## 1. Alethic pluralism about truth: a plurality of properties


### 1.1 Strength




The pluralist's thesis that there are many ways of being true
is typically construed as being tantamount to the claim that the number
of truth properties is greater than one. However, this basic
interpretation,


* (1) there is more than one truth property.




is compatible with both moderate as well as more radical
precisifications. According to moderate pluralism, at least one way of
being true among the multitude of others is universally shared:


* (2) there is more than one truth property, some of which are had by
all true sentences.




According to strong pluralism, however, there is no such universal
or common way of being true:


* (3) there is more than one truth property, none of which is had by
all true sentences.




Precisifying pluralism about truth in these two ways brings several
consequences to the fore. Firstly, both versions of pluralism conflict
with strong monism about truth:


* (4) there is exactly one truth property, which is had by all true
sentences.




Secondly, moderate--but not strong--pluralism is
compatible with a moderate version of monism about truth:


* (5) there is one truth property, which is had by all true
sentences.




(2) and (5) are compatible because (5) does not rule out the
possibility that the truth property had by all true sentences might be
one among the multitude of truth properties endorsed by the moderate
pluralist (i.e., by someone who endorses (2)). Only strong pluralism in
(3) entails the denial of the claim that all true sentences are true in
the same way. Thus, moderate pluralists and moderate monists
can in principle find common ground.


### 1.2 Related kinds of pluralism and neighboring views




Not infrequently, pluralism about truth fails to be distinguished
from various other theses about associated conceptual, pragmatic,
linguistic, semantic, and normative phenomena. Each of these other theses involves
attributing plurality to a different aspect of the analysandum
(explanandum, definiendum, etc.). For instance, linguistically, one may
maintain that there is a plurality of truth predicates (Wright 1992;
Tappolet 1997; Lynch 2000; Pedersen 2006, 2010). Semantically, one may
maintain that alethic terms like 'true' have multiple
meanings (Pratt 1908; Tarski 1944; Kolbel 2008, 2013; Wright 2010).
Cognitively or conceptually, one may maintain that there is a
multiplicity of truth concepts or regimented ways of conceptualizing
truth (Kunne 2003; cf. Lynch 2006). Normatively, one might think
that truth has a plurality of profiles (Ferrari 2016, 2018).




These parameters or dimensions suggest that pluralism is itself not
just a single, monolithic theory (see also Sher 1998; Wright
2013). Any fully developed version of pluralism about truth is likely
to make definitive commitments about at least some of these other
phenomena. (However, it hardly entails them; one can consistently be
an alethic pluralist about truth, for instance, without necessarily
having commitments to linguistic pluralism about truth predicates, or
about concepts like fact or actuality.) Nonetheless, theses about
these other phenomena should be distinguished from pluralism about
truth, as understood here.




Likewise, pluralism about truth must be distinguished from several
neighbouring views, such as subjectivism, contextualism, relativism, or
even nihilism about truth. For example, one can maintain some form of
subjectivism about truth while remaining agnostic about how many ways
of being true there are. Or again, one can consistently maintain that
there is exactly one way of being true, which is always and everywhere
dependent on context. Nor is it inconsistent to be both a pluralist and
an absolutist or other anti-relativist about truth. For example, one
might argue that each of the different ways of being true holds
absolutely if it holds at all (Wright 1992). Alternatively, one might
explicate a compatibilist view, in which there are at least two kinds
of truth, absolute and relative truth (Joachim 1905), or deflationist
and substantivist (Kolbel 2013). Such views would be, necessarily,
pluralistic. Occasionally, pluralists have also been lumped together
with various groups of so-called 'nihilists',
'deniers', and 'cynics', and even associated
with an 'anything goes' approach to truth (Williams 2002).
However, any version of pluralism is prima facie inconsistent with any
view that denies truth properties, such as nihilism and certain forms
of nominalism.


### 1.3 Alethic pluralism, inflationism, and deflationism




The foregoing varieties of pluralism are consistent with various
further analyses of pluralists' ideas about truth. For instance,
pluralists may--but need not--hold that truth properties are
simply one-place properties, since commitments to truth's being
monadic are orthogonal to commitments to its being monistic. However,
most pluralists converge on the idea that truth is a substantive
property and take this idea as the point of departure for articulating
their view.




A property is substantive just in case there is more to its nature
than what is given in our concept of the property. A paradigmatic
example of a substantive property is the property of being water. There
is more to the nature of water--being composed of H\(\_2\)O,
e.g.--than what is revealed in our concept of water (the
colourless, odourless liquid that comes out of taps, fills lakes,
etc.)




The issue of substantiveness connects with one of the major issues
in the truth debate: the rift between deflationary theories of truth
and their inflationary counterparts (Horwich 1990; Edwards 2013b;
Kunne 2003; Sher 2016b; Wyatt 2016; Wyatt & Lynch 2016). A common way to understand the divide between
deflationists and inflationists is in terms of the question whether or
not truth is a substantive property. Inflationists endorse this idea,
while deflationists reject it. More specifically, deflationists and
inflationists can be seen as disagreeing over the following claim:


* (6) there exists some property \(F\) (coherence,
correspondence, etc.) such that any sentence, if true, is so in virtue
of being \(F\)--and this is a fact that is not transparent in
the concept of truth.




The inflationist accepts (6). According to her, it is not
transparent in the concept of truth that being true is a matter of
possessing some further property (cohering, corresponding, etc.). This
makes truth a substantive property. The deflationist, on the other
hand, rejects (6) because she is committed to the idea that everything
there is to know about truth is transparent in the concept--which,
on the deflationist's view, is exhausted by the disquotational
schema ('\(p\)' is true if, and only if, \(p)\), or some principle
like it.




Deflationists also tend to reject a further claim about
truth's explanatory role:


* (7) \(F\) is necessary and sufficient for explaining the truth
of any true sentence \(p\).




Inflationists, on the other hand, typically accept both (6) and
(7).




Strong and moderate versions of pluralism are perhaps best
understood as versions of a non-traditional inflationary theory (for an exception, see Beall 2013; for refinements, see Edwards 2012b and Ferrari & Moruzzi forthcoming).
Pluralists side with inflationists on (6) and (7), and so, their views
count as inflationary. Yet, traditional inflationary theories are also
predominantly monistic. They differ about which property
\(F\)--coherence, identity, superwarrant, correspondence,
etc.--truth consists in, but concur that there is precisely one
such property:


* (8) there is a single property \(F\) and truth
consists in a single property \(F\).




The monistic supposition in (8) is tantamount to the claim that
there is but one way of being true. In opposing that claim, pluralism
counts as non-traditional.


## 2. Motivating pluralism: the scope problem




Pluralists' rejection of (8) typically begins by rendering it as a
claim about the invariant nature of truth across all regions of
discourse (Acton 1935; Wright 1992, 1996; Lynch 2000, 2001; for more
on domains see Edwards 2018b; Kim & Pedersen 2018, Wyatt 2013; Yu
2017). Thus rendered, the claim appears to be at odds with the
following observation:


* (9) the plausibility of each inflationist's candidate for the
property \(F\) differs across different regions of discourse.




For example, some theories--such as correspondence
theories--seem intuitively plausible when applied to truths about
ladders, ladles, and other ordinary objects. However, those theories
seem much less convincing when applied to truths about comedy, fashion,
ethical mores, numbers, jurisprudential dictates, etc. Conversely,
theories that seem intuitively plausible when applied to legal, comic,
or mathematical truths--such as those suggesting that the nature
of truth is coherence--seem less convincing when applied to truths
about the empirical world.




