## 1. What is a Truth-maker?



Truth-makers are often introduced in the following terms (Bigelow
1988: 125; Armstrong 1989c: 88):



(*Virtue-T*)
a truth-maker is that in virtue of which something is true


The sense in which a truth-maker "makes" something true is
said to be different from the causal sense in which, e.g., a potter
makes a pot. It is added that the primary notion of a truth-maker is
that of a *minimal* one: a truth-maker for a truth-bearer
*p* none of whose proper parts or constituents are truth-makers
for *p*. (Whether every proposition has a minimal truth-maker
is contentious.) We are also cautioned that even though people often
speak as if there is a unique truth-maker for each truth, it is
usually the case that one truth is made true by many things
(collectively or severally).



Whether (*Virtue-T*) provides a satisfactory elucidation of
truth-making depends on whether we have a clear understanding of
"in virtue of". Some philosophers argue this notion is an
unavoidable primitive (Rodriguez-Pereyra 2006a: 960-1). But
others are wary. Thus, for example, Bigelow finds the locution
"in virtue of" both obscure and, as will see, avoidable
"we should not rest content with an explanation which turns on
the notion of *virtue*!" (Bigelow 1988). These kinds of
concern provides a significant motivation for establishing whether it
is possible to elucidate the concept of *truth-making* in terms
of notions that enjoy a life independently of the circle of notions to
which *in virtue of* and *truth-making* belong.


### 1.1 Truth-making as Entailment



One influential proposal for making an elucidatory advance upon
(*Virtue-T*) appeals to the notion of *entailment* (Fox
1987: 189; Bigelow 1988: 125-7):



(*Entailment-T*)
 a truth-maker is a thing the very existence of which entails that
something is true.


So *x* is a truth-maker for a truth *p* iff *x*
exists and another representation that says *x* exists entails
the representation that *p*. It is an attraction of this
principle that the key notion it deploys, namely entailment, is
ubiquitous, unavoidable and enjoys a rich life outside
philosophy--both in ordinary life and in scientific and
mathematical practice.



Unfortunately this account threatens to over-generate truth-makers for
necessary truths--at least if the notion of entailment it employs
is classical. It's a feature of this notion that anything
whatsoever entails a necessary truth *p*. It follows as a
special case of this that any claim that a given object exists must
entail *p* too. So it also follows--if
(*Entailment-T*) is granted--that any object makes any
necessary truth true. But this runs counter to the belief that, e.g.,
the leftovers in your refrigerator aren't truth-makers for the
representation that 2+2=4. Even worse, Restall has shown how to
plausibly reason from (*Entailment-T*) to "truth-maker
monism": the doctrine that every truth-maker makes every truth
true (whether necessary or contingent). Every claim of the form
*p* [?] ~*p* is a necessary truth. So every existing
thing *s* is a truth-maker for each instance of this form (see
preceding paragraph). Now let *p* be some arbitrary truth
(grass is green) and *s* any truth-maker for *p* [?]
~*p* (a particular ice floe in the Antarctic ocean). Now it is
intuitively plausible that something makes a disjunction true
*either* by making one disjunct true *or* by making the
other disjunct true (Mulligan, Simons, & Smith 1984: 316). This is
what Restall calls "the disjunction thesis". It follows
from this thesis that either *s* makes *p* true or
*s* makes ~*p* true. Given that *p* is true,
neither *s* nor anything else makes it true that ~*p*.
So *s* (the ice floe) must make it true that *p* (grass
is green)! But since *s* and *p* were chosen arbitrarily
it follows that all truth-makers are on a par, making true every truth
(Restall 1996: 333-4).



The unacceptability of these results indicates that insofar as we have
an intuitive grip upon the concept of a truth-maker it is constrained
by the requirement that a truth-maker for a truth must be relevant to
or about what it represents as being the case. For example, the truths
of pure arithmetic are not about what's at the back of your
refrigerator; what's there isn't relevant to their being
true. So we're constrained to judge that what's there
cannot be truth-makers for them. This suggests that operating at the
back of our minds when we issue these snap judgements there must be
something like the principle:



(*Relevance*) 
what makes something true must--*in some
sense*--be what it is "about".


