Mixed Inferences: Not a Problem for Pluralism about Truth

1.Background

1.1 Roadmap

Christine Tappolet posits that mixed inferences seem to pose problems for pluralistic theories about truth (Tappolet, 1997; 2000). I argue that responses to the problem on behalf of pluralists successfully meet Tappolet’s challenge, and that the most viable responses to the challenge focus, at the heart, on the idea that while a stipulated generic truth predicate seems to do the work at explaining the validity of mixed inferences, it is the other truth predicates that do the work in explaining why the premises and conclusion are true to begin with. The premises and conclusion of Tappolet’s mixed inference might be true in the generic sense, but only because they are first true in some other way—as a result of social agreement or correspondence to the facts, or some further way.

To begin with, I will first sketch a background on pluralistic theories about truth and review the challenges posed by mixed inferences. After this, I will analyze several philosophers’ responses to these problems and explain how (some of) these responses successfully reply to Tappolet’s challenge.

1.2 Pluralism About Truth

Pluralism is the idea that there are different ways of being true. More specifically, in different discourses, or subject matters, the truth predicate attributes different properties (Wrenn, 2015: 133). For example, a pluralist about truth might place the proposition Wet cats are funny in the domain of comedy, where one way of being true, Tsa, would apply because all propositions that fall under this domain are truth-assessable in terms of social agreement. The proposition This cat is wet might be placed in the domain of scientific claims or claims about the state of affairs of the world, and a different way of being true, Ta, would apply because all propositions that fall under this domain are truth-assessable in terms of correspondence to the facts.

Tappolet’s problem of mixed inferences might seem especially well-postured to pose a deathblow to Strong Alethic Pluralism, which is the view that there is more than one truth property, and that no one truth property can explain the truth of true propositions (Pedersen, 2006: 106).

1.3 Mixed Inferences

Tappolet demonstrates that mixed inferences pose a problem to pluralist theories about truth by testing the pluralists’ central claim that different types of truth predicates correspond to sentences of different subject matters (Tappolet, 1997: 209–210). She presents the following deductively valid argument, or ‘mixed inference,’ whose premises are sentences from two different subject matters—and thus, two different truth predicates would apply, if the pluralist about truth is correct (Tappolet, 1997: 209–210):

  1. Wet cats are funny.
  2. This cat is wet.
  3. Therefore, this cat is funny.

In the above argument, (i) is a type of sentence that, according to the pluralist about truth, does not involve realism about the entities of the sentence, and is truth-assessable in terms of a minimal or ‘lightweight’ truth (pluralists would classify comical or moral sentences under this type). For (i), the pluralist about truth might think of the truth predicate in the same way a coherence theorist about truth would.

And (ii) is a type of sentence that the pluralist about truth holds is truth-assessable in terms of a ‘heavyweight’ truth that implies a realist view of the subject matter. While (i) is an allegedly non-descriptive sentence, in that it does not assert any fact of the matter about the world, (ii) is a descriptive sentence. A pluralist about truth might think of the truth predicate here in the same way a correspondence theorist about truth would.

Tappolet argues that if the pluralist about truth is correct, and one type of truth predicate explains the truth of (i) and a different type of truth predicate explains the truth of (ii), then the argument would not be valid. However, it clearly is valid, and so therefore, Tappolet argues, there must be only one truth predicate that applies to all three sentences. She further argues that since the argument is valid, both (i) and (ii) must be assessable in terms of the same truth predicate—not different ones as the pluralist about truth maintains.

In explaining the above argument, Tappolet advocates that truth is what is preserved in valid inferences. Her challenge to the pluralist about truth is this: if we already have one truth predicate that seems to apply to all three sentences in the argument above, why do we need multiple truth predicates?

