ means ‘x made y exist’. However, even if this claim is intuitively true, I doubt that the inference from (6a) to (6b) would strike most people as intuitively valid. (And I suspect that it would strike many as intuitively invalid).

Schaffer has a potential response: the inference from (6a) to (6b) is intuitive when we get the right reading of (6b). According to Schaffer, ‘[…] intuitions directly targeted to non-existence can be explained away via quantifier domain restriction’ (Schaffer 2009, author's italics: 360). The idea is this: Someone who judges that (the fictional character) Holmes does not exist is simply judging that Holmes is not among some subset of all the things there are.⁹ Which subset? Three possibilities come to mind: (a) Holmes is not among the concrete entities; (b) he is not among the mind-independent entities; or (c) he is not among the actual entities.

Daly & Liggins (2014) argue against this suggestion. ‘There’-sentences are often subject to quantifier domain restriction. For example: If I inspect my garage and find that there are no bicycles, then it may be appropriate to say ‘there are no bicycles’. Here, the sentence ‘there are no bicycles’ is true because the domain of quantification has been implicitly restricted to things in my garage. But it's not plausible that ‘exist’-sentences are subject to domain restriction in the same way, as Walton (2003: 240–1) and Everett (2013: 147–52) have shown. For example: I cannot describe the situation in my garage by saying ‘bicycles don’t exist’.

However, even if ‘exist’-sentences are not subject to domain restriction at the semantic level, it's plausible that they are subject to domain restriction at the pragmatic level. We often read ‘exists’ as ‘exists concretely’ (etc.), for pragmatic reasons, just as we often read ‘milk’ as ‘cow milk’, for pragmatic reasons. Does this explain our judgment that Holmes does not exist, even on the assumption that he was created by Doyle? In order to validate this explanation, Schaffer needs to show that some sentences that assert the existence of fictional characters are clearly true when we interpret them correctly. In a footnote, Schaffer offers the following example, due to van Inwagen:

• (7)

  To hear some people talk, you would think that all of Dickens's working-class characters were comic grotesques; although such characters certainly exist, there are fewer of them than is commonly supposed. (van Inwagen 2000: 245, quoted in Schaffer 2009, n. 12: 359).

In the same paper, van Inwagen offers another example:

• (8)

  Sarah just ignores those characters that don’t fit her theory of fiction. She persists in writing as if Anna Karenina, Tristram Shandy, and Mrs Dalloway simply didn’t exist. (van Inwagen 2000: 245).

Unfortunately, these examples are unpersuasive. Consider (7). The relevant sentence in (7) is the following:

• (9)

  Such characters exist.

(9) means ‘characters of this kind’ where ‘this’ refers back to what was said in the previous sentence, namely, that ‘all of Dickens's working-class characters were comic grotesques’. Further, it is understood that ‘Dickens's working-class characters’ describes the (fictional) working-class characters in the novels of Dickens. Given this, there are at least two interpretations of (9):

• (9’)

  Comically grotesque, (fictional) working-class characters exist, in the novels of Dickens.

• (9”)

  Comically grotesque, (fictional) working-class characters in the novels of Dickens exist.

(9”) is committed to the existence of fictional characters; (9’) is not. But (9’) is a more plausible interpretation of (9). In any case, the existence of both interpretations makes this an unpersuasive example. Now consider (8). The relevant sentence in (8) is the following:

• (10)

  Sarah persists in writing as if Anna Karenina, Tristram Shandy, and Mrs Dalloway simply didn’t exist.

(10) is not committed to the existence of fictional characters. (10) does not say (e.g.) that Shandy exists, only that Sarah writes as if he doesn’t. However, it's implied that Sarah ought to write as if these characters exist, which raises two further questions. First, what does it mean (in this context) to write as if a fictional character exists? Second, why should Sarah write this way? One answer goes like this: To write as if a fictional character exists is to assert, or presuppose, that this character exists and Sarah should write this way because Karenina, Shandy, and Dalloway do, in fact, exist.

However, there is another answer: To write as if a fictional character exists is to formulate a theory of fiction that applies to this character and Sarah should write this way because a theory of fiction that doesn’t apply to Karenina, Shandy, and Dalloway is inadequate. To my mind, the second set of answers is more plausible than the first. In any case, the existence of both answers makes this an unpersuasive example.

At this point, Schaffer might change tack. Consider an extended version of (6):

• (11) a.

  Arthur Conan Doyle created the fictional character Sherlock Holmes.

• b.

  Therefore, there is a fictional character that Arthur Conan Doyle created (namely, Sherlock Holmes).

• c.

  Therefore, the fictional character Sherlock Holmes exists.

• d.

  Therefore, a fictional character exists.

The inference from (11a) to (11b) is intuitively valid; the inference from (11b) to (11c) is not (and may be intuitively invalid). But didn’t Quine teach us that every ‘there’-sentence entails a corresponding ‘exist’-sentence? Schaffer leans into this idea when he writes: ‘[t]o my mind (and here I follow Quine), [‘there are numbers’] just says that numbers exist’ (2009: 258).

What is the relevant Quinean view? To begin with, there is a metaphysical view and a linguistic view. The metaphysical view is that there is no distinction between being and existence. So, necessarily, an entity has being iff it exists. The linguistic view is that every sentence of the form ‘a is’ or ‘Fs are’ entails a sentence of the form ‘a exists’ or ‘Fs exist’, and vice versa. These views are mainstream, and for good reason; they’re very plausible. However, they don’t say that every ‘there’-sentence entails a corresponding ‘exist’-sentence.

