The Frege-Geach problem (sometimes called the embedding problem) is a challenge to moral non-cognitivism – the view that moral judgements (e.g. “Stealing is wrong”) do not express beliefs that can be true or false, but instead express emotions, attitudes, or prescriptions that are neither true or false.
The embedding problem argues that this non-cognitivist view does not fit with certain ways we use moral judgements – particularly moral reasoning and the embedding of moral judgements in conditional statements.
Non-cognitivism
Emotivism is probably the most straightforward form of non-cognitivism. It says that when someone says “Stealing is wrong”, what they really mean is something like “Booo! Stealing!” – an expression of their own emotional disapproval, rather than a description or belief about the world that could be true or false.
There are other forms of non-cognitivism, like prescriptivism, which says “stealing is wrong” is more like an instruction – “don’t steal!”. But for the purposes of this post, I’ll focus on the emotivist interpretation of moral judgements to explain the Frege-Geach problem.
The point with all these non-cognitivist views of moral language is that moral judgements are not truth-apt – they’re neither true or false.
| Cognitive |
Non-cognitive |
| Descriptions or beliefs of how the world is | Not descriptions or beliefs, things like attitudes and emotions |
| Truth-apt: They are either true or false | Not truth-apt: Neither true or false |
Examples:
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Examples:
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The Frege-Geach embedding problem
The Frege-Geach problem was first raised by Peter Geach, drawing on ideas from the logician Gottlob Frege. The issue is that moral judgements can appear not only as stand-alone sentences, like:
Stealing is wrong
But the same moral judgement can also embedded within larger logical constructions – such as conditionals, arguments, or negations – and they still seem to retain their meaning and logical role. For example:
If stealing is wrong, then getting your little brother to steal is also wrong
This whole sentence – “if stealing is wrong, then getting your little brother to steal is wrong” – makes perfect sense. But, if non-cognitivism is correct, what this sentence really means is something like:
If boo! Stealing!, then getting your little brother to steal is also wrong
And this doesn’t make sense – expressions of emotion don’t combine in the same structured, truth-preserving way that truth-apt propositions do. This conditional statement only makes sense if the antecedent – “stealing is wrong” – is capable of being true or false.
Or we can use the moral judgement in a moral argument like this:
- Stealing is wrong.
- If stealing is wrong, then getting your little brother to steal is also wrong.
- Therefore, getting your little brother to steal is wrong.
And this seems to be a perfectly valid argument – the conclusion (3) follows logically from the premises (1) and (2).
But here’s the problem: if the moral judgement is not a statement expressing a truth-apt belief, then the argument above would not count as valid under non-cognitivism, even though it looks valid to us.
In short, if moral non-cognitivism is correct, it becomes very hard to explain how moral judgements can appear in conditional statements, how moral judgements can appear in logical arguments, how such arguments can be valid, or how moral reasoning works at all.
The fact that moral judgements make sense in conditional statements and logical arguments suggests they are truth-apt, i.e. that moral cognitivism is correct and moral non-cognitivism is false.
Summary
- Moral non-cognitivism says moral judgements (e.g. “stealing is wrong”) are not truth-apt.
- E.g. Emotivism says “stealing is wrong” means “boo! stealing!”.
- The Frege-Geach problem shows that moral judgements appear in logical arguments and embedded in conditional statements but still retain their meaning.
- E.g. “If stealing is wrong, then getting your little brother to steal is also wrong”.
- But if moral non-cognitivism were correct, moral judgements couldn’t be logically combined or embedded in this way.
- E.g. The following doesn’t make sense: “If boo! stealing!, then getting your little brother to steal is also wrong”.
- So moral non-cognitivism is false.