Conceptual Relativity and Metaphysical Realism
Terry Horgan and Mark Timmons
Is conceptual relativity a genuine phenomenon? If so, how is it properly understood? And if it does occur, does it undermine metaphysical realism? These are the questions we propose to address. We will argue that conceptual relativity is indeed a genuine phenomenon, albeit an extremely puzzling one. We will offer an account of it. And we will argue that it is entirely compatible with metaphysical realism.
Metaphysical realism is the view that there is a world of objects and properties that is independent of our thought and discourse (including our schemes of concepts) about such a world. Hilary Putnam, a former proponent of metaphysical realism, later gave it up largely because of the alleged phenomenon that he himself has given the label ‘conceptual relativity’. One of the key ideas of conceptual relativity is that certain concepts—including such fundamental concepts as object, entity, and existence—have a multiplicity of different and incompatible uses (Putnam 1987, p. 19; 1988, pp. 110-14). According to Putnam, once we recognize the phenomenon of conceptual relativity we must reject metaphysical realism:
The suggestion . . . is that what is (by commonsense standards) the same situation can be described in many different ways, depending on how we use the words. The situation does not itself legislate how words like “object,” “entity,” and “exist” must be used. What is wrong with the notion of objects existing “independently” of conceptual schemes is that there are no standards for the use of even the logical notions apart from conceptual choices.” (Putnam 1988, p. 114)
Putnam’s intriguing reasoning in this passage is difficult to evaluate directly, because conceptual relativity is philosophically perplexing and in general is not well understood. In this paper we propose a construal of conceptual relativity that clarifies it considerably and explains how it is possible despite its initial air of paradox. We then draw upon this construal to explain why, contrary to Putnam and others, conceptual relativity does not conflict with metaphysical realism, but in fact comports well with it. Our paper has two main parts.
In part I we dwell on the phenomenon itself. We explain why conceptual relativity is so puzzling—indeed, why it initially appears impossible. We identify three interrelated assumptions lying behind this apparent impossibility—assumptions about concepts, meanings, and affirmatory conflict—and we argue that in order to make sense of conceptual relativity, all three must be rejected. We then set forth an account of relativity-susceptible concepts and meanings that explains how conceptual relativity is possible and why it is actual—an account that eschews the three problematic assumptions.
In part II, we turn to the issue of the compatibility of conceptual relativity and metaphysical realism. Our main task here is to explain how the two can be reconciled. In doing so, we sketch a general account of truth that in previous writings we have called “contextual semantics.” We argue that the framework provided by contextual semantics smoothly accommodates the phenomenon of conceptual relativity (as explicated in part I), while at the same time allowing this kind of relativity to be combined with metaphysical realism.
I. UNDERSTANDING CONCEPTUAL RELATIVITY
1. Why conceptual relativity seems impossible
Putnam uses the expression ‘conceptual relativity’ for a property of intentional notions including truth, reference, and meaning. He says that conceptual relativity “is a property which has only emerged as central in the twentieth century, and its very existence is still most often ignored, if not actually denied” (Putnam 1988, p 110). In fact, there is an air of paradox surrounding the various illustrations of this alleged phenomenon. Consider, for instance, one of Putnam’s illustrations of conceptual relativity—the well-known example of Carnap and the Polish logician (Putnam 1987, pp. 18-20).
In this scenario (slightly modified), Carnap and the Polish logician are presented with a number of objects (say, books lying on a table) and each of them is asked how many objects there are on the table. Carnap, employing the ordinary concept of object, reports that there are exactly three objects on the table: O1, O2, and O3. By contrast the Polish logician, who accepts a particular mereology of objects according to which for every two particulars there is an object that is their “mereological sum,” counts the objects on the table and reports that there are exactly seven: O1, O2, O3, O1+O2, O1+O3, O2+O3, and O1+O2+O3.
This case seems to be one in which we have conflicting but equally correct judgments about the number of objects on the table. We might express this combination of ideas in terms of two principles:
Principle of affimatory conflict. There is a genuine conflict in what Carnap and the Polish logician are respectively affirming about how many objects there are: Carnap’s claim that there are exactly three objects on the table conflicts with the Polish logician’s claim that there are exactly seven.
Principle of mutual correctness. Both Carnap and the Polish logician are correct in their respective claims about how many objects there are on the table, because each of them is making a claim which, relative to a specific way of using the concept of object, is true.
It seems to us that Putnam is pointing to a genuine, and important, phenomenon. In a significant sense, Carnap’s way of counting objects and the Polish logician’s way are in conflict; they are not just talking past one another. And yet, given the principles for counting that they each are employing, they are both making claims that are correct.
But although the phenomenon in question seems real, on reflection it is also quite puzzling because, initially anyway, these principles appear to be mutually incompatible. Here are two complementary arguments that make the point.
The argument from affirmatory conflict. According to the first principle, there is a genuine conflict between the claims of Carnap and the Polish logician about how many objects there are. Now in order for there to be genuine conflict in this case, Carnap and the Polish logician must be employing the same concept of object and using the associated term with the same meaning. Otherwise, there is no genuine conflict between their respective claims; they are just talking past one another. But if they are employing the same concept of object and so using the term ‘object’ with the same meaning, then their conflict must consist in the mutual inconsistency of their respective claims about how many objects are on the table. But if the two claims are inconsistent, then they cannot both be correct! And this means that the other key ingredient in the phenomenon of conceptual relativity—the principle of mutual correctness—is false. In this way, reflection on one side of the phenomenon of conceptual relativity leads to the denial of the other.
The argument from mutual correctness. We get a similar result if we begin with the principle of mutual correctness, according to which Carnap and the Polish logician, given their uses of the concept of object, are both correct in their respective claims about the number of objects on the table. If each of their claims is correct, then those claims cannot be inconsistent with one another. Furthermore, if the respective claims are not mutually inconsistent—if, that is, when Carnap says there are exactly three objects on the table his claim does not contradict the Polish logician’s claim that there are exactly seven—then they must be employing different concepts of object and using the term ‘object’ with different meanings. But if they are employing different concepts of object and using the term ‘object’ with different meanings, then their claims are really not in conflict after all! Thus, if Carnap and the Polish logician are both correct in their respective claims, then they are just talking past one another—contrary to the principle of affirmatory conflict. Again, reflection on one of the key ingredients involved in conceptual relativity (this time the principle of mutual correctness) leads, by a series of seemingly plausible steps, to the denial of the other ingredient.