Of course the notions of "about" and
"relevance" are notoriously difficult to pin down (Goodman
1961). And a speaker can know something is true without knowing
everything about what makes it true. Often it will require empirical
research to settle what makes a statement true. Moreover, what is
determined *a posteriori* to be a truth-maker may exhibit a
complexity quite different from that of the statement it makes true
(Mulligan, Simons, & Smith 1984: 299). Nevertheless, it is clear
that unless (*Entailment-T*) is constrained in some way it will
generate truth-makers that are unwanted because their presence
conflicts with (*Relevance*).



One way to restore accord between them would be to abandon the
Disjunction Thesis that together with (*Entailment-T*) led us
down the path to Truth-maker Monism. Indeed isn't the
Disjunction Thesis dubious anyway? Consider examples involving the
open future. Can't we imagine a situation arising that makes it
true that one or other of the horses competing in a race will win, but
which neither makes it true that one of the horses in particular will
win nor makes it true that another will (Read 2000; Restall 2009)? For
further discussion of issues surrounding truthmaking entailment, the
Disjunctive Thesis and the Conjunctive Thesis, i.e. the principle that
a truthmaker for a conjunction is a truthmaker for its conjuncts, see
Rodriguez-Pereyra 2006a, 2009, Jago 2009, Lopez de Sa (2009) and
Talasiewicz (et al) (2012). 



But even if the Disjunction Thesis is given up still this leaves in
place the embarrassing consequence of defining what it is to be a
truth-maker in terms of classical entailment, *viz.* that
*any* existing thing turns out to be a truth-maker for
*any* necessary truth. Some more radical overhaul of
(*Entailment-T*) is needed to avoid over-generation. One
possibility is to redefine what is to be a truth-maker in terms of a
more restrictive notion of "relevant entailment" (in the
tradition of Anderson & Belnap) that requires what is entailed to
be relevant to what it is entailed by (Restall 1996, 2000; Armstrong
2004: 10-12). Whether exploring this avenue will take us very
far remains a matter of dispute. Simons, for example, reflects, 



> 
> 
> In truth however I suspect our intuitions about truth-makers may be at
> least as robust as our intuitions about what is good for a logical
> system of implication, and I would not at present attempt to explicate
> truth-making via the arrow of the relevance logic system
> **R**. (2008: 13)
> 
> 
> 



Nevertheless since truth-making concerns the bestowal of truth,
entailment its preservation, there must *at some level* be an
important connection to be made out between truth-making and
entailment; the effort expended to make out such a connection will be
effort spent to the advantage of metaphysicians and logicians alike.
But even granted this is so there are reasons to be doubtful that any
overhaul of (*Entailment-T*), however radical, will capture
what it is to be a truth-maker. One vital motivation for believing in
truth-makers is this. Positing truth-makers enables us to make sense
of the fact that the truth of something depends on how things stand
with an independently given reality. This is how Bigelow reports what
happens to him when he stops believing in truth-makers: 



> 
> 
> I find I have no adequate anchor to hold me from drifting onto the
> shoals of some sort of pragmatism or idealism. And that is altogether
> uncongenial to me; I am a congenital realist. (1988: 123) 
> 
> 
> 



Truth-makers are posited to provide the point of semantic contact
whereby true representations touch upon an independent reality, upon
something non-representational. Since entailment is a relation between
representations it follows that the notion of a truth-maker cannot be
fully explicated in terms of the relation of
entailment--regardless of whether representations are best
understood as sentences or propositions or some other candidate
truth-bearer (Heil 2000: 233-4; 2003: 62-5; Merricks 2007:
12-13). Ultimately (*Entailment-T*), or a relevance logic
version if it, will leave us wanting an account of what makes a
representation of the existence of a truth-maker--whatever it
entails--itself beholden to an independent reality.


### 1.2 Truth-making as Necessitation



This difficulty arises because entailment is a relation that lights
upon representations at both ends. Appreciating this Armstrong
recognised that truth-making 



> 
> 
> cannot be any form of entailment. Both terms of an entailment relation
> must be propositions, but the truth-making term of the truth-maker
> relation is a portion of reality, and, in general at least, portions
> of reality are not propositions. (2004: 5-6; see also Lowe 2006:
> 185)
> 
> 
> 



Accordingly Armstrong made a bold maneuver. He posited a
metaphysically primitive relation of necessitation (i.e., one not
itself defined in terms of possible worlds because Armstrong is
"opposed to the extensional view proposed by those who put
metaphysical faith in possible worlds" preferring an
'intensional account' of modality instead (1997: 151,
2004: 96)). The relation in question lights upon a portion of reality
at one end and upon a truth at the other. In the simplest case that
means that the truth making relation is one that "holds between
any truthmaker, *T*, which is something in the world, and the
proposition" that *T* exists (2004: 6). Armstrong then
defined what is to be a truth-maker in terms of this metaphysical
bridging relation:



(*Necessitation-T*)
 a truth-maker is a thing that necessitates something's
being true.


