Remarks on the problem of Sense in a pragmatic reading: an interpretation of Dummett on the intensional problem

Observações sobre o problema do sentido em uma leitura pragmática: uma interpretação de Dummett sobre o problema intensional

Lucas Ribeiro Vollet[a]

Universidade Federal de Santa Catarina (UFSC), Brasil

Esta obra está bajo una Licencia Creative Commons Atribución 4.0 Internacional.

Como citar: VOLLET, L. Remarks on the problem of Sense in a pragmatic Reading: na interpretation of Dummet on the intencional problem. Revista de Filosofia Aurora, Curitiba, v. 34, n. 63, p. 173-191, out./dez. 2022

Among the first puzzles of analytic philosophy there is one that still gives rise to intrigue and reflection. The referential identity between the expressions Hesperus and Phosphorus does not guarantee that they can be substituted for the other in any compound sentence without changing the truth value:

...since, e.g., the thought of the sentence "The morning star is a body illuminated by the sun" differs from that of the sentence "The evening star is a body illuminated by the sun." Anybody who did not know that the evening star is the morning star might hold the one thought to be true, the other false. The thought, accordingly, cannot be the referent of the sentence, but must rather be considered as the sense. (FREGE, 1948, p. 215)

Frege's solution was to explain that these expressions have the same reference but differ in Sense. In addition to reference (Bedeutung), expressions also have sense (Sinn). In indirect or oblique speech, where what is at stake is the Sense, we cannot rely on Leibniz's law of intersubstitution salva veritate.

The artificiality of this solution was not ignored. The idea of Sense seems to appear in Frege's thought as an emergency valve, not to diagnose and solve the paradox, but to neutralize its inconvenient logical consequences without enriching our knowledge of its causes. The artificiality of this solution can be explained in part by the fact that Frege had little interest in linguistic problems arising from the intensional nature of certain expressions. For him, the important question was how to explain the information gained from "a=a" to "a=b". Frege's interest was in the nature of a mathematical problem related to identity, according to Dummett (The Interpretation of Frege's Philosophy): "The real topic of Grundlagen 63-9 is how to transition from saying that there are as many F's as G's to say that the number of F's is the same as the number of G's" (1981, p. 335). Moreover, more direct references from the text certainly leave a lasting impression that by Sinne the author means only the "mode of presentation" of the reference, which in the case of the proposition would be the conditions under which it could be said to be true. As K. Klement has correctly noted, attention to this particularity can mislead a reading of Frege:

The problem with such a literal interpretation of a Sinn as an “Art des Gegebenseins” is that it would imply that the Sinn (Gedanke) of a whole proposition is the means of determining its truth value, i.e., the means of verifying or falsifying it. This would attribute to Frege a verificationist account of meaning, which there is little evidence to support, and is most likely incompatible with the rest of his philosophy. (KLEMENT, 2002, p. 60)

Nevertheless, we must ask: What distinguishes knowledge of Sense from knowledge of Reference? For Dummett, "A and B have the same Sense if, once one recognizes either as truth, but does not recognize the other, it follows that he could not understand the Sense of at least one of them" (1981, p. 323). This criterion is uncomfortably general. It vaguely presupposes the state of knowledge of someone who fails to make an ascription of identity. One knows that he would not recognize any difference between the identity patterns projected by the expressions. But that is all we can know. However, this leaves open what he does not grasp. We can make it more precise by saying that there is a rule for knowing how to use A and B meaningfully. And second, this rule gives us the knowledge of the indifference between A and B under certain conditions. A consolidated, but admittedly unsupported by Frege's text, interpretation is that the idea of Sense was an anticipation of the tools for mapping possibilities that were later pursued by the semantics of possible worlds. We can attribute this interpretation mainly to Hintikka:

Frege said that the intension (Sinn) of a name must include . . . the way in which this reference is given (die Art des Gegebenseins . . . ). Now the functional dependence which this phrase ‘way of being given’ clearly means can—and must—be spelled out by specifying how the reference depends on everything it might depend on, which in the last analysis is the whole possible world we are dealing with. (HINTIKKA, 1973, p. 377)

The possibility offered by language itself of assigning different names to the same object testifies to the ability to describe the same object in more than one way, and allows speakers of a language to explore (what we may call) superidentifications in the sense of describing identity between objects under a particular condition (as in classes of possible worlds). Another way of saying this is to say that these identifications are made in a space of possibilities, or that they exclude a class of specific possibilities.

