We started with the observation that mutual understanding and communication between the proponents of two distinct scientific languages are difficult, problematic, and even unattainable. Following Kuhn, I suggested that incommensurability is a semantic phenomenon closely related to the problem of how two scientific language communities can effectively understand and successfully communicate with one another. Cross-language communication breakdown is the landmark of incommensurability. Intuitively, to say that two scientific languages are incommensurable is to say that a necessary common measure of some sort is lacking between them and that thereby the cross-language communication between the two language communities breaks down. By introducing the notion of P-language, I have identified such a common measure as M-presuppositions: The M-presuppositions of two P-languages have to be compatible to facilitate successful communication between them. In abnormal discourse in which the M-presuppositions of two distinct P-languages are incompatible, the communication between them is inevitably partial; in other words, communication breakdown in abnormal discourse is inevitable. In this case, the two P-languages are incommensurable. To put things in a coherent perspective, let us briefly review how we reached this conclusion in the last five chapters.
Presumably, to argue for the essential role of M-presuppositions (as a necessary condition) in cross-language understanding and communication, we need to clarify the notions of linguistic understanding and communication. In chapter 12, based on the notion of effective propositional understanding, I found that a P-language is fully intelligible only if its M-presuppositions are conceptually recognized and comprehended. Thus, the knowledge of the M-presuppositions of a P-language is necessary for effective understanding of it. In abnormal discourse, due to lack of comprehension of the M-presuppositions of a P-language to be understood, interpreters tend to project the scheme of their own language onto it. Such a projective approach to understanding in abnormal discourse often leads to the failure of understanding which then results in complete communication breakdown between the two language communities.
The failure of the projective understanding in abnormal discourse does not mean that mutual understanding between two P-language communities with incompatible M-presuppositions is unattainable in principle. The thesis of incommensurability does not lead to radical relativism according to which we are enclosed in a prison house of our own language. The question then becomes how to make an alien language intelligible without distorting it? In chapter 13, after rejecting the adoptive approach to understanding in abnormal discourse, I argued that we have to go beyond propositional understanding. Our attention is thereby shifted from propositional understanding to Gadamer’s hermeneutic understanding, which is supposed to avoid antithetical poles and provide us with a way beyond the absolutistic-projective and the relativistic-adoptive approaches to understanding. The chapter ended with a cautious note: Although hermeneutic understanding does have a considerable advantage over propositional understanding in abnormal discourse, hermeneutic understanding, as we have argued in chapter 14, is not propositional understanding. Success of hermeneutic understanding does not guarantee the success of propositional understanding; on the contrary, it is when propositional understanding fails that hermeneutic understanding takes over. In addition, Gadamer’s notion of coming to understanding oriented toward agreement through conversation, as argued in chapter 15, is in fact a process of dialogical communication. Since an undistorted full cross-language communication between two incompatible P-languages cannot be achieved, a complete, full (hermeneutic) understanding in abnormal discourse is not feasible either.
Many would argue that language learning seems to provide us an effective way of understanding the alien language in abnormal discourse so that full communication between two incompatible P-languages could be restored. I agree that partial understanding through language learning is possible and feasible. The process of language learning for an interpreter is, in essence, a process of hermeneutic interpretative understanding (chapter 13), which, I argued, cannot restore full propositional understanding. Another challenge may be posted based on bilingualism: A bilingual can surely understand (in the sense of propositional understanding) both P-languages as any competent native speaker does. If so, understanding should not be an insurmountable obstacle for cross-language communication, at least in the case in which both the interpreter and the speaker are bilinguals. Instead of questioning bilingualism, I decided to take it for granted for the sake of argument. To justify the conclusion that communication breakdown is inevitable in abnormal discourse, I argued in chapter 14 that it is necessary to distinguish propositional understanding as comprehension from informative communication based on the standard transmission model of communication; for propositional understanding is necessary but not sufficient for cross-language informative communication. I concluded that shared or compatible M-presuppositions between two P-languages are necessary for carrying out a successful communication between the two distinct P-languages. Therefore, cross-language (informative) communication in abnormal discourse is inevitably partial.
At the end of chapter 14, I found that the notion of informative communication based on the transmission model could not reveal the essence of a genuine communication in the Platonic sense. We need to go beyond the transmission model of communication. In chapter 15, I argued that, for Gadamer, the process of substantive hermeneutic understanding—the process of’coming-to-an-understanding’ oriented toward ‘coming-to-an-agreement’ through genuine conversation—is, in essence, communication. Through analysis and criticism of Gadamer’s common language requirement in terms of a full fusion of horizons, I reached the same conclusion as I did in chapter 14: Based on Gadamer’s conversation model, cross-language communication in abnormal discourse is inevitably partial.
However, Gadamer’s conversation model apparently departs from the basic line of argument that I have been pursuing, namely, the essential role of M-presuppositions and truth-related claims in cross-language understanding and communication. Neither Gadamer’s notion of tradition nor that of horizon could be lined up formally with my notion of M-presupposition. The notion of truth also does not play any significant role in Gadamer’s conversation model, as it should. In chapter 16, I turned to Habermas’s discourse model of communication to rescue these two insights lost in Gadamer’s model. Habermas’s theory of communicative action brings the essential roles played by both M-presuppositions and truth-related claims in cross-language communication back to the central stage. For Habermas, cross-language communication is carried out through communicative speech acts oriented toward reaching both comprehension and agreement on the status of the truth claims raised and presupposed by what is said (utterances). Such comprehension and agreement can only be reached through discursive argumentation in dialogue. Thus, for Habermas, dialogical communication is in essence (hermeneutic) understanding.