Pluralists typically take traditional inflationary theories of truth
to be correct in analyzing truth in terms of some substantive property
\(F\). Yet, the problem with their monistic suppositions lies with
generalization: a given property \(F\) might be necessary and
sufficient for explaining why sentences about a certain subject matter
are true, but no single property is necessary and sufficient for
explaining why \(p\) is true for all sentences \(p\), whatever its subject
matter. Subsequently, those theories' inability to generalize
their explanatory scope beyond the select few regions of discourse for
which they are intuitively plausible casts aspersion on their candidate
for \(F\). This problem has gone by various names, but has come to
be known as 'the scope problem' (Lynch 2004b, 2009; cf. Sher
1998).




Pluralists respond to the scope problem by first rejecting (8) and
replacing it with:


* (10) truth consists in several properties \(F\_1 ,
\ldots ,F\_n\).




With (10), pluralists contend that the nature of truth is not a
single property \(F\) that is invariant across all regions of
discourse; rather the true sentences in different regions of discourse
may consist in different properties among the plurality
\(F\_1 , \ldots ,F\_n\) that
constitute truth's nature.




The idea that truth is grounded in various properties
\(F\_1 , \ldots ,F\_n\) might be
further introduced by way of analogy. Consider water. We ordinarily
think and talk about something's being water as if it were just
one thing--able to exist in different states, but nevertheless
consisting in just one property (H\(\_2\)O). But it would be a
mistake to legislate in advance that we should be monists about water,
since the nature of water is now known to vary more than our intuitions
would initially have it. The isotopic distribution of water allows for
different molecular structures, to include hydroxonium
(H\(\_3\)O), deuterium oxide (D\(\_2\)O), and so-called
'semi-heavy water' (HDO). Or again, consider sugar, the
nature of which includes glucose, fructose, lactose, cellulose, and
similar other such carbohydrates. For the pluralist, so too might truth
be grounded as a plurality of more basic properties.




One reason to take pluralism about truth seriously, then, is that it
provides a solution to the scope problem. In rejecting the
'one-size-fits-all' approach to truth, pluralists formulate
a theory whose generality is guaranteed by accommodating the various
properties \(F\_1 , \ldots ,F\_n\) by
which true sentences come to be true in different regions of discourse.
A second and related reason is that the view promises to be
explanatory. Variance in the nature of truth in turn explains why
theories of truth perform unequally across various regions of
discourse--i.e., why they are descriptively adequate and
appropriate in certain regions of discourse, but not others. For
pluralists, the existence of different kinds of truths is symptomatic
of the non-uniform nature of truth itself. Subsequently, taxonomical
differences among truths might be better understood by formulating
descriptive models about how the nature of truth might vary between
those taxa.


## 3. Prominent versions of pluralism


### 3.1 Platitude-based strategies




Many pluralists have followed Wright (1992) in supposing that
compliance with platitudes is what regiments and characterizes the
behavior and content of truth-predicates. Given a corollary account of
how differences in truth predicates relate to differences among truth
properties, this supposition suggests a platitude-based strategy for
positing many ways of being true. Generally, a strategy will be
platitude-based if it is intended to show that a certain collection of
platitudes \(p\_1 , \ldots ,p\_n\) suffices for
understanding the analysandum or explanandum. By
'platitude', philosophers generally mean certain
uncontroversial expressions about a given topic or domain. Beyond that,
conceptions about what more something must be or have to count as
platitudinous vary widely.


#### 3.1.1 Discourse pluralism/minimalism




A well-known version of platitude-based pluralism is discourse
pluralism. The simplest versions of this view make the following four
claims. Firstly, discourse exhibits natural divisions, and so can be
stably divided into different regions \(D\_1 , \ldots ,D\_n\). Secondly, the platitudes subserving some
\(D\_i\) may be different than those subserving
\(D\_j\). Thirdly, for any pair \((D\_i,
D\_j)\), compliance with different platitudes
subserving each region of discourse can, in principle, result in
numerically distinct truth predicates \((t\_i,
t\_j)\). Finally, numerically distinct truth predicates
designate different ways of being true.




Discourse pluralism is frequently associated with Crispin Wright
(1992, 1996, 2001), although others have held similar views (see, e.g.,
Putnam 1994: 515). Wright has argued that discourse pluralism is
supported by what he calls 'minimalism'. According to
minimalism, compliance with both the disquotational schema and the
operator schema,


* (11) '\(p\)' is true if, and only if, \(p\).
* (12) it is true that \(p\) if, and only if, \(p\).




as well as other 'parent' platitudes, is both necessary
and sufficient for some term \(t\_i\) to qualify as
expressing a concept worth regarding as TRUTH (1992: 34-5).
Wright proposed that the parent platitudes, which basically serve as
very superficial formal or syntactic constraints, fall into two
subclasses: those connecting truth with assertion
('transparency'),


* (13) To assert is to present as true.
* (14) Any attitude to a proposition is an attitude towards its
truth.




and those connecting truth with logical operations
('embedding'),


* (15) Any truth-apt content has a negation which is also
truth-apt.
* (16) Aptitude for truth is preserved under basic logical operations
(disjunction, conjunction, etc.).




Any such term complying with these parent platitudes, regardless of
region of discourse, counts as what Wright called a
'lightweight' or 'minimal' truth predicate.
Yet, the establishment of some \(t\) as a minimal truth predicate
is compatible, argued Wright, with the nature of truth consisting in
different things in different domains (2001: 752).




Wright (2001) has also suggested that lightweight truth predicates
tend to comply with five additional subclasses of platitudes, including
those connecting truth with reality ('correspondence') and
eternity ('stability'),


* (17) For a sentence to be true is for it to correspond with
reality.
* (18) True sentences accurately reflect how matters stand.
* (19) To be true is to "tell it like it is".
* (20) A sentence is always true if it ever is.
* (21) Whatever may be asserted truly may be asserted truly at any
time.




and those disconnecting truth from epistemic state
('opacity'), justification ('contrast'), and
scalar degree ('absoluteness'),


* (22) A thinker may be so situated that a particular truth is beyond
her ken.
* (23) Some truths may never be known.
* (24) Some truths may be unknowable in principle.
* (25) A sentence may be true without being justified and
vice-versa.
* (26) Sentences cannot be more or less true.
* (27) Sentences are completely true if at all.




The idea is that \(t\) may satisfy additional platitudes beyond
these, and in doing so may increase its 'weight'. For
example, some \(t\_i\) may be a more heavyweight truth
predicate than \(t\_j\) in virtue of satisfying
platitudes which entail that truth be evidence-transcendent or that
there be mind-independent truth-makers. Finally, differences in what
constitutes truth in \(D\_1 , \ldots ,D\_n\) are tracked by differences in the weight of
these predicates. In this way, Wright is able to accommodate the
intuition that sentences about, e.g., macromolecules in biochemistry
are amenable to realist truth in a way that sentences about
distributive welfare in ethics may not be.




