The Frege-Geach Problem

A Challenge to Moral Non-Cognitivism

Moral non-cognitivism is the metaethical account that denies that moral statements are truth-apt, or in other words, capable of being either true or false. For example, a non-cognitivist would claim that the sentence “murder is wrong” is not an expression of anything that is subject to being either true or false, in the same way that beliefs or knowledge are normally subject to assessments of truth or falsity. Moral claims are not cognitive (like beliefs or knowledge) because they do not “pick-out” or allude to some real proposition or property out in the world. My utterance that “Plato was the student of Socrates” is a proposition about a certain state of the world at some point in history, and is therefore, truth-apt. Non-cognitivists argue that sentences like “murder is wrong” do not belong in the same category as a belief like “Plato was the student of Socrates” because moral statements are more like expressions of desires or attitudes that one has about something. Accordingly, when I claim that “murder is wrong”, I am saying something more like “I disapprove of murder” or “you should not murder” (with no appeal to moral responsibility).

While many flavors of non-cognitivism exist, I won’t get into them much here. What’s important is the broad understanding of non-cognitivism as a metaethical theory in which moral statements aren’t describing anything in the world at all and more aptly serve as declarations of our desires, commands, and other such “non-cognitive” states. Under one subdivision of non-cognitivism, “murder is wrong” is likened to claiming I disapprove of murder, under another subdivision, it is likened to claiming Murder?!?! Boo!!!, and so forth. This is wildly different from our commonplace understanding and interpretation of ethical statements. However, the contention that moral language is rooted in emotions might have some appeal, given the vast and seemingly perpetual disagreement on moral issues. Could moral non-cognitivism be an elegant solution or explanation for moral relativism rather than just serving as some absurd theory? The answer is most likely no; non-cognitivism faces an almost insurmountable issue.

Before we get into where non-cognitivism runs into trouble, let’s do a small lesson on logic:

1.    If stealing is bad, then murder is bad.

2.    Stealing is bad.

C. Murder is bad.

The structure of the above argument is very common in logic and philosophy. Statements 1 & 2 are called premises while the last statement, the one preceded by “C”, is the conclusion of the argument. This form of argument, where an “if…then” statement is followed by the antecedent alone (the phrase after the “if”) and then the consequent alone (the phrase after the “then”), is called a modus ponens.* A simple form of a modus ponens:

1.    If A, then B

2.   A

C. B

*Knowing these terms isn’t necessary for understanding the logic of this argument but I do think they sound cool and you can throw them around with your friends as a nice flex.

An argument in logic is valid if the conclusion necessarily follows from the premises. The argument above is clearly valid because the conclusion murder is bad is necessarily true if we assume the truth of the conditional statement and the truth of stealing is bad. Note that an argument being valid doesn’t necessarily mean it’s absolutely true; we assumed that the premises were true and in doing so, the conclusion must follow. An argument is sound if it is valid and if its premises are absolutely true.

The Frege-Geach Problem in philosophy describes the ultimate challenge to non-cognitivism and essentially consists of a difficulty for the non-cognitivist in explaining how the logical properties of sentences can be preserved for moral claims (which again, aren’t about anything that can be true or false) in more complex, embedded contexts. We’ve seen how an argument like the modus ponens demonstrates the logical property of validity; the conclusion necessarily follows from the premises. A further requirement for the preservation of validity is that the meanings of the premises in an argument must remain constant, otherwise we commit the fallacy of equivocation. For the moral cognitivist, the premise “stealing is bad” means that the property of wrongness applies to the act of stealing; this sentence would have to mean the exact same thing in a more complex phrase, such as the if-then conditional, to avoid equivocating on meaning. For clarity, here is an example of equivocation:

1.    Aubrey Graham Drake is a star.

2.    A star is a ball of gas.

C.   Aubrey Graham Drake is a ball of gas.

This argument is not valid because we have equivocated on the meaning of the word “star”; in the first premise, “star” is meant to describe a very popular person (someone ask Drake when Certified Lover Boy is dropping) while in the second premise, “star” refers to the scientific term. Because the word has two different meanings in the argument, the conclusion does not follow.

Ultimately, the non-cognitivist commits an error of equivocation in a modus ponens with moral phrases such as “murder is wrong” when they are embedded into more complex phrases:

1.    If stealing is wrong, then murder is wrong.

2.    Stealing is wrong.

C. Murder is wrong.

Let’s break down the meaning of each of these sentences from the perspective of a non-cognitivist: “stealing is wrong” must mean something more like “I disapprove of stealing” and “murder is wrong” must mean something more like “I disapprove of murder”. But what exactly does “if stealing is wrong, then murder is wrong” mean? The first part of that conditional must mean the exact same thing as premise 2 to avoid equivocating on meaning, but the non-cognitivist cannot adequately explain how the two are the same. “If stealing is wrong…” could be interpreted as meaning “I wonder if I disapprove of stealing” or “If it were the case that I disapproved of stealing”, which is not the same thing at all as “I disapprove of stealing” outright - it seems that moral claims in more complex language constructions, such as the conditional, do not express the same disapproval that simple moral claims do, as argued by the moral non-cognitivist. Thus, the non-cognitivist is unable to construct valid modus ponens arguments using moral language without committing an error of equivocation.

While the Frege-Geach Problem continues to puzzle non-cognitivists, several solutions have been proposed in favor of an emotional basis for moral claims. In the next post, I’ll describe an ethical framework called quasi-realism, proposed by philosopher Simon Blackburn, and its purported solution to the Frege-Geach Problem.