Habermas identifies three conditions of dialogical cross-language communication: (i) the knowledge of the truth claims raised and presupposed by the utterances of the other language; (ii) the redemption of those truth claims through argumentation in rational dialogue; and (iii) reaching agreement on the validity of the truth claims in dispute discursively. Since the most fundamental truth claims presupposed by the utterances of the language are actually what we call M-presuppositions, condition (i) is the same as the condition of propositional understanding I have identified in chapter 12. Failure of mutual recognition and comprehension of the truth claims raised by the other language results in complete communication breakdown between the two languages. But dialogical communication requires much more than mere propositional understanding or comprehension. One can disagree with the speaker from the other language on the status of the truth-claims raised with the language based on one’s recognition and comprehension of the claims. In fact, it is precisely one’s ability to comprehend the other language that explores the inability of communicating successfully with the other. To fulfill the two other conditions, I argued, two P-languages have to compatible. Again, I reached the same conclusion as I did in chapters 14 and 15: Based on Habermas’s discourse model, full cross-language communication in abnormal discourse is doomed to failure. Cross-language communication in abnormal discourse is inevitably partial. It is such partial communication breakdown in abnormal discourse that gives the real theoretical thrust of the thesis of incommensurability as communication breakdown. Most classical cases of incommensurability identified by Kuhn, Feyerabend, and many others are cases of partial communication breakdowns.
Communication breakdown in the case of incommensurability, no matter whether it is complete or partial, occurs only in abnormal discourse. It should be distinguished from other kinds of communication breakdowns, especially communication breakdown in normal discourse. Communication between two distinct language communities in normal discourse can fall short of the ideal in many other ways. For example, a communication breakdown may occur between any two languages simply due to a divergence of the speaker’s language-meaning from the interpreter’s language-meaning. For example, there are cases in which the interpreter does ascribe some meaning to the sentence uttered by the speaker such that there is the interpreter’s language-meaning. However, the meaning attributed to the speaker by the interpreter is not the same as the speaker’s language-meaning, namely, how the speaker intends the sentences to be understood. The interpreter misunderstands the speaker. In such cases, an act of communication is not successful. However, the communication breakdown in this case is not as threatening as that due to incompatible M-presuppositions. In the case of misunderstanding, both sides agree on the truth-value status of the sentences in discourse, but specify different truth conditions for these sentences such that the interpreter attributes different meanings to the sentences in the speaker’s language. Actually, these are the cases that the standard interpretation identifies as incommensurability as untranslatability due to meaning variance. This kind of communication breakdown due to misunderstanding is restorable since misunderstanding can be overcome in the process of on-going partial communication.
We observed in chapter 5 the emergence of a (conceptually possible) truth-value gap between the Chinese medical language and the Western medical language and the occurrence of a (actual) truth-value gap between the Newtonian language and the Leibnizian language of space. By a truth-value gap between two P-languages PL1 and PL2, as defined formally in chapter 9, I mean the occurrence of a massive number of truth-valueless sentences of PL1, when considered within the context of PL2, due to the failure of the M-presuppositions of PL1 from PL2’s point of view. Based on the distinction between conceptually possible truth-value and actual truth-value given in chapter 9, we can further distinguish two kinds of truth-value gaps. If massive numbers of truth-valueless sentences of PL1 (say, the language of Chinese medical theory) occur because the speaker of the competing language PL2 (say, the advocate of Western medical theory) cannot recognize its M-presuppositions, we say that there is a conceptually possible truth-value gap between the two languages. If numerous truth-valueless sentences of PL1 (say, the Newtonian language of space) occur because its M-presuppositions are suspended or rejected by the advocate of the other (say, the Leibnizian), then we say that there is an actual truth-value gap between them.
In chapter 12, I identified a strong semantic correlate of the failure of effective understanding between two distinct P-languages—the occurrence of a conceptually possible truth-value gap between them. More precisely, if the core sentences of one P-language, when considered within the context of the other, lack conceptually possible truth-values, then it indicates the failure of effective understanding on the interpreter’s side. Moreover, as argued in chapters 14, 15, and 16, compatible M-presuppositions are necessary for any successful communication between two distinct P-languages. When two P-languages are incompatible, the conflict in M-presuppositions would render massive core sentences of one language actually truth-valueless when considered within the context of the competing language; in other words, there is an actual truth-value gap between two P-languages with incompatible M-presuppositions. Then the occurrence of an actual truth-value gap between two P-languages indicates that the communication between them is in principle incomplete. In this case, even if the speaker of one language PL1 is able to identify and comprehend the M-presuppositions of the other language PL2, many core sentences of PL1, which are meaningful for the speaker of PL1, are not factually meaningful.
Therefore, the occurrence of a truth-value gap between two P-languages is a strong semantic indicator of the communication breakdown between them. Specifically, the occurrence of a conceptually possible truth-value gap corresponds to a complete communication breakdown while the emergence of an actual truth-value gap correlates with a partial communication breakdown.
Be aware that the occurrence of a truth-value gap between two competing P-languages discussed above is caused by two incompatible sets of M-presuppositions embedded in the two languages. The occurrence of a truth-value gap between two languages is measured by the occurrence of a massive number of truth-valueless sentences. However, not all occurrences of truth-valueless sentences count as a truth-value gap in the sense defined above. Many individual truth-valueless sentences could occur within a language due to purely syntactic, pragmatic, or semantic matters other than the failure of the M-presuppositions of the languages involved. For illustration, let us take a brief look at a variety of reasons responsible for the occurrence of truth-valueless (declarative) sentences.
