Skip to content

The Frege-Geach Problem (wonkish)

by Bill Meacham on October 7th, 2023

Back in 1965 British analytic philosopher Peter Geach published an insightful and engaging paper titled “Assertion,” which has been the source of a certain amount of controversy ever since. Geach, a professor of Logic, maintains that the same proposition has the same meaning whether or not it is asserted as true, a view he attributes to Frege. He goes into quite a lot of detail about the context, sometimes explicit and sometimes implicit, in which certain statements are made and how to represent them in logical form. If you like that sort of thing, as I do, it’s quite entertaining.

The controversy comes from a short section near the end:

The theory that to call a kind of act “bad” is not to describe but to condemn it is open to similar objections. Let us consider this piece of moral reasoning:

If doing a thing is bad, getting your little brother to do it is bad.
Tormenting the cat is bad.
Ergo, getting your little brother to torment the cat is bad.

The whole nerve of the reasoning is that “bad” should mean exactly the same at all four occurrences—should not, for example, shift from an evaluative to a descriptive or conventional or inverted-commas use. But in the major premise the speaker (a father, let us suppose) is certainly not uttering acts of condemnation: one could hardly take him to be condemning just doing a thing.(1)

By “not to describe but to condemn” he refers to the meta-ethical view called “non-cognitivism,” that moral statements do not express propositions and thus cannot be true or false. They don’t express propositions because they don’t refer to objective moral facts; there are no such things say the non-cognitivists. Instead they express the speaker’s attitude and are equivalent to statements that are either merely emotional (“Boo to killing!”) or prescriptive (“Don’t kill!”).(2)

Ever since, Geach’s argument has been known as the “Frege-Geach Problem” even though Frege himself knew nothing of it. In a recent issue of Philosophy Now magazine, Justin Bartlett explores the issue in some detail.(3) I’m pleased that the magazine has published letters in response from both me and my colleague, Mark Gold.(4) Here they are, Mark’s first.

Letter from Mark Gold

Justin Bartlett questions non-cognitivism in ethics by referring to the Frege-Geach Problem. (“The Cognitive Gap” Philosophy Now Issue 156, July/July 2023) If “Killing is wrong” amounts to no more than “Boo to killing” then a seemingly valid argument turns out to be nonsense, he says. The valid argument, taken in a cognitivist interpretation, is this:

P1: Killing is wrong.

P2: If killing is wrong, then getting your little brother to kill is wrong.

C: Therefore, getting your little brother to kill is wrong.

Substituting equivalent phrases, he says, we get this:

P1: Boo to killing!

P2: If ‘Boo to killing!’, then getting your little brother to kill is wrong.

C: Therefore, getting your little brother to kill is wrong.

Proposition 2 makes no sense, so therefore non-cognitivism must be false.

But Bartlett doesn’t take the substitution far enough. To be consistent he ought to equate “Getting your little brother to kill is wrong” with “Boo to getting your little brother to kill.” Doing so yields this argument:

P1: Boo to killing!

P2: If ‘Boo to killing!’, then ‘Boo to getting your little brother to kill.’

C: Therefore, ‘Boo to getting your little brother to kill.’

On the face of it, this seems valid. One might object that “Boo to killing” is not a truth-apt proposition and hence cannot play a role in logical inference. Very well, we can replace “Boo to killing” with the proposition “I strongly disapprove of killing” and “Getting your little brother to kill is wrong” with “I strongly disapprove of getting my little brother to kill.” The argument then becomes this:

P1: I strongly disapprove of killing.

P2: If I strongly disapprove of killing, then I strongly disapprove of getting my little brother to kill.

C: Therefore, I strongly disapprove of getting my little brother to kill.

The latter is a valid argument and poses no problem for the non-cognitivist.


Mark Gold

Letter from Bill Meacham

The epistemological argument between moral cognitivism and non-cognitivism (“The Cognitive Gap,” Philosophy Now issue 156) parallels the ontological argument between moral realism and anti-realism. The realists say that moral properties such as rightness and wrongness are mind-independent parts of objective reality. Hence, propositions about them can be true or false because they refer to things that actually exist. Anti-realists say that moral properties have no objective reality; they are mere human constructs or at best mistaken ideas and have no objective referent. Hence propositions about them can be neither true nor false, so they must be mere expressions of our emotions or at best admonitions to behave in a certain way.

The arguments for moral anti-realism are strong. One of them, the Argument from Queerness cited by the late J.L. Mackie (Ethics: Inventing Right and Wrong, 1997) asserts that if there were objective values they would be entities of a very strange sort, utterly different from anything else in the universe. Moral entities such as the wrongness of murder or the obligation to tell the truth are neither physical nor mathematical/logical, but have characteristics of both. Like mathematical/logical entities but unlike physical objects, they lack perspective, mass, extension in space, velocity, acceleration and color. Like both mathematical and physical objects, they persist in time. If someone thinks murder is wrong today, that person will most likely think it wrong tomorrow. Like physical objects but unlike mathematical/logical entities, moral entities seem to change over time. Slavery was common and accepted in ancient Greece and Rome; today we find it morally wrong. Unlike both, moral properties intrinsically motivate us to act. We may wish to pick a nice, ripe apple, but it is our hunger that motivates us, not anything intrinsic to the apple.

