THE FREGE–GEACH PROBLEM, MODUS PONENS, AND LEGAL LANGUAGE*

This paper proposes a new pragmatic interpretation of the Frege–Geach problem and presents a possible solution using a model of ascriptive legal language. The first section includes the definition of the Frege–Geach problem. In the second section, I analyze the content of Geach’s critical argument against prescriptivism in ethics. I discuss what Geach means by ascriptivism, why he mixes it with prescriptivism, and why a particular article by Herbert Hart became the subject of criticism by Geach. The third section proposes a possible solution to the Frege–Geach problem based on the explication of the assertoric force of ascriptive legal utterances and the performativity of legal language.

The Frege-Geach Problem, formulated by Peter Geach as a critical argument against the prescriptive theory of Richard Hare, proved to be so enduring that the subsequent development of noncognitivism in ethics was concerned with comprehending the problem, describing it, and seeking a solution to it. It was through a refutation of the Frege-Geach problem that such ethical concepts as normative expressivism (Gibbard 2014) and prescriptivism (Hare 1952; * A previous version of this paper was presented at the XXVIII World Congress on the Philosophy of Law and Social Philosophy (IVR) in Lisbon in July 2017, where I benefited from comments by the participants of the special workshop "Law and Language". I would like to thank also Jean Kollantai for her review of style and anonymous reviewers for they helpful comments and suggestions, which led to making my arguments clearer.
The work on this paper was supported by the Council for Grants of the President of the russian Federation for State Support of Young Russian Scientists, Award Number MD-1530MD- .2018 Singer 1993) arose. But despite the definite diversity in the character of argumentation, all noncognitivist theories in ethics have one important substantive claim: Ethical utterances are neither true nor false, that is, they lack truth-values (Schroeder 2008: 703). A refutation of this assertion, as well as a defense of it, remains the subject of intense academic debate today, moving far beyond the boundaries of ethics and the philosophy of language. Therefore, analyzing the Frege-Geach problem in other contexts (for example, the philosophy of law) remains relevant.
The particular logical and linguistic problem posed by Geach in relation to a particular prescriptive theory then became transformed into a fundamental theoretical and methodological paradigm of modern philosophy (Alwood 2010;Charlow 2014;Eklund 2009). It is true that the explication of the Frege-Geach problem has been widely discussed in ethical theories; however, the application of this problem in other discourses has received insufficient attention. analyzing the views of Frege and Geach through the terms of legal language provides an opportunity to give new impetus to the discussion around the Frege-Geach problem and highlight new facets of what would seem to be a thoroughly studied topic.

Formulating the Frege-Geach Problem
In his article "Assertion", Geach puts forth a thesis that questions any noncognitivist theory: "A thought may have just the same content whether you assent to its truth or not; a proposition may occur in discourse now asserted, now unasserted, and yet be recognizably the same proposition" (Geach 1965: 449). This dictum later became the classic formulation of the Frege-Geach problem (Horwich 2005: 78). Meanwhile, Geach himself calls this viewpoint "the Frege point" because in his opinion Frege was the first logician who clearly stated it (Geach 1965: 449).
What exactly does Geach mean by the Frege point? How are his views similar to those of Frege? and what conclusions did Frege himself reach? that is what I would like to examine before attempting to explicate this problem in the context of legal language, using the example of a specific type of utterance -ascriptive legal utterances (Hart 1951: 145-166).
In considering a thought to be the content of a sentence, Frege never attempted to explain in what way thought relates to reality. Frege's aim was limited only to an analysis that was focused on the language used to express the conclusion. He does not tell us what language is but does stipulate that, if in language conclusions and proofs must be expressed and something must be acknowledged as truth, then the use of language must have a specific structure. this structure must be clearly established with the help of certain expressive means of a formal nature. Refuting the principle of logical stress, Frege proposes his own understanding of sentence structure. What is being defined meanwhile becomes not the form that connects concepts but the conditions for the truthfulness of the utterance. From this point of view, the elements of the logical structure of an utterance must be defined only by the role they play in the establishment of its true meaning.
