The Frege-Geach Problem
By Ryan W
Gottlob Frege and Peter Geach, the two philosophers whose ideas contributed to the formulation of this famous problem.
The Frege-Geach problem is one of the most important quandaries in the field of metaethics, as it is perhaps the biggest obstacle facing the non-cognitivist school of thought regarding moral language.
Before delving deeper into the problem itself, it would be helpful to illuminate what is meant by non-cognitivism. Theories such as emotivism, expressivism, and prescriptivism are all examples of a non-cognitive approach to moral language, which essentially boils down to the claim that moral assertions are not truth-apt (that they have no true or false condition), and that all they consist of is an expression of emotion, attitude, or desire. So for instance, a non-cognitivist would claim that the statement “murder is wrong” is not true or false, but that it is essentially like saying “I disapprove of murder and you should too.” It is also famously often phrased in terms of boo and hurrah, which means saying “murder is wrong” is really like saying “boo murder!”
Now, back to the problem at hand. It is a fact that moral language has logical properties and can appear in complex sentences. The phrase “murder is wrong” for instance is logically incompatible with “murder is right,” and complex conditional phrases such as “if murder is wrong, then getting your friend to commit murder is wrong” are logically sound. It is when a moral assertion is embedded within a deductive argument with a complex conditional phrase that the non-cognitivist begins to have a hard time defending their position. Take the following example of a valid argument:
(Original)
Premise 1) If murder is wrong, then getting your friend to commit murder is wrong
Premise 2) Murder is wrong
Conclusion) Therefore, getting your friend to commit murder is wrong
Because premise 1 is a conditional statement that does not contain any moral assertions, the non-cognitivist is not able to translate it into any of their terms. Meanwhile, premise 2 does contain a moral assertion, and would therefore be translated. So, the same argument can also be written as follows:
(Non-cognitivist translation)
Premise 1) If murder is wrong, then getting your friend to commit murder is wrong
Premise 2) Boo murder!
Conclusion) Therefore, getting your friend to commit murder is wrong
As you can see now, the argument seems to no longer be valid. This is because the non-cognitivist has committed themselves to saying that the moral language in premise 2 means something completely different from the moral language in premise 1, but we know that this cannot be. To do that would be to commit a fallacy of equivocation, where the same language is used with different meanings in the same argument. With the original argument, we can see that this is NOT the case, as the meaning of “murder is wrong” has not changed from premise 1 to premise 2. However, the non-cognitivist cannot explain what has happened in their translation, as “murder is wrong” in premise 2 means the expression of an attitude or emotion, whereas “murder is wrong” in premise 1 has not been changed in meaning from the original. The non-cognitivist therefore must conclude that this is an invalid argument to stay consistent with their framework, even though the argument is deductively true by modus ponens and is without equivocation.
So, the onus is on the non-cognitivists to somehow make sense of this argument and any similar logical moral argument, as well as explain how moral language can have logical properties and how moral arguments can be logically valid yet not be truth-apt, functioning solely as expressions of attitudes. In the future, we will explore one attempt to do just that, the Quasi Realist approach.