Why anti-realist semantics cannot work

A technical worry

[Epistemic status: I don’t do ethics!]

Introduction

Some time ago I wrote a post on this issue, but I am still unsatisfied. This is a revamp of the argument from that old post.

Meta-ethicists are typically divided into two camps: Realists and Anti-realists. Realists believe that there are moral facts that are true independent of the stances of any people. In contrast, anti-realists deny that there are any moral facts of this sort, they deny that there are moral facts that are stance-independently true. The anti-realist’s rejection of stance-independent moral facts are variously motivated. Some reject realism because they believe moral facts are true stance-dependently, some because they don’t believe any moral facts are true, still more reject realism because they don’t believe moral statements concern ‘facts’ at all.

Rather than argue against any particular anti-realist view, I wish to note a constraint on any such project. Many anti-realists wish to provide the truth conditions, or the meaning, of moral statements. “The proposition expressed by the sentence ‘X is good’ is true, iff, the person who uttered the sentence prefers/desires X” or “‘X is good’ means ‘Yay X!’ (or something near enough).” The candidate definiens, or analysans, suggested by realists are often ill suited for this project.

Moral statements constitute an extensional context. If a moral statement M is true, then a statement identical to M with all terms replaced with co-extensional ones, M’, is also true. It follows that the set of all true moral statements is closed under substitution of co-extensional terms. Thus, an analysis or definition provided for moral statements must also be closed under the substitution of co-extensional terms. I’ll first elaborate on this argument, and then show why this constraint poses a difficulty for at least one form of anti-realism.

The constraint

A proposition is extensional if its truth is preserved under substitution of co-extensional terms. Two terms are co-extensional if they have the same extension. The idea of extension is easiest to grasp with names, though it also applies to properties.

Consider the sentence “Robert Zimmerman wrote Mr. Tambourine Man.” This sentence is true. It is also true that “Bob Dylan wrote Mr. Tambourine Man” because Bob Dylan is Robert Zimmerman. The name ‘Bob Dylan’ has one person in its extension, and that person is the same person contained in the extension of ‘Robert Zimmerman.’ With names, it is easiest to think of extension as synonymous with referent.

Now, consider the predicate “egg laying mammal with a bill.” Platypi are egg laying mammals with bills, indeed, only platypi are egg laying mammals with bills. So we can infer from the sentence “A platypus destroyed my destructinator” that “An egg laying mammal with a bill destroyed my destructinator.” This is because the predicate ‘platypus’ and ‘egg laying mammal with a bill’ are co-extensional. The extension of a predicate is the set of all things the predicate is true of, so the extension of the predicate ‘platypus’ includes all platypi.

Certain contexts are extensional, and others are not. Clearly, the above sentences express extensional propositions, but in some contexts the sentences at hand will typically express non-extensional propositions. The non-extensional context par excellence is belief. Suppose I believe “Bob Dylan wrote Mr. Tambourine Man”. You cannot infer that I believe “Robert Zimmerman wrote Mr. Tambourine Man.” If you handed me a test with the question of who wrote Mr. Tambourine Man, it is clearly possible that I honestly answer that Bob did, but Robert did not. This is even clearer with predicates. Suppose I believe “a platypus destroyed my destructinator.” We cannot infer that I believe “an egg laying mammal with a bill destroyed my desctructinator.” If we could infer such a thing, then every child who had beliefs about platypi would know what mammals were!

Moral contexts are unlike belief contexts, they are extensional. Suppose it is true that “It would be wrong to murder Bob Dylan.” We can infer that “It would be wrong to murder Robert Zimmerman.” Suppose “it would be good to own an egg laying mammal with a bill,” we can infer that “it would be good to own a platypus.” The astute reader will note that moral contexts are not always extensional. It may not follow from “It would be good for you to believe that Bob Dylan wrote Mr. Tambourine Man” that “It would be good for you to believe that Robert Zimmerman wrote Mr. Tambourine Man.” One might also demur from this judgement, but I’m happy to grant it for the sake of argument. Clearly, this is a case where a non-extensional proposition is embedded in the moral sentence. We can say that moral contexts are extensional so long as a non-extensional proposition is not embedded within the proposition expressed by the relevant moral sentence in this way.

Finally, we can say that extensional contexts are closed under co-extensional substitution. More formally, if we consider a set of propositions Φ which corresponds to a context C, if C is extensional then for any proposition P expressed by a sentence of the context C, P is a member of Φ and any proposition P’ which follows from P by co-extensional substitution is a member of Φ, and P’ iff P.

Given moral contexts are extensional, it follows that they are closed under co-extensional substitution. We can then consult the narrower range of true moral sentences. These will still be extensional, as the relevant sentences are a subset of the broader extensional moral context. Therefore the set of true moral sentences will be closed under co-extensional substitution.

