The Grice point and the Geach point

The Geach point (also known as the “embedding problem”) is used as the main “test” to understand rationality in non-cognitivist theories.

The problem was posed in P. Geach’s article “Assertion” but the discussion starts back from Geach’s article “Imperatives and Deontic Logic”.

In particular, Geach used his own test to attack non-cognitivist claims.

In fact, if we find a positive solution to the Geach point we are de facto giving significance to non-cognitivist moral reasoning.

On the contrary, if no solution to the problem is provided, the only option left open to moral reasoning is cognitivism or excluding ethics into the realm of rationality (likewise radical forms of emotivism such as Ayer).

Briefly, the Geach point is that sentences that express moral judgments can form part of semantically complex sentences in a way that an expressivist cannot easily explain.

According to Geach, the sentence

Telling the lies is wrong
Eating people is wrong -- "The Reluctant Cannibal" (discussed by Speranza and Mark Silcox).

has the same meaning regardless of whether it occurs on its own or as the antecedent of “If telling the lies is wrong, then getting your little brother to tell lies is also wrong”.

This must be so, since we may derive “Telling your little brother to tell lies is wrong” from them and both by modus ponens without any fallacy of equivocation. Yet nothing is expressed (in the relevant sense) by “Telling lies is wrong” when it forms the antecedent of the conditional, since the antecedent is not itself the same illocutionary force as the premise, and so its meaning (regardless of where it occurs) apparently cannot be explained by an expressivist analysis. Analogous problems within other kinds of embedded contexts (Unwin, 1999).

However, Geach recommends attention to Frege’s distinction between assertion and predication, or in other words, between illocutionary force and propositional content, respectively. In fact, if we assume the role of the illocutionary force, there would be a slight change in the meaning of the word “wrong” in the antecedent of the conditional “If telling the lies is wrong, then getting your little brother to tell lies is also wrong” and in its occurrence as consequence in the same conditional sentence. This problem is even clearer using modus ponens:

1. If tormenting the cat is wrong, then getting your little brother to torment the cat is also wrong
2. Tormenting the cat is wrong
Therefore, getting your little brother to torment the cat is wrong.

In the case above it is difficult to say that the occurrence of “wrong” as antecedent of the 1st conditional (which appears to be descriptive) has exactly the same meaning as “wrong” in the 2nd sentence (which appears to be normative).

We saw non-cognitivism is characterized by the assumption that norms lack truth-values.

Yet, the contexts introduced by ordinary logic operators such as “and”, “not”, “or”, “if… then”, and the quantifiers, together with predication itself, are normally explicated in terms of the more basic semantic concepts of truth. Therefore, it seems that this option is not available to non-cognitivists, in general, and in particular to expressivists.

Blackburn  redefines the Geach Problem in terms of whether expressive theories can cope with unasserted contexts in such a way as to allow sentences the same meaning within them, as they have when they are asserted.

According to Blackburn, we use evaluative sentences as if they were not different from assertions (because of our projective attitude), and, therefore, we intuitively treat them as if they were bearing truth-values and linked to descriptive sentences.

The problem will be about the interpretation of connectives to be used to build up more complex commitments having in their own several illocutionary characteristics (such as in a conditional). Blackburn suggests commitments are used to create more complex sentences which is accepted only if all its parts are accepted, according to the following solution: “the notion of commitment is then capacious enough to include both ordinary beliefs, and these other attitudes, habits and prescriptions” (Blackburn, ibid., p. 192).

  Therefore a conditional will express someone’s endorsement to an attitude (which is an expression of a moral standpoint, too) preceded by a belief. In other words, it expresses a higher-order attitude, that is, an expression of disapproval or approval toward a combination of attitudes (such as of lying). Conditionals, as they are used in ordinary language, show the way we express an endorsement over involvement of commitments – which is expression of a moral standpoint. In other words, we can see that using conditional forms (in normative contexts) is a higher level form (compared to simple sentences like “it’s wrong telling lies”) which serves to express one’s attitudes on attitudes, or meta-attitudes.

Blackburn introduces these kinds of sentences formally in the following way:

H! (B!p → B!q)

Where H! stands for the

“Hooray” operator (expressive counterpart of the deontic operator “O” – for obligation), B! is the “Booh” operator (expressive equivalent to the deontic “F” – for forbidden).

What appears between slashes shows that our argument is an attitude or a belief, which express a first order attitude (such as “The playing for West Ham is wrong”).

The main limit of Blackburn’s solution of the Frege-Geach problem concerns the nature of the H! and B! operators, while iterated in a higher order sentence.

Blackburn’s formulation does not make clear the illocutionary role of the operator.

If we interpret all the operators in the formula (a) in an expressive (or prescriptive) way, (that is lacking of truth-values), the whole expression will not make sense.

According to Barcan Marcus, iteration of normative operators looks like stammering.