Distinctions among truth predicates, according to the discourse
pluralist, are due to more and less subtle differences among platitudes
and principles with which they must comply. For example, assuming that
accuracy of reflection is a matter of degree, predicates for truth and
truthlikeness diverge because a candidate predicate may comply with
either (18) or else either of (26) or (27); to accommodate both, two
corollary platitudes must be included to make explicit that accurate
reflection in the case of truth is necessarily maximal and that degrees
of accuracy are not equivalent to degrees of truth. Indeed, it is not
unusual for platitudes to presuppose certain attendant semantic or
metaphysical views. For example,


* (28) A sentence may be characterized as true just in case it
expresses a true proposition.




requires anti-nominalist commitments, an ontological commitment to
propositions, and commitments to the expression relation (translation
relations, an account of synonymy, etc.). Discourse pluralists
requiring predicates to comply with (28) in order to count as
truth-predicates must therefore be prepared to accommodate other claims
that go along with (28) as a package-deal.


#### 3.1.2 Functionalism about truth



'Functionalism about truth' names the thesis that truth
is a functional kind. The most comprehensive and systematic development
of a platitude-based version of functionalism comes from Michael Lynch,
who has been at the forefront of ushering in pluralist themes and
theses (see Lynch 1998, 2000, 2001, 2004c, 2005a, 2005b, 2006, 2009, 2012, 2013; Devlin
2003). Lynch has urged that we need to think about truth in terms of
the 'job' or role, \(F\), that true sentences stake
out in our discursive practices (2005a: 29).




Initially, Lynch's brand of functionalism attempted to
implicitly define the denotation of 'truth' using the
quasi-formal technique of Ramsification. The technique commences by
treating 'true' as the theoretical term \(\tau\)
issued by the theory \(T\) and targeted for implicit definition.
Firstly, the platitudes and principles of the theory are amassed
\((T: p\_1 , \ldots ,p\_n)\) so that
the \(F\)-role can be specified holistically. Secondly, a certain
subset \(A\) of essential platitudes \((p\_i ,
\ldots ,p\_k)\) must be extracted from \(T\),
and are then conjoined. Thirdly, following David Lewis, \(T\) is
rewritten as


* (29) \(R(\tau\_1,\ldots ,
\tau\_n , \omicron\_1,\ldots , \omicron\_n )\)




so as to isolate the \(\tau\)-terms from the non-theoretical
('old, original, other') \(o\)-terms. Fourthly, all
instances of 'true' and other cognate or closely related
\(\tau\)-terms are then replaced by subscripted variables
\(x\_1 , \ldots ,x\_n\). The resulting
open sentence is prefixed with existential quantifiers to bind them.
Next, the Ramsey sentence is embedded in a material biconditional; this
allows functionalists to then specify the conditions by which a given
truth-apt sentence \(p\) has a property that plays the \(F\)-role:


* (30) \(p\) has some property \(\varrho\_i\) realizing the
\(F\)-role \(\equiv \exists x\_1 , \ldots ,\exists x\_n [R(x\_1 ,
\ldots ,x\_n , \omicron\_1,\ldots , \omicron\_n ) \amp p\) has
\(x\_1\)],




where, say, the variable \(x\_1\) is the one that
replaced 'true'. Having specified the conditions under
which \(p\) has some property realizing \(F\), functionalists can then
derive another material biconditional stating that \(p\) is true iff \(p\) has
some property realizing the \(F\)-role.




However, as Lynch (2004: 394) cautioned, biconditionals that specify
necessary and sufficient conditions for \(p\) to be true still leave open
questions about the 'deep' metaphysical nature of truth.
Thus, given the choice, Lynch--following up on a suggestion from
Pettit (1996: 886)--urged functionalists to identify truth, not
with the properties realizing the \(F\)-role in a given region of
discourse, but with the \(F\)-role itself. Doing so is one way to
try to secure the 'unity' of truth (on the presumption that
there is just one \(F\)-role). Hence, to say that truth is a
functional kind \(F\) is to say that the \(\tau\)-term
'truth' denotes the property of having a property that
plays the \(F\)-role, where the \(F\)-role is tantamount to
the single unique second-order property of being \(F\).
Accordingly, this theory proposes that something is true just in case
it is \(F\).




Two consequences are apparent. Firstly, the functionalist's
commitment to alethic properties realizing the \(F\)-role seems to
be a commitment to a grounding thesis. This explains why Lynch's
version of alethic functionalism fits the pattern typical of
inflationary theories of truth, which are committed to (6) and
(7) above. Secondly, however, like most traditional inflationary
theories, Lynch's functionalism about truth appears to be
monistic. Indeed, the functionalist commitment to identifying truth
with and only with the unique property of being \(F\) seems to
entail a commitment to strong alethic monism in (5) rather than
pluralism (Wright 2005). Nonetheless, it is clear that Lynch's
version does emphasize that sentences can have the property of being
\(F\) in different ways. The theory thus does a great deal to
accommodate the intuitions that initially motivate the pluralist thesis
that there is more than one way of being true, and to finesse a fine
line between monism and pluralism.




For pluralists, this compromise may not be good enough, and critics
of functionalism about truth have raised several concerns. One
stumbling block for functionalist theories is a worry about epistemic
circularity. As Wright (2010) observes, any technique for implicit
definition, such as Ramsification, proceeds on the basis of explicit
decisions that the platitudes and principles constitutive of the
modified Ramsey sentence are themselves true, and making explicit
decisions that they are true requires already knowing in advance what
truth is. Lynch (2013a) notes that the problem is not peculiar to
functionalism about truth, generalizing to virtually all approaches
that attempt to fix the denotation of 'true' by appeal to
implicit definition. Some might want to claim that it generalizes even
further, namely to any theory of truth whatsoever. Another issue is
that the \(F\)-role becomes disunified to the extent that
\(T\) can accommodate substantially different platitudes and
principles. Recall that the individuation and identity conditions of
the \(F\)-role--with which truth is identified--are
determined holistically by the platitudes and principles constituting
\(T\). So where \(T\) is constituted by expressions of the
beliefs and commitments of ordinary folk, pluralists could try to show
that these beliefs and commitments significantly differ across
epistemic communities (see, e.g., Naess 1938a, b; Maffie 2002;
Ulatowski 2017, Wyatt 2018). In that case, Ramsification over
significantly different principles may yield implicit definitions of
numerically distinct role properties
\(F\_1, F\_2 , \ldots ,F\_n\), each of which is a warranted claimant to being
truth.


### 3.2 Correspondence pluralism




The correspondence theory is often invoked as exemplary of
traditional monistic theories of truth, and thus as a salient rival to
pluralism about truth. Prima facie, however, the two are consistent.
The most fundamental principle of any version of the correspondence
theory,


* (31) Truth consists in correspondence.




specifies what truth consists in. Since it involves no covert
commitment about how many ways of being true there are, it does not
require denying that there is more than one (Wright & Pedersen
2010). In principle, there may be different ways of consisting in
correspondence that yield different ways of being true. Subsequently,
whether the two theories turn out to be genuine rivals depends on
whether further commitments are made to explicitly rule out
pluralism.




Correspondence theorists have occasionally made proposals that combine
their view with a version of pluralism. An early--although not
fully developed--proposal of this kind was made by Henry Acton
(1935: 191). Two recent proposals are noteworthy and have been
developed in detail. Gila Sher (1998, 2004, 2005, 2013, 2015, 2016a) has
picked up the project of expounding on the claim that sentence in
domains like logic correspond to facts in a different way than do
sentences in other domains, while Terence Horgan and colleagues
(Horgan 2001; Horgan & Potrc 2000, 2006; Horgan & Timmons
2002; Horgan & Barnard 2006; Barnard & Horgan 2013)
have elaborated a view that involves a defense of the claim that not
all truths correspond to facts in the same way.