Therefore, the subject of Frege's logical analysis becomes only those sentences in which something is communicated as an assertion. These include "these exclamations in which one vents one's feelings, groaning, sighing, laughing, unless it has been decided by some agreement that they are to communicate something" (Frege 1956: 293). Interrogative and assertive sentences contain the same thought, but assertive sentences contain something more, which is the assertion itself. Frege proposes that two things be differentiated in an assertive sentence -its content and assertion -while noting that both are closely connected in assertive sentences and their separateness may be difficult to observe. While trying to prove that the meaning of a sentence is its truth-value, he concluded that the question of truth arises only when we move from simple statement of a thought to an assertion. That is why, in Frege's view, it is necessary to differentiate, in the structure of an assertive sentence: (1) the apprehension of a thought -thinking; (2) the recognition of the truth of a thought -judgment; and (3) the manifestation of this judgment -assertion (Frege 1956: 294). Although Frege insists on the necessity of differentiating between these three levels of an assertive sentence, this is not at all simple to do, because they truly are closely related. Frege notes the rendering of judgment when a thought is recognized to be true. this act of recognition is called judgment. Judgment is manifested in a sentence stated with assertive force. However, it is possible to grasp and express a thought without recognizing it as true, that is, without rendering judgment. In addition, he states that in an assertive sentence there is no special component corresponding to assertion; the fact that something is being stated is part of the form of that sentence.
Perhaps it is that thesis about the three-level structure of an assertive sentence to which Geach refers as the the Frege point, because the idea of isolating assertion in its structure as a separate part is, in my opinion, key to understanding the Frege-Geach problem. In fact, in natural language, the difference between the content of a sentence and its assertion is hidden in the form of expression itself. In the structure of an indicative sentence, there is nothing that would allow for the differentiation between a simple statement of a thought and the recognition of that thought as true. We express the recognition of truth in the form of an assertive sentence. At the same time, Frege notes: We do not have to use the word "true" for this. and even when we do use it the real assertive force lies, not in it, but in the form of the indicative sentence and where this loses its assertive force the word "true" cannot put it back again (Frege 1956: 294).
Frege believes that it is necessary to introduce the isolation of a special assertive force into the formal language of the description of logical structures where all differences must be clearly articulated. For this purpose, he introduces a special symbol ⊢, in mathematical logic called a "turnstile". Incorporating this symbol into the structure of expressing a thought, Frege notes that this symbol expressing assertive force can never be included in the content of a dependent clause. according to Frege, the sentence ascribed to the performance has an indirect entry into the expression and, as such, has sense and meaning distinct from the sense and meaning of the original sentence. therefore, in order to assert that something is true we need the special symbol ⊢, the symbol of the name of the truth-value, from which follows that the recognition of truth is expressed in the form of the assertive sentence. An example that illustrates the possibility of introducing the argument of assertive force connected to the form of the indicative (assertive) sentence in natural language and the symbol ⊢ in Frege's calculation is the special case with Modus Ponens. In the conclusion is already present in the conditional premise. However, if the symbol ⊢ is introduced into this deduction, then the petitio principii hidden in the form of the conditional categorical deduction can be avoided. In the conclusion is not contained in the conditional premise, because ⊢ B does not coincide with B. Perhaps Geach meant this by the Frege point when he said that in the opposite case "arguments of the pattern 'if x is true (if w is bad), then p; but x is true (w is bad); ergo p' contained a fallacy of equivocation 1 , whereas they are in fact clearly valid" (Geach 1960: 223). Now, I would like to examine key elements of Frege's philosophy that are important in the analysis and solution of the Frege-Geach problem. I will turn to these theses not only as instruments to describe the Frege-Geach problem, but also as the source and theoretical foundation of a new interpretation of it. The Frege point is based on the following theses: 1) only those sentences that are expressed with assertive force (i.e., the thoughts that correspond to them) must be recognized as true and can be elements of the conclusion; 2) in an assertive sentence, there is no special component corresponding to assertion, and the fact that something is being stated is included in the form of the sentence; 3) a special symbol is needed so that we can assert something to be true, 1 In logic, equivocation (calling two different things by the same name) is an informal fallacy that results from the use of a particular word or expression in multiple senses throughout an argument, leading to a false conclusion. For an argument to be valid, words must have the same meaning every time they appear in its premises or conclusion. Arguments that switch between different meanings of words equivocate, and thus do not work. this is because the change in meaning introduces a change in subject. If the words in the premises and the conclusion mean different things, then the premises and the conclusion are about different things, and so the former cannot support the latter. In short, equivocation is a fallacy by which a key word or phrase in an argument is used with more than one meaning, and is also known as semantic equivocation. and ⊢ is the symbol of the name of the truth-value; and 4) the recognition of truth is expressed in the form of the assertive sentence.