The problem is how to find a straightforward interpretation that assigns truth or falsehood to the sentence asserting the identity of Hesperus and Phosphorus. The whole problem is how to program a semantic theory to afford those values to be absolute and not interpretations relative to the description one has in mind. This difficulty is compounded when ordinary language contains sentences that cannot be judged by uniform rules and therefore do not admit of a testable semantic theory. The state of affairs has been very well summarized by Donald Davidson (Truth and Meaning):

what would emerge as the deep problems are the difficulties of reference, of giving a satisfactory semantics for modal sentences, sentences about propositional attitudes, mass terms, adverbial modification, attributive adjectives, imperatives, and interrogatives; and so on through a long list familiar, for the most part, to philosophers. (2001, p. 63)

Now we can better outline what would be a criticism of the existence of Sinne, as an independent element in the list of properties of meaning. What would someone have to say who denies the existence of this aspect of meaning (Sense)? He would have to say that at no point in our linguistic competence do we need two rules of interpretation. One rule is sufficient to give the instruction of a semantic nature about what is said; and if more than one rule is required, the instruction will not be unambiguous (non-straightforward). Hillary Putnam was a pioneer who formulated this question in similar terms. The name of his 1975 article, Meaning of Meaning, hints at the question of this unnecessary duplication. For him, "...the extension of a term is not fixed by a concept that the individual speaker has in his head." (PUTNAM, 1975, p. 245). This issue has also been discussed in the context of linguistics and its interfaces with cognitive psychology:

One viewpoint (e.g., Chomsky, 1965), which has been dominant in many theoretical approaches to language, starts by assuming a strong separation between linguistic competence (i.e., an abstract specification of the speaker/hearer’s knowledge of the language) and linguistic performance (the processes by which this abstract competence is deployed in language processing) (...) An opposing viewpoint suggests that no such abstract linguistic competence exists — rather, acquiring language is no more than acquiring the ability to process language” (CHATER, MCCAULER & CHRISTIANSEN, 2016, p. 3)

Skepticism about this doubling of rules, which divides use of language into a matter of productive competence and a matter of performance, was the catalyst for the externalist critique of intensional foundationalism. This critique took place in the second half of the 20th century. We can summarize the challenge as follows: If the rules used to obtain unambiguous (straightforward) semantic values do not conflict with each other, we can unify them into a more general and unambiguous rule. However, if the rules conflict, they will split their instructions and confuse those who have mastered them, making it impossible for them to unlock direct interpretations. It makes no difference to hold them in independent positions, as if they were two inescapable realities of the nature of Meaning. Dummett has a possible answer:

The only way in which a speaker of the object-language can specify the Bedeutung of one of its terms is by using some co-referential term, which he recognizes as such by his grasp of statements of identity (DUMMETT, 1995, p.16-17)

To be fair, the externalist would not be impressed by the usefulness of discourse on Sense to spot co-referentiality: He would say that there is no need for Platonic identities if all we want to do is detect the correspondence between A and B by writing an algorithm to check for possible discrepancies between them. We can program a computer to detect this identity. The computer program is not a Platonic object and can work according to the rules of physics. When we talk about Sense, we can talk about the conditions under which the convergence between A and B can be mechanically generalized. Some recursive properties must be sufficient to generate this identification. So we are left with this one reason to talk about Sinn: It is that which we are talking about when we need to refer to this "identity". We can say that what characterizes Sinn is the mastery of these learnable recursive features:

If the theory is to display the existing or intended Sinne of the expressions of the object language, it must embody only what anyone who has a mastery of the object language will know (DUMMETT, 1995, pp. 16-17).