To begin with, sentences that do not have any potential (i.e., logically possible) truth-value, such as ‘Three sapdlaps sat on a bazzafrazz’, are definitely truth-valueless. A sentence containing a connotationless and denotationless singular term (a proper name or description) as its subject, such as ‘Florkyyzzxxm loves glork’, is truth-valueless since its subject is a meaningless particle. Similarly, as to the so-called genuine or logically proper singular terms (primarily demonstratives and proper names), if B. Russell and K. Donnellan are right that these terms have a purely referential use only and have no hidden semantic structure, then we can treat them as meaningless particles if, as singular terms, they are connotationless and denotationless. Hence, a sentence containing an empty logically proper singular term, such as ‘Snow White was born at midnight’, is neither true nor false. In contrast, a so-called superficial singular term (primarily a description) contributes meaning to the sentence in which it occurs, irrespective of whether or not it has a referent; for the primary function of such a term is attributive, such as ‘the present king of France’ in the sentence, ‘The present king of France is bald’. As we have discussed at length in chapter 8, truth-valuelessness of such an existential sentence is due to the failure of its semantic presuppositions, such as, ‘There exists a present king of France’.
Sentences containing unspecified hidden parameters have truth-values only relative to specific contexts in which the parameters are specified. A sentence containing a vague property is a typical case for this kind of sentences. We know that many predicates, such as ‘blue’, ‘small’, ‘bald’, ‘heap’, do not have definite extensions. When such predicates are applied to objects on the borderline, the result will be sentences with no truth-values. For example, whether or not Bill’s belief that Rex is big has a truth-value depends on the specification of a reference-class (‘big for what’ or ‘big compared to what’).
The truth-value status of some sentences depends on adoption of different linguistic conventions for reading the sentences. A sentence, ‘Snow White was born around midnight’, along the suggestion of Russell, can be read as ‘There is one and only one person who is Snow White and that person was born around midnight’. That is, ∃x [Born-at-Midnight(x) & ∀y(y = Snow-White ↔ x = y)]. According to this reading, the sentence is simply false. But according to Strawson’s reading, which we have adopted, the sentence is neither true nor false since its presupposition, i.e., ‘Snow White is a real person’ is false. A similar analysis applies to the sentences committing category mistakes. For a sentence, ‘The Earth is more honest than Mars’, one way of reading it is to treat it as false (W. Lycan); another way is to treat it as meaningless (Ryle); still another way is to treat it as truth-valueless (This is the reading I adopt).
Lastly, the truth-valuelessness of a sentence may be caused by the failure of one of its semantic presuppositions. The failure of any one of them will make the sentence truth-valueless. But these semantic presuppositions usually have different roles in the language containing the sentences. For illustration, imagine two chemists, Dr Bennett and Dr Braxton, who disagree on the truth-value status of sentence (30) of phlogiston theory:
(30) Element a contains more phlogiston than element b.
Here, ‘a’ and ‘b’ stand for some definite descriptions or proper names of two chemical elements. Suppose that Braxton is working within phlogiston theory while Bennett within the framework of modern chemistry. Suppose further that for some reason, (30) is either true or false for Braxton, but is neither true nor false for Bennett. Obviously, there are many possible reasons leading to the disagreement on the truth-value status of (30) between Bennett and Braxton.
Let us first suppose that Bennett thinks that the term ‘a’ fails to denote anything because such a chemical element does exist. But Braxton thinks that the term really refers to a real chemical element. Assume that both persons accept Strawson’s notion of semantic presupposition. Then (30) is either true or false for Braxton since the presupposition of (30), i.e., (30c), is held to be true for him.
(30c) Element a exists.
On the contrary, (30) is neither true nor false for Bennett since she holds (30c) to be false. However, the falsity of (30c) can be fully explained within phlogiston theory without violating any M-presuppositions of phlogiston theory. In other words, the truth-valuelessness of (30) can be derived from a factually meaningful statement within phlogiston theory itself that element a does not exist. Therefore, denial of (30c) does not bring any harm to the integrity of phlogiston theory.
Alternatively, let us suppose that Dr Bennett, as the speaker of the language of modern chemistry, categorically denies the truth of a M-presupposition underlying (30), namely,
(30a) Phlogiston exists.
Be aware that Bennett’s denial of (30a) is not based on her personal belief about its truth-value. Instead, her belief about the falsity of (30a) is derived from modern chemistry theory. Here we touch the heart of the debate. The failure of (30a) renders (30), when considered within modern chemistry theory, truth-valueless. However, denial of the existence of phlogiston cannot be derived from other expressible beliefs in phlogiston theory without casting doubt on the integrity of phlogiston theory as a whole. This is because (30a) is presupposed in the very linguistic setup of phlogiston theory. For this reason, rejection of (30a) cannot be carried out within phlogiston theory itself, but has to resort to another competing language, in our case, modern chemistry. There is a (actual) truth-value gap occurring between the two theories.