Thus, we arrive at the apparent conclusion that conceptual relativity, understood as involving the two principles in question, is impossible.
2. Questionable assumptions
As we have said, we do think that conceptual relativity is a genuine phenomenon, and thus should be accounted for. Also, the phenomenon does indeed involve the features described by the principles of affirmatory conflict and mutual correctness. So something must be wrong with the reasoning that leads to the rejection of this phenomenon. When confronted with a philosophical puzzle of this sort, the thing to do is to look for one or more underlying assumptions—ones that, while perhaps common and initially plausible, should be challenged. What are they?
In connection with the identity of concepts and meanings, there is a pair of related assumptions that we question. Both involve semantic standards that govern the correct employment of concepts and words—that is, standards that determine the conditions under which statements employing the words, and judgments employing the concepts those words express, are true. Regarding concepts, the assumption involved is this:
I1 If the semantic standards governing the correct employment of concept C1, as employed by person P1 at time t1, differ from the semantic standards governing the correct employment of concept C2, as employed by person P2 at time t2, then C1 ¹ C2.
That is, any difference between two persons with respect to the semantic standards governing their respective usage of certain concepts is sufficient to make it the case that they thereby are employing non-identical concepts. (Likewise for one person’s usage at two different times.) Here is a parallel assumption, with respect to words and their meanings:
I2 If the semantic standards for the correct employment of word W, as it is used by person P1 at time t1, differ from the semantic standards for the correct employment of W, as it is used by person P2 at time t2, then the meaning of W as used by P1 at t1 ¹ the meaning of W as used by P2 at t2.
That is, any difference between two persons with respect to the semantic standards governing their respective usage of a certain word is sufficient to make it the case they thereby are employing that word with non-identical meanings. (Likewise for one person’s usage at two different times.) We dub the view of concepts and meanings captured by I1 and I2 the invariantist view. The idea is that the semantic standards that govern concepts and words cannot vary from one usage to another, insofar as the same concept of word-meaning is employed in both usages: any difference in governing semantic standards reflects a distinct concept or word-meaning. Concepts and word-meanings never preserve their self-identity under changes of the semantic standards that govern them.
But, in addition to these assumptions, the pair of arguments challenging conceptual relativity rests on a certain conception of genuine affirmatory conflict, namely:
DI All cases of genuine affirmatory conflict—cases in which what person P1 affirms at time t1 conflicts with what person P2 affirms at time t2—involve straightforward inconsistency between what P1 and P2 are thinking or saying.
Call this the direct-inconsistency conception of affirmatory conflict.
If indeed conceptual relativity is a genuine phenomenon—as we contend it is—then these various assumptions will have to be rejected. In order to make sense of conceptual relativity, one needs to explain how the members of the following list of ideas can be mutually compatible:
1. Persons P1 and P2 are making conflicting claims. [Principle of affimatory conflict]
2. So they must be employing the same concept of object and using the term ‘object’ with the same meaning.
3. But they are also making claims that are mutually correct. [Principle of mutual correctness]
4. So their claims cannot be flatly inconsistent.
The gist of the puzzle is to explain how all four of these claims can be correct. Doing so should also thereby explain why and how it is that although Carnap’s statement and the Polish logician’s statement do indeed conflict semantically, nevertheless this conflict between them is not a theoretically weighty one, but rather is “no big deal”—as they themselves might well both acknowledge.
Executing this explanatory project requires accomplishing three interrelated tasks. First, we must replace the invariantist view of concepts and meanings with what we will call a variantist conception. The key idea is that the semantic standards that govern certain concepts can vary from one usage to another even though the same concept is employed on both occasions—and even though the word expressing it has the same meaning on both occasions. Such semantic differences in correct usage are identity-preserving differences in concepts and meanings. The task is to explain why and how it is that some concepts and meanings actually do conform to this variantist conception.
Second, we must harness the account of identity-preserving semantic differences in order to explain the principle of mutual correctness. The task is to explain why it is that Carnap and the Polish logician, despite the fact that they are employing a single concept of object and using the term ‘object’ with a single meaning, are both correct in their respective claims about how many objects are on the table.
Third, we also must harness the account of identity-preserving semantic differences to explain the principle of affirmatory conflict. The task is to explain why it is that the respective claims of Carnap and the Polish logician, despite the fact that they are both correct, nevertheless do conflict with one another in some fairly robust way. Such an explanation must repudiate the third assumption identified above—the direct-inconsistency conception of affirmatory conflict—and must replace it with an alternative conception. This alternative must identify a tension-relation R that obtains between Carnap’s claim and the Polish logician’s claim, and that exhibits these two features: (i) R is compatible with the mutual correctness of the two claims, and yet (ii) R still has enough bite, qua tension-relation, to count as a genuine form of affirmatory conflict (albeit conflict that is, in an important sense, “no big deal”).
Accomplishing all three tasks will provide an explanation of how items 1-4 can all be true, and thus how conceptual relativity is possible. Let us now proceed to the first task.
3. The variantist view of concepts and meanings
Entities of various sorts certainly can change in some ways—can alter through time—without thereby losing their identity. Persons, for instance, change as they grow older, and yet they retain their self-identity all the while. They undergo identity-preserving changes, and the differences between a person at one moment in time and that same person at another moment of time are identity-preserving differences.