The following semantic condition exhausts all that one needs to know in order to be in possession of the assertoric content of a sentence: 'To grasp the content of an assertion, one needs to know only what possibilities it rules out" (DUMMETT, 1993, p. 47). Straightforward stipulations of truth are those that are unproblematic for assertion contexts. Ceteris paribus, the truth or falsity of the sentence is not challenged. Tarski has shown that any technique for identifying instances of true sentences is nothing more than a repetition of the sentence in a biconditional that correlates it with its translation in a metalanguage. Tarski's lesson means that knowing a criterion for meaning does not allow us to draw conclusions about the sentence's ability to be verified or compared to something else. When we try to compare the sentence with something external, we cannot distinguish all extensionally compatible interpretations: "When we try to provide a serious semantics for reference to facts, we discover that they melt into one; there is no telling them apart" (DAVIDSON, 2015, p. 5). Thus, it is not necessary to know an identity predicate. Meaning is just a trivial expression of the fact that the predicate "truth" can be generalized in a language with its own syntax proper to express a certain semantic transparency: "once we have a Fregean syntax, are not the details of classical semantics thereby determined?" (DUMMETT, 1993, p. 24). As Dummett pointed out in The Logical Basis of Metaphysics:

it must always be possible to frame a straightforward stipulation with respect to truth. I believe this to be so, indeed to be virtually evident, since amounts to no more than that we can always have a notion of truth for which Tarski's schema holds (1993, p. 19).

We will return to the Hesperus and Phosphorus paradox. The problem is that these expressions denote the same object, although they also mark different ways of determining it according to a rule. Of course, semantics should be used to find rules that are suitable to unify other rules, by giving straightforward references to any kind of problematic interpretation or ambiguity. If there is controversy about an interpretation, the semantic part of that interpretation must be the solution that projects a sufficiently narrow margin to characterize the difference between the worst and best interpretive hypothesis - the floor and ceiling of the interpretation. Only what lies far outside this curve can be called extra-semantic. But even semantics cannot hold the consistency of interpretation in some contexts. No classical semantic rule can assign a consistent extension or straightforward interpretation to sentences occurring in oblique contexts such as "Flaubert thought that Hesperus is Phosphorus." Frege's solution, which states that in addition to a reference, these expressions have a Sense (Sinn), alleviates the discomfort of this problem, even if it does not eliminate its enigmatic aspect. The stars seem to agree extensionally, but may disagree intensionally. How can we interpret this chaotic circumstance in a simple unambiguous way? The problem with classical logic and semantics is that we must not resort to non-straightforward interpretations of logical constants. As Dummett noted:

for classical logic, we can specify the conditions for the truth (under an interpretation) of a complex formula only by means of absolutely or relatively straightforward stipulations relating to each of its logical constants; whereas, for a non-classical logic, we may also be able to frame non-straightforward account of at least some of the logical constants. (DUMMETT, 1993, p. 28)

What are the commonalities in cases where the semantic value cannot be stated directly? The semantic problem of finding a straightforward interpretation for a sentence is the problem of fixing the reference in a way that is not just a proxy. Since some references cannot be fixed without relativizing them to possible worlds, the problem is not so easy to solve. It seems that some interpretations must be oblique. This becomes particularly problematic in defining the stable object of a belief ascription such as "Flaubert believed that Mount Everest is in Nepal." In normal contexts, the problem of the truth or falsity of "...is in Nepal" for Mount Everest is straightforward. It needs nothing more than to know the solution to the problem of the truth or falsity of "...is in Nepal" for the Biggest Mountain in the world (since both map directly to the same thing). It does not matter how much information is added by substituting Mount Everest for the largest mountain, because the logical problem here is one of truth, and that must be straightforward. Now this is not so unproblematic if the proposition is subordinated to a belief ascription. Let us assume that Flaubert does not know whether Mount Everest is the biggest mountain on earth. Then the problem with the truth of one is not the same problem as with the truth of the other, at least not as long as the sentence is subordinated to the ascription.

The simplest solution to this problem is to stabilize the value of the alternatives for "...is in Nepal". Expressions that introduce instability into semantic composition, such as expressions that have different references in different possible worlds, must be stabilized. The simplest way to do this is to map the expression to a neutral second-order value that gives a class of alternatives a uniform 'de re' interpretation. According to Dummett:

that there is predicative or de re thought, belief, and knowledge, is not to be called into question. (…). This would be a knowledge of the truth of which did not rest on any piece of proposition (de dicto) knowledge” (DUMMETT, 1981, p. 590).