1.4 Tappolet’s Trilemma

According to Tappolet, in the face of the above challenge, the pluralist must do one of three things: first, claim that in addition to the one, generic truth predicate that seems to apply to all three sentences, there are different truth predicates that apply to different sorts of sentences (Tappolet, 2000: 382–383). The problem is, Occam’s razor should hold. That is, if both monistic theories about truth and pluralistic theories about truth can explain the truth of the argument equally well, then we should rally behind the simplest theory (i.e. monistic theories about truth in general, or a generic truth predicate in particular) (Tappolet, 2000: 383). The bulk of responses to Tappolet’s challenge focus on this horn of the trilemma.

Second, the pluralist about truth might deny that mixed inferences are valid. The problem is, they clearly are valid. None of the responses this paper concerns itself with go this route—and it would seem strange to do so, because mixed inferences seem intuitively valid.

Third, the pluralist about truth may deny the classical account of validity, which says that an argument is valid if and only if the truth of the premises necessitates the truth of the conclusion. The problem is, it seems that the classical account of validity should hold and our theories about truth should not haphazardly throw it out. While none of the responses this paper concerns itself with go this route either, one plausible alternative might be to expand the definition to account for mixed inferences, if needed, rather than throw out the classical account of validity altogether. However, this paper will say nothing more on this matter, and instead turn to responses that tackle the first horn of Tappolet’s trilemma, which seems a far more fruitful approach.

2. Proposed Solutions to the Problem of Mixed Inferences

2.1 Beall’s Solution

JC Beall sidesteps Tappolet’s trilemma by appealing to many-valued logics, which allow for the possibility of there being more than one way for a proposition to be true, and do not restrict the number of truth values to just two, true and false; rather, Beall seems to imply there are as many designated values as there are different ways of being true (Beall, 2000: 381–382). By appealing to the concept of designated value, where every way of being true is a designated value, the standard account of validity as necessary truth preservation holds (Lynch, 2004: 388–389).

Using many-valued logics, we can represent the truth of (i) by 1 and the (different) truth of (ii) by ½ (Beall, 2000: 381–382). For this example, Beall assumes there is exactly one way to be not-true, which we can represent by 0 (Beall, 2000: 381–382). In many-valued logics, an argument is valid if and only if the conclusion cannot be false (0) if all the premises are designated (1 or ½) (Beall, 2000: 382). Alternatively, an argument is valid if there is no case where the premises are designated (1 or ½) and the conclusion fails to be designated (0) (Beall, 2000: 382).

Thus, Beall argues, pluralists may simultaneously maintain that: 1. (i) and (ii) represent different ways of being true, and 2. The argument above is valid, so long as there is no case where the premises are designated (1 or ½) and the conclusion fails to be designated (Beall, 2000: 382).

Beall’s appeal to many-valued logics fails to deliver a deathblow to Tappolet’s argument. Tappolet herself makes a good point; if all three sentences are designated, is that not a kind of truth? (Tappolet, 2000: 384). Michael P. Lynch makes a similar point: designation is a thinly-veiled truth concept and is doing all the work in explaining the validity of the mixed inference (Lynch, 2004: 389).

However, a response to Tappolet’s rejoinder might go something like this: Beall himself says that designated values are the same as the different ways of being true, and so does not dispute that they are kinds of truth. What is at issue is Tappolet’s contention that sentences with designated values (e.g. 1 or ½) can be further reduced to something more elemental—to just the fact that the sentences are designated. Surely this is not something to hang one’s hat on, as each designated value maps onto a different way of being true—a way of being true that cannot be further reduced. For example, the designated value of 1 maps onto something being true as a result of social agreement, and a designated value of ½ maps onto something being true as a result of correspondence to the facts. Being designated in the general sense might be akin to being true in some generic sense. However, while the premises and conclusion of Tappolet’s mixed inference might be true in the generic sense, this is only because they are first true in some other way—as a result of social agreement or correspondence to the facts, or some further way. Thus, being designated in the general sense is dependent on being designated in a particular sense (e.g. 1 or ½). So, it seems that Tappolet has it backwards: the designation of 1 or ½ cannot be further reduced to being designated in general; being designated in general has to do first with being designated in some other way.