This conception of truth making avoids the "category"
mistake that results from attempting to define truth-making in terms
of entailment. It also makes some advance upon (*Virtue-T*) and
its primitive use of "in virtue of" because at least
(*Necessitation-T*) relates the notion of truth making to other
modal notions, like that of necessity, upon which we have some
independent handle. But what is there positively to be said in favour
of conceiving of truth-makers in terms of "necessitation"?
Suppose that *T* is a candidate truth-maker for a truth
*p* even though *T* fails to necessitate *p*.
Then it is possible for *T* to exist even when *p* is
false. Armstrong now reflects "we will surely think that the
alleged truth-maker was insufficient by itself and requires to be
supplemented in some way" (1997: 116). Suppose this
supplementary condition is the existence of another entity,
*U*. Then "*T*+*U* would appear to be the
true and necessitating truth-maker for *p*" (2004: 7).
Armstrong concludes that a truth-maker for a truth must necessitate
the truth in question.



Unfortunately this argument takes us nowhere except around in a
circle. (*Necessitation-T*) embodies the doctrine that it is
both necessary and sufficient for being a truth-maker that a thing
necessitates the truth it makes true. Armstrong's argument for
this doctrine relies upon the dual assumptions: (1) anything that
fails to necessitate *p* (witness *T*) cannot be a
truth-maker for *p*,whereas (2) anything that succeeds in
necessitating *p* (witness *T*+*U*) must be. But
(1) just is the claim that it is necessary, and (2) just the claim
that it is sufficient for being a truth-maker that a thing
necessitates the truth it makes true. Since it relies upon (1) and
(2), and (1) and (2) are just equivalent to
(*Necessitation-T*), it follows that Armstrong's argument
is incapable of providing independent support for the conception he
favours of what it is to be a truth-maker.



Even though this argument may be circular, does
(*Necessitation-T*) at least have the favourable feature that
adopting it enables us to avoid the other difficulty that beset
(*Entailment-T*), *viz*. over-generation? Not if there
are things that necessitate a truth whilst still failing to be
sufficiently relevant to be plausible truth-makers for it. If the
necessitation relation is so distributed that it holds between any
contingently existing portion of reality, e.g., an ice-floe, and any
necessary truth, e.g., 2+2=4, then we shall be no further forward than
we were before. So Armstrong needs to tell us more about the
cross-categorial relation in question to assure us that such cases
cannot arise. Smith suggests another problem case for
(*Necessitarian-T*). 



> 
> 
> Suppose that God wills that John kiss Mary now. God's willing
> act thereby necessitates the truth of "John is kissing
> Mary". (For Malebranche, all necessitation is of this sort.) But
> God's act is not a truth-maker for this judgement. (Smith 1999:
> 6)
> 
> 
> 



If such cases are possible then (*Necessitation-T*) fails to
provide a sufficient condition for being a truth-maker.



In fact the commitment already emerges from (*Necessitarian-T*)
if the necessitation relation it embodies is conceived as internal in
the following sense: "An internal relation is one where the
existence of the terms entails the existence of the relation"
strung out between the terms; otherwise a relation is external
(Armstrong 1997: 87). Armstrong argues that the relation of
truth-making has to be internal (in just this sense) because if it
weren't then we would have to allow that, absurdly,
"anything may be a truth-maker for any truth" (1997: 198).
But then nothing but propositions--conceived in the
self-interpreting sense--can be truth-bearers that are internally
related to their truth-makers. Any other candidate for this
representational role, as we've already reflected--a token
belief state or utterance--could have been endowed with a
different representational significance than the one it possesses. So
the other eligible candidates, by contrast to propositions,
aren't internally related to what makes them true.