The claim we want to make, by way of rejecting the invariantist view as expressed in theses I1 and I2, is this: whatever exactly concepts and meanings are, they are subject to certain kinds of identity-preserving differences in correct usage. One and the same concept can be used by two persons (or by one person, at different times) in ways that are governed by somewhat different semantic standards, while still being the same concept. Likewise, one and the same word can be used in two ways involving somewhat different semantic standards, while still possessing the same meaning under both uses. A concept or word as used by one person can differ somewhat in its semantically proper employment from its proper employment as used by another person (or by the same person at a different time), and yet it is the same concept or word anyway: the differences are identity-preserving. Adapting a useful philosophical term from Derrida, we will say that an identity-preserving difference in two uses of a given concept, or in the meaning of a given word, is a diffèrance in concepts (or in meaning).
Let us consider some examples. Putnam himself has noted the diachronic version of the phenomenon we are calling diffèrance in concepts and meaning—although he does not call it by this name, and he does not link it directly to conceptual relativity (as we will do presently). One of his examples features the concept of momentum in physics:
In Newtonian physics the term momentum was defined as “mass times velocity.” (Imagine, if you like, that the term was originally equated with this definens by the decision of a convention of Newtonian physicists.) It quickly became apparent that momentum was a conserved quantity.... But with the acceptance of Einstein’s Special Theory of Relativity a difficulty appeared. Einstein...showed that the principle of Special Relativity would be violated if momentum were exactly equal to (rest) mass times velocity. What to do?... Can there be a quantity with the properties that (1) it is conserved in elastic collisions, (2) it is closer and closer to “mass times velocity” as the speed becomes small, and (3) its direction is the direction of motion of the particle? Einstein showed that there is such a quantity, and he (and everyone else) concluded that that quantity is what momentum is. The statement that momentum is exactly equal to mass times velocity was revised. But this is the statement that was originally a “definition”! And it was reasonable to revise this statement; for why should the statement that momentum is conserved not have at least as great a right to be preserved as the statement “momentum is mass times velocity” when a conflict is discovered?... When the statements in our network of belief have to be modified, we have “trade-offs” to make; and what the best trade-off is in a given context cannot be determined by consulting the traditional “definitions” of terms. (Putnam 1988, pp. 9-10).
According to Putnam, then, the term ‘momentum’ and its associated concept has undergone, over time, an identity-preserving change. In this example and others like it, the meaning of at least some terms, and the nature of their associated concepts, depends to some extent upon a certain network of background beliefs; when those change sufficiently, the concept and meaning change in certain ways. But the difference between the concept and meaning at an earlier stage, and the concept and meaning at a later stage, is an identity-preserving difference—a diffèrance. As Putnam remarks about this phenomenon:
If this seems strange, it is because we are not used to thinking of meanings as being historic entities in the sense in which persons or nations are historic entities.... There are practices which help us decide when there is enough continuity through change to justify saying that the same person still exists. In the same way, we treat “momentum” as referring to the same quantity that it always referred to, and there are practices which help us decide that there is enough continuity through change to justify doing this. Meanings have an identity through time but no essence. (Putnam 1988, p. 11)
Turn next to synchronic cases of diffèrance (which will be particularly important for purposes of understanding conceptual relativity). Here a given concept, and the meaning of a term expressing the concept, both have a certain structural feature: viz., possessing one or more implicit semantic aspects or dimensions that are subject to contextual variation across different uses of the term or concept. We will call such an aspect a contextually variable parameter; it is what David Lewis (1979/1983) called a component of the “score in the language game.” Consider, for example, competing uses of the term ‘flat’, with respect (e.g.) to whether or not a particular sidewalk is flat. Lewis has this to say, concerning Peter Unger’s views about flatness:
Peter Unger has argued that hardly anything is flat. Take something you claim is flat; he will find something else and get you to agree that it is even flatter. You think that the pavement is flat—but how can you deny that your desk is flatter? But flat is an absolute term: it is inconsistent to say that something is flatter than something that is flat. Having agreed that your desk is flatter than the pavement, you must concede that the pavement is not flat after all. Perhaps you now claim that your desk is flat; but doubtless Unger can think of something that you will agree is even flatter than your desk. And so it goes. Some might dispute Unger’s premise that “flat” is an absolute term, but...I think he is right.... The right response to Unger, I suggest, is that he is changing the score on you. When he says that the desk is flatter than the pavement, what he says is acceptable only under raised standards of precision. Under the original standards the bumps on the pavement were too small to be relevant either to the question whether the pavement is flat or to the question whether the pavement is flatter than the desk. (Lewis 1983, pp. 245-6)
We claim, with Lewis, that the semantically correct use of the notion of flatness depends upon certain implicit, contextually operative, standards of precision—standards that can permissibly vary somewhat from one usage to another. The standards of precision that govern a particular use constitute the specific current setting of what may be called the precision parameter for flatness. As the passage from Lewis makes clear, this parameter is contextually variable: it can take on different specific settings in particular contexts. This contextual variability is semantically built into the single concept flatness, and into the meaning of the term ‘flat’. What you mean when you use ‘flat’ in such a way that the sidewalk counts as flat is somewhat different from what Unger means when he uses ‘flat’ in such a way that it doesn’t; likewise, mutatis mutandis, for the nature of the concept of flatness as employed by you, as distinct from its nature as employed by Unger. But these differences in meaning, and in concept, are identity-preserving differences. There is a diffèrance in meaning, and in concept, between yourself and Unger.
In light of these observations we propose to replace the invariantist view of concepts and meanings with what we will call the variantist conception, which recognizes the phenomenon of identity-preserving differences. Thus, we replace I1 with:
V1 The semantic standards for the correct employment of C1, as C1 is employed by person P1 at time t1, may differ in certain permissible ways from the semantic standards for the correct employment of concept C2, as C2 is employed by person P2 at time t2, while C1 = C2. When this occurs we have diffèrance in concepts.
And a similar principle about the meanings of words replaces I2:
V2 The semantic standards for the correct employment of word W, as it is used by person P1 at time t1, may differ in certain permissible ways from the semantic standards for the correct employment of W, as it is used by person P2 at time t2, and yet the meaning of P1’s word W = the meaning of P2’s word W. When this occurs we have a diffèrance in meanings.