If Mount Everest stands as a de re belief ascription for Flaubert, it stands as the thing that is Mount Everest^[2]. It stands as a possible instance of a function. The straightness of the interpretation is reached.

The possibility of expressing a de re knowledge, or, in Dummett's words, an irreducibly predicative knowledge of the thing believed, represents a considerable departure from Frege's conception that every expression has a Sense and a reference: 'There can be no thought about an object not involving its being picked out in some particular way' (DUMMETT, 1981, p. 592). In this Fregean conception, the full characterization of the semantic role of "Mount Everest" cannot be simulated by its de re characterization. The way in which it is selected or specified - its Sense - will be missing. But, still following Dummett, "That there can be no irreducibly predicative thought does not imply that there can be no purely referential term" (DUMMETT, 1981, p. 592).

Even if you do not know that (i) Mount Everest is (ii) the largest mountain on earth, substituting (i) for (ii) in the statement "Flaubert believes of the (x that is the) Mount Everest that it is in Nepal" cannot reverse the value from true to false or from false to true. This is because the problem is settled when the reference fixation is settled. It is not duplicated in a Sense problem: "If I say 'The man I am pointing at might not been in Rome, I do not invite the retort 'How could you point at him if he was in Rome'" (DUMMETT, 1981, p. 599).

Let us summarize what we have learned. Assuming no obliquity is spotted, the semantic structure of the sentence, or the way it guides a possibility of instantiation, restricts what counts as a counter-instance for the sentence. It can give an unambiguous interpretation of the sentence, an absolute answer to the question of whether it is true or false. This answer cannot be challenged lightly. If the sentence is true, it cannot be false. The semantic structure that maps instances to a sentence projects the logical problem of constraining the ways to investigate the truth of the proposition. In this de re constraint, Flaubert's ignorance of whether an instance of "... is in Nepal" would still be an instance of it in other worlds will not reopen the problem of its truth or falsity. The truth (or falsity) of the sentence "...is in Nepal" is settled once and for all, once an instance satisfies it or not, even if there is a possible world (the possible worlds represented by Flaubert's beliefs) in which it is an open problem whether the Mount Everest is the largest mountain on earth.

In the last chapter we saw that even beliefs can have a straightforward interpretation – they can be true or false in just one way, and not as answers to two different problems – by locking an "object" of belief. We have concluded that changing the semantic value of a sentence by replacing a term with a coreferential term is possible only in contexts where the semantic object is indirectly or propositionally referenced (de dicto). However, we can learn a lot from these non-linear contexts. Problems with Sense can only duplicate the problems of deciding the truth or falsity of a sentence in oblique contexts. The question not explicitly posed in Frege, but which Dummett brings into the first scene, is why we should duplicate the question of the truth of a sentence. What is the goal if we consider the truth of a sentence in a way that is relative to the (de dicto) oblique way we understand its reference? The explanation is quite simple: we need semantic technologies – whatever they may be – to fix the reference of expressions that vary from world to world or from time to time. Only because we can fix the reference in this way do we have access to solutions to the truth or falsity of hypothetical propositions. But from the fact that we can reasonably distinguish different hypothetical propositions, it does not follow for Dummett that we have a metaphysical superconcept of truth (or non-falsity) for modal propositions. This is the limit of straightforwardness.

Semantics cannot help us on this path. There is no "super-parameter" by which one could easily assign truth instances to possible or necessary true propositions. Projections are inherently an estimate based on an upper and lower bound, the maximum and minimum that can be asserted by an interpretation. But this does not give us a unit value for the set of possibilities. It merely gives us a curve of consistent interpretations. We can, of course, offer a truth approximation, a partial model, or something relative, but then – according to Dummett – we are trying to establish an ingredient value that does not involve extension. Once we have moved to the ingredient value, the extensional aspect will not be sufficient to provide the relevant knowledge.

