Is the argument convincing? Not as stated, but I will argue that both premises can be improved.

Premise 1 would certainly be rejected by contemporary philosophers, as verificationism has long been rejected,Footnote 8 and such Carnapian arguments are usually dismissed on the grounds that they presuppose verificationism.

But we can now see the key point: verificationism is a dispensable part of the argument. At the heart of Carnap’s argument is a claim about justification. I think this is what Carnap was really getting at, but, more importantly, it improves the argument. If we go back to Carnap’s example of the two geographers, the root of the unease about the dispute between realism and idealism is that ‘these two theses...go beyond experience [evidence]’, and disputes that go beyond evidence are problematic because it is unclear how we can have justification to believe one side over the other. So I suggest we replace:

1. If sentence S has factual content then evidence which would support S or \(-\hbox {S}\) is conceivable (Verificationism)

with:

1’. If we can have justification for S then evidence which would support S over \(-\hbox {S}\) is conceivable.Footnote 9

Let’s move on to premise 2:

2. It is not the case that evidence which would support S or \(-\hbox {S}\) is conceivable.

At this point we need to say something about the concept of support. Fortunately, there is wide agreement that the best analysis of the concept of support (confirmation) is the Bayesian probability raising account that, where P expresses an agent’s degree of belief,

$$\begin{aligned} \hbox {E supports S iff P}(\hbox {E}{\vert }\hbox {S}) > \hbox {P}(\hbox {E}{\vert }-\hbox {S}) \end{aligned}$$

Footnote 10,Footnote 11

(Whether P can stand for rational belief will be a key issue later.) So premise 2 says that for any conceivable evidence \(\hbox {E}, \hbox {P}(\hbox {E}{\vert }\hbox {S}) = \hbox {P}(\hbox {E}{\vert }-\hbox {S})\). We can think of premise 2 as saying that S is immune to evidence. But now we face a problem.

Which sentences are immune to evidence? Plausibly, none, due to confirmation holism. That is, given the right background information, any sentence can confirm any other sentence. For example, take a paradigm sentence that looks immune to evidence: ‘19 angels can dance on the head of a pin’. And suppose our background information includes ‘if I see a red flash then 19 angels can dance on the head of a pin’. Now ‘19 angels can dance on the head of a pin’ is not immune to evidence. This is a toy example, but the point should be clear—given the right background information, for any sentence, there is some evidence that would confirm itFootnote 12 \(^,\) Footnote 13. Thus, few, if any, candidates for S satisfy premise 2.

I think this objection can be answered. The key is to notice, first, that in many metaphysical debates a sentence is contrasted, not with its negation, but with an alternative.Footnote 14 And second, the alternatives are usually intended to predict all the same evidence. For example, consider the debate between the realist and the idealist above:

H1 \(=\) The mountain is real (and goes beyond our perceptions) H2 \(=\) Only our perceptions are real.

The realist and the idealist will both set up their hypotheses so that they predict the same evidence.Footnote 15 H1 and H2 are empirically equivalent i.e. they predict exactly the same evidence, so for any \(\hbox {E}, \hbox {P}(\hbox {E}{\vert }\hbox {H1}) = \hbox {P}(\hbox {E}{\vert }\hbox {H2})\). If follows that no conceivable evidence supports H1 over H2. Given a debate that has been carefully circumscribed in this way, the point about confirmation holism will have no force. We can grant that any sentence can be confirmed by any other (given particular background beliefs), but no evidence will support realism over idealism or vice versa (given that they predict exactly the same evidence). To put it another way, for any two theories, if conceivable evidence E confirms one over the other, the two theories cannot be realism and idealism.

Applying this to premise 2, the improved version says that the target sentences are empirically equivalent. So we replace:

2. It is not the case that evidence which would support S or \(-\hbox {S}\) is conceivable

with:

2C. It is not the case that evidence which would support S over T is conceivable.

In many cases, metaphysicians engaged in a debate intend that their competing hypotheses should be empirically equivalent. However, if hypotheses are not empirically equivalent then 2C will not apply, and the range of debates for which evidence is relevant is highly contentious. For example, consider the debate about whether numbers exist. If there could be evidence confirming that there is a prime number between 4 and 6 (e.g. a proof that 5 is not divisible by 2, 3 or 4), then 2C will not apply. Similarly, if finding a best theory of the world that quantifies over numbers would be evidence for the existence of numbers, then 2C will not apply.Footnote 16 \(^,\) Footnote 17 So the epistemological argument we are developing deflates debates that can not be resolved by evidence and vindicates debates that can be resolved by evidence; whether a debate is scientific, philosophical or metaphysical does not come into it. We’ll come back to this in Sect. 6, where the upshot will be that whether our argument applies will have to be assessed on a case-by-case basis, varying with the topic, and even with the philosopher.

One final modification. In order for 2C to fit the first premise, we have to compare S with T in the first premise too. So we replace

\(1'\). If we can have justification for S then evidence which would support S over \(-\hbox {S}\) is conceivable.

with

1C. If we can have justification for S over T then evidence which would support S over T is conceivable.Footnote 18

Putting these together, we arrive at the challenge to contemporary metaphysics.

Epistemological Argument 1C. If we can have justification for S over T then evidence which would support S over T is conceivable. 2C. It is not the case that evidence which would justify S over T is conceivable. 3C. Therefore we cannot have justification for S over T.

This argument is not semantic, but epistemic. Instead of saying that metaphysical theses can’t be stated, it says that we can have no justification to believe them. The result is almost as devastating for metaphysics. If we can have no justification to believe a metaphysical hypothesis, there is no point trying to have a rational metaphysical debate—so there is no point doing metaphysics.Footnote 19

To recap, Carnap’s argument ran: Verificationism + Metaphysics can’t be justified = Metaphysics has no content

Once we reject verificationism, the conclusion that metaphysics has no content can’t be defended. But the heart of the argument, that metaphysics can’t be justified, remains.

To reject the Epistemological Argument we’d have to argue either that some metaphysical theses can be justified by the evidence (thus rejecting 2C) or that we can have non-evidential justification for some metaphysical hypothesis (thus rejecting 1C). I’ll come back to this in part 6.

Before moving on I’ll briefly compare three recent works by Karen Bennett, Ted Sider and Uriah Kriegel that make related points.Footnote 20 Bennett (2009) suggests a similar epistemic conclusion, but for different reasons. She suggests that often ‘there is little justification’ (p. 42) for opposing metaphysical hypotheses. Her reasoning is that as most metaphysicians want to minimize the difference between their own view and their opponent’s, the resulting views end up so similar that arguments against one view rebound against the other view.Footnote 21 She seems to grant that we do have non-evidential justification, but thinks this justification often ends up being weak. In my terms, Bennett denies 1C, but offers a different path to 3C (or perhaps a weaker version of 3C).

Sider (2011) notes a similar challenge in passing:

One complaint [about metaphysical disputes, and in Sider’s example about extended simples] is purely epistemic. It admits that the dispute is substantive, but claims that the considerations offered by the enthusiasts [metaphysicians] are inadequate to resolve it. We do not know whether there exist extended simples, it is alleged, and the enthusiasts [metaphysicians] arguments aren’t helping. (p. 80)

Although Sider quickly dismisses three other complaints (p. 82) there is no quick dismissal of this one.Footnote 22

Kreigel (2013) provides the most detailed discussion of this epistemic challenge, and his discussion is in the same spirit as my own. In my terms, he defends 1C and 2C, but ends up suggesting that there must be some way to avoid 3C. I will briefly suggest a way in part 6, which discusses objections to the Epistemological Argument. But in the intervening part I will discuss objections to this interpretation of Carnap.