For Sher, truth does not consist in different properties in
different regions of discourse (e.g., superwarrant in macroeconomics,
homomorphism in immunology, coherence in film studies, etc.). Rather,
it always and everywhere consists in correspondence. Taking
'correspondence' to generally refer to an \(n\)-place
relation \(R\), Sher advances a version of correspondence
pluralism by countenancing different 'forms', or ways of
corresponding. For example, whereas the physical form of correspondence
involves a systematic relation between the content of physical
sentences and the physical structure of the world, the logical form of
correspondence involves a systematic relation between the logical
structure of sentences and the formal structure of the world, while the
moral form of correspondence involves a relation between the moral
content of sentences and (arguably) the psychological or sociological
structure of the world.




Sher's view can be regarded as a moderate form of pluralism.
It combines the idea that truth is many with the idea that truth is
one. Truth is many on Sher's view because there are different
forms of correspondence. These are different ways of being true. At the
same time, truth is one because these different ways of being true are
all forms of correspondence.




For Sher, a specific matrix of 'factors' determines the
unique form of correspondence as well as the correspondence principles
that govern our theorizing about them. Which factors are in play
depends primarily on the satisfaction conditions of predicates. For
example, the form of correspondence for logical truths of the form


* (32) Every \(x\) either is or is not self-identical.




is determined solely by the logical factor, which is reflected by
the universality of the union of the set of self-identical things and
its complement. Or again, consider the categorical sentences


* (33) Some humans are disadvantaged.




and


* (34) Some humans are vain.




Both (33) and (34) involve a logical factor, which is reflected in
their standard form as I-statements (i.e., some \(S\) are \(P)\), as well as
the satisfaction conditions of the existential quantifier and copula; a
biological factor, which is reflected in the satisfaction conditions
for the predicate 'is human'; and a normative factor, which
is reflected in the satisfaction conditions for the predicates
'is disadvantaged' and 'is vain'. But whereas
(34) involves a psychological factor, which is reflected in the
satisfaction conditions for 'is vain', (33) does not. Also,
(33) may involve a socioeconomic factor, which is reflected in the
satisfaction conditions for 'is disadvantaged', whereas
(34) does not.




By focusing on subsentential factors instead of supersentential
regions of discourse, Sher offers a more fine-grained way to
individuate ways in which true sentences correspond. (Sher supposes
that we cannot name the correspondent of a given true sentence since
there is no single discrete hypostatized entity beyond the
\(n\)-tuples of objects, properties and relations, functions,
structures (complexes, configurations), etc. that already populate
reality.) The upshot is a putative solution to problems of mixed
discourse (see SS4 below): the truth of sentences like


* (35) Some humans are disadvantaged and vain.




is determined by all of the above factors, and which
is--despite the large overlap--a different kind of truth than
either of the atomic sentences (33) and (34), according to Sher.




For their part, Horgan and colleagues propose a twist on the
correspondence theorist's claim that truth consists in a
correspondence relation \(R\) obtaining between a given
truth-bearer and a fact. They propose that there are exactly two
species of the relation \(R\): 'direct'
(\(R\_{dir}\)) and 'indirect correspondence'
(\(R\_{ind}\)), and thus exactly two ways of being true.
For Horgan and colleagues, which species of \(R\)--and thus
which way of being true--obtains will depend on the austerity of
ontological commitments involved in assessing sentences; in turn, which
commitments are involved depends on discursive context and operative
semantic standards. For example, an austere ontology commits to only a
single extant object: namely, the world (affectionally termed the
'blobject'). Truths about the blobject, such as


* (36) The world is all that is the case.




if it is one, correspond to it directly. Truths about things other
than the blobject correspond to them indirectly. For example, sentences
such as


* (37) Online universities are universities.




may be true even if the extension of the predicate
'university' is--strictly speaking--empty or what
is referred to by 'online universities' is not in the
non-empty extension of 'university'. In short, \(p\) is
true\(\_1\) iff \(p\) is \(R\_{dir}\)-related to the
blobject given contextually operative standards \(c\_i,
c\_j , \ldots ,c\_m\).
Alternatively, \(p\) is true\(\_2\) iff \(p\) is
\(R\_{ind}\)-related to non-blobject entities given
contextually operative standards \(c\_j,
c\_k , \ldots ,c\_n\). So, truth
always consists in correspondence. But the two types of correspondence
imply that there is more than one way of being true.


## 4. Objections to pluralism and responses


### 4.1 Ambiguity




Some take pluralists to be committed to the thesis that
'true' is ambiguous: since the pluralist thinks that there
is a range of alethically potent properties (correspondence, coherence,
etc.), 'true' must be ambiguous between these different
properties. This is thought to raise problems for pluralists. According
to one objection, the pluralist appears caught in a grave dilemma.
'True' is either ambiguous or unambiguous. If it is, then
there is a spate of further problems awaiting (see
SS4.4-SS4.6 below). If it is not, then there is only one
meaning of 'true' and thus only one property designated by
it; so pluralism is false.




Friends of pluralism have tended to self-consciously distance
themselves from the claim that 'true' is ambiguous (e.g.,
Wright 1996: 924, 2001; Lynch 2001, 2004b, 2005c). Generally, however,
the issue of ambiguity for pluralism has not been well-analyzed. Yet,
one response has been investigated in some detail. According to this
response, the ambiguity of 'true' is simply to be taken as
a datum. 'True' is de facto ambiguous (see, e.g., Schiller
1906; Pratt 1908; Kaufmann 1948; Lucas 1969; Kolbel 2002, 2008;
Sher 2005; Wright 2010). Alfred Tarski, for instance, wrote:



> 
> 
> 
> The word 'true', like other words from our everyday
> language, is certainly not unambiguous. [...] We should reconcile
> ourselves with the fact that we are confronted, not with one concept,
> but with several different concepts which are denoted by one word; we
> should try to make these concepts as clear as possible (by means of
> definition, or of an axiomatic procedure, or in some other way); to
> avoid further confusion we should agree to use different terms for
> different concepts [...]. (1944: 342, 355)
> 
> 
> 




If 'true' is ambiguous de facto, as some authors have
suggested, then the ambiguity objection may turn out to
be--again--not so much an objection or disconfirmation of the
theory, but rather just a datum about 'truth'-talk in
natural language that should be explained or explained away by theories
of truth. In that case, pluralists seem no worse off--and possibly
better--than any number of other truth theorists.




A second possible line of response from pluralists is that their
view is not necessarily inconsistent with a monistic account of either
the meaning of 'true' or the concept TRUTH. After all,
'true' is ambiguous only if it can be assigned more than
one meaning or semantic structure; and it has more than one meaning
only if there is more than one stable conceptualization or concept
TRUTH supporting each numerically distinct meaning. Yet, nothing about
the claim that there is more than one way of being true entails, by
itself, that there is more than one concept TRUTH. In principle, the
nature of properties like being true--whether homomorphism,
superassertibility, coherence, etc.--may outstrip the concept
thereof, just as the nature of properties like being water--such
as H\(\_2\)O, H\(\_3\)O, XYZ, etc.--may outstrip the
concept WATER (see, e.g., Wright 1996, 2001; Alston 2002; Lynch 2001,
2005c, 2006). Nor is monism about truth necessarily inconsistent with
semantic or conceptual pluralism. The supposition that TRUTH is both
many and one (i.e., 'moderate monism') neither rules out
the construction of multiple concepts or meanings thereof, nor rules
out the proliferation of uses to express those concepts or meanings.
For example, suppose that the only way of being true turns out to be a
structural relation \(R\) between reality and certain
representations thereof. Such a case is consistent with the existence
of competing conceptions of what \(R\) consists in: weak
homomorphism, isomorphism, 'seriously dyadic'
correspondence, a causal \(n\)-place correspondence relation, etc.
A more sensitive conclusion, then, is just that the objection from
ambiguity is an objection to conceptual or semantic pluralism, not to
any alethic theory--pluralism or otherwise.