Two potential sources of diffèrance in concepts and meanings have been mentioned in this section. One source, manifested in diachronic cases of diffèrance like Putnam’s example of momentum, is the fact that the synchronic nature of a concept or a word-meaning at a particular moment in history depends partly upon certain background beliefs prevalent at that time; concepts and meanings can change through time, when the pertinent background beliefs change in certain ways. A second source of diffèrance, which can be manifested synchronically in cases like competing uses of the term ‘flat’, is the fact that such terms, and the concepts they express, are semantically governed by implicit, contextually variable, parameters. This second form of diffèrance, we will suggest, is at the heart of conceptual relativity.
4. Mutual correctness
The next task we face is to harness the synchronic form of diffèrance in order to explain the mutual-correctness aspect of conceptual relativity. Return to the case of Carnap and the Polish logician. Our suggestion is that the concept of object bears a structural similarity to concepts like flat; and likewise for the meanings of the respective terms expressing these concepts. That is, the concept of object is semantically governed by an implicit, contextually variable, parameter—in this case a parameter that affects matters of counting and mereology. We will call it the mereology parameter. The idea is that on different occasions of use the setting of this mereology parameter may vary. In the case at hand, Carnap employs the concept of object in a way that is semantically governed by one particular setting of the mereology parameter, while the Polish logician employs the same concept in a way that is semantically governed by another, somewhat different, setting of the same mereology parameter. Given the mereological parameter-setting that governs Carnap’s usage, he correctly judges that there are exactly three objects on the table. Given the different mereological parameter-setting that governs the Polish logician’s usage, she correctly judges that there are exactly seven objects on the table. Each is right, as each respectively is employing the concept of object. Although the concept as employed by Carnap does differ from the concept as employed by the Polish logician (since the mereology parameter has different settings in the two cases), it is the same concept nonetheless; likewise, mutatis mutandis, for the meaning of the term ‘object’ as employed by Carnap and by the Polish logician respectively. We have here a diffèrance in concept and in meaning—that is, an identity-preserving difference.
5. Why content should not be relativized
So far we have completed two of the three tasks that need to be accomplished in order to explain conceptual relativity: articulating a variantist conception of concepts and meanings, and harnessing it to explain the principle of mutual correctness. The third task remains: to develop an account of affirmatory conflict that avoids the idea that all such conflict involves direct inconsistency, and yet identifies a form of semantic tension that is robust enough to deserve the label ‘conflict’ anyway. In order to see more clearly what must be done in order to accomplish this third task, let us now consider a tempting but mistaken way of elaborating our variantist treatment of relativity-susceptible concepts and terms. This approach will run afoul of the principle of affirmatory conflict. Seeing why a given path leads to a dead end can help reveal the right path.
Consider what we call the relativized content view of relativity-susceptible concepts and terms. As applied to the example of Carnap and the Polish logician, it involves three main ingredients. First, it embraces the variantist idea that Carnap and the Polish logician are using the same concept of object—one that allows for a diffèrance in their respective uses of that concept. Second, it also embraces the contention that the source of this diffèrance is the fact that the concept of object is semantically governed, in various different contexts, by specific settings of a contextually variable mereology parameter. Both of these ingredients are taken from the account we ourselves offered above. But now comes a third ingredient: viz., the contention that both Carnap and the Polish logician are making claims whose full content is more than what is explicitly expressed by their words, and is really an implicit relativity claim—a claim to the effect that the explicit content obtains relative to a specific setting of the mereology parameter. If one were to spell it out, making such implicit aspects of content explicit, Carnap would be saying: There are exactly three objects on the table, relative to such and such mereological principles for ‘object’, while the Polish logician would be saying: There are exactly seven objects on the table, relative to so and so mereological principles for ‘object’.
The problem, of course, is this: relativizing content in this way is obviously at odds with the phenomenon of conceptual relativity because the statements being expressed, even if they are both correct, do not involve genuine affirmatory conflict at all. Intuitively, this problem is something like a use/mention conflation. What is actually going on in the Carnap-Polish logician example is that each of these parties is using a certain conceptual scheme, a certain way of “carving” the world into objects. But according to the relativized-content view, in effect what each is doing is mentioning (implicitly) a certain way of carving, and then asserting that there are thus-and-such many objects relative to that way of carving. Both of these relativity claims are correct, all right, but they do not really conflict in any interesting way at all. Instead, their apparent conflict is entirely a surface phenomenon, one that dissolves entirely when one makes explicit the full content of the two respective relativity claims. Indeed, once the content of the respective relativity claims is made explicit, both Carnap and the Polish logician could perfectly well affirm both statements.
But Carnap and the Polish logician are not making relativity claims; implicit reference to a setting of the mereology parameter is not a component of the content of what either of them is saying. Rather, both Carnap and the Polish logician are speaking and judging categorically, from within respective semantic stances in which they are employing the notion of object in a way that is semantically governed by a specific parameter-setting. On our view, the content of what Carnap is saying is properly expressed this way: There are exactly three objects on the table, while the content of what the Polish logician is saying is properly expressed this way: There are exactly seven objects on the table. Both statements are categorical, and thus neither of them is an implicit relativity claim. Although the respective statements are semantically governed by different settings of the mereology parameter, and although each statement is correct under the particular parameter-setting that governs it in context, neither statement is implicitly about its own governing parameter-setting.
6. Affirmatory conflict
The relativized content view is an instructive failure, with respect to the task of explaining the kind of affirmatory conflict that Carnap’s claim and the Polish logician’s bear to one another. The reason why there is no real affirmatory conflict, under this approach, is that it allows for a way of reformulating what each party is supposedly claiming—a way of making each party’s respective relativity-claim fully explicit—such that Carnap and the Polish logician each can happily affirm both statements (as reformulated) and thus can happily affirm the conjunction of the two statements.
This lesson helps triangulate the kind of affirmatory conflict we seek to understand. A crucial feature of it should be this: there is no way to reformulate the respective claims of person P1 at time t1 and person P2 at time t2 such that a single person at a single time could correctly affirm both statements (as reformulated) and thus could correctly affirm their conjunction. As we will put it, the two statements are not correctly co-affirmable.
