Cutting the Gordian Knot of Frege-Geach James Coley (

Famously, J. L. Mackie thought that moral sentences – those that include moral predicates like good, bad, right and wrong – mean in ordinary language exactly what the moral realist thinks they do, but that moral realism as a metaphysical thesis is nevertheless false, and thus that all these sentences are in error. What if he were right? Would that mean we should call for the end of ethics?

I think not. An alternative to moral nihilism is here provided by a general philosophical method I call constructionism. According to this method, revision is the way to go in philosophy, in this case and many others. We kick troublesome ordinary language to the curb, more or less, and stipulate new meanings. The philosopher as conceptual engineer constructs homonyms for moral predicates, proposed as successors.

For the constructionist, by the way, a counterexample from ordinary language may not be fatal for a theory, particularly if it is a far-fetched counterexample. Since its definitions are stipulative, constructionism may allow any such examples to apply for the homonym, and far-fetched ones will be the least problematic deviations from common usage. At the same time, the stipulated meanings must align with ordinary language well enough that we are not changing the subject. I begin with the premise that Mackie was right about ordinary language, and I want to construct a metaethical theory that walks this fine revisionist line.

Like Mackie, I take an irrealist view. So whatever metaethical theory I propose, constructionist or not, must withstand that nemesis, not just of expressivism, but of irrealism in general. I mean, of course, the Frege-Geach problem. It starts as a set of adequacy conditions for any theory of moral sentences.

The theory must, first of all, provide accounts for moral predicates in embedded as well as stand-alone instances and, secondly, these accounts must be the same, in part because, thirdly, the theory must account correctly for valid arguments like this version of the little-brother argument. (The second condition prevents equivocation in examples like this one.)

(1) Lying is wrong.

(2) If lying is wrong, then getting little brother to lie is wrong.

Therefore, (3) Getting little brother to lie is wrong.

This is shop-worn, and it isn’t even the original example in Peter Geach’s 1965 paper. But it will serve my purposes well enough, and I will stick to the example of wrong. It should be easy to see how to apply my account to other moral predicates.

I’ve identified what I call the Frege-Geach adequacy conditions. My problem is how an irrealist constructionist theory might meet these conditions. A somewhat different problem is explaining embedded contexts and valid arguments like this one for ordinary moral language. But as far as that is concerned, I’ve already cut the Gordian Knot of Frege-Geach.

The reason ordinary moral language seems realist is that it is. If the Frege-Geach problem is explaining why, despite the appeal of expressivism for the irrealist, it does not seem to capture certain surface characteristics of moral language, the solution is to concede the point and embrace the error theory, as far as ordinary language is concerned.

The constructionist wants to move on to craft something that is revisionist but aligns largely with ordinary language, where that alignment is something more than a convenience, but not an exceptionless requirement. In any case, what I have fashioned seems to meet the Frege-Geach adequacy conditions and might even recommend itself to the philosopher who rejects constructionism and clings to old-fashioned conceptual analysis.

Of course, Frege-Geach does not exhaust the adequacy conditions for a theory of moral sentences. Under constructionism, philosophers will argue about what the adequacy conditions should be, just as architects argue about the aesthetic, cultural and even functional purposes of buildings and related structures, composers argue about the meaning of music, and so on. Philosophers argue about adequacy conditions for their theories anyway, constructionism aside.

I call the theory I have fashioned value prescriptivism. It is a form of prescriptivism in which, roughly speaking, it is values that are prescribed instead of behavior. If expressivism likens “Murder is wrong” to “Murder: Boo!” and standard prescriptivism likens it to “Don’t murder!” then value prescriptivism likens it to “Have a value system that prohibits murder!”

Before giving a full presentation of value prescriptivism, I will consider a different approach: semantic relativism. Others might call it indexicalism. One reason for looking at semantic relativism first is that, along the way, we will see other adequacy conditions emerge, besides those I call “Frege-Geach.” After the full presentation of value prescriptivism, I will argue that it meets all these adequacy conditions.

Lots of things can be called “relativism” and value prescriptivism might face the accusation of being relativistic. Any view that explicates a one-place predicate as a two-place predicate might draw imputations of this label, although I will use a different term (“relationism”) for this.

In some sense, I can’t, and have no need to, evade the charge of relativism. But I want to distance value prescriptivism from the label for two reasons. First of all, my view is not normative relativism, the ridiculous idea that if a person, society or culture says that something is right or wrong, it is right or wrong, at least as these predicates apply to them. Second, value prescriptivism attempts to satisfy adequacy conditions that semantic relativism does not satisfy.