### 4.2 The scope problem as a pseudo-problem




According to the so-called 'Quine-Sainsbury objection',
pluralists' postulation of ambiguity in metalinguistic alethic
terms is not actually necessary, and thus not well-motivated. This is
because taxonomical differences among kinds of truths in different
domains can be accounted for simply by doing basic ontology in
object-level languages.



> 
> 
> 
> [E]ven if it is one thing for 'this tree is an oak' to
> be true, another thing for 'burning live cats is cruel' to
> be true, and yet another for 'Buster Keaton is funnier than
> Charlie Chaplin' to be true, this should not lead us to suppose
> that 'true' is ambiguous; for we get a better explanation
> of the differences by alluding to the differences between trees,
> cruelty, and humor. (Sainsbury 1996: 900; see also Quine 1960: 131)
> 
> 
> 




Generally, pluralists have not yet developed a response to the
Quine-Sainsbury objection. And for some, this is because the real force
of the Quine-Sainsbury objection lies in its exposure of the scope
problem as a pseudo-problem (Dodd 2013; see also Asay 2018). Again, the idea is that
traditional inflationary theories postulate some candidate for
\(F\) but the applicability and plausibility of \(F\) differs
across regions of discourse. No such theory handles the truths of
moral, mathematical, comic, legal, etc. discourse equally well; and
this suggests that these theories, by their monism, face limitations on
their explanatory scope. Pluralism offers a non-deflationary solution.
Yet, why think that these differences among domains mark an alethic
difference in truth per se, rather than semantic or discursive
differences among the sentences comprising those domains? There is more
than one way to score a goal in soccer, for example (via corner kick,
ricochet off the foot of an opposing player or the head of a teammate,
obstruct the goalkeeper, etc.), but it is far from clear that this
entails pluralism about the property of scoring a goal in soccer.
(Analogy belongs to an anonymous referee.) Pluralists have yet to
adequately address this criticism (although see Blackburn 2013; Lynch 2013b, 2018; Wright 1998 for further discussion).


### 4.3 The criteria problem




Pluralists who invoke platitude-based strategies bear the burden of
articulating inclusion and exclusion criteria for determining which
expressions do, or do not, count as members of the essential subset of
platitudes upon which this strategy is based (Wright, 2005). Candidates
include: ordinariness, intuitiveness, uninformativeness, wide use or
citation, uncontroversiality, a prioricity, analyticity,
indefeasibility, incontrovertibility, and sundry others. But none has
proven to be uniquely adequate, and there is nothing close to a
consensus about which criteria to rely on.




For instance, consider the following two conceptions. One conception
takes platitudes about \(x\) to be expressions that must be
endorsed on pain of being linguistically incompetent with the
application of the terms \(t\_1 , \ldots ,t\_n\) used to talk about \(x\) (Nolan 2009).
However, this conception does not readily allow for disagreement: prima
facie, it is not incoherent to think that two individuals, each of whom
is competent with the application of
\(t\_1 (x), \ldots ,t\_n (x)\), may differ as to whether some \(p\)
must be endorsed or whether some expression is genuinely platitudinous.
For instance, consider the platitude in (17), which connects being
true with corresponding with reality. Being linguistically competent
with terms for structural relations like correspondence does not force
endorsement of claims that connect truth with correspondence; no one
not already in the grip of the correspondence theory would suppose that
they must endorse (17), and those who oppose it would certainly suppose
otherwise. Further inadequacies beleaguer this conception. It makes no
provision for degrees of either endorsement or linguistic incompetence.
It makes no distinction between theoretical and non-theoretical terms,
much less restrict \(t\_1 (x), \ldots ,t\_n (x)\) to non-theoretical terms. Nor does
it require that platitudes themselves be true. On one hand, this
consequently leaves open the possibility that universally-endorsed but
false or otherwise alethically defective expressions are included in
the platitude-based analysis of 'true'. An old platitude
about whales, for example--one which was universally endorsed on
pain of being linguistically incompetent--prior to whales being
classified as cetaceans--was that they are big fish. The worry,
then, is that the criteria may allow us to screen in certain
'fish stories' about truth. This would be a major problem
for advocates of Ramsification and other forms of implicit definition,
since those techniques work only on the presupposition that all input
being Ramsified over or implicitly defined is itself true (Wright
2010). On the other hand, making explicit that platitudes must also be
true seems to entail that they are genuine 'truisms'
(Lynch 2005c), though discovering which ones are truly indefeasible is
a further difficulty--one made more difficult by the possibility
of error theories (e.g., Devlin 2003) suggesting that instances of the
\(T\)-schema are universally false. Indeed, we are inclined to say
instances of disquotational, equivalence, and operator schemas are
surely candidates for being platitudinous if anything is; but to say
that they must be endorsed on pain of being linguistically incompetent
is to rule out a priori error theories about instances of the
\(T\)-schema.




A second, closely related conception is that platitudes are
expressions, which--in virtue of being banal, vacuous, elementary,
or otherwise trivial--are acceptable by anyone who understands
them (Horwich 1990). The interaction of banality or triviality with
acceptance does rule out a wide variety of candidate expressions,
however. For instance, claims that are acceptable by anyone who
understands them may still be too substantive or informative to count
as platitudinous, depending on what they countenance. Similarly, claims
that are too 'thin' or neutral to vindicate any particular
theory \(T\) may still be too substantive or informative to count
as genuinely platitudinous on this conception (Wright 1999). This is
particularly so given that nothing about a conception of platitudes as
'pretheoretical claims' strictly entails that they reduce
to mere banalities (Vision 2004). Nevertheless, criteria like banality
or triviality plus acceptance might also screen in too few expressions
(perhaps as few as one, such as a particular instance of the
\(T\)-schema). Indeed, it is an open question whether any of the
principles in (11)-(28) would count as platitudes on this
conception.




An alternative conception emphasizes that the criteria should
instead be the interaction of informality, truth, a prioricity, or
perhaps even analyticity (Wright 2001: 759). In particular, platitudes
need not take the form of an identity claim, equational definition, or
a material biconditional. At the extreme, expressions can be as
colloquial as you please so long as they remain true a priori (or
analytically). These latter criteria are commonly appealed to, but are
also not without problems. Firstly, a common worry is whether there are
any strictly analytic truths about truth, and, if there are, whether
they can perform any serious theoretical work. Secondly, these latter
criteria would exclude certain truths that are a posteriori but no less
useful to a platitude-based strategist.


### 4.4 The instability challenge




Another objection to pluralism is that it is an inherently instable
view: i.e., as soon as the view is formulated, simple reasoning renders
it untenable (Pedersen 2006, 2010; see also Tappolet 1997, 2000; Wright
2012). This so-called *instability challenge* can be presented
as follows. According to the moderate pluralist, there is more than one
truth property \(F\_1 , \ldots ,F\_n\). Yet, given \(F\_1 , \ldots ,F\_n\), it seems we should recognize another truth
property:


* (38)
 \(\forall p[F\_U (p) \leftrightarrow F\_1 (p) \vee \cdots \vee F\_n (p)]\).