We can now talk about how Dummett rescues Frege's theory against modal logic, illuminating an aspect of the classical semantic perspective that can be extended without crossing over into a metaphysical conception of possible worlds. In the chapter on Kripke in his book, Dummett criticizes modal logic and its attempt to build a metaphysical model of truth in which certain assertions can be asserted in terms of a set of worlds: "when modal discourse is in question, there is little obvious alternative to represent modal expressions as operators on sentences or predicates; but it is far from evident that our theory is to be framed in terms of particular possible worlds" (DUMMETT, 1981, p. 598). The author does not doubt that we can construct values to interpret hypothetical sentences:

if we are devising a semantic theory, the linguistic phenomena by its accordance with which it is to be judged correct or incorrect are our judgments as to truth or falsity of statements of natural language, to which our opinions about how we judge in hypothetical cases are excellent guides (DUMMETT, 1981, p. 598).

However, he doubts that this can be done straightforwardly. The question remains: what happens when we add the predicate "is assertible" to sentences referring to time or possible worlds? We illuminate the hypothetical condition under which assertion of the untrue proposition, though not true, might nevertheless be rewarding. These are the conditions under which asserting the proposition would be strategically rewarding, since it contributes to an investigation of possible truth. Rewardable differs from true in specific but important respects. First, the idea of reward invokes an aspect of the concept of meaning capable of reconciling an idea of truth and the idea of justification or warrant assertion - like the score in a game. This connection was described by Davidson in the process of the formation of a regularity of assertive use through a scoring system:

at the start, the learner does not register anything more than an association between an object or situation and sound and gesture. The value of the association is supplied by the teacher or the environment in the form of reward (DAVIDSON, 2005, p. 14).

But the idea of reward is not just the primitive way of teaching children before they can convert their concept of trial and error into thought and belief. In the case of sentences whose meaning seems to exceed the ability to be described by the features of the predicate "truth" because their assertibility depends on complex, unstable, or nonsimple conditions, the only way to maintain the testability of the meaning of our beliefs is to return to the stability provided by the concept of reward. The case of non-straightforward contexts invites us to be children again, in the sense that we must return to security. We move from the highly idealized concept of truth to that of reward, since in these cases the only way to maintain the correctness rule for our assertions is to devise rational defense strategies provided by a theoretical framework of truth prediction. Dummett also brought this dimension of the problem to the fore in his “Truth” article:

It has become a commonplace to say that there cannot be a criterion of truth. (...). In the same sense, there could not be a criterion for what constitutes the winning of a game, since learning what constitutes winning is an essential part of learning what the game is. (...) (DUMMETT, 1959, p. 7)

This teaches us that the concept of "truth" is a widely abstract form of idealization, applicable only in rare cases to sentences placed in extremely favorable strategic contexts. These favorable strategic contexts appeared sublimated in the position in Tarski's hierarchy in which the assignment of the predicate "is true" to that sentence is straightforward – not reversible to falsity or to paradox. This idealization can only be discussed, negotiated, and revised if we bring the problem into a setting where we can talk about more or less true sentences, as sentences that are given a relative non-false value – as hypothetical sentences.

For Dummett, this should not scandalize anyone, because the value of the concept of "truth" to semantic knowledge is overestimated: "It may well be doubted that truth really is the central notion for characterization of valid inferences" (DUMMETT, 1993, p. 41). What we know when we know the unique interpretation of a sentence is not the empirical conditions of its truth, but the equality of its truth with all propositions whose truth is assigned under similar enough conditions. To speak again with Dummett (Frege's Philosophy of Language):

Facts, as true thoughts, belongs, not to the reign of reference, but to that of sense. (...) there are no two things between which comparison has to be made in order to find out if they correspond" (1973, p. 443).

What we know by knowing that two expressions can be interchanged salva veritate, even in modal contexts, is not their extensionality but their similar ingredient value. We know this by theorizing about their rewarding properties. In other words, we know that the assertion can be rewarded or score under the same strategic conditions as all sentences with the same ingredient contribution.

The whole problem is: how to make a semantic mapping that is fair enough to assign a non-dogmatic semantic value to hypothetical rewardable statements? If we want to know when the assertion of a hypothesis has fair onus, we need to know how it can be understood in the context of a discussion of its possible truth or the conditions under which its truth is favorable. A hypothesis is judged not by how much it asserts, but by how much it proves. Here we see part of Dummett's reasons for moving from a classical concept of truth to an intuitionistic concept of provability.