As a preliminary to my digression on semantic relativism, allow me to define a few terms. They are among the building blocks I will also use in the full explanation of my theory. To work up to a more formal presentation of the main idea of value prescriptivism, it is important to understand the notions of values and value systems.

First, I stipulate that a valuation is a conditional disposition to have an attitude of approval or disapproval about something given that one believes it meets a particular criterion. What I call values are a proper subset of valuations, where the criteria are abstractly characterized. Exactly how they must be characterized is hard to say, but all I have in mind here is that, for example, if I approve of something because I believe it to be chocolate, I will call that a valuation, but I don’t want to call it a value. By way of contrast, if I approve of something because I believe it to be courage, I will say that it is a value of mine, and that I value courage. This is related to the way “courage” requires a more abstract characterization than “chocolate.”

A person’s value system encompasses their values, and need not be all that systematic. I need a notion like that of a normative system or perspective, as we see them developed by other philosophers including Gibbard, Ridge and many others. One way to make this more precise is to say that a value system includes both values and beliefs, from which some attitudes the person also has may be inferred. Some degree of inferential structure is what I have in mind, but it does not really matter all that much exactly what it is.

What I call relatonism is the strategy of explicating moral predicates as relations to value systems. My example is will be the explication of wrong as the violation of a value system. I predicate murder wrong because it violates my value system, and this suggests the following biconditional.

Murder is wrong ↔ Murder violates V

The right-hand side of the biconditional is an instantiation of the relational schema for the moral predicate wrong, and V is a variable ranging over all conceivable value systems. There are relational schemata for all the moral predicates.

Semantic relativism – henceforth relativism for short – is the theory of the semantic content of moral predicates as pegged to particular value system. Consider a hypothetical conversation between myself and Sarah Palin. When she says “Gay marriage is wrong,” according to relativism, she means that gay marriage violates her bibliolatrous value system Vb. When I say the same sentence, although I don’t believe it to be true, what I mean is that gay marriage violates my humanistic value system Vh. There are two problems with this.

First, we mean different things, according to relativism. She means something to do with Vb while I’m talking about something different, Vh. This is a problem because it seems that we do not disagree in a way that we certainly do disagree. We can’t really, fully disagree about the moral sentence “Gay marriage is wrong” if we are talking past each other. Certainly we do not agree in our value systems, and would recommend contrary social policies, and so on. But we disagree in a deeper sense as well with respect to the judgments we make about the moral sentence as understood to have a common semantic content.

The second problem is apparent once we notice that, according to relativism, what Sarah says is true. Gay marriage certainly does violate her value system Vb. But I want to preserve the features of ordinary language that enable me to say that, when she says “Gay marriage is wrong” she has said something false. Of course, when I say “Gay marriage is not wrong” she will say I have said something false. This is all to be expected, and is just more of what follows from our having a genuine disagreement, given that we have very different value systems. I don’t mean to suggest that a theory of moral sentences should bias the outcome in this case in my favor, but I certainly don’t want metaethics alone to necessitate that Sarah’s utterance is true. At the very least, I ought to be able make sense of being able to say that what Sarah says is false.

So two more adequacy conditions for a metaethical theory of moral sentences have emerged. First, the theory must account for common semantic content even in cases of genuine, deep disagreements. Second, the theory must enable us to make sense of moral sentences being judged true or false, not on the basis of the value system of the one uttering the sentence, but instead on the basis of the value system of the person making that judgment of truth or falsity.

Now the time has come for the full presentation of value prescriptivism. This will require definition of two more building blocks, that of the characteristic schema of a moral sentence, and that of a particular value system satisfying a characteristic schema. These will allow the formulation of the basic statement of value prescriptivism. After presenting the basic statement, I will show how value prescriptivism satisfies the three adequacy conditions of Frege-Geach, as well as the two other adequacy conditions for a theory of moral sentences that relativism fails to satisfy.

For any moral sentence S there is a corresponding characteristic schema S´ which is an open sentence resulting from the uniform replacement in S of each instance of any moral predicate with its corresponding relational schema. So any characteristic schema S´ is an open sentence, and it is open in the variable V that ranges over all conceivable value systems.

A particular value system named Vi satisfies a characteristic schema S´ just in case uniformly replacing V with Vi yields a true descriptive sentence.

The basic statement of value prescriptivism is this: To say a moral sentence is to prescribe acceptance of any value system that satisfies the characteristic schema of the sentence.

To restate this using the notation developed: To say S is to prescribe acceptance of any Vi that satisfies S´.

Consider how value prescriptivism applies to the premises of the little brother argument. According to this theory of moral sentences, to say “Lying is wrong” is to prescribe acceptance of any value system Vi such that lying violates Vi. To say “If lying is wrong, then getting little brother to lie is wrong” is to prescribe acceptance of any value system Vi such that if lying violates Vi then getting little brother to lie violates Vi.