Observe that \(F\_U\) is not merely some property
possessed by every \(p\) which happens to have one of
\(F\_1 , \ldots ,F\_n\). (The property
of being a sentence is one such a property, but it poses no trouble to
the pluralist.) Rather, \(F\_U\) must be an alethic
property whose extension perfectly positively covaries with the
combined extension of the pluralist truth properties
\(F\_1 , \ldots ,F\_n\). And since
nothing is required for the existence of this new property other than
the truth properties already granted by the pluralist, (38) gives a
necessary and sufficient condition for \(F\_U\) to be had
by some \(p\): a sentence \(p\) is \(F\_U\) just in case \(p\) is
\(F\_1 \vee \cdots \vee F\_n\). Thus,
any sentence that is any of \(F\_1 , \ldots ,F\_n\) may be true in some more generic or universal
way, \(F\_U\). This suggests, at best, that strong
pluralism is false, and moderate monism is true; and at worst, there
seems to be something instable, or self-refuting, about pluralism.




Pluralists can make concessive or non-concessive responses to the
instability challenge. A concessive response grants that such a truth
property exists, but maintains that it poses no serious threat to
pluralism. A non-concessive response is one intended to rebut the
challenge, e.g., by rejecting the existence of a common or universal
truth property. One way of trying to motivate this rejection of
\(F\_U\) is by attending to the distinction between
sparse and abundant properties, and then demonstrating that alethic
properties like truth must be sparse and additionally argue that the
would-be trouble-maker \(F\_U\) is an abundant property.
According to sparse property theorists, individuals must be unified by
some qualitative similarity in order to share a property. For example,
all even numbers are qualitatively similar in that they share the
property of being divisible by two without remainder. Now, consider a
subset of very diverse properties \(G\_1 , \ldots ,G\_n\) possessed by an individual \(a\). Is there
some further, single property of being \(G\_1\), or
..., or \(G\_n\) that \(a\) has? Such a further
property, were it to exist, would be highly disjunctive; and it may
seem unclear what, if anything, individuals that were
\(G\_1\), or ..., or \(G\_n\) would
have in common--other than being \(G\_1\), or
..., or \(G\_n\). According to sparse property
theorists, the lack of qualitative similarity means that this putative
disjunctive property is not a property properly so-called. Abundant
property theorists, on the other hand, deny that qualitative similarity
is needed in order for a range of individuals to share a property.
Properties can be as disjunctive as you like. Indeed, for any set
\(A\) there is at least one property had by all members of
\(A\)--namely, being a member of \(A\). And since there
is a set of all things that have some disjunctive property, there is a
property--abundantly construed--had by exactly those things.
It thus seems difficult to deny the existence of \(F\_U\)
if the abundant conception of properties is adopted. So pluralists who
want to give a non-concessive response to the metaphysical instability
challenge may want to endorse the sparse conception (Pedersen 2006).
This is because the lack of uniformity in the nature of truth across
domains is underwritten by a lack of qualitative similarity between the
different truth properties that apply to specific domains of discourse.
The truth property \(F\_U\) does not exist, because truth
properties are to be thought of in accordance with the sparse
conception.




Even if the sparse conception fails to ground pluralists'
rejection of the existence of the universal truth property
\(F\_U\), a concessive response to the instability
challenge is still available. Pluralists can make a strong case that
the truth properties \(F\_1 , \ldots ,F\_n\) are more fundamental than the universal truth
property \(F\_U\) (Pedersen 2010). This is because
\(F\_U\) is metaphysically dependent on
\(F\_1 , \ldots ,F\_n\), in the sense
that \(F\_U\) is introduced in virtue of its being one of
\(F\_1 , \ldots ,F\_n\), and not
vice-versa. Hence, even if the pluralist commits to the existence of
\(F\_U\)--and hence, to moderate metaphysical
monism--there is still a clear sense in which her view is
distinctively more pluralist than monist.


### 4.5 Problems regarding mixed discourse


#### 4.5.1 Mixed atomic sentences




The content of some atomic sentences seems to hark exclusively from
a particular region of discourse. For instance, 'lactose is a
sugar' concerns chemical reality, while '\(7 + 5 = 12\)'
is solely about the realm of numbers (and operations on these). Not all
discourse is pure or exclusive, however; we often engage in so-called
'mixed discourse', in which contents from different regions
of discourse are combined. For example, consider:


* (39) Causing pain is bad.




Mixed atomic sentences such as (39) are thought to pose problems for
pluralists. It seems to implicate concepts from the physical domain
(causation), the mental domain (pain), and the moral domain (badness)
(Sher 2005: 321-22). Yet, if pluralism is correct, then in which
way is (39) true? Is it true in the way appropriate to talk of the
physical, the mental, or the moral? Is it true in neither of these
ways, or in all of these three ways, or in some altogether different
way?




The source of the problem may be the difficulty in classifying
discursive content--a classificatory task that is an urgent one
for pluralists. For it is unclear how they can maintain that regions of
discourse \(D\_1 , \ldots ,D\_n\)
partially determine the ways in which sentences can be true without a
procedure for determining which region of discourse
\(D\_i\) a given \(p\) belongs to.




One suggestion is that a mixed atomic sentence \(p\) belongs to
no particular domain. Another is that it belongs to several (Wyatt 2013). Lynch (2005b:
340-41) suggested paraphrasing mixed atomic sentences as
sentences that are classifiable as belonging to particular domains. For
example, (39) might be paraphrased as:


* (40) We ought not cause pain.




Unlike (39), the paraphrased (40) appears to be a pure atomic
sentence belonging to the domain of morals. This proposal remains
underdeveloped, however. It is not at all clear that (40) counts as a
felicitous paraphrase of (39), and, more generally, unclear whether all
mixed atomic sentences can be paraphrased such that they belong to just
one domain without thereby altering their meaning, truth-conditions, or
truth-values.




Another possible solution addresses the problem head-on by
questioning whether atomic sentences really are mixed, thereby denying
the need for any such paraphrases. Consider the following
sentences:


* (41) The Mona Lisa is beautiful.
* (42) Speeding is illegal.




Prima facie, what determines the domain-membership of (41) and (42)
is the aesthetic and legal predicates 'is beautiful' and
'is illegal', respectively. It is an aesthetic matter
whether the Mona Lisa is beautiful; this is because (41) is true in
some way just in case the Mona Lisa falls in the extension of the
aesthetic predicate 'is beautiful' (and mutatis mutandis
for (42)). In the same way, we might take (39) to exclusively belong to
the moral domain given that the moral predicate 'is
bad'. (This solution was presented in the first 2012 version of this entry; see Edwards 2018a for later, more detailed treatment.)




It is crucial to the latter two proposals that any given mixed
atomic sentence \(p\) has its domain membership essentially, since such
membership is what determines the relevant kind of truth. Sher (2005,
2011) deals with the problem of mixed atomic sentences differently. On
her view, the truth of a mixed atomic sentence is not accounted for by
membership to some specific domain; rather the 'factors'
involved in the sentence determine a specific form of correspondence,
and this specific form of correspondence is what accounts for the truth
of \(p\). The details about which specific form of correspondence obtains
is determined at the sub-sentential levels of reference, satisfaction,
and fulfillment. For example, the form of correspondence that accounts
for the truth of (39) obtains as a combination of the physical
fulfillment of 'the causing of \(x\)', the mental
reference of 'pain', and the moral satisfaction of
'\(x\) is bad' (2005: 328). No paraphrase is
needed.