Refuting Critical arguments against ascriptivism
as noted above, Geach forms his critical argument against noncognitivism in ethics in an article "Assertion" (1965). However, his first attempts to explicate the Frege point can be found in his earlier works "Ascriptivism" (1960) and "Imperative and Deontic logic" (1958); for the purposes of this article, it is the former, "Ascriptivism", that is of particular interest. In it, Geach provides a fairly detailed description of Frege's arguments in relation to prescriptivism (replacing it with the term "ascriptivism"), set forth, in his opinion, in an article by Herbert Hart, "The Ascription of Responsibility and rights" (1951). What does Geach mean by ascriptivism? Why does he mix it with prescriptivism? And why did this particular article by Hart become the subject of criticism from Geach? 2 2 although neither the essay nor its author is mentioned by name, Hart himself acknowledged that this criticism was addressed to him. It should be noted that Hart took this criticism very seriously, saying: "There were some things which were quite useful and true in it, but I think there was a central mistake. I claimed that the statement that a person has done an action is not a description but an ascription -let's say, a way of saying it's your responsibility. And I think that's wrong" (Sugarman 2005: 276). Moreover, in the introduction to his Punishment and Responsibility. Essays in Philosophy of Law, Hart claims: "I have not reprinted here, in spite of some requests, my earliest venture into this field: 'The Ascription of Responsibility and Rights' […]. My reason for excluding it is simply that its main contentions no longer seem to me defensible, and that the main criticism of it made in recent years are justified" (Hart 1968: 6). Nevertheless, on the basis of these brief comments, it is difficult to conclude exactly what points of ascriptivism In "Ascriptivism", although Hart is not named, reference is made to "some Oxford philosophers", called "Ascriptivists", and Geach offers a critical conception, explicating and refuting ascriptivism, whose content he defines in the following manner: Ascriptivists hold that to say an action x was voluntary on the part of an agent A is not to describe the act x as caused in a certain way, but to ascribe it to A, to hold A responsible for it.
[…] And so, Ascriptivists argue, there is no question here of truth or falsehood, any more than there is for moral judgments (Geach 1960: 221).
At the foundation of ascriptivism, in Geach's opinion, lie theories that "have had quite a vogue", such as those that use utterances like "to say 'it is bad to get drunk' is not to describe or characterize drunkenness but to condemn it" (Geach 1960: 222). This line of reasoning is flawed for the following reasons. Let us denote the moral predicate "bad" as P. In this utterance, Р is used not as a description, but as a particular type of performative. However, the difference between calling a thing by "P" and predicating "P" of a thing is often ignored. this difference is that Р may be predicated of a thing in dependent clauses of a conditional clause without that thing being called Р. Geach claims that to say "If gambling is bad, inviting people to gamble is bad" is not to say that either gambling or an invitation to gamble is bad. But theories of nondescriptive performances 3 , as a rule, only focus on Hart rejected, and whether he rejected them at all. In this paper, I do not want to consider whether he was right or not in so doing. Here I try only to prove that the explication of the assertoric force of ascriptive legal utterances could be used in a solution to the Frege-Geach Problem. 3 Geach does not specify to what kind of theories of nondescriptive performances he refers, and it is not at all clear whether by the word "nondescriptive" he means one of the potential uses of Р -specifically, the use of calling something Р. at the same time, predications of "bad" in dependent clauses of a conditional sentence are simply ignored (Geach 1960: 223).