So moral entities do indeed appear to be queer in Mackie’s sense. They are not real in the familiar way that physical objects are, nor in the way that mathematical/logical entities seem to be. They have some characteristics of both and one characteristic, that they inherently motivate us, shared by neither. If moral realism means to be real in the manner of physical objects or of mathematical/logical entities, then moral realism is false and moral anti-realism, true.

But that’s not the whole story. There is another way to be real.

Following John Searle (The Construction of Social Reality, 1995) I assert that moral properties and entities are socially constructed institutional facts. There are quite a number of such facts. Searle mentions money, property, marriages, governments, tools, restaurants, schools and many others. They exist only because we believe them to exist. Take money for instance. Bits of paper with certain markings on them are money—that is, media of exchange and stores of value—not because of their physical characteristics but only because human beings use them as money and have rules that govern their use as money.

Ontologically, the manner of being of moral entities is to be socially constructed. They exist independently of any particular person, but they are not independent of conscious agents altogether as physical and (arguably) mathematical/logical entities are. Moral entities are socially constructed within a community of practice, a social group, a culture or a society. Within such a community or society, everybody agrees (more or less) on what they are, everybody treats them the same way and everybody acts as if they are real. Just as there are consequences for the way we deal with physical objects, there are real consequences for the way we abide by moral rules or not, namely the reactions of others in the community. So, for members of such a community they are real. The ontological status of morality is that it is a socially constructed reality.

Recognition of this fact cuts through the debate about moral realism. As with many conceptual issues, this one depends on definitions of terms. If “real” means to be real as physical entities are, then moral anti-realism and non-cognitivism are true. If “real” means to be real in any fashion at all, then they are false and their opposites, realism and cognitivism, are true.

The issue has practical as well as theoretical implications, which space does not permit me to pursue here. Please see my “Reassessing Morality” at


Bill Meacham

(1) Geach, pp. 463-464.

(2) Wikipedia, “Non-cognitivism.”

(3) Bartlett, “The Cognitive Gap.”

(4) Philosophy Now, Issue 157, August/September 2023, p. 47. Online publication as of 7 October 2023.


Bartlett, Justin. “The Cognitive Gap.” Philosophy Now Issue 156. Online publication as of 1 September 2023.

Geach, P.T. “Assertion.” The Philosophical Review, Oct., 1965, Vol. 74, No. 4 (Oct., 1965), pp. 449-465. Online publication as of 6 October 2023.

Mackie, J.L. Ethics: Inventing Right and Wrong. London and New York: Penguin Books, 1977.

Searle, John R. The Construction of Social Reality. New York: The Free Press, 1995.

Wikipedia. “Non-cognitivism.” Online publication as of 7 October 2023.

From → Philosophy

  1. John Mackie sees moral entities and properties as exceptionally unlike anything else in the Universe. Perhaps a failure of imagination on his part. A tool’s manufacture and use are dependent on the human mind, our being able to imagine what it will be used for, and to imagine how it needs to be shaped in order for it to do what we imagine it could do. The tool involves those who can use their imaginations this way exclusively. The human imagination may be a queer thing that is unique in the universe, but that’s because, along with having an imagination we are able to share its contents with each other and to pass on significant contents from generation to generation. Morality is a collective tool for social and self regulation of behaviour. Its reality is not in moral concepts, principles, or theories, it’s a reality of participation and practice. The queer thing about morality is that everyone finds themselves subject to its rules; it applies universally, as if it were a law of nature; but it is exactly not a law of nature, it is a code of conduct we agree applies to everyone who is able to choose whether or not to follow it, unlike a law of nature, which simply determines physical reality.

  2. George H permalink

    Thanks for the articles. I might push a little harder from Searle’s starting point. If socially construction is able to create real rules and objects associated with these rules, might this whole effort be mirroring a more general reality which allows humans within societies to flourish? Could these not be observer independent morals? Stop signs piggyback off of traffic congestion, perhaps rules against murder piggyback off the safety humans need to flourish.


    • Well, I agree. But in order to do that we need somehow to overcome our tribal instincts, which we still have because of our evolutionary history. Perhaps an economic model based on cooperation would help. Take a look at my blog essay about Mondragon Cooperatives:


  3. Leonard Hough permalink

    There is something about your colleague’s name…

Leave a Reply

Note: XHTML is allowed. Your email address will never be published.

Subscribe to this comment feed via RSS