Armstrong's commitment to the truth-making relation's
being internal clashes with his naturalism (David 2005: 156-9).
According to Armstrong, 



> 
> 
> Truth attaches in the first place to propositions, those propositions
> which have a truth-maker. But no Naturalist can be happy with a realm
> of propositions. (Armstrong 1997: 131) 
> 
> 
> 



So Armstrong counsels that we don't take propositions with
"ontological seriousness": 



> 
> 
> What exists are classes of intentionally equivalent tokens. The
> *fundamental* correspondence, therefore, is not between
> entities called truths and their truth-makers, but between the token
> beliefs and thoughts, on the one hand, and truth-makers on the other.
> (Armstrong 1997: 131)
> 
> 
> 



But naturalistically kosher token beliefs and thoughts aren't
internally related to what makes them true. So Armstrong's
naturalism commits him to denying that the truth-making relation is
internal after all. Heil has also inveighed in a naturalistic spirit
against incurring a commitment to propositions that are designed to
have their own "built-in intentionality" whilst continuing
to maintain that truth-making is an internal relation (2006:
240-3). Since we have no idea of what a naturalistic
representation would look like that was internally related to what
made it true, this appears to be an impossible combination of views.
Our inability to conjure up a credible class of truth-bearers that are
internally related to their truth-makers provides us with a very
strong incentive for supposing that the truth-making relation is
external. The long and short of it: if we are wary, as many
naturalists are, of the doctrine that truth-bearers are propositions,
then we should also be wary of thinking that the truth-making relation
is internal. This spells trouble for (*Necessitarian-T*) and
any other account of truth making which invoke internal relations to
propositions.


### 1.3 Truth-making as Projection



Smith tries to get around this problem by adding to
(*Necessitation-T*) the further constraint that a truth-maker
for a given truth should be part of what that truth is *about*:
"roughly: it should fall within the mereological fusion of all
the objects to which reference is made in the judgment" (1999:
6). His suggestion is that a typical contingent judgement *p*
not only makes singular reference to the objects whose antics it
describes but also "generic reference" to the events,
processes and states that are associated with the main verb of the
sentence that is used to express the judgement in question. So, for
example, the judgement that John is kissing Mary incorporates not only
singular reference to John and Mary but also generic reference to all
kisses. Smith identifies the *projection* of a judgement with
the fusion of all these things to which it refers (singularly or
generically). He then defines what is to be a truth-maker in terms of
this notion:



(*Projection T*) 
a truth-maker for a judgement *p* is something that
necessitates *p* and falls within its projection


Since God's act of willing isn't one of the things to
which the judgement that John is kissing Mary makes singular or
generic reference--it doesn't fall within the projection of
this judgement--His act isn't a truth-maker for this
judgement. But that fateful kiss does fall within the generic
reference of the judgement that John is kissing Mary *and*
necessitates the truth of that judgement; so the kiss is a truth-maker
for it.



Whether taking up (*Projection-T*) will avoid classifying
malignant cases of necessitating things as truth-makers will depend
upon whether the notion of projection can be made sufficiently precise
to vindicate the intuition that the net cast by a judgement
won't catch these unwanted fishes with the rest of its haul;
whether if the judgement that ph*x* incorporates singular
reference to *x* and generic reference to ph-ings, it
doesn't incorporate (even more) generic reference to anything
else that may (waywardly) necessitate ph*x*. (Here
"ph" indicates the place for a verb phrase and
"*x*" a place for a name.)



Smith attempts to make the notion of projection precise using just
mereology and classical entailment. Something belongs to the
projection of a judgement that ph*x* only if it is one of
the things to which the judgement is existentially committed (Smith
1999: 7). In order to capture the "generic" as well as the
singular consequences of a judgement, Smith includes amongst its
existential consequences the fusions that result from applying the
mereological comprehension principle (*T*[?])
([?]*x*ph*x* iff there exists a unique fusion of
all and only those *x* such that ph*x*) to the
immediate commitments of the judgement. For example, the judgement
that Nikita meows is immediately committed to the existence of a meow
and thereby to the unique fusion of all and only meows. Because
God's act of willing John to kiss Mary doesn't fall within
the class of logical-cum-mereological consequences of the judgement
that John is kissing Mary, His act isn't a truth-maker for
it.