In fact, if we emphasize the assertion (or "calling", in the words of Geach, although by all appearances, what is meant is definitely assertion), then we cannot use Modus Ponens, because it will then contain a logical fallacy.
If doing a thing is bad, getting your little brother to do it is bad (in this premise, "doing a thing is bad" is not an assertion).
Tormenting the cat is bad (in this premise, "doing a thing is bad" is an assertion).
therefore, getting your little brother to torment the cat is bad. this reasoning contains ambiguity in the assertion, or a logical fallacy of equivocation 4 . But Modus Ponens is valid. that is why we should look not to assertion (or calling), but to predication, because predication is found even where there is no assertion. For the use of a sentence in which P is predicated of a thing to count as an act of calling the thing P, that must be used assertively. this is very distinct from the predication, because P can still be predicated of the thing even when the dependent clause in which it occurs is used "ascriptive". For the sake of simplicity, in this article I use "nondescriptive" as a synonym for "ascriptive", because I think it is appropriate to Geach's reasoning as well as to Hart's approach. 4 In the above example, distinct meanings of the word "bad" are implied in the contexts of the first and second premises. It is difficult to say that the occurrence of "bad" as an antecedent of the first premise has exactly the same meaning as "bad" in the second premise. But according to Geach, the word "'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" (Geach 1965: 463-464). nonassertively. Consequently, calling a thing P must be explained in terms of predicating P of the thing but not the other way around (Geach 1960: 223). From Geach's point of view, if I say, in all seriousness, "If gambling is bad, inviting people to gamble is bad", I do not thereby condemn either gambling or inviting people to gamble, though I do predicate "bad" of these kinds of acts. this forces Geach to dismiss ascriptivism and move on to the assertion that sentences in the form of "He did it" are not ascriptions or condemnations, but descriptions of the cause of action. Geach is a proponent of the "natural view" that to ascribe the completion of an act to a person is a causal description of the act, something that is the most widespread example of causal statements. He wishes to demonstrate thereby that ascribing an action must be implemented through the action that caused it (Geach 1960: 224).
the essence of this reasoning is that the term "'bad' should mean exactly the same at all occurrences […] 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" (Geach 1965: 463-464). With this argument, Geach illustrates the theoretical unsoundness of defining the meanings of moral terms (using the example of the word "bad") through certain acts of utterance or assertion. In his understanding, the meaning of a word is not constituted by its being uttered or asserted (this is what Geach sees as the main lesson that Frege left for us) because there are contexts in which terms appear as unasserted positions (these include questions, denials, expressions of hope or surprise, disjunctive and conjunctive constructions, and others).

Resolving the Frege-Geach Problem
an analysis of the philosophical reasoning Geach set forth in "Ascriptivism" demonstrates that he uses the term ascriptivism too freely to mean all kinds of noncognitivist ethical doctrines and theories of nondescriptive performances. Let us consider this below. When analyzing moral judgments, critics of emotivism (such as Geach) doubt that it is possible to wholly explicate the meaning of moral propositions in terms of reactions of acceptance or rejection. In particular, the Frege-Geach problem, which uses grammatical linguistic arguments to prove the similarity in semantics of moral and factual propositions, thereby destroys and casts into doubt the main position of noncognitivist metaethics, which contended the fundamentally distinct functioning of the language of morals from the functioning of descriptive language. Geach attempts to show that there are contexts in which the usual emotivist analysis of the meaning of moral terms does not work.
This type of analysis can be applied to any type of nondescriptive discourse, according to Geach. and the result of this analysis is an assertion that apparently is the formulation of the Frege-Geach problem, specifically: If moral (or any nondescriptive) propositions are used to express a logical conclusion, then they must, without fail, be true or false, but moral propositions are neither true nor false; therefore, they cannot be used to express a conclusion without violating the laws of logic. In addition, Geach notes that the occurrence of moral terms in conditional and assertive premises of Modus Ponens must have the same meaning and be subject to standard rules of logic 5 .
