The Frege Geach Embedding Problem

Moral cognitivists are moral theorists that hold that moral or ethical statements are propositional, and are truth apt, meaning that a statement such as “Stealing is wrong” is a statement which can be either True or False.

It follows then, that to the moral cognitivists, if a propositional, or declarative statement can be true or false, then one can hold a dispositional of belief towards the propositional content. In other words, the moral cognitivist can believe “stealing is wrong” and use the statement “stealing is wrong” in a propositional argument as it has a truth value of being either true or false.

The moral non-cognitivist takes an opposing view, and denies moral cognitivism. To the moral non-cognitivist, statements such as “stealing is wrong” do not express propositions which are true or false, but express something about the state of mind of the person making the declarative statement.

In other words, when a moral non-cognitivist asserts ‘stealing is wrong,’ they are expressing something other than the proposition that ‘stealing is wrong’ being true or false.

There are various types of moral non-cognitivists, such as emotivists who believe statements such as “stealing is wrong” are just assertive utterances which express some type of emotional attitude about the statement, such as approval or disapproval. This is why emotivism is often referred to as the “boo-yay” theory. An emotivist who argues ‘stealing is wrong’ essentially encounters the Frege-Geach embedding problem because, in emotivism, ‘stealing is wrong’ is not truth-apt. This then raises the question of how such a statement can function as a moral premises in deductive arguments or within complex sentences.

In moral theory, specifically metaethics, there are two main types of moral theorists.The ones who are referred to as moral cognitivists, and the others, unsurprisingly are called moral non-cognitivists.

Saying “boo stealing!”, or if they argue “Charity is virtuous” they are arguing “Charity, yay!” expressing their approval for charity.

Another form of moral non-cognitivism would be prescriptivism, where a moral statement such as “stealing is wrong” is inferred to be more of a directive, sometimes known as an imperative, as in “Don’t steal!”, and is understood as a command not to steal. Although it could be argued that an imperative has a stronger connotation than a directive.

While Moral Non-cognitivism generally deals more with what is called “speech act theory” about normative sentences, which I will try to get to in another video, it is in essence, a meta-ethical theory about normative ethics, which are ethics about what actions are right or wrong, and what action an ethical agent should take.

With all that in mind, let’s get to the Frege Geach embedding problem.

German philosopher, and logician, Gottlob Frege, and British philosopher and professor of logic Peter Geach independently both discussed this problem, but Geach, who had discussed in other articles, first formally posed the problem in an article called “assertion”, in the 1965 edition of The Philosophical review.

In his article, Geach argues that the term “proposition” has been essentially appropriated by some moral theorists from the general understanding of the word, which was to refer to something profounded, or put forward for consideration, or basically that a proposition is a proposal put forth to be evaluated as being True of False.

Geach argued that some theorists included propositions to include what he referred to as “timeless abstract ‘intentional’ objects”, which he felt lacked what he referred to as “formulable criterion” of what constituted such an abstraction to be considered as a proposition. In other words, what makes something like an emotional attitude something worthy of being considered to be a moral statement, and how could one use such abstract objects in logical arguments.

Geach also points out how Frege makes a distinction between an assertion and a predication, which relates to the illocutionary force of the statement being asserted, as opposed to the actual propositional content itself. This can lead to a form of equivocation, making it difficult for the non-cognitivist to argue moral statements in logical arguments. 

Example:

p->q If stealing is wrong, then telling your friend to steal is wrong.
p stealing is wrong
q telling your friend to steal is wrong

In the conditional statement, p implies q, “wrong” is used in a way that allows for truth-functional logic to operate, but truth functional logic only operates on statements which are propositional and truth-apt. 

In the antecedent of the conditional, the word “wrong” is acting as a description, “stealing is wrong” is describing a morally impermissible act. However, the word “wrong” in the consequent is being used in a more normative sense, meaning that it is the action of telling your friend to steal is wrong, not the act of stealing that is wrong. 

And if it expresses a normative claim, and if “wrong” is interpreted as merely an expression of disapproval, then how can it then be used with logical connectives to form a valid argument?

This is the crux of the Frege-Geach embedding problem. That by adopting a metaethical moral theory that doesn’t hold moral statements as being propositional and truth apt. The embedding problem also points out that moral terms, such as “good” or “wrong,” can appear in complex logical sentences dealing with conditionals and negations, where they don’t seem to express emotions, nor prescribe actions directly, yet, these sentences can still be used in logically valid arguments.

This creates a dilemma, as either the meaning of moral terms changes when embedded in these contexts, such as embedding in a simple modus ponens in my prior example of stealing is wrong, leading to a fallacy of equivocation, or non-cognitivist theories must explain how non-truth-apt expressions can function in truth-preserving logical inferences. 

The Frege-Geach problem presents a significant challenge to non-cognitivist ethical theories. It argues that moral language cannot be fully or adequately explained merely through expressions of emotion, attitudes, directives, or prescriptions. The problem implies that for moral reasoning to function as we observe in everyday life, and in our discourse and philosophical arguments, moral statements need to be truth-apt to serve as evaluable content in logical arguments—a requirement that non-cognitivist theories explicitly reject.

And I happen to agree with that implication.