Based on the above brief survey, I think it is necessary to draw a distinction between two kinds of truth-valuelessness: the truth-valuelessness due to the failure of M-presuppositions and that due to other factors. I call the former a truth-valuelessness with ontological significance. Since an M-presupposition is an absolute presupposition underlying a substantial number of core sentences of a P-language, when it is suspended by the other competing language, the occurrence of truth-valuelessness is not restricted to a few individual sentences, but rather spreads to the whole language and leads to a massive number of (actual) truth-valueless sentences. Strictly speaking, only in this case can we say that there is a truth-value gap occurring between two P-languages. In contrast, truth-valuelessness is of no ontological significance if it is due to factors other than the rejection of M-presuppositions. Since these factors are usually associated with some isolated individual sentences only, the occurrence of this kind of truth-valueless sentence is restricted to some individual sentences.
The occurrence of a truth-value gap between two competing P-languages PL1 and PL2 due to incompatible M-presuppositions plays a double role in our presuppositional interpretation of the incommensurability relation between them. On the one hand, the occurrence of a truth-value gap between PL1 and PL2 indicates, at the epistemic level, a cross-language communication breakdown between the two language communities. On the other hand, such a gap is caused by, and can be used to indicate semantically, an ontological incompatibility between PL1 and PL2 at the ontological level. Because a truth-value gap between PL1 and PL2 plays such a double role in the emergence of incommensurability, it is more appropriate to use the occurrence of a truth-value gap caused by incompatible M-presuppositions, signified by cross-language communication breakdown, as a touchstone of incommensurability. By definition,
Two P-languages are incommensurable (in a broad sense) when the core sentences of one language, which have truth-values when considered within its own context, lack (either actually or conceptually possible) truth-values when considered within the context of the other. The occurrence of a truth-value gap between the two P-languages indicates that the communication between the two language communities is inevitably partial.
Incommensurability so defined (in a broad sense) admits degrees since there are two kinds of truth-value gaps corresponding to two kinds of communication breakdowns. Specifically, when there is a conceptually possible truth-value gap between two P-languages, which indicates a complete communication breakdown between the two language communities because the speaker of one language cannot recognize and comprehend the M-presuppositions of the other, we say that two P-languages are radically incommensurable. I have argued that complete communication breakdown can be overcome in principle in terms of either language learning or hermeneutic understanding. That means that the radical incommensurability relation between two competing P-languages associated with a complete communication breakdown can be overcome in principle.
However, communication between two disparate P-languages with incompatible M-presuppositions is inevitably partial. When there is an actual truth-value gap between two P-languages, corresponding to a partial communication breakdown between the two language communities due to incompatible M-presuppositions, we say that the two P-languages are moderately incommensurable. Radically incommensurable languages are rare phenomena. Most classical incommensurable scientific languages identified by Kuhn, Feyerabend, and many others are moderately incommensurable. The moderate incommensurability relation between two competing P-languages, associated with a partial communication or a communication breakdown per se, is the incommensurability of real metaphysical significance.
Based on the notion of semantic presupposition (chapter 8), the notions of presuppositional language (chapter 9) and metaphysical presupposition (chapters 10 and 11), a truth-value conditional account of propositional understanding (chapter 12), Gadamer’s notion of hermeneutic understanding (chapter 13), and the transmission model and the dialogue model of cross-language communication (chapters 14, 15, and 16), my presuppositional interpretation of incommensurability is, I believe, semantically sound, epistemologically well-established, and metaphysically profound. The interpretation enables us to explore the genuine nature and sources of incommensurability. By doing this, we establish the integrity and tenability of the notion of incommensurability, and confirm the reality of the phenomenon of incommensurability.
The presuppositional interpretation avoids many difficulties faced by the translation-failure interpretation. The translation-failure interpretation is parasitic on the concepts of meaning, reference, and translation. By sidestepping questions of meaning, reference, and translation, the presuppositional interpretation presumably avoids many intriguing and often unsolvable semantic issues concerning meaning and reference, such as the coherence and tenability of the contextual theory of meaning/reference, which are the theoretical foundation of the translation-failure interpretation. Of the four standard objections to the translation-failure interpretation (chapter 2), there is only one left that needs to be addressed here: In what sense can we say that two languages are rivals or compete with each other if they are semantically so disparate that there can be no meaning-referential continuity between them? The answer to this question is not hard to see from the perspective of presuppositional interpretation. Two P-languages are rivals or compete with one another if their underlying M-presuppositions are incompatible, which is signified by the occurrence of a truth-value gap between them.
Nevertheless, the critic might dismiss the above advantages of the presuppositional interpretation over the translation-failure interpretation by casting doubt on the independence of the former over the latter:
Well, perhaps the presuppositional interpretation does grasp an important aspect of incommensurability, namely, the occurrence of a truth-value gap between two incommensurable languages. But truth-value gaps are exactly what incommensurable languages are supposed to lead to on the translation-failure interpretation. When there is a truth-value gap between two competing languages, truth-preserving translation between them inevitably fails; for there is no way to match up sentences with the same truth-values in two languages respectively. If so, the occurrence of truth-value gaps entails some species of untranslatability. Thus, one cannot help wondering whether the presuppositional interpretation is a real alternative to the translation-failure interpretation.1
If the above argument stands, it is really not necessary to introduce the presuppositional interpretation in the first place, not to mention its advantages over standard interpretation.
However, it is not clear at all how meaning-reference variance between two languages can, in the translation-failure interpretation, lead to a truth-value gap. Clearly, change in the meanings of some constituents of a sentence in itself does not make the sentence truth-valueless. For instance, suppose that, if the contextual theory of meaning was right, the term ‘mass’ in the sentence, ‘The mass of a particle does not change with its velocity’, has different meanings in Newtonian physics and relativity theory. If the sentence sounds truth-valueless when considered within the language of relativity theory, it is not because of change in the meaning of the term, but because a universal principle presupposed by the sentence, namely, that properties like shapes, masses, and periods inhere in objects and change only by direct physical interactions, is suspended by relativity theory.