I suppose that Geach is wrong in claiming that ascriptivism has much in common with prescriptivism, and in denying the truth-values of utterances about rights and responsibilities. It is clear that Hart would be incorrect if he asserted that utterances with the form "This is mine" or "He did it" could not be true or false. But because the main purpose of such utterances is to claim or ascribe a right or responsibility, that absolutely does not prevent individual specific cases of claiming or ascribing from being verified as true or false. My assertion "This car is mine" would be false if, actually, it belonged to someone else, and my utterance "He did it" could be the proper performance of an obligation to tell the court nothing but the truth (in terms of responsibility for bearing false witness). Hart does not deny this. In fact, he admits that claims or accusations can be refuted with the facts on which they are based (Hart 1951: 147) and that they can have a direct descriptive use. However, he draws our attention to more interesting cases of their use. When the situation is not so well defined, when it is possible to establish the performative na-5 Jørgensen's Dilemma, named after Jørgen Jørgensen (see Jørgensen 1937: 288-296), is a very complicated problem that is similar to the Frege-Geach Problem. Indeed, the Frege-Geach Problem and Jørgensen's Dilemma address the same issue. 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 there is the interpretation of connectives and logical operators in contexts that are partially lacking truth-values. Jørgensen's Dilemma, on the other hand, deals with making inferences between norms, that is, sentences that are lacking in truth-values. I attempt to develop here a fresh approach to the solution of the Frege-Geach Problem in the context of legal language and by means of ascriptive statements.
ture of the use of ascriptive legal terms and uncover contradictions between descriptive ascriptive utterances: the case to which I wish to draw attention is that where we use such sentences not to transfer or confer rights, but to ascribe or recognize them. For here, like a judge, the individual decides, on certain facts, that somebody else has certain rights, and his recognition is like a judgement, a blend of fact and rule if not of law (Hart 1951: 158).
Hart seeks to attach claims of responsibility to claims of action in the same way that legal consequences attach to legal pronouncements: The sentences "I did it", "you did it", "he did it" are, I suggest, primarily utterances with which, we confess or admit liability, make accusations, or ascribe responsibility […]. Indeed, the descriptive use of verbs of action is so important as to obscure even more in their case than in the case of "this is yours", "this is his", etc., the non-descriptive use, but the logical character of the verbs of action is, I think, betrayed by the many features which sentences containing these verbs, in the past tense, have in common with sentences in the present tense using the possessive pronouns ("this is his", etc.), and so with judicial decisions by which legal consequences are attached to facts (Hart 1951: 160).
Hart's main point here, as Ronald Loui says, is very important: the "principal function is" ascription, and there are "primarily utterances with which" we ascribe (Loui 1995: 22). Nevertheless, it does not suffice to refute Hart by citing examples in which ascription of action is possible without ascription of responsibility. In Hart's examples, a legal judgment of murder incontrovertibly carries responsibility. We do not know in advance what that responsibility entails as punishment. But it already seems to differ from a legal judgment of manslaughter, which ascribes a different responsibility. It appears that any kind of action sentence can be used either descriptively or ascriptively; it depends on the tense in which the action verbs are used. Therefore, responsibility presupposes both descriptive and nondescriptive uses.
I will attempt to develop this idea of Hart's that plays a key role in my solution to the Frege-Geach problem. To solve the Frege-Geach problem using the model of ascriptive legal language, we need: (1) to use for the explication of the assertoric nature of legal utterances (like Frege) the argument of "assertive force" and grant that it corresponds to the form "X did…"; (2) to assume that "X did…" is an ascription. These assumptions do not simply correspond to the logic of Hart's reasoning but are an implicit expansion of the argumentation he presents in "The Ascription of Responsibility and Rights". The theses I present are closely interconnected; one logically follows from the other, but the second argument plays a decisive role in my proposed solution.
In attempting to substantiate the performativity of legal language, Hart concluded that it was possible to do so only with the "correct interpretation" of the use of the verb "to do": The verb "to do" and generally speaking the verbs of action, have an important descriptive use, especially in the present and future senses, their ascriptive use being mainly in the past tense, where the verb is often both timeless and genuinely refers to the past as distinguished from the present (Hart 1951: 160).