Now, any analysis or candidate definition of some set or type of sentences will constitute an extensional context if the target sentences constitute an extensional context, because there must be at least one translation sentence for every translated sentence, and the translation sentences must be of the same truth value as the translated sentences. An analysis or definition for a sentence or term will take any instance of that sentence or term, and provide a new sentence with the same truth value. If “John is a bachelor” is true then we can apply an analysis and get the (true) sentence “John is an unmarried man.” Therefore any analysis or translation of moral sentences must be A. truth-value preserving, and B. closed under extensional substitution. (A) is a necessary condition of any analysis and (B) is a necessary condition of any analysis of sentences in an extensional context. Another way to put this is that every member of the set of translated sentences must be true iff the sentence it translates is true, and the set of translated sentences must be closed under extensional substitution.

Applying the constraint

Whence cometh the puzzle? Suppose some anti-realist provides the following translation of moral sentences:

The sentence S: “X is good” is true, iff, the person who utters S approves of X.

This is rough, but suitable for our purposes. The target analysandum is some set of moral sentences, namely those moral sentences about what is good. The analysans will lead to a set of sentences about the speaker’s approval. We can now apply the constraint. Is the set of sentences generated by the analysans closed under extensional substitution? No! The fact that someone approves of X does not mean they will approve of some extensionally equivalent proposition X’. If I approve of Bob Dylan playing rock music, it does not follow that I approve of Robert Zimmerman playing rock music. If you asked me “Would you like to hear a Robert Zimmerman song?” I might reasonably, and emphatically, say no! “Tower of Babble approves of Bob Dylan playing rock music” is not true if and only if “Tower of Babble approves of Robert Zimmerman playing rock music.”

Indeed, this constraint also poses a puzzle for emotivists.¹ Our reactions can’t be closed under co-extensional substitution, since reactive attitudes are non-propositional; but less trivially, facts about our reactive attitudes are also not closed under co-extensional substitution. From the fact that I always say ‘Yay Bob Dylan playing music’ it does not follow that I will say ‘boo Robert Zimmerman playing music,’ for I might not know that Bob Dylan is Robert Zimmerman. It also does not follow from the fact that I have the yay attitude towards Bob Dylan that I have the yay attitude towards Robert Zimmerman, for similar reasons. People can clearly have conflicting attitudes about the same thing, particularly in cases of co-referential names, and this renders facts about our attitudes incredibly ill suited as an analysans, or definiens, for statements of moral fact! Moral facts cannot conflict in virtue of co-extensional substitution! Not only are moral facts closed under entailment (to my mind, this also poses a problem for emotivism, one which goes unsolved by solutions to the embedding problem), they are closed under co-extensional substitution; not so with attitudinal contexts.

Avenues of response

So what is an anti-realist to do? A few options. The first path is to be an error theorist. You can accept the conventional realist account about the object of moral discourse, deny that there are facts of the relevant kind, and thus all statements about them are false. Refuse to ‘reduce’ moral discourse to attitudinal discourse in any way, instead claim that attitudinal discourse is good enough on its own. I don’t really like this option, because error theory strikes me as the most obviously crazy form of anti-realism (“It is wrong to torture babies” being false is a really bad look for a meta-ethical theory, even if “It is right to torture babies” is also false on that theory), but if you have a way to sweeten some bullets, this route is promising.

You could also deny that moral contexts are extensional. I’m suspicious this will work, because we often use evaluative terms to describe states of affairs, e.g. “It would be better if there were an elephant here, than if there were a monkey.” It seems clear that we will be able to carve out some subset of states of affairs which are amenable to the extensionality of moral statements made about them. If you find any area of our moral language that constitutes an extensional context, the constraint will apply to any view ambitious enough to claim that it can analyze or translate all moral sentences. In other words, so long as there is some portion of the broader moral context which is extensional, any theory which claims to translate all sentences in a moral context will still face the constraint articulated when they get to that extensional portion. So long as the relevant anti-realist view is so ambitious, it will struggle to avoid the constraint.

Finally, an anti-realist could find a suitable analysans, or definiens for their project. Maybe you pound the table: “No! Attitudinal contexts are extensional!” Or an anti-realist could suggest a new candidate that I have not addressed here. Obviously I believe the former does not work, given my arguments to the contrary, but I’m not overly confident on that point, and it is equally as obvious that (for all I know) the second option is still live. I have no argument that nothing could serve the anti-realists purposes here.

Conclusion

The upshot is simple enough. Moral statements constitute an extensional context, a circumstance where truth is preserved under co-extensive substitution. Most candidates for anti-realist translation thesis are not extensional context, and thus, are not suitable for a translation or analysis of moral statements.

1. What follows is a thought I had in embryonic form during my recent conversation with Philosophical Convictions - Ed (sorry I didn’t have this fully worked out at the time, needed to write it out!)