I have to admit that the critic is right about one direction of the relationship between truth-value gaps and untranslatability. The existence of a truth-value gap does entail some species of untranslatability in the sense of truth-preserving translation. If two languages are incommensurable, there is necessarily a truth-value gap between them based on the presuppositional interpretation. Truth-preserving translation cannot proceed when both sides do not agree on the truth-value status of the sentences of the other language. Hence, incommensurable languages are necessarily untranslatable. This means that the presuppositional interpretation, as one will expect, can do justice to the translation-failure interpretation, which should be considered as one of its advantages. However, it is not valid to move from untranslatability to truth-value gap. Truth-preserving is necessary but not sufficient for truth-preserving translation. Untranslatability does not entail truth-value gap. Therefore, untranslatability will not necessarily, and usually will not, lead to incommensurability since the occurrence of a truth-value gap, in the presuppositional interpretation, is necessary for incommensurability. Furthermore, not all truth-value gaps lead to incommensurability. Only the truth-value gaps with ontological significance do. Therefore, the presuppositional interpretation cannot be reduced to the translation-failure interpretation.
Even if the presuppositional interpretation is distinct from the translation-failure interpretation and overcomes some typical difficulties faced by the latter, the critic may argue, it still faces its own problems. For instance, the interpretation seems to face a dilemma:
The presuppositional interpretation seems to presuppose a common ground between two incommensurable languages: the speaker of one language regards the M-presuppositions of the other incommensurable language as true or false. But two languages have to have a rich enough common language in order for them to agree on the truth-value status of one another’s M-presuppositions (when they disagree on the truth-value status of the sentences). If so, the existence of a sort of common language is inevitable between two incommensurable languages according to the presuppositional interpretation. If the above argument were sound, then the presuppositional interpretation would face a fatal dilemma: On the one hand, two incommensurable languages are supposed to lack a common language between them. On the other hand, the very existence of incommensurability, in the presuppositional interpretation, has to be based on the existence of a common language. Then, in what sense can we say that two languages are incommensurable on a global scale since they share such a common language?2
To respond, let me point out first that incommensurability does not necessarily presuppose shared truth-value status of the M-presuppositions of two P-languages involved. As I have pointed out, incommensurability admits degrees. There are two kinds of incommensurability. When two P-languages are moderately incommensurable, the speaker of one language can understand the other by recognizing its M-presuppositions. But the speaker does not hold them to be true. So the two sets of M-presuppositions are incompatible. In this moderate case, it is true that both sides accept the positive truth-value status of the M-presuppositions of one another’s language. However, when two P-languages are radically incommensurable, the M-presuppositions of one language might be beyond the conceptual reach of the interpreter from the other language such that the interpreter cannot attribute any truth-value status to these M-presuppositions; for one has to understand them first in order to assign truth-value status to them. In this radical case, each side does not accept the positive truth-value status of the M-presuppositions of the other language. We might say, if you like, that the two languages are incommensurable ‘on a global scale’ in the sense that there is no common language whatsoever shared by both languages. Thus, the presuppositional interpretation does allow the possibility of incommensurability ‘on a global scale’. But I have to emphasize again that radical incommensurability, or the incommensurability ‘on a global scale’, is a rare phenomenon and can be overcome in principle.
Return to the case of moderate incommensurability in which the speakers of two P-languages can understand the M-presuppositions of one another’s language but disagree on their truth-values. In this case, there does exist some common ground between the two languages, namely, the shared truth-value status of each other’s M-presuppositions. This conclusion is actually presupposed by the doctrine of universality of understanding that I adopt. In order for the speakers of two different languages to understand one another, there has to be some common ground between them. Otherwise mutual understanding is impossible. This sounds like a tautology. The real issue at stake is whether there exists a rich enough common language, not just any form of common ground, between two incommensurable languages so that both languages can be fully expressed. When Kuhn and Feyerabend contend that there are incommensurable languages, they do not argue against the existence of any form of common ground between them. Instead, what they strive against is the existence of a common language into which both incommensurable languages can be translated without loss and by which to make a point-to-point comparison between their cognitive contents. Even in our moderate case of incommensurability, there does not exist such a common language.
Actually, the existence of a common ground—in our case, shared truth-value status of the M-presuppositions—between two moderately incommensurable P-languages provides a necessary platform for theory comparison as I will address it shortly. Such a common ground should be regarded as a virtue, instead of a flaw, of presuppositional interpretation.
Although the concept of incommensurability has its own merits in the explication of cross-language understanding and communication, the critic might continue, the concept has stirred up many heated debates in the past four decades primarily because of its many alleged undesirable metaphysical and epistemological consequences, especially for rationalistic, realistic-minded philosophers. The thesis of incommensurability allegedly makes rational theory comparison and choice impossible, and accordingly undermines our image of science as a rational, progressive enterprise. Any theory of incommensurability would be incomplete if it did not address the issue of theory comparison, especially if it did not render rational theory comparison possible. In this respect, the presuppositional interpretation seems to fare no better than the standard one. If there is no common language between two competing P-languages, especially if there is no truth-functional connection between two languages, how can rational theory comparison and choice be possible?