Otherwise. if we interpret (according to Blackburn) the external operator H! in an expressive (or prescriptive) way and those into the slashes as descriptive ones, we will have a correct way of interpreting operators but no solution to the Frege-Geach problem. The formula (a) above, indeed, is formally correct but does not solve the problem about the identity of meaning for example between the antecedent of the 1st conditional in the Modus Ponens shown above (which is descriptive) and its 2nd sentence (which is normative).

Gibbard tries to solve the Frege-Geach problem using a slightly modified version of possible worlds semantics that he labeled as “factual-normative worlds”.

Factual-normative worlds are an ordered pair where “w” is a possible world (or a set of facts) and “n” is a complete system of general norms. The pair constitutes a creedal-normative state completely opinionated (Gibbard, 1990, p. 95).
According to Gibbard, any particular normative judgment holds or not, as a matter of logic, in the factual-normative world . That is, the pair is a set of sound and complete norms where, for each possible human behavior, we can state the normative status (Forbidden, Obligatory or Indifferent) associated with it. In this way each individual can understand the normative qualification of his or her action.
Consider a human observer who is uncertain both factually and normatively. When the observer will think about the rightness of a normative judgment, she or he will rule out any possible action which is not included into a set constituted by all the factual elements and all the normative elements in which that normative judgment is valid. Let’s take for instance, the modus ponens above:

1. If tormenting the cat is wrong, then getting your little brother to torment the cat is also wrong
2. Tormenting the cat is wrong
Therefore, getting your little brother to torment the cat is wrong.

The first premise rules out all the combinations in which it is not wrong to get your little brother to tell lies. The second premise rules out the set of combination between norms and facts in which is wrong to torment the cat. Therefore both premises together rules out the whole set of norms and facts in which it is not wrong to get your little brother to torment the cat; including any combination that the conclusion rules out.

What does it mean for a sentence to be valid in a particular factual-normative world?

According to Gibbard it means that for each sentence containing a normative predicate there is a n-corresponding descriptive version which makes a normative predicate (such as “rational”) refer to a particular set of norms (that is “rational” according to the system n). Hence, Gibbard concludes, for any logically complex sentence S containing normative predicates in embedded contexts, we may construct the descriptive sentence Sn that arises from replacing all normative predicates in S by their n-corresponding version. Therefore we can operate with embedded contexts saying the sentence S holds in if and only if Sn holds in a possible world .

Actually Gibbard’s solution to the Geach-Frege problem is rather a bypass method to avoid the problem because he explains the functioning of normative language by means of descriptive language and semantical models. According to Sinnot-Armstrong’s criticism (1993), Gibbard’s analysis appears to be compatible with a realist view on norms because of his ambiguous use of normative judgment (which is a state of mind) and his use of possible world semantics.


The Geach problems and Jorgensen’s Dilemma are faces of the same coin.

The first deals with the problem of mixed, or embedded, contexts (normative and descriptive) and how it is possible to deal with mixed sentences. The main problem here is the interpretation of connectives and logical operators in contexts that are partially lacking truth-values.

Jorgensen’s Dilemma, on the other hand, deals with making inferences between norms, that is, sentences that are lacking of truth-values, and to create a logical foundation that makes sense of inferences between norms we actually find sound in the everyday discourse. The Jorgensen’s Dilemma also tries to explain the very nature lying behind moral disagreements and the way we can rationally deliberate on them.
Both are questions involving the different illocutionary role of normative/expressive sentences and their solution represents a challenge to non-cognitivism. A positive solution to both challenges would open a room to the rationality of non-cognitive discourse in ethics. On the contrary, a negative one would show that the only option for rationalism in ethics is cognitivism or — in the worst case scenario — to irrationality and ethical nihilism.

Finally it is worth notice that while both cover a similar perspective, the Frege-Geach problem is more popular in moral philosophy, whereas Jorgensen’s Dilemma is more popular in the philosophy of law. It is difficult to understand the reasons for that different interest. We can only guess that it was because the analysis of sentences in terms of the Frege-Reichenbach model was popular among moral philosophers while it was virtually unknown (until the works by Alchourron and Bulygin, 1971) among philosophers of law.

The following scheme is a development from R. M. Hare’s A Taxonomy of Ethical Theories (Hare, 1997, p. 42)

Descriptivism:
Meanings of moral sentences are wholly determined by syntax and truth conditions.

Naturalism:
Truth conditions of moral sentences are non-moral properties.

Objectivistic naturalism:
These properties are objective.

Subjective naturalism:
These properties are subjective.

Intuitionism:
Truth conditions of moral sentences are sui generis moral properties.

Non-descriptivism:
Meanings of moral sentences are not wholly determined by syntax and truth conditions.

Emotivism:
Moral sentences are not governed by logic.

Rationalistic non-descriptivism:
Moral sentences are governed by logic.

Universal prescriptivism:
The logic, which governs moral sentences, is the logic of universal prescriptions.

Expressivism:
The moral sentences are about beliefs and/or commitments; their logic is different from the logic of descriptive sentences.

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