It should be apparent that value prescriptivism easily satisfies the first Frege-Geach adequacy condition. It provides an account of stand-alone instances of moral predicates, such as “Lying is wrong,” as well as embedded cases such as “If lying is wrong, then getting little brother to lie is wrong.” Compositionality is not a problem because the account applies to whole sentences, not the moral predicates. To put this another way, compositionality is handled through the characteristic schema of the sentence, prior to the introduction of normativity in the account.

It should also be apparent that the accounts provided by value prescriptivism for embedded and stand-alone cases are the same, and thus that the second Frege-Geach adequacy condition is easily satisfied. Value prescriptivism always accounts for all moral sentences in precisely the same way.

The third and final Frege-Geach adequacy condition is that a theory of moral sentences must account correctly for valid arguments. Again, consider how value prescriptivism applies to the little brother argument. Here we see Hare’s points about how imperatives and other prescriptions exhibit logical relationships coming to the fore. Even if prescriptions do not have truth-conditions, at least in an obvious way, they do have compliance conditions, and these are isomorphic to truth-conditions with respect to validity.

There is no way a value system can satisfy the characteristic schema of “Lying is wrong” as well as the characteristic schema of “If lying is wrong, then getting little brother to lie is wrong” without also satisfying the characteristic schema of “Getting little brother to lie is wrong.” Thus, there is no way to comply with the prescription related to the first premise, as well as the prescription related to the second premise, without also complying with the prescription related to the conclusion.

Although a complete development of how value prescriptivism can account for validity in normative and mixed arguments is beyond the present scope, the idea here is that logical relations between compliance conditions for prescriptions, along with the way the theory applies to whole sentences, provides the resources needed for such an account.

Consider this illustration of the rough idea. Suppose I send you to the video store – remember video stores? – to get a movie for us, and I say “Get a Hitchcock movie,” although I don’t know that you will not return with one by another director instead. I remember that Psycho is not one of my favorites, and that I prefer the 1956 remake of The Man Who Knew Too Much to the original 1934 version, and so I also say “If you get a Hitchcock movie, get one in color.” It is impossible for you to comply with both of these prescriptions unless you get a movie that is in color.

Unlike a relativist theory, value prescriptivism easily accounts for disagreements. When Sarah says “Gay marriage is wrong” she means exactly the same thing, according to my theory, that I would mean were I to say this. There is no reference to any particular value system in the accounts given by value prescriptivism, as there is an existential quantifier involved instead, and this prevents the problem of there being no common semantic content between me and Sarah.

When Sarah says “Gay marriage is wrong” she prescribes that I and everyone else accept some value system or other such that gay marriage violates it. Were I to say it, I would mean the same thing. She says what she says because gay marriage violates her value system, and because, in the familiar manner of universal prescriptivism, she is willing to prescribe that others have value systems like hers, at least in this one respect linked to the semantic content of the sentence.

Were I to say “Gay marriage is wrong” I would make the same prescription. But since gay marriage does not violate my value system, I don’t make any such prescription. Nevertheless, Sarah and I are not talking past each other; the moral sentence has the same content for both of us.

Thus, my theory satisfies the first of the two adequacy conditions we identified in the consideration of relativism. I will end with some indication of how I think value prescriptivism can also satisfy the second of these two conditions, the one related to the possibility of my judging the moral sentence “Gay marriage is wrong” false.

Value prescriptivism is resolutely irrealist and offers no account for moral sentences of truth simpliciter, and regards the notion in this case as inappropriate if not incoherent. However, my theory does have a straightforward deflationist account of what it is for someone to say that a moral sentence is true or false. To say, for example, that “Murder is wrong” is true is to prescribe acceptance of any value system satisfying the characteristic schema of the sentence, and to say that it is false is to prescribe acceptance of any value system satisfying the characteristic schema of “Murder is not wrong.” This will, of course, track whether murder violates one’s own value system. As gay marriage does not violate my value system, it makes sense for me to say that, when Sarah says “Gay marriage is wrong,” she says something false. It equally well makes sense for her to say that, when I say “Gay marriage is not wrong,” I am saying something false.

Of course, this raises all kinds of questions usually raised about relativist accounts although, for reasons I have explained, I do not classify value prescriptivism as a relativist view. I will not be able to settle these questions now, but I hope it will suffice to point out that a theory of moral sentences, as a creature of metaethics, can not be expected to settle normative disagreements such as the one about gay marriage, or even one about murder. At some point, Sarah and I must discuss our value systems.


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