In Hart's view, both traditional and modern approaches to the interpretation of the concept "action" were incorrect because they were aimed at defining the concept of an action through the development of the necessary and sufficient conditions for its application. For example, to say "X did action A" means, from the point of view of traditional and modern analysis, saying something that can be expressed in categorical propositions that describe, accordingly, the movements of X's body and his or her psychological relationship to what was committed. Hart said that the logic of these approaches was false, because it supposes that the concept of an action can be defined only through descriptive utterances related to one individual. Descriptive utterances are not suitable for the analysis of sentences such as, "He did it". That is why we should acknowledge as false an analysis of action that identifies the meaning of a nondescriptive utterance ascribing responsibility with factual circumstances that support or are good reasons for the ascription. It is not possible to draw a distinction between the utterances "His body moved in violent contact with another's" and "He hits her" without reference to the nondescriptive use of sentences by which responsibility is ascribed. Therefore, rejecting the physical and psychological components of action enabled Hart to assert first that utterances such as "He hits her" do not merely describe, but ascribe, rights and responsibilities, and second that it is not possible to interpret utterances of this type without taking into account their nondescriptive (and in this case ascriptive) nature.
Hart's main point is that responsibility can be used either descriptively or ascriptively: It depends on a tense of action verbs. and if we take this argument into account, then a conclusion from ascriptive utterances (where the verbs are used in a past tense) under Modus Ponens will not contain a logical fallacy. I will represent "X did…" as ⊩, a special symbol indicating an assertive force of an ascriptive sentences ("X did…" corresponds to the symbol ⊢ in Frege's notation). Then, the main use of legal utterances under Modus Ponens can be formally represented as a conclusion from then petitio principii, hidden in the form of conditional categorical deductions, can be avoided. at the same time, Hart argues (and he diverges from Frege on this as well) that predication of P in dependent clauses of conditional ascriptive sentences can be defeasible 6 (Hart 1951: 153, 160). Consequently, such predication can produce a defeasible utterance: "⊩ If A, then B; ⊩ A, therefore, ⊩ B" is not a description of "X did…", that is, does not describe it completely, because along with the purely descriptive component, a nondescriptive component is also revealed (see Chisholm 1964: 614). 6 Hart's views on action and responsibility face many objections, but that is not the case here (see Bix 2012: 198-199). What is of interest here is Hart's argument, which is based on what he calls the "defeasible" character of judgments of the form "X ϕ-ed" (see fruitful discussion about this concern D'Almeida 2016: 10-14). I especially agree with D'Almeida that we can attribute to Hart the following thesis: "When uttering a token of 'X ϕ-ed' in non-embedded contexts a speaker is characteristically (performing the non-descriptive speech act of) ascribing responsibility to X" (D'Almeida 2016: 12). I do not use here "defeasibility" as a legal notion, rather I consider it from a semantic point of view, because this reasoning corresponds to Hart's approach: "This can be seen by examining the distinctive ways in which legal utterances can be challenged" (Hart 1951: 147).

Conclusion
taking into account the argument of assertive force (designated ⊩) and the presence of a nondescriptive component in the concept of an action, I will explain my reasoning using this example: If the murder was committed by John, then he should be held responsible.
John committed the murder. Therefore, he should be held responsible.
Here, the assertive force will be the fact that the murder was in fact committed and the ascription "John committed the murder" will be defeasible (we might learn, for example, that the killing was accidental or done in self-defense). as I have noted, the predication of P in dependent clauses of conditional ascriptive sentences can be defeasible; therefore, if the conditional premise "If the murder was committed by John, then he should be held responsible" contains a defeasible consequent, then the whole conditional proposition is defeasible (by analogy, a conditional proposition is false when and only when a false consequent follows from a true antecedent). Bear in mind that Hart clearly indicates that what is defeasible is not the action itself (the action occurs -someone really killed someone), but the responsibility (for instance, in the case of manslaughter). Moreover, because this deduction is defeasible, then the sentence "John committed the murder" does not fully describe John's behavior, because the description contains within itself a nondescriptive component. Therefore, assertive force in a sentence with the form of "X did…", the thesis of the defeasible character of ascriptive legal utterances, and