One way that two statements can fail to be correctly co-affirmable, of course, is for them to be directly inconsistent with one another. But, given our above account of synchronic diffèrance, this is not the only way. Another way arises from the fact that the various permissible settings for contextually variable semantic parameters are mutually exclusionary; i.e., for a single person P at a single time t, no more than one parameter-setting for a given concept or word can semantically govern correct usage, by P at t, of that concept or word. So, suppose that two statements S1 and S2 both contain a common word W that is semantically governed by a contextually variable parameter p; suppose also that person P1 affirms S1 at time t1 under a setting ap of p, and that person P2 affirms S2 at time t2 under a distinct setting bp of p. The relevant form of affirmatory conflict, obtaining between P1’s affirmation of S1 at t1 and P2’s affirmation of S2 at t2, is this:
(1) There is at least one circumstance C such that
(a) in C, S1 is true under ap and S2 is false under ap, and
(b) in C, S2 is true under bp and S1 is false under bp, and
(2) there is no circumstance C* such that either
(a) in C*, S1 and S2 are both true under ap, or
(b) in C*, S1 and S2 are both true under bp.
Under these conditions, statements S1 and S2 are not correctly co-affirmable—even though they are not directly inconsistent with one another.
The affirmatory conflict at work in cases of conceptual relativity, we suggest, occurs when two claims made by two different persons (or by one person at two different times) exhibit the features just described. The two statements fail to be correctly co-affirmable, and this failure stems from the fact that they are respectively semantically governed by mutually exclusionary settings of some contextually variable semantic parameter. The respective claims of Carnap and the Polish logician fail to be correctly co-affirmable for just that reason; and this feature constitutes their affirmatory conflict with one another.
We can express this kind of affirmatory conflict by coining a philosophical term (again, in the spirit of Derrida); let us say that the respective claims of Carnap and the Polish logician are inconsistant, even though they are not directly inconsistent. The two parties are not just “talking past one another” by using two non-identical concepts and employing the term ‘object’ with two non-identical meanings, and they also are not just directly contradicting one another either. They are doing something in between, something that emerges as a genuine possibility once we recognize (i) that there can be diffèrance in concepts and meanings, (ii) that the source of synchronic diffèrance is contextually variable semantic parameters, and (iii) that such diffèrance is the basis for conceptual relativity. This in-between relation in their respective claims is one under which both claims are correct despite conflicting with one another in the sense of not being mutually co-affirmable. Although the semantic conflict is genuine, it is also “no big deal” insofar as both parties are speaking and judging correctly under the semantic parameter-settings that govern their respective use of the notion of object. This distinctive semantic-conflict relation is what we are calling inconsistance.
This completes the three tasks that needed accomplishing in order to secure the mutual compatibility of items 1-4 in section I.2, thereby explaining conceptual relativity. To summarize: The first task was to explain why and how it is that some concepts and meanings conform to the variantist conception. We did so by identifying two forms of diffèrance—the diachronic version illustrated by Putnam’s example of momentum, and the synchronic version illustrated by Lewis’s treatment of the concept of flatness—and by highlighting the respective sources of identity-preserving difference for both kinds of case. In synchronic cases, the source is implicit, contextually variable, semantic parameters.
The second task was to harness this source of synchronic diffèrance in order to explain the principle of mutual correctness. This we did by pointing out that although Carnap and the Polish logician are employing a single concept of object, and are using the term ‘object’ with a single meaning, nevertheless their respective uses are semantically governed by different settings of the implicit mereology-parameter. Each of their respective claims is true under the specific setting of the mereology parameter that governs the claim.
The third task was to harness the source of synchronic diffèrance in order to explain the principle of affirmatory conflict. This we did by pointing out that the respective settings of the mereology parameter that respectively govern Carnap’s statement and the Polish logician’s statement are mutually exclusionary, and that there is no single setting of the mereology parameter under which both statements are true at once. Thus, the two statements are not mutually co-affirmable, and this constitutes their affirmatory conflict. Although the two statements are not inconsistent, they are indeed inconsistant.
II. Combining Conceptual Relativity with Metaphysical Realism
We turn now to the question of the relation between conceptual relativity and metaphysical realism. We will draw upon our account in Section I to argue that these two theses are compatible, and in fact comport well with one another. Doing so will require specific attention to the concept of truth.
1. Conceptual relativity, direct correspondence, and the denial of metaphysical realism
Metaphysical realism asserts that there is a mind-independent, discourse-independent, world—a world containing mind-independent, discourse-independent, objects that instantiate mind-independent, discourse-independent, properties and relations. Hereafter, it will be useful to adopt Putnam’s capitalization convention to order to speak of this putative world and these putative objects, properties, and relations; this makes unambiguously clear when we mean to be talking about the kinds of entities whose existence the metaphysical irrealist denies. (More below on how to construe the capitalization convention, given what will be said about truth.)
Conceptual relativity is often thought to be incompatible with metaphysical realism. An initially plausible line of reasoning, leading from conceptual relativity to the denial of metaphysical realism, goes as follows. According to conceptual relativity, there are various incompatible ways of “carving” reality—e.g., incompatible forms of mereology, yielding incompatible ways of counting objects, each of which is equally right. But if there is really a WORLD of OBJECTS that instantiate various PROPERTIES and RELATIONS, then it couldn’t be that these incompatible ways of “carving” are all correct; for, the only correct way of carving would be the one that corresponds to how THE WORLD is in itself—that is, the carving that picks out the genuine, mind-independently real, OBJECTS, and that employs predicates expressing the genuine, mind-independently real, PROPERTIES and RELATIONS. Thus, if conceptual relativity obtains, then metaphysical realism is false. So, given that conceptual relativity does obtain, metaphysical realism is false.
This line of reasoning assumes the following direct-correspondence conception of what truth would have to be, given metaphysical realism.
DC If metaphysical realism is correct, then truth must be a matter of straightforward, direct, correspondence between the content of language and thought, on one hand, and how things are with THE WORLD on the other hand.