2.2 Cotnoir’s Solution

Aaron J. Cotnoir’s solution to Tappolet’s problem of mixed conjunctions, while only indirectly related to the problem of mixed inferences, can also be applied to meet Tappolet’s challenge. Mixed conjunctions are those with conjuncts from different subject areas (for example, ‘this cat is wet and it is funny’) (Tappolet, 2000: 384–385). Tappolet’s challenge is this: mixed conjunctions can obviously be true (Tappolet, 2000: 384–385). But if the pluralist about truth is correct, and each conjunct is true in a different way, in what way is the conjunction itself true? It seems that the conjunction itself should be true in the same way its conjuncts are—in the generic sense.

Cotnoir sees no reason to think that a generic truth predicate would make other ways of being true redundant, and suggests that a generic truth predicate is not incompatible with pluralism, if the generic property is defined by, or dependent on, the other ways of being true (Cotnoir, 2009: 478). This sounds very close to Douglas Edwards’s view about mixed conjunctions, where the truth of the conjunction is entirely dependent on the truth of its conjuncts (i.e. p & q is true because p is true in one way, T1, and q is true in a different way, T2) (Edwards, 2008: 147).

Cotnoir successfully answers Tappolet’s challenge about why we should let in other ways of being true into a theory about truth, as opposed to just the one generic truth property. That is, the generic truth property in and of itself lacks all explanatory power as to why a proposition is true to begin with; that is, a proposition is generically true only if it is true in some further way. Being true in the generic sense is defined by, or dependent on, the other ways of being true.

2.3 Pedersen’s Solution

Nikolaj Jang Linding Pedersen maintains that mixed inferences fail to make a dent in strong alethic pluralism (Pedersen, 2006: 107). He posits that alethic pluralists can appeal to a sparse view of properties to get around Tappolet’s assertion that there must be one generic truth predicate that applies to all three sentences in her mixed inference (Pedersen, 2006: 108). Sparse properties ‘carve things up at the qualitative joints’; abundant properties do not (Pedersen, 2006: 108). For example, the property of being a cat is a sparse property; all items in the set cats are qualitatively similar—they share similarities in terms of appearance, behavior, evolutionary history, et cetera (Pedersen, 2006: 108). However, the property of being either a cat or a real number is an abundant property—there is no qualitative similarity between being a cat or a real number (Pedersen, 2006: 108). That is, the only property that all items in the set cat or real number have in common is being a member of this set (Pedersen, 2006: 108).

It seems that Pedersen’s point can be expanded thusly: say we take Tappolet’s lead and maintain that all three propositions—Wet cats are funny, This cat is wet, and the conclusion that necessarily follows, This cat is funny—must belong to the set generically true in order for the traditional notion of validity to hold. Under the sparse conception of properties, since there is no qualitative similarity between the ways the propositions are true (for example, what makes it true that wet cats are funny, which might be the result of something like social agreement, is not qualitatively similar to what makes it true that a particular cat is wet, which might be true as a result of something like correspondence to the facts), the property of being generically true does not qualify as a property at all (Pedersen, 2006: 109). This is because Tappolet’s posited generic truth property is not a qualitative property, but only a logical one (Pedersen, 2006: 109).

While Pedersen makes an interesting point, he seems to leave something out. Since mixed inferences are deductively valid, it seems evident that there is a generic truth property, whether it is qualitative or not. That is, truth is what is preserved in any valid inference, and for our purposes, we will assume that the truth that is preserved is the generic truth property. The generic truth property plays an important role which makes it so that the truth of Wet cats are funny is comparable to the truth of This cat is wet, and facilitates the logical leap so that the conclusion, This cat is funny, necessarily follows. However, upon close examination, the generic truth property is merely a bucket that captures all other ways of being true, one which arises out of logical necessity. It does no work in explaining why the premises or conclusion are true to begin with (or, as Pedersen might say, the generic truth property is an abundant property, and the only thing that the premises and conclusion have in common is that they are in the same set, generically true) (Pedersen, 2006: 109). In other words, the fact that the premises and conclusion are generically true is dependent on the ways that each of the premises and the conclusion are (independently) true.