Before I clarify the position of the presuppositional interpretation of theory comparison, I have to dismiss one quite influential misunderstanding of the relation between incommensurability and theory comparison. It is commonly held that rational comparison between two theories is possible only if the statements made in each theory respectively stand in a strict logical relationship—such as logical incompatibility, inconsistency, contradiction, or logical consequence—which in turn requires that the meaning/reference-related contents of those statements overlap to some extent. According to the alleged standard argument for incommensurability based on the contextual theory of meaning/reference, no statement made in one theory is in a logical relation to any statement made in the other incommensurable one. This is because the proponents of two incommensurable theories, such as the wave and the particle theories of light, mean distinct concepts and refer to different entities by the same term, in this case ‘light’. As a result, the apparently contradictory statements made in the two incommensurable theories respectively are in fact not contradictory. In other words, the incommensurable theories are not in logical conflict. In addition, since the contents of incommensurable theories are formulated in different, untranslatable languages without shared meanings and references, the cognitive contents of one theory cannot be expressed in the other. Thus their contents do not overlap. Now, in the absence of content overlap and a genuine logical relationship between two incommensurable theories, it is unclear how theory choice between them could be made on a rational ground. For this reason, many insist that incommensurability amounts to or can be reduced to incomparability, since the latter is a logical consequence of the translation-failure interpretation of incommensurability.3 The thesis that theories are incommensurable turns out to be the thesis that theories may be rationally incomparable due to meaning and/or reference variance of the theoretical terms contained. This is actually another influential interpretation of incommensurability, i.e., incommensurability as incomparability due to meaning/reference variance.
Whether the incommensurables are rationally comparable has been a central issue related to incommensurability and the most controversial aspect of the thesis of incommensurability. In fact, the most persistent attacks on the thesis of incommensurability have come from those who either equate incommensurability with or reduce it to incomparability. The thesis of incommensurability so construed has been attacked both ‘directly’ and ‘indirectly’. Many argue that the thesis could not be true since it directly contradicts our intuitive idea of science as a rational enterprise. By reductio ad absurdum, the thesis has to be rejected due to its absurd consequence, i.e., incomparability. Direct criticism, on the other hand, confronts the thesis head-on, trying to prove that the thesis is simply false since theories are rationally comparable in many effective ways.
It is well known that Kuhn and Feyerabend repeatedly denied the interpretation of incommensurability as incomparability.4 I agree with Kuhn and Feyerabend on this. The notion of comparability itself is ill-defined and ambiguous. The term ‘rational comparison’ could mean totally different concepts. We can at least distinguish the following three senses of ‘rational comparison’ in the literature, (a) Systematic, point-by-point comparison: This is the strictest sense of rational comparison, which is possible only if there is an exact translation available between the languages of two theories to be compared (systematically identical mapping between meanings and references of the terms used by the two theories).5 (b) Meaning/reference-related content comparison: Theory comparison means to compare meaning/reference-related contents—such as cognitive or empirical contents—of two theories, for instance, consequence classes, empirical predictions, observational evidences, truthfulness or truthlikeness, or any other such considerations relating to meaning/reference-contents. This kind of comparison is possible only if there is enough meaning/reference overlap or continuity between the terms of two theories, (c) Pragmatic comparison: Comparison between two theories can be carried out by appealing to other non-semantic aspects of the theories, such as cognitive norms or values, methodological considerations, pragmatic efficiency, etc.
As Kuhn and Feyerabend point out repeatedly, the thesis of incommensurability as untranslatability does not amount to or cannot be reduced to incomparability in general. There are many effective ways to make rational comparison between two incommensurable theories. Not only is pragmatic comparison feasible between two incommensurable theories, but also are some types of content comparison.6 What Kuhn and Feyerabend deny is point-by-point comparison between the incommensurables and some content comparison that depends upon the invariance of meaning and/or reference. Therefore, incommensurability, in the translation-failure interpretation, does not amount to or cannot be reduced to rational incomparability in general. It at most leads to some kinds of incomparability, such as the impossibility of point-by-point comparison.
Therefore, incommensurability and incomparability are two separate issues; the latter is not a necessary ingredient of the former. Incomparability has nothing whatsoever to do with the nature of incommensurability. It is at most an epistemological consequence (not a logical consequence) of incommensurability, not the very definition of it. For me, it is an open question whether two incommensurable theories are rationally comparable. It is open because the answer depends upon many related notions, such as the concept of incommensurability, the concept and standards of rational comparison, the concept of semantic relation between theories, and even the notion of theory.7 It is my intention to leave it open whether two incommensurable theories, in the presuppositional interpretation, are rationally comparable.
It is obvious that rational comparison between the incommensurables differs from and is more problematic than that between the commensurables. Classical point-by-point comparison, which requires the existence of a common language into which both languages to be compared can be translated without loss, has to be given up in the case of incommensurability. Similarly, classical content-comparison based on the sameness of meaning/reference cannot be carried out between two incommensurable theories. Unfortunately, the critic quickly jumps from this observation to the conclusion that the thesis of incommensurability not only makes classical rational comparison problematic, but also makes rational comparison in general impossible.
Notice that the question of concern here is the possibility, not the feasibility, of rational comparison. In fact, to say that two theories are rationally comparable is to say that it is possible to make a rational comparison between them. So what we want to know is whether rational comparison between the incommensurables is possible. If it is not, then the thesis of incommensurability, no matter how it is interpreted, indeed threatens to undermine our image of science as a rational enterprise.