Under the direct-correspondence conception of truth, an atomic statement ‘Fa’, for instance, is true iff there exists some OBJECT O and some PROPERTY P such that (i) ‘a’ denotes O, (ii) ‘F’ expresses P, and (iii) O INSTANTIATES P. An existential statement ‘($x)Fx’ will be true iff there exists some OBJECT O and some PROPERTY P such that (i) ‘F’ expresses P, and (ii) O INSTANTIATES P. And so forth for logically more complex statements, in accordance with the recursion clauses in a Tarski-style truth characterization.
It has very often been supposed that the direct-correspondence conception of truth is mandatory for metaphysical realism. Indeed, some philosophers (notably Dummett and Putnam) actually build this assumption into their characterization of metaphysical realism—something we are not doing here. And once one conjoins the direct-correspondence conception with metaphysical realism, then this package deal does appear incompatible with conceptual relativity. With respect to Carnap and the Polish logician, for example, the package-deal view would entail that they cannot both be right in how they count objects, because at most only one of their competing mereology/counting schemes generates the truth about such matters—in particular, the truth about how many OBJECTS are on a given table at a given moment.
2. Truth as indirect correspondence
But the metaphysical realist need not—and should not, we maintain—acquiesce in the direct-correspondence conception of truth. Rather, the realist can—and should—construe truth as correspondence of a more generic kind—a genus that has various species. Direct correspondence is one species but there are also various other kinds of truth-constituting correspondence.
In a number of prior writings, we have articulated and defended a general approach to truth that incorporates this idea; we call it contextual semantics. Here we will briefly sketch some central themes of contextual semantics in enough detail to serve our purpose of explaining how conceptual relativity can mesh with metaphysical realism.
One fundamental claim of contextual semantics is this: although truth is correspondence between content (in language or thought) and the WORLD, often our language and thought work in such a way that the relevant kind of correspondence is indirect rather than direct—so that that there need not be any OBJECTS that answer to the singular terms or the quantifiers in a given statement, or PROPERTIES that answer to the predicates. Take, for instance, this statement:
Beethoven’s fifth symphony has four movements.
Its truth does not require that there be some genuine OBJECT answering to the term ‘Beethoven’s fifth symphony’, and also instantiating a genuine PROPERTY expressed by the predicate ‘has four movements’. Rather, the relevant correspondence-relation is less direct than this. Especially germane is the behavior by Beethoven that we would call “composing his fifth symphony.” But a considerably wider range of goings-on is relevant too: in particular, Beethoven’s earlier behavior in virtue of which his later behavior counts as composing his fifth symphony; and also a broad range of human practices (including the use of handwritten or printed scores to guide orchestral performances) in virtue of which such behavior by Beethoven counts as “composing a symphony” in the first place.
Another fundamental claim of contextual semantics, intimately connected to the notion of indirect correspondence, is that truth is semantically correct affirmability under contextually operative semantic standards. Likewise, falsity is semantically correct deniability, under such standards. The relevant notion of semantic correctness has nothing to do with matters of etiquette; a statement can be semantically correct, in the relevant sense, even if it would be impolite, impolitic, or otherwise inappropriate to utter it. Semantic correctness is also distinct from epistemic warrant: a statement can be epistemically warranted but semantically incorrect, and can be semantically correct but epistemically unwarranted. (Suppose that Beethoven engaged in behavior correctly describable as “composing his tenth symphony,” and that no traces of this fact exist—perhaps because he burned his score and sketchbooks and never mentioned the project to anyone. Then the statement ‘Beethoven composed only nine symphonies’ is semantically incorrect despite being epistemically warranted.)
Contextual semantics also stresses that semantic standards vary somewhat from one sociolinguistic context to another. In the limit case, the applicable standards require direct referential linkages connecting a statement’s basic subsentential constituents to OBJECTS and PROPERTIES. In this limit case, truth (i.e., semantically correct affirmability) is direct correspondence. But the contextually operative standards also can work in such a way that the requisite goings-on in the world need not involve OBJECTS or PROPERTIES answering to the statement’s basic subsentential constituents. In such cases, truth is indirect correspondence.
Limit-case semantic standards frequently come into operation in philosophical contexts where ontological issues are under discussion. It is plausible that they also are operative in various scientific contexts, for instance in discussions in physics about the subatomic constituents of matter. But for typical uses of numerous kinds of non-scientific discourse—including discourses in which statements like “Beethoven’s fifth symphony has four movements” would naturally occur—it is plausible that the contextually operative semantic standards are not limit-case standards. Thus, for statements in such discourses, truth (i.e., semantically correct affirmability) typically is indirect correspondence.
3. The compatibility of metaphysical realism and conceptual relativity
We maintain that contextual semantics is a plausible and theoretically attractive approach to truth; elsewhere we have set forth various arguments in support of it (as well as articulating it more fully). Our present objective is to explain why metaphysical realism and conceptual relativity can be naturally, and simultaneously, accommodated within the framework of contextual semantics. This means, of course, that metaphysical realism and conceptual relativity are entirely compatible with one another.
So consider, first, metaphysical realism—which asserts that there is a WORLD containing OBJECTS instantiating various PROPERTIES and RELATIONS. Contextual semantics comports well with this thesis. For one thing, contextual semantics is perfectly consistent with it. Moreover, in contexts where language and thought are governed by limit-case semantic standards, truth is a matter of direct correspondence between language/thought content on one hand, and how things are with these OBJECTS and their PROPERTIES and RELATIONS on the other hand. Under direct-correspondence standards conceptual relativity cannot be operative.
Even under limit-case semantic standards of course, one must still be employing certain specific concepts in certain specific ways: one must be thinking and judging with those specific concepts, and from within those context-specific semantic standards. In this mundane sense, one’s judgments and assertions are still relative to a specific “conceptual scheme.” But it is just a non sequitur to infer from this kind of conceptual-scheme relativity that metaphysical realism is false. For, when one is employing concepts under limit-case semantic standards, one purports to be carving THE WORLD at its mind-independently real joints; one’s judgments and statements are true iff they directly reflect how things are with OBJECTS, in terms of the PROPERTIES and RELATIONS they instantiate.