For example, it is true, Tsa, that Wet cats are funny, because in the domain of comedy, in which funniness is decided by something like social agreement, it is the case that wet cats are funny; and it is true, Tc, that This cat is wet, because in the domain of scientific claims or states of affairs of the world, in which whether or not something is wet is decided by correspondence to the facts, it is the case that this cat is wet. Taking this example further, if a proposition is true (in this case, by correspondence to the facts or social agreement), then it is true in a further way: generically true, Tg. This provides an answer to Tappolet’s question, ‘why should we need the many truth predicates instead of the one that does the inferential job…?’ (Tappolet, 2000: 384). The generic truth property facilitates logical inference, but holds no other meaning in itself.

3.3 Conclusion

One of the main motivations behind pluralism about truth is that all monistic theories of truth share a common weakness: the Scope Problem (Wrenn, 2015: 134). That is, monistic theories about truth do not seem to successfully apply to truths of all subject matters (Wrenn, 2015: 134). For example, a correspondence theory of truth seems to explain very well why a particular cat might be wet, but seems to do a poor job of explaining why wet cats might be funny. A generic truth predicate would explain the truth of both why a particular cat is wet and why wet cats are funny (and all true propositions, for that matter) the same way, which seems wrong, because this sidesteps why the propositions are true to begin with.

In this paper, I pursued two main tasks. First, I sketched a background on pluralism in general and strong alethic pluralism in particular, and on Tappolet’s problem of mixed inferences; second, I outlined several responses to the problem and reflected on each of these in turn.

In the first horn of her trilemma (and the horn that is most easily tackled), Tappolet argues that the pluralist about truth must claim that in addition to the one, generic truth predicate that seems to apply to all three parts of the mixed inference, there are further truth predicates that apply (Tappolet, 2000: 382–383). I argue that the most viable responses to Tappolet’s challenge focus, at the heart, on the idea that while a stipulated generic truth predicate seems to do the work at explaining the validity of mixed inferences, it is the other truth predicates, for example, Tsa and Tc, that do the work in explaining why the component propositions are true to begin with. The premises and conclusion of Tappolet’s mixed inference might be true in the generic sense, but only because they are first true in some other way—as a result of social agreement or correspondence to the facts.

Mixed inferences might pose a problem for pluralists, but they also pose a problem for monists about truth—in a different way. A correspondence theorist about truth, for example, might very easily explain why it is true that a particular cat is wet, but struggle to explain why wet cats are funny; a theorist who subscribes to a social agreement theory about truth might very easily explain why it is true that wet cats are funny but struggle to explain why a particular cat is wet. Monistic theories about truth would have a hard time explaining why all parts of a mixed inference are true. How, then, could we ever make the logical leap to this cat is funny?

References

Beall, JC. (2000). On Mixed Inferences and Pluralism about Truth Predicates. The Philosophical

Quarterly, 50.200: 380–382.

Cotnoir, A. J. (2009). Generic truth and mixed conjunctions: some alternatives. Analysis, 69.3:

473–479.

Edwards, D. (2008). How to Solve the Problem of Mixed Conjunctions. Analysis, 68.2: 143–149.

Lynch, M. P. (2004). Truth and Multiple Realizability. Australasian Journal of Philosophy, 82.3:

384–408.

Pedersen, N. J. L. (2006). What Can the Problem of Mixed Inferences Teach Us About Alethic

Pluralism? The Monist, 89.1: 102–117.

Tappolet, C. (1997). Mixed inferences: a problem for pluralism about truth predicates. Analysis,

57.3: 209–210.

Tappolet, C. (2000). Truth Pluralism and Many-Valued Logics: A Reply to Beall. The

Philosophical Quarterly, 50.200: 382–385.

Wrenn, C. (2015). Truth. Cambridge: Polity Press.

 

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