Of course, one cannot deny that the distinctness of hypothetical statements is achieved by some theory (semantic or otherwise), otherwise natural science would be impossible. But it is not clear that this distinctness is a new knowledge, like the knowledge about extratemporal "things":

we have no clear conception of what metaphysical necessity and essential properties are, and no defense against the suspicious that, if modal discourse does rest on these notions, then it is, in fact, pointless" (DUMMETT, 1981, p. 598).

Rather, we should say that trying to discern what a hypothesis says (its semantic instruction) is trying to explain its burden or the (strategic) cost of asserting it, not just assigning different non-true-or-false values to its assertion.

For Dummett, the fact that we have to improvise non-straightforward interpretations for modal and counterfactual propositions arises from another necessity: "We need the notion only in order to explain the contribution of that sentence to the content of more complex sentences of which it is a constituent" (DUMMETT, 1981, p. 582). In addition to the assertoric value of the sentence that might be assigned (in a Tarskian fashion), we can also give semantic stipulations or referential mappings to expressions and sentences that contribute in part to the truth or falsity, or that capture part of the truth or what would be true if more information were added.

We are now in a position to determine the conditions under which a theory of the meaning of Frege's style – doubled into two problems (the extensional and the intensional) – can be recovered from a pragmatist point of view. To do so, however, we must concede an extension of the extensional thesis to a less straightforward form: the form of Dummett's thesis of ingredient values. We intend to rescue the main classical insights of a bipolar theory of meaning, but other classical insights will be lost in the process. We will extend these classical insights to cases where the assertion has no uniform label of truth or falsity. Because assertions may be rewarded differently, their truth or falsity can contribute to a broader strategy of reasoning in different ways (being true or false in complex, relative, or approximate ways). These are cases where semantic value is merely an ingredient of an assertion strategy. On this reading, we do not need a correct, straightforward truth assignment for identity assertions. We can just stick to the idea of grasping the Sense

:the interesting notions, in connection with sense, are those of grasping a sense and of expressing sense, and a great deal may be said about these without the need for a sharp criterion of identity of sense" (DUMMETT, 1981, p. 342).

According to this view, the conceptual interest in grasping the Sense of Hesperus and Phosphorus is the interest, in an astronomical theory, of knowing that one cannot assert a sentence that assigns P to the first and deny the same P to the second. This "cannot" is to be understood as: "it is not strategically asserted" or "it is not rewardable". To support this reading, we will follow some steps.

The semantic content provided by the Sense is the way the sign is coordinated with the Reference. In contrast to a model that provides a slightly simplified and extensionally generalized interpretation, that is, a fully truth-functional "semantic value", Sense locates a less straightforward and more subtle and refined content projection. This operation is not harmlessly generalizable by a quantifier (since it is not an extension). But it still has a semantic ingredient; it has a certain general value (which needs a pragmatic explanation). It complements the projection of a rule of interpretation. In order to understand this quality of the Sense, we need to be clear about its possible ingredient contribution. Moreover, we must recognize the character of its contribution in contexts of ambiguity, approximation, relative reference, or what we call "speculative" semantic conditions. For example, we need to consider the cases in which a sentence can be untrue (undesignated) in more than one way.

... the distinction between different undesignated values (...) is irrelevant to the assertoric content; it serves only to designate the ingredient sense - how the sentence affects the assertoric content of more complex sentences of which it is part (DUMMETT, 1993, p. 48).

This is particularly interesting for evaluating hypothetical sentences, since they can be false under more than one condition. The challenge is to find the meaning – or the straightforward stipulation – under which they can be rationally asserted to be false. The challenge is to distinguish rational scientific false hypotheses from mere superstition and dogma.

Mastery of knowledge of the Sense is a state of maturation of the intensional profile of a sign system. The test for identifying a semantic contribution consistent with the intensional profile of the sentence is whether it projects a single assertion or a single assertive contribution - a straightforward value. But instead of saying that the sentence is classified as true, we must say that it can be rewarded under the same strategic conditions. Changing this way of speaking is decisive. The test is whether it encodes a single semantic reaction when interacting with possible supports and objections. It must transform the crude, naive, and enigmatic concept of "verification" (or confirmation) into the more refined semantic picture of "truth sensitivity." But then we will discover that some sentences that have a modal profile have different truth sensitivities because they are asserted under different rewarding conditions.