Furthermore, as I have shown above, the debate over the issue of comparability does not concern whether rational comparison in general between the incommensurables is possible, but rather concerns what kind of rational comparison is possible. Especially, the controversy arises regarding whether semantic comparison between two incommensurable theories is possible. By semantic comparison, I mean the rational comparison between semantic contents of the theories involved. Both point-by-point comparison and content comparison are two classical types of semantic comparison. But the concept of semantic comparison I adopt here is broader than these two. The semantic contents to be compared in semantic comparison not only include meaning/reference-related contents at the theoretical level, such as consequence classes, empirical predictions, observational evidences, truthfulness or truthlikeness, but also include semantic-presupposition-related content at the meta-theoretical level as I will clarify shortly. Value-related contents, such as cognitive norms or values, methodological considerations (simplicity, coherence, etc.), or pragmatic efficiency (problem-solving ability, predictability, etc.), are dealt with in pragmatic comparison, not in semantic comparison. So we might divide rational comparison into two subcategories, semantic comparison versus pragmatic comparison.
Now it should become clear that the question of comparability related to the thesis of incommensurability is a Kantian one. It is a question of ‘possibility’: Is semantic comparison between the incommensurables possible? It is not the question of ‘how to’: How to make a rational comparison between two incommensurable theories?
Semantic comparison is in principle possible if there is a certain semantic . relationship, whatever it is, holding between the languages of two theories to be compared. There is nothing in principle that prevents pooling together all the potential semantic resources of two competing theories, no matter how disparate they are, so as to bring them into some semantic relation. Therefore it is my conviction that semantic comparison is always possible between any two competing theories. Otherwise, it does not even make sense to say that they are competing with one another if they do not stand in any semantic relation with one another whatsoever. That means that some semantic comparison between the incommensurables should be in principle possible. The real trouble for semantic comparison between the incommensurables is that the languages of two incommensurable theories may be related to one another semantically in such a hidden way at a meta-language level which is normally ignored. In this case, whether two incommensurable languages can be semantically connected depends on how to locate such a crucial semantic connection between the incommensurable P-languages.
To confirm the above intuition, we need to specify a certain kind of semantic relationship needed for semantic comparison between competing theories. Presumably, semantic incompatibility is such a semantic relation we need. If two theories are semantically incompatible, then we can identify a situation or a possible world in which they cannot both be true. In such a case, it is possible to make a rational comparison about their relative merits based on some commonly accepted criteria of comparison. Thus, two theories are semantically comparable if the languages of the theories are semantically incompatible. Now our task is to identify a semantic incompatibility relationship between two incommensurables.
There are at least two types of semantic incompatibility of concern here. One is what I will call truth-theoretical incompatibility; the other is what I will call presuppositional incompatibility. Truth-theoretical incompatibility includes logical and quasi-logical incompatibility. Logical incompatibility is a strict logical relation defined as follows:
Suppose: (a) Two theories T1 and T2 have predicates F1 and F2. (b) Terms a1 and a2 are in the core paradigmatic part of T1 and T2, respectively, (c) There exist some theory of meaning M and theory of reference R shared by both T1 and T2 so that Meaning (F1) = Meaning (F2), Reference (F1) = Reference (F2), Meaning (a1) = Meaning (a2), Reference (a1 = Reference (a2). If {T1, T2, M, R} ├¬[True(F1(a1)) ∧ True(F2(a2))], then T1 and T2 are logically incompatible.
I will call the semantic comparison based on logical incompatibility defined above logical comparison, which is actually the counterpart of point-by-point comparison. Clearly, logical incompatibility requires sameness of meaning and reference. According to the translation-failure interpretation, logical comparison between two incommensurable theories is impossible due to variance of meaning and reference.
In contrast, quasi-logical compatibility allows difference of meanings as long as there is a partial overlap of reference. By definition:
Suppose: (a) Two theories T1 and T2 have predicates F1 and F2. (b) Terms a1 and a2 are in the core paradigmatic part of T1 and T2, respectively, (c) [Overlapping-reference hypothesis H]: The referents of F1, F2, a1, and a2 overlap somehow according to an available theory of reference R: Reference (F1) ∩ Reference (F2) ≠ Ø, Reference (a1) ∩ Reference (a2) ≠ Ø. If {T1, T2, R, H} ├ ¬[True(F1(a1)) ∧ True(F2(a2))], then T1 and T2 are quasi-logically incompatible.
The critics of Kuhn and Feyerabend who take the referential alternative to the semantic values of scientific terms contend that sameness of meaning and reference is not required for semantic comparison. Semantic comparison between two incommensurable theories is possible as long as they are quasi-logically incompatible. Since such a relation only requires overlap of reference, not sameness of meaning and reference, the semantic comparison between incommensurables is possible.
However, according to my presuppositional interpretation, semantic comparison based on quasi-logical incompatibility, which I will call quasi-logical comparison, between the incommensurables is also impossible. One reason is that, as I have argued in chapter 2, the critic is unsuccessful in providing us with the referential continuity required by quasi-logical incompatibility. Another reason is more significant. I find that both logical incompatibility and quasi-logical incompatibility exclusively focus on the meaning-referential relationship between theories. They are intended to be used to represent the confrontation of truth-values of the statements of two incommensurable theories. This in turn presupposes that the same truth-value status can cross the boundary of two incommensurable P-languages employed by the theories. Then, we can reduce both logical and quasi-logical incompatibility to a broader framework, namely, truth-theoretical incompatibility:
Suppose (a) two theories T1 and T2 and their languages L(T1) and L(T2), (b) a metalanguage M ∩ {L(T1) ∧ L(T2)}, (c) a truth theory TR formulated in M, and (d) core sentences S1 and S2, S1 ∈ L(T1) and S2 ∈ L(T2). T1 and T2 are truth-theoretically incompatible if {T1, T2, L(T1), L(T2), M, TR} ├ ¬ [True(S1) ∧ True(S2)].