Quine also argued that if you want to use a ‘there’-sentence (or any other sentence) to express an ontological commitment, then you should interpret this sentence as ‘∃’-sentence in first-order logic. This is not a descriptive claim about the meaning of ‘there’-sentences in ordinary English; it's a normative claim about the language you ought to use to express your ontological commitments. This view is also mainstream, although I find it less plausible. In any case, it doesn’t say that every ‘there’-sentence entails a corresponding ‘exist’-sentence.

Further, although some ‘there’-sentences clearly entail a corresponding ‘exist’-sentence, and this is plausibly an instance of a general pattern, it is not clear what the general pattern is. For example: The truth of ‘there are things that don’t exist’ arguably does not entail the truth of ‘things that don’t exist exist’.

I conclude that the inference from (6a) to (6b) is not intuitively valid. The question remains: Is the validity of this inference a matter that we cannot seriously question? The problem, for Schaffer, is that it's relatively easy to make a defensible case for the invalidity of this inference.

According to Schaffer, ‘x created y’ means ‘x made y exist’ (i.e., ‘x brought y into existence’). As we’ve seen, the inference from ‘Doyle created Holmes’ to ‘Holmes exists’ isn’t intuitively valid. However, the inference from ‘Doyle made Holmes exist’ (i.e., ‘Doyle brought Holmes into existence’) to ‘Holmes exists’ is intuitively valid. This is a prima facie problem for Schaffer's semantic view and must be explained. I have already considered, and rejected, one explanation—that the inference from ‘Doyle created Holmes’ to ‘Holmes exists’ is intuitive when we get the right reading of the conclusion. Another explanation is that this inference is not intuitive because we can’t access the relevant semantic facts merely by drawing on our linguistic competence. Fair enough, but other explanations are available.

According to Everett & Schroeder (2015), ‘Doyle created Holmes’ may be a shorthand for ‘Doyle created the idea of Holmes’. If it is (and ‘x created y’ means ‘x made y exist’), then Doyle made the idea of Holmes exist (i.e., he brought this idea into existence). However, this entails the existence of ideas, not fictional characters. So, the inference from (6a) to (6b) is not valid.¹⁰ According to Brock (2002), ‘Doyle created Holmes’ is a shorthand for ‘according to a certain metafiction in which fictional entities exist, Doyle created Holmes’.¹¹ So, again, the inference from (6a) to (6b) is not valid. It is an open question which of these explanations is correct (or whether some other explanation is correct). However, the inference from (6a) to (6b) is only valid on one of these explanations. So, we can seriously question the validity of this inference.

Here is another argument for the invalidity of the inference from (6a) to (6b). Sherlock Holmes is a fictional character because he's a character (roughly: a person) according to some fiction. His pipe is a fictional pipe because it's a pipe according to some fiction. But his city—London—is a fictionalised city, not a fictional one, even though it's a city according to some fiction. So, what distinguishes a fictional character (or object) from a fictionalised one?

One answer is that (by definition) a fictionalised character exists; a fictional character does not. On this view, (6b) states a contradiction. So, either (6a) also states a contradiction or the inference from (6a) to (6b) is invalid. Since (6a) expresses a Moorean belief, we have a strong reason to believe that the inference from (6a) to (6b) is invalid.¹² Of course, Schaffer will offer a different answer: A fictional character is a character whose existence depends on the existence of some fiction; a fictionalised character is a character whose existence does not depend on the existence of any fiction. But even if Schaffer's answer is correct, it is far from obvious. So, clearly, there is a serious debate here about the meaning of ‘fictional’ and the validity of the inference from (6a) to (6b).

Further arguments for the invalidity of this inference can be found in the literature on fictional entities. But I’ve said enough to make my point. I conclude that we can seriously question whether the inference from (6a) to (6b) is valid. Since I have also argued that this inference is not intuitive, I conclude that this inference is not trivially valid. So, (6) cannot be defended as an easy argument. More importantly, if the truth of ‘Doyle created Holmes’ doesn’t trivially entail the truth of ‘Holmes exists’, then Schaffer cannot defend (3) as an easy argument for God. So, his argument for permissivism fails.

One question remains: Are there other easy arguments for the existence of fictional characters or God? If there are, then perhaps Schaffer can reboot his argument for permissivism with another easy argument for the existence of God in place of (3). Consider the following example:

• (12) a.

  The fictional character Sherlock Holmes is more famous than any living detective.

• b.

  Therefore, the fictional character Sherlock Holmes exists.

Arguably, God is also more famous than any living detective. So, if (12) is sound, then there is a sound easy argument for the existence of God. However, the inference from (12a) to (12b) is not intuitively valid (and may be intuitively invalid). Further, it's relatively easy to make a defensible case for its invalidity. For example: It can be argued that (12a) should be analysed as ‘Holmes is better known than any living detective’ and that this should be analysed as ‘the number of people who know of Holmes is greater than the number of people who know of any living detective’.

However, if this analysis is correct, then the inference from (12a) to (12b) is analogous to the inference from ‘Bob wanted (dreamt about, searched for, etc.) a unicorn’ to ‘a unicorn exists’ and arguably they are both invalid for similar reasons. Further, even if Schaffer argues that the inference from ‘Bob wanted (etc.) a unicorn’ to ‘a unicorn exists’ is valid, he can’t argue that it is trivially valid because its validity is not intuitive and can be seriously questioned.

Of course, I can’t discuss every potential easy argument for the existence of fictional characters. Hopefully, I’ve said enough to convince you that these arguments suffer a similar fate, for similar reasons.¹³ And if that's the case, then Schaffer's argument for permissivism fails.¹⁴

Footnotes

REFERENCES