#### 4.5.2 Mixed compounds




Another related problem pertains to two or more sentences joined by
one or more logical connectives, as in


* (43) Killing innocent people is wrong and \(7 + 5 = 12\).




Unlike atomic sentences, the mixing here takes place at the
sentential rather than sub-sentential level: (43) is a conjunction,
which mixes the pure sentence '\(7 + 5 = 12\)' with the pure
sentence 'killing innocent people is wrong'. (There are, of
course, also mixed compounds that involve mixed atomic sentences.) For
many theorists, each conjunct seems to be true in a different way, if
true at all: the first conjunct in whatever way is appropriate to moral
theory, and the second conjunct in whatever way is appropriate to
arithmetic. But then, how is the pluralist going to account for the
truth of the conjunction (Tappolet 2000: 384)? Pluralists owe an answer
to the question of which way, exactly, a conjunction is true when its
conjuncts are true in different ways.




Additional complications arise for pluralists who commit to facts
being what make sentences true (e.g., Lynch 2001: 730), or other such
truth-maker or -making theses. Prima facie, we would reasonably expect
there to be different kinds of facts that make the conjuncts of (43)
true, and which subsequently account for the differences in their
different ways of being true. However, what fact or facts makes true
the mixed compound? Regarding (43), is it the mathematical fact, the
moral fact, or some further kind of fact? On one hand, the claims that
mathematical or moral facts, respectively, make \(p\) true seem to betray
the thought that both facts contribute equally to the truth of the
mixed compound. On the other hand, the claim that some third
'mixed' kind of fact makes \(p\) true leaves the pluralist with
the uneasy task of telling a rather alchemist story about
fact-mixtures.




Functionalists about truth (e.g., Lynch 2005b: 396-97) propose
to deal with compounds by distinguishing between two kinds of realizers
of the \(F\)-role. The first is an atomic realizer, such that an
atomic proposition \(p\) is true iff \(p\) has a property that realizes the
\(F\)-role. The second is a compound realizer, such that a
compound \(q \* r\) (where \(q\) and \(r\) may themselves be complex) is true
iff


* (44) \({\*} = \wedge : q \wedge r\) has the property of being an instance of
the truth-function for conjunction with conjuncts that both have a
property that realizes the \(F\)-role.
* (45) \({\*} = \vee : q \vee r\) has the property of being an instance of the
truth-function for disjunction with at least one disjunct that has a
property that realizes the \(F\)-role.
* (46) \({\*} = \rightarrow : q \rightarrow r\) has the property of being an
instance of the truth-function for material conditional with an
antecedent that does not have the property that realizes the
\(F\)-role for its domain or a consequent that has a property that
realizes the \(F\)-role.




The realizers for atomic sentences are properties like
correspondence, coherence, and superwarrant. The realizer properties
for compounds are special, in the sense that realizer properties for a
given kind of compound are only had by compounds of that kind. Witness
that each of these compound realizer properties requires any of its
bearers to be an instance of a specific truth-function. Pure and mixed
compounds are treated equally on this proposal: when true, they are
true because they instantiate the truth-function for conjunction,
having two or more conjuncts that have a property that realizes the
\(F\)-role (and mutatis mutandis for disjunctions and material
conditionals).




However, this functionalist solution to the problem of mixed
compounds relies heavily on that theory's monism--i.e., its
insistence that the single role property \(F\) is a universal
truth property. This might leave one wondering whether a solution is
readily available to someone who rejects the existence of such a
property. One strategy is simply to identify the truth of conjunctions, disjunctions, and conditionals with the kind of properties specified by (44), (45), and (46), respectively (as opposed to taking them to be realizers of a single truth property). Thus, e.g., the truth of any conjunction simply \(is\) to be an instance of the truth-function for conjunction with conjuncts that have the property that plays the \(F\)-role for them (Kim & Pedersen 2018, Pedersen & Lynch 2018 (Sect. 20.6.2.1). Another strategy is to try to use the resources of multi-valued logic. For example, one can posit an ordered set of designated
values for each way of being true \(F\_1 , \ldots ,F\_n\) (perhaps according to their status as
'heavyweight' or 'lightweight'), and then take
conjunction to be a minimizing operation and disjunction a maximizing
one, i.e., \(v(p \wedge q) = \min\{v(p), v(q)\}\)
and \(v(p \vee q) = \max\{v(p), v(q)\}\).
Resultingly, each conjunction and disjunction--whether pure or
mixed--will be either true in some way or false in some way
straightforwardly determined by the values of the constituents. For
example, consider the sentences


* (47) Heat is mean molecular kinetic energy.
* (48) Manslaughter is a felony.




Suppose that (47) is true in virtue of corresponding to physical
reality, while (48) true in virtue of cohering with a body of law; and
suppose further that correspondence \((F\_1)\) is more
'heavyweight' than coherence \((F\_2)\).
Since conjunction is a minimizing operation and \(F\_2 \lt F\_1\), then 'heat is mean molecular
kinetic energy and manslaughter is a felony' will be
\(F\_2\). Since disjunction is a maximizing operation,
then 'heat is mean molecular kinetic energy or manslaughter is a
felony' will be \(F\_1\).




The many-valued solution to the problem of mixed compounds just
outlined is formally adequate because it determines a way that each
compound is true. However, while interesting, the proposal needs to be
substantially developed in several respects. For example, how is
negation treated--are there several negations, one for each way of
being true, or is there a single negation? Also, taking 'heat is
mean molecular kinetic energy and manslaughter is a felony' to be
true in the way appropriate to law betrays a thought that seems at
least initially compelling, *viz.* that both conjuncts
contribute to the truth of the conjunction. Alternatively, one could
take mixed compounds to be true in some third way. However, this would
leave the pluralist with the task of telling some story about how this
third way of being true relates to the other two. Again substantial
work needs to be done.




Edwards (2008) proposed another solution to the problem of mixed
conjunctions, the main idea of which is to appeal to the following
biconditional schema:


* (49) \(p\) is true\(\_i\) and \(q\) is true\(\_j\) iff \(p \wedge q\)
is true\(\_k\).




Edwards suggests that pluralists can answer the challenge that mixed
conjunctions pose by reading the stated biconditional as having an
order of determination: \(p \wedge q\) is true\(\_k\) in
virtue of \(p\)'s being true\(\_i\) and \(q\)'s being
true\(\_j\), but not vice-versa. This, he maintains,
explains what kind of truth a conjunction \(p \wedge q\) has when its
conjuncts are true in different ways; for the conjunction is
true\(\_k\) in virtue of having conjuncts that are both
true, where it is inessential whether the conjuncts are true in the
same way. Truth\(\_k\) is a further way of being true
that depends on the conjuncts being true in some way without reducing
to either of them. The property true\(\_k\) is thus not a
generic or universal truth property that applies to the conjuncts as
well as the conjunction.




As Cotnoir (2009) emphasizes, Edwards' proposal provides too
little information about the nature of true\(\_k\). What
little is provided makes transparent the commitment to
true\(\_k\)'s being a truth property had only by
conjunctions, in which case it is unclear whether Edwards's
solution can generalize. In this regard, Edwards' proposal is
similar to Lynch's functionalist proposal, which is committed to
there being a specific realizer property for each type of logical
compound.