The concept of truth-theoretical incompatibility assumes that a sufficient neutral metalanguage can be found to establish a unitary truth theory accepted by both theories. We can identify a confrontation on truth-values since truth-value status is preserved across the theories. But this assumption cannot be held in the case of incommensurability based on the presuppositional interpretation. I have argued that there is a truth-value gap between the languages of two incommensurable theories. Therefore, we simply cannot compare the truth-values of the core sentences in two incommensurable languages since they differ on truth-value status. We cannot identify the confrontation of truth-values between core sentences of two incommensurable theories. Consequently, the truth-theoretical incompatibility relation is not available between them. That means that the semantic comparison based on truth-theoretical incompatibility, which I will call truth-theoretical comparison, is impossible.
One obvious objection to the presuppositional interpretation emerges immediately: ‘Your presuppositional interpretation actually brings more damage to the image of science as a rational enterprise than the translation-failure interpretation does. Based on the translation-failure interpretation, the semantic comparison between the incommensurables is still possible as long as a quasi-logical incompatibility relationship between them remains. But in the presuppositional interpretation, even quasi-logical incompatibility between the incommensurables is excluded a priori. Then the presuppositional interpretation implies that semantic comparison is impossible between the incommensurables. It is more radical than the traditional interpretation.’
The critic here is too hurried to jump from the impossibility of truth-theoretical incompatibility to the impossibility of semantic incompatibility between the incommensurables. Truth-theoretical incompatibility is neither the only nor the most interesting aspect in which two competing theories can be incompatible. I have argued that it is the truth-value functional relation between competing theories, instead of the meaning-referential relation, that constitutes the dominant semantic relation between two incommensurable theories. The disagreement between two incommensurable theories is not in what counts as truth, but rather in what counts as truth-or-falsity. This is in turn determined by the M-presuppositions underlying each theory. When the M-presuppositions of two competing theories are incompatible, the two theories are incommensurable. The incompatibility between the M-presuppositions of two incommensurable theories is the fundamental semantic incompatibility needed for semantic comparison. By definition:
Suppose (a) two theories T1 and T2 and their languages L(T1) and L(T2), (b) two built-in truth theories TR1 and TR2 for L(T1) and L(T2), respectively, and (c) the M-presuppositions MP1 and MP2 underlying L(T1) and L(T2), respectively. T1 and T2 are presuppositionally incompatible if {T1, T2, L(T1), L(T2), TR1, TR2} ├ ¬ [True(MP1) ∧ True(MP2)].
The subscript ‘L’ indicates that both MP1 and MP2 are considered within the context of one language, either L(T1) or L(T2). We have identified many presuppositionally incompatible scientific languages before. I will not belabor them here.
Since the presuppositional incompatibility relation exists between two incommensurable theories, semantic comparison based on it is possible. I will call such comparison presuppositional comparison. The virtues of presuppositional comparison are obvious. Compared with much stronger requirements of logical or quasi-logical comparison, presuppositional comparison asks much less. It does not require that there exist a neutral language into which both theories can be translated without loss; it does not require that there exist a unitary truth theory accepted by both languages; it does not require sameness or overlap of meaning or reference. Actually, it sidesteps many problems caused by meaning, reference, and translation. As long as we can show that the M-presuppositions of two incommensurable theories, when considered within the context of one theory, cannot both be held to be true, we know that they are semantically incompatible, which makes semantic comparison between the two theories possible. Unlike truth-theoretical comparison which focuses on the contents of corresponding statements of two incommensurable theories, presuppositional comparison starts from the bottom up, namely, to compare and evaluate the incompatible M-presuppositions of two incommensurable theories at the meta-theoretical level. The most effective way of pooling together two incommensurable theories is to bridge the ontological gap caused by incompatible M-presuppositions. Presuppositional comparison provides a promising way to do this.
1 Both Ruth Millikan and Austen Clark pointed out this potential connection between the two interpretations.
2 This potential dilemma was pointed out by Samuel Wheeler III.
3 I. Scheffler, 1967, pp. 81-6; C. Kordig, 1971, pp. 22, 52; L. Laudan, 1977, pp. 139-42; 1990, pp. 121-3; M. Devitt, 1979, p. 29; W. Newton-Smith, 1981, p. 148; D. Shapere, 1984, pp. 66, 83; D. Pearce, 1987, p. 3.
4 Kuhn, 1976, pp. 191, 198; 1970b, pp. 234, 266; 1983b, p. 671; 1977a, pp. 320-39. Feyerabend, 1970, 1977.
5 For a clear illustration of one-by-one comparison, please refer to W. Balzer, 1989.
6 Feyerabend, in his 1965a, lists a few ways to make content comparison.
7 According to W. Stegmuller’s (1979) structuralist interpretation of incommensurability, a pair of incommensurable theories may be semantically incomparable if they are viewed as classes of sentences or statements, since they are not logically related so construed in the case of incommensurability. However, when those theories are construed as structure of a certain sort, not as statements, they are semantically comparable since the structures of two incommensurable theories can be canonically related where statements cannot.