Dummett believes that "truth" is overrated. What is needed for communication of propositional content is a notion of proof strategies (borrowed from intuitionism): "A proposition is a decidable classification of constructions (into those that are and those that are not proofs of the statement)" (DUMMETT, 1993, p. 29). This thesis was popularized as Dummett's additions to classical semantics (The Logical Basis of Metaphysics):

It indeed requires an argument to show that the notion of truth does play such a part in an account of language; simply assume that it does is to take as already known a large sector of such an account should make explicit (1993, p. 33).

This theory helps individualize the category of contribution that each expression makes to truth, even in a non-truth-functional way, i.e., as an ingredient contribution to a comprehensive context of proof. Here, the notion of truth is not bound to the classical format, and the semantic modeling of an expression can be classified as its non-straightforward contribution:

the semantic value of a sentence is here a principle of classification (...). The semantic value of a sentence is, in effect, the class of all plays (succession of moves) following a move consisting in the production of that sentence" (DUMMETT, 1993, p. 34).

Two people in an interpretive dispute over the semantic content of a sentence would simultaneously test different keys of intensional generalization. Normally, a dispute of this type is considered infeasible because one cannot theoretically predict how a disagreement about meaning might be semantically encoded. Thus, there would be no possible test for identifying a Sense (Sinn). According to Davidson (Truth and Meaning), a staunch extensionalist, a testable theory about the meaning of a sentence is a theory about the unity of the standard of truth to which the proposition conforms: "The evidence to which we are appealing is (...): mainly questions of the loss or preservation of truth-value under transformations" (DAVIDSON, 2001, p. 64). Davidson, however, offers too narrow a view of the realm of the theorizable. What he overlooks is the value of a theory of Sense for answering questions about the consistency standard used to evaluate a claim. In contexts where interpretive disputes are at stake, theorizing about this standard is our only chance to achieve stability and to set rewardable strategies. When we ask someone to spell out the standard by which they have judged an assertion, we are asking for a non-dogmatic answer so that we can justify the strategic expectation that they will judge similarly in similar cases. In a legal context, this is much clearer. We ask for answers about the standard of judgment and its precedents so that we can test the compatibility of that standard with future judgments as well as with current legislation and, in the case of further argument, with international law. The theory of "Sense" (or the theory of supercompatibilities between patterns and codes) that we acquire by collecting these answers is the only human defense against dogmatic and arbitrary application of consistency standards. Thus, there is nothing anti-theoretical or pseudo-scientific about a theory of "Sense," for without it we would have no defense either to justify an interpretive disagreement (in contexts of translation or legal hermeneutics) or to justify an expectation about how an assertion will be judged or how an assertion strategy will be rewarded.

Frege's division of the problem of meaning into a theory of Reference and a theory of Sense gives us the following advantage. It allows us to identify the problem of meaning with a deep and fine-grained level. The price is that the general knowledge generated in this way is not straightforwardly extensional, so it cannot be rationally corrected or criticized in two easy ways: empirically or computationally. The difficult way, however, is the most rewarding. One must pragmatically interrogate the whole knowledge of language and its categories in order to offer adjustments, corrections, or revisions to the intensional profile.

To summarize: For Frege, we cannot be interested only in reference when working to solve a problem of meaning (of absolute or straightforward interpretation) and the determination of a semantic value, for example, to determine the compatibility of an interpretation with the straightforward coordinate encoded by the sentence. Sense theory in Frege creates the conditions for giving a deeper level to a semantic theory. It can identify content that is coordinated or aligned not only by extensional generality but also by an organic affinity of propositional and inferential profile. This ability would cause two languages, codes, or consistency patterns to match in depth, although on the surface they would also match in their ability to produce similar Tarski's biconditionals (straightforward true or false sentences). As a sign system, they would not only be able to refer to the same extensions. They would also be able to convey similar deductive inferences. Intensional theories are classifications of ingredients into those that contribute to the same inferential mediation. They are super-extensional ways of classifying the affinity of propositional contents. One can achieve this affinity dogmatically or pragmatically. Rational semantics is engaged with the latter.