#### 4.5.3 Mixed inferences




Mixed inferences--inferences involving truth-apt sentences from
different domains--appear to be yet another problem for the
pluralist (Tappolet 1997, 2000; Pedersen 2006). One can illustrate the
problem by supposing, with the pluralist, that there are two ways of
being true, one of which is predicated of the antecedent of a
conditional and the other as its consequent. It can be left open in
what way the conditional itself is true. Consider the following
inference:


* (50) Satiated dogs are lazy.
* (51) Our dog is satiated.
* (52) Our dog is lazy.




This inference would appear to be valid. However, it is not clear
that pluralists can account for its validity by relying on the standard
characterization of validity as necessary truth preservation from
premises to conclusion. Given that the truth properties applicable to
respectively (51) and (52) are different, what truth property is
preserved in the inference? The pluralist owes an explanation of how
the thesis that there are many ways of being true can account for the
validity of mixed inferences.




Beall (2000) argued that the account of validity used in
multi-valued logics gives pluralists the resources to deal with the
problem of mixed inferences. For many-valued logics, validity is
accounted for in terms of preservation of designated value, where
designated values can be thought of as ways of being true, while
non-designated values can be thought of as ways of being false.
Adopting a designated-value account of validity, pluralists can simply
take \(F\_1 , \ldots ,F\_n\) to be the
relevant designated values and define an inference as valid just in
case the conclusion is designated if each premise is designated (i.e.,
one of \(F\_1 , \ldots ,F\_n)\). On
this account, the validity of (mixed) arguments whose premises and
conclusion concern different regions of discourse is evaluable in terms
of more than one of \(F\_1 , \ldots ,F\_n\); the validity of (pure) arguments whose premises
and conclusion pertain to the same region of discourse is evaluable in
terms of the same \(F\_i\) (where \(1 \le i \le n)\). An immediate rejoinder is that the term
'true' in 'ways of being true' refers to a
universal way of being true--i.e., being designated simpliciter
(Tappolet 2000: 384). If so, then the multi-valued solution comes at
the cost of inadvertently acknowledging a universal truth property. Of
course, as noted, the existence of a universal truth property poses a
threat only to strong pluralism.


### 4.5 The problem of generalization




Alethic terms are useful devices for generalizing. For instance,
suppose we wish to state the law of excluded middle. A tedious way
would be to produce a long--indeed,
infinite--conjunction:


* (53) Everything is either actual or non-actual, and thick or not
thick, and red or not red, and ...




However, given the equivalence schema for propositions,


* (54) The proposition that \(p\) is true iff \(p\).




there is a much shorter formula, which captures what (54) is meant
to express by using 'true', but without loss of explanatory
power (Horwich 1990: 4):


* (55) Every proposition of the form \(\langle\)everything is \(G\) or
not\(-G\rangle\) is true.




Alethic terms are also useful devices for generalizing over what
speakers say, as in


* (56) What Chen said is true.




The utility of a generalization like (56) is not so much that it
eliminates the need to rely on an infinite conjunction, but that it is
'blind' (i.e., made under partial ignorance of what was
said).




Pluralists seem to have difficulty accounting for truth's use
as a device for generalization. One response is to simply treat uses of
'is true' as elliptical for 'is true in one way or
another'. In doing so, pluralists account for generalization
without sacrificing their pluralism. A possible drawback, however, is
that it may commit pluralists to the claim that 'true'
designates the disjunctive property of being \(F\_1
\vee \cdots \vee F\_n\). Granting the existence of
such a property gives pluralists a story to tell about generalizations
like (55) and (56), but the response is a concessive one available only
to moderate pluralists. However, as noted in SS4.2.3, the existence
of such a property is not a devastating blow to all pluralists, since
the domain-specific truth properties \(F\_1 , \ldots ,F\_n\) remain explanatorily basic in relation to the
property of being \(F\_1 \vee \cdots \vee F\_n\).


### 4.6 The problem of normativity




As is often noted, truth appears to be normative--i.e., a
positive standard governing immanent content (Sher 2004:
26). According to one prominent tradition (Engel 2002, 2013;
Wedgwood 2002; Boghossian 2003; Shah 2003; Gibbard 2005; Ferrari 2018; Lynch 2009; Whiting 2013),
truth is a doxastic norm because it is the norm of correctness for
belief:


* (57) \(\forall p\)(a belief that \(p\) is correct iff \(p\) is true).




Indeed, many take it to be constitutive of belief that its norm of
correctness is truth--i.e., part of what makes belief the kind of
attitude that it is. If correctness is understood in
prescriptive--rather than descriptive--terms, then (57)
presumably gives way to the following schema:


* (58) \(\forall p\)(one ought to believe
that \(p\) when \(p\) is true).




A third normative schema linking truth and belief classifies truth
as a good of belief (Lynch, 2004a, 2005b: 390, 2009: 10; David
2005):


* (59) \(\forall p\)(it is prima facie good to
believe that \(p\) when \(p\) is true).




What these schemas suggest is that the apparent doxastic and
assertoric normativity of truth appears to be entirely general, in a
manner analogous to which winning appears to be a general norm that
applies to any competitive game (Dummett 1978: 8; Lynch 2005b: 390).
Hence, if \(p\) is true, then it is correct and good to believe that \(p\), and
one should believe that \(p\)--regardless of whether \(p\) concerns
fashion or physics, comedy or chemistry. And again, the generalized
normativity of truth appears to make trouble for pluralists, insofar as
the thesis that there are several ways of being true apparently implies
a proliferation of doxastic truth norms. Yet, instead of truth being
the single normative property mentioned in (57), (58), and (59), the
pluralist commits to a wide variety of norms--one for each
domain-specific truth property \(F\_1 , \ldots ,F\_n\). For example, for any given trigonometric
statement p, it is prima facie good to believe \(p\) when \(p\) is true in the
way appropriate to trigonometry, while the prima facie goodness of
believing a truth about antibodies is tied to whatever truth property
is apropos to immunology. Hence, whereas the normative aspects of truth
seem characterized by unity, pluralism renders disunity.




As before, a concessive response can be given by granting the
existence of a disjunctive, universal truth property: the normative
property of being \(F\_1 \vee \cdots \vee F\_n\). Although this amounts to an endorsement
moderate pluralism, it poses no threat to the importance of the
domain-specific norms \(F\_1 , \ldots ,F\_n\), insofar as these properties are explanatorily
more basic than the normative property of being \(F\_1 \vee \cdots \vee F\_n\). However, at the same time,
they do provide the unity needed to maintain that the predicate *is
true* in (57), (58), and (59) denotes a single, universally
applicable norm:


* (60) \(\forall p\)(a belief that \(p\) is correct iff \(p\) is
\(F\_1 \vee \cdots \vee F\_n)\).
* (61) \(\forall p\)(one ought to believe \(p\) when \(p\) is
\(F\_1 \vee \cdots \vee F\_n)\).
* (62) \(\forall p\)(it is prima facie good to believe that \(p\) when \(p\) is
\(F\_1 \vee \cdots \vee F\_n)\).




Likewise, functionalists once again respond to the challenge by
invoking the monist aspect of their view. There is a single normative
property--the property of having a property that realizes the
\(F\)-role--that delivers a uniform understanding of (57),
(58), and (59).