Now consider conceptual relativity, as explicated in part I above. Contextual semantics comports well with this thesis too. The key point is this: insofar as the contextually operative semantic standards governing the correct usage of a person’s concepts and words only require indirect correspondence rather than direct correspondence, the items to which one’s judgments and statements are “ontologically committed” by Quinean standards need not be mind-independently real; they need not be OBJECTS. Thus, for example, different contextually specific semantic standards governing the notion of object could involve different, mutually incompatible, mereology parameters—say, Carnap’s on one hand, and the Polish logician’s on the other. As long as Carnap and the Polish logician are not both employing limit-case, direct-correspondence, semantic standards, there is no reason why they cannot each be employing the notion of object in such a way that under the respectively operative settings of the mereology parameter, each of them is counting objects correctly. In short: contextually variable semantic standards often work in such a way that truth—that is, semantic correctness under contextually operative standards—is indirect correspondence rather than direct correspondence; and conceptual relativity is accommodated by the range of different potential forms of indirect correspondence, involving different settings of contextually variable semantic parameters.
Although our principal example of conceptual relativity has been Putnam’s case of Carnap and the Polish logician—which on our account involves different settings of an implicit mereology-parameter governing the notion of object—we emphasize that the phenomenon of conceptual relativity extends well beyond matters of counting and part/whole relations. It also covers, for example, entire domains of entities that count as legitimate posits under various kinds of non-limit-case semantic standards. Plausible examples include (inter alia) nations, universities, symphonies, and numbers. Under contextual semantics, there need not be genuine OBJECTS answering to thought and talk that carries Quinean ontological commitment to such entities; and we doubt that there are such OBJECTS. Thus, an ontologically minded philosopher might claim that nations do not exist, whereas someone employing nation-talk under more typical contextually operative semantic standards would claim that of course nations exist. Both claims could well be correct, we maintain, given the differing contextually-operative semantic standards that govern their respective uses of the nation-notion. Thus, matters of existence and non-existence are subject to conceptual relativity too.
4. Ontology in light of conceptual relativity
Given contextual semantics, numerous entities to which our language and thought carries Quineian “ontological commitments” might turn out to be only mind-dependently, discourse-dependently, real, in this sense: although statements positing such entities are true under various sorts of indirect-correspondence semantic standards that often are contextually operative, such statements are not true under limit-case, direct-correspondence, standards. This means that questions of ontology, about what OBJECTS there are and what PROPERTIES and RELATIONS they instantiate, are methodologically subtle, within the framework of contextual semantics. In inquiring into them, one needs to attend carefully to whether language and thought are, or are not, being employed under limit-case semantic standards—and also to questions about what sorts of items are, or are not, appropriate to posit when one is speaking and judging under those standards. In principle, however, there is no clear reason why such matters should not be open to human theoretical investigation—including scientifically informed investigation.
One can, if one so chooses, deliberately undertake serious ontological inquiry—thereby employing discourse governed by limit-case semantic standards—to ask questions about what EXISTS. (The capitalization convention is a device for overtly signaling that one is employing direct-correspondence standards.) In this rarified form of thought and discourse, conceptual relativity no longer holds sway. Thus, if Carnap and the Polish logician both were to deliberately shift into direct-correspondence discourse, and also both were to persist in their respective claims about the number of objects, then their dispute would thereby become a “big deal” ontologically. For, although Carnap and the Polish logician can both be right about how many objects are on the table when at least one of them is speaking and judging under indirect-correspondence semantic standards, nevertheless if they intend their dispute to be a genuine metaphysical conflict about how many OBJECTS are on the table, then they cannot both be correct.,
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 See Lynch (1998) for an illuminating attempt to make sense of conceptual relativity which, because of space considerations, we are not able to consider in this paper. But see note 7 below for an indication of why we think Lynch’s view does not really handle the phenomenon of conceptual relativity.
 For expository convenience, we have formulated these two principles in a way that makes them specifically about just the one case of Carnap and the Polish logician. But such principles can also be formulated more abstractly, to apply to cases of conceptual relativity in general. Of course, it need not always be the case that each of the persons in affirmatory conflict is actually making a true statement (relative to the given person’s own way of using relativity-susceptible concepts); for, the affirmed statement might happen to be false even relative to the speaker’s own way of using the relevant concepts.
 See also Van Inwagen (this volume), who also argues that conceptual relativity is not really possible.
 The account we offer will not constitute a full theory of concepts and meanings, by any means. Rather, it potentially could be incorporated into various alternative general theories.
 It is important to distinguish the phenomenon of diffèrance in concepts from what Putnam (1981, p. 116-19) calls difference in conception (even though the distinction is somewhat fuzzy). The latter is a matter of different beliefs about a given subject matter, not differences in concepts and in meaning. Diffèrance, on the other hand, does involve differences in concepts and in meaning—albeit identity-preserving ones.
 Different settings of the mereology parameter do not appear to conform to any simple ordering, however; in this respect the mereology parameter differs from the precision parameter for flatness.
 These remarks are further supported by reflecting on the attempt to accommodate the phenomenon of conceptual relativity in Lynch (1998), pp. 91-3. Lynch appears to accept a version of what we are calling the relativized content view (although the text is not completely unambiguous about this), and in order to make sense of the principle of affirmatory conflict, he claims that the statements made by Carnap and the Polish logician are in conflict in the sense that “if these propositions were relative to the same scheme, they would be inconsistent” (p. 93). But this sort of conflict is merely counterfactual; it does not constitute or explain the actual affirmatory conflict that is present in the claims that are actually made by Carnap and Polish logician. Yet once one embraces a relativized content view about the claims in question, one seems forced to make a move like Lynch’s in trying (unsuccessfully) to accommodate the idea that there is genuine affirmatory conflict in the actual claims being made in the Carnap-Polish logician case.
