Unbelievable Errors is a remarkable new book by Bart Streumer. In it he makes the case for a generalized error theory, one that covers all normative judgements. Normative judgements on this view are uniformly false. Streumer believes his reasoning shows this to be true. Similar works in the past, which were confined to moral judgements, were offered by J.L. Mackie, Richard Joyce, and Jonas Olson. Unbelievable Errors is distinctive in three ways. First, he doesn't rest his case on queerness arguments, or on the related claim that scientific information somehow informs us that, as a matter of metaphysics, nonnatural moral properties cannot exist. Second, Streumer endorses the claim that we cannot believe the error theory, including himself: ‘Like everyone else, I cannot believe the error theory’ (7). Third, it is the reason that Streumer gives for this claim that is the most novel feature of his book. People that consider moral error theory for the first time will agree that they cannot believe it, either because it is too crazy to be true, or because its implications are morally abhorrent. Streumer, on the other hand, holds that the unbelievability of the error theory is simply an implication of the error theory. The book may be divided into two parts: the major part, the case for the error theory and the minor part, why we cannot believe it.

What is the error theory? It holds that ‘normative judgements are beliefs that ascribe normative properties, but that normative properties do not exist. It therefore entails that all normative judgements are false’ (ix). The approach that Unbelievable Errors takes to making the case for the error theory is a common one in ethics. Various theories of normative judgments are offered for consideration. Arguments are given to eliminate each one. The survivor of the destructive process is the error theory. And none of the arguments applied to the alternative theories destroys the error theory. Many of these reductio ad absurdum arguments rely on quite abstract propositions. When Streuemer is moving from one variation of a given view to another, he adjusts his argument to target each new variation. The organization of this portion of the book, like the organization of the whole, is quite well arranged, so an assessment of one view can be applied to the assessment of the next view. The mechanical precision with which Streumer conducts the process is impressive. And view after view is seemingly dispatched, at some points in very little space.

To give a sense of Streumer's argumentative approach consider his argument against the traditional target of error theory, nonnaturalism. In his attempted takedown of non-reductive realism, as he calls it, he uses certain considerations of properties to show that there are no irreducibly normative properties. At the center of this reduction argument is the proposition (N): ‘Two predicates ascribe the same property if and only if they are necessarily coextensive’ (11). By using this principle along with various considerations and thought experiments, he arrives at the conclusion: If there are normative properties, these properties are identical to descriptive properties. If this is true, then non-reductive realism is clearly in trouble. So much depends on the details of the reduction argument. Throughout this portion of the book, Streumer is very thorough. If you are dissatisfied with the reduction argument he offers, he provides second and third versions of it. If you have objections to his arguments, responses are given to several objections.

Non-reductive realists will strongly resist concluding that, if there are normative properties, these properties are identical to descriptive properties. In the service of bolstering the argument for this proposition, Streumer handles a common non-reductionist counterclaim: there are predicates that have the same extension yet signify distinct properties. Here is a case that illustrates how this can be so: ‘The predicates “has three angles” and “has three sides” are necessarily coextensive but ascribe different properties’ (13). And the way to show this is by considering, first, a triangle, a figure with three angles and three sides, and second, an open figure in which there are three sides but only two angles. Streumer attempts to disable this counterclaim with a counterclaim of his own. He states, with supporting reasons, that the claim should be, ‘The predicates “is a closed figure that has three sides” and “is a closed figure that has three angles” are necessarily coextensive but ascribe different properties’ (14). Even if it is correct to say that the original counterclaim too easily supports non-reductionism, it is also correct to say Streumer's own counterclaim too easily undermines it. It would seem that if we could find a proposition halfway between them, that would decide the dispute. The two predicates ‘is a figure that has three sides’ and ‘is a figure that has three angles’ are coextensive for triangles, but signify distinct properties when we consider an open three-sided figure.

Despite Streumer's thoroughness and care, the problem we have in evaluating his overall performance is a familiar one in metaethics. It seems that he is either right, or on the right track, in his arguments against every other theory but the one the reader favors. Streumer's attempted takedown of the view I favor, non-reductive realism, at several points made me wonder if there were not some serious weaknesses in this brand of realism. At the same time, the abstractness of some of his crucial propositions and arguments made me also wonder how such reasoning could decisively eliminate the possibility that an entire class of properties exists. This in turn made me wonder just how strong his arguments are against other views such as reductionism, non-cognitivism, constructivism, and so on. It would seem that the best way to know this is to have proponents of the different theories he covers provide their assessments of his reductio arguments.

It is the minor claim of Unbelievable Errors, however, that makes this work most distinctive. It also makes error theory more plausible, as Streumer claims. Eliminating all of the various theories of normative judgements, and thereby concluding that there are no normative properties, implies that there are no reasons for belief. Since there are no reasons for belief, there are no reasons to believe the error theory. (This is precisely where the generalization of the error theory comes in handy). Therefore, on the very terms that establish the error theory, we can conclude that we cannot believe the error theory. Besides, as he states, he himself is not at all inclined to give up his own normative judgments (138).

Although Streumer's basic argument for the claim can be put as simply as that, he employs his characteristic thoroughness in an attempt to ensure the argument works. Included in his discussion are the conditions he claims are requisite for an agent to have a belief, a sizeable discussion of reasons for acting and reasons for believing, and a handling of objections to the views being offered. The reason Streumer's ‘cannot believe’ claim makes error theory more plausible is, in my opinion, because we're not inclined to believe the error theory as it is. His argument for the minor claim rests on the matter of the conditions under which we can hold in belief incompatible propositions. As applied to Streumer's major and minor claims, it is clear that unless one believes the major claim, there will be no inclination to believe the minor one on that basis. That means the controversy over the minor claim is likely to matter most to other error theorists.

In my view Unbelievable Errors is most valuable for its most prominent feature. The series of destructive arguments he offers against theories of normative judgements will be useful for testing them. Although, as I've said, I'm unsure that Streumer's arguments undermine non-reductive realism, I do believe I'll be using these arguments to test the theory. The kind of abstract argumentation that Streumer engages in, as I've said, often leaves one unsure that it has hit its intended mark. What it does show, however, is that he is very confident in the power of abstract, even a priori, reasoning to show that purported properties don't exist. What he seems not to recognize is that with such a confidence, Streumer makes way for the possibility of there being a priori reasoning that shows such properties do exist. If such a possibility is considered, and succeeds, then the reason we cannot believe the error theory can find a more straightforward explanation. We continue to really think that murder is wrong, rape is wrong, keeping promises is right, and so on, because each such proposition is true.