 It is crucial to this kind of affirmatory conflict that the two statements are not reformulable in a way that allows for correct co-affirmability by one person at one time. Suppose, for instance, that Jones correctly says “I am over 6 feet tall” and Smith correctly says “I am not over six feet tall.” Neither of them can correctly affirm the conjunctive sentence “I am over 6 feet tall and I am not over 6 feet tall.” However, each of them has a way of reformulating the other’s statement that will make the two statements co-affirmable under reformulation. (Jones, for instance, can correctly say “I am over 6 feet tall and Smith is not over 6 feet tall.”) So Jones’ and Smith’s respective claims about their own heights, both of which employ the indexical term ‘I’, are not in affirmatory conflict.
 Nor are they direct contraries of one another either—that is, statements that can be mutually false but cannot be mutually true. Being direct contraries is a form of content-conflict which—like being directly contradictory—runs afoul of the principle of mutual correctness.
Although you say that the respective claims of Carnap and the Polish logician are not co-affirmable, you yourselves affirm the principle of mutual correctness; i.e., you yourselves affirm that Carnap and the Polish logician are both correct in their respective claims. But to affirm that they are both correct is to affirm what each of them is saying! So there is a way of correctly co-affirming their claims after all—which shows that there is no genuine affirmatory conflict between them.
Reply: The principle of mutual correctness employs the term ‘correct’—and also the word ‘true’—in a relativistic way: the principle asserts that both Carnap and the Polish logician are making a claim which, relative to a specific way of using the concept of object, is true. When one employs the notion of truth in this relativistic way vis-a-vis a statement S, one does not thereby categorically affirm that S is true—and hence one does not commit oneself to S itself. Thus, in affirming the principle of mutual correctness one does not thereby co-affirm Carnap’s claim and the Polish logician’s claim. Cf. note 19 below.
 In Putnam (1982, p. 272), for instance, metaphysical realism is characterized as a view that assumes the following:
1. A world consisting of a definite totality of discourse-independent properties and objects
2. ‘Strong bivalence’, i.e., that an object either determinately has or determinately lacks any property P that may significantly be predicated of that object
3. The correspondence theory of truth in a strong sense of ‘correspondence’, i.e., a predicate corresponds to a unique set of objects, and a statement corresponds to a unique state of affairs, involving the properties and objects mentioned in (1), and is true if that state of affairs obtains and false if it does not obtain. (p. 272)
Putnam ascribes to Michael Dummett the same three-part characterization of metaphysical realism. We ourselves are taking metaphysical realism to comprise only the thesis of mind-independent, discourse-independent, OBJECTS, PROPERTIES, and RELATIONS—which Putnam articulates as claim (1) of the package-deal view that he himself calls metaphysical realism. Presently we will reject claim (3), Putnam’s formulation of the direct-correspondence conception of truth. We also deny that claim (2) should be built into the very definition of metaphysical realism (although we remain officially neutral about this claim), because metaphysical realists disagree among themselves about whether there are, or can be, vague OBJECTS or PROPERTIES—and if so, whether or not they obey the principle of strong bivalence.
 See Horgan (1986a, 1986b, 1991, 1995a, 1995b, 1996, 1998, 2001), Horgan and Potrc (2000), Horgan and Timmons (1993), and Timmons (1999). Originally Horgan called the view “language-game semantics” and later called it “psychologistic semantics,” before Horgan and Timmons decided on the current name. The overall framework includes theses not only about truth and falsity per se, but also about meaning, ontology, thought, and knowledge.
 Although contextual semantics denies that truth can be construed epistemically—say, as epistemically warranted affirmability, or as some kind of idealization of epistemically warranted affirmability—nevertheless contextual semantics does posit an intimate connection between semantic standards for correct affirmability on one hand, and epistemic standards for warranted affirmability on the other hand. By and large, the epistemic standards we actually employ in assessing the epistemic warrant-status of various statements are appropriate to the contextually operative semantic standards governing semantically correct affirmability. This explains why, for example, one need not concern oneself about the ontological status of musical works of art in order to be well warranted in affirming the statement that Beethoven’s fifth symphony contains four movments (given the plausible assumption that this statement, as ordinarily employed, is governed by indirect-correspondence semantic standards).
 Although this is initially plausible, there also are considerations that count against it, having to do with conceptual problems that threaten the possibility of ontological vagueness. See Horgan and Potrc (2000).
 See the texts cited in note 12.
 Pendlebury (1986) shows how it is possible to make sense of a realist truthmaking relation that does not presuppose that the object language cuts nature at the joints. This approach, which is similar in spirit to contextual semantics, also appears to lend support to the contention that metaphysical realism is compatible with conceptual relativity.
 Putnam appears to commit this fallacy in the third sentence of the passage we quoted in the second paragraph of this paper.
 Even if neither Carnap nor the Polish logician is employing semantic standards requiring direct correspondence to OBJECTS and their PROPERTIES and RELATIONS, one of them might happen to be employing mereological principles that are actually obeyed by OBJECTS themselves. But this could only be so for one of their mereological schemes at most—not for both.
 The concept of truth is itself subject to conceptual relativity, according to contextual semantics: it too is governed by implicit, contextually variable, semantic parameters. Typically—but not invariably—the contextually operative parameter-settings mesh with those governing first-order discourse in such a way that the claim that statement S is true entails S, and conversely. One important alternative way to employ the truth predicate is a non-categorical, explicitly relativistic usage: one says of statement S that it is true under (or, true relative to) such-and-such semantic standards (or mode of usage, or conceptual scheme, etc.). The truth predicate is used in this relativistic way in our formulation of the principle of mutual correctness in section I.1, and also in our account of affirmatory conflict in the third paragraph of section I.6. Such a non-categorical truth-attribution to a statement S does not entail S.
 We do acknowledge the worry that perhaps nothing could settle such ontological issues, even in principle—and the fact that this worry potentially threatens metaphysical realism. As is emphasized by Lynch (1998), one need not be a verificationist about meaning to feel the grip of this line of thought. But addressing it is a matter for another occasion.
 For a discussion that construes their dispute as a genuine metaphysical conflict, and argues that they are both wrong, see Van Inwagen (this volume).
 We thank Elizabeth Giles, Michael Lynch, Michael Pendlebury, and John Tienson for helpful comments and discussion.