But this still threatens to over-generate truth-makers (Gregory 2001).
The judgement that John is kissing Mary has amongst it existential
consequences that someone exists. Since Smith assumes that
"*x* exists", like "*x* meows"
and "*x* kisses Mary", is a predicate, it also
follows via (*T*[?]) that the projection of this judgement
includes the fusion of all and only existing things (Smith 1999: 10).
But since (*ex hypothesi*) God's act exists--and so
belongs to the aforementioned fusion and thereby the projection of the
judgement in question--and necessitates that John is kissing
Mary, it fails to rule out God's act as a truth-maker for
it!



The projection of a judgement needs to be made far more relevant to
what a judgement is intuitively about; the logical-mereological notion
of a projection supplied doesn't even provide a basis for
affirming that singular judgements don't generically refer to
every existing thing. An initial attractive move to avoid this
particular problem would be to deny that "exists" is a
predicate. But more generally, it remains to be seen whether an
appropriate notion of a judgement's referential net, its
projection, can be made out that's isn't too
permissive--thereby including illegitimate
truth-makers--without having to deploy resources that are not
obviously clearer or more problematic than that of truth-making itself
(see Smith 2002 and Schnieder 2006b for contrasting prognoses).


### 1.4 Truthmaking in terms of Essentialism



Others attempt to avoid over-generating truth-makers by appealing to
the notion of *essence*, a notion that purports to be far more
discriminating than *necessitation* (Fine 1994; Lowe 1994). The
difference in grain between these notions becomes evident when we
reflect that although it is (supposed to be) necessarily the case that
if Socrates exists then his singleton does too, it isn't part of
the essence of Socrates that he belongs to this set. If these notions
really are different then we will need to distinguish between those
entities that merely necessitate a true claim on the one hand and
those that are also part of its essence on the other. This suggests a
strategy for ruling out spurious truth-makers: they're the ones
that only necessitate true claims, whereas the real ones are also
implicated (somehow) in the essences of the claims they make true.



This brings us back to the question of truth-bearers. If truth-makers
are implicated in the essences of truth-bearers then truth-bearers can
neither be sentences nor judgements. Truth-bearers of these kinds only
bear their representational features accidentally; they could have
been used to say or think something different, or occurred in contexts
where they lacked significance altogether. Since they could have meant
something different, or nothing at all, the truth-makers of these
truth-bearers can hardly be implicated in their essences. Accordingly
truth-bearers that essentially implicate their truth-makers must be
creatures that could not have shifted or lacked their representational
features. They must be *propositions* in the deep sense of
being items that are incapable of meaning anything other than they do.
Conceiving of propositions only in this sense and appealing to their
essences, what is to be a truth-maker admits of the following
definition (Mulligan 2003: 547, 2006: 39, 2007; Lowe 2006:
203-10, 2009: 209-15):



(*Essential-T*) 
a truth-maker of a proposition is something such that it is part
of the essence of that proposition that it is true if that thing
exists.


If this definition is adopted then it is plausible to maintain that
many of the spurious cases of truth-makers, which have afflicted
accounts of truth-making in terms of entailment, necessitation or
projection, will thereby be weeded out (Lowe 2006: 202-3). It
isn't part of the essence of the proposition that John is
kissing Mary that it is true if there exists an act of God's
willing it. Nor is it part of the essence of the proposition that
2+2=4 that it is true if there is a particular ice floe in the
Antarctic. It isn't even part of the essence of the proposition
that 2+2=4 that it is true if p exists. So none of these things are
(spuriously) classified, if (*Essential-T*) is our touchstone,
as truth-makers for these propositions. In this respect, the
essentialist conception of truth-making has conspicuous advantages
over its aforementioned rivals.



Nevertheless, on the downside, it may be questioned whether our grip
upon the notion of the essence of a proposition is any firmer than the
notion of truth-maker for it. Moreover, the benefits of adopting
(*Essential-T*) come at a cost. The idea of a truth-maker is
introduced as "intuitively attractive" (Lowe 2006: 207).
But (*Essential-T*) requires propositions that are not only
abstract--already anathema to naturalists--but also
mysterious, because they are, so to speak, self-interpreting, i.e.
propositions that mean what they do irrespective of what speakers or
thinkers ever do with the signs or judgements that express them. So
the idea of a truth-maker turns out to be far less intuitive and
attractive than it initially seemed. Nonetheless, this is a commitment
some may accept anyway (Lowe 2009: 178-80), or may be willing to
accept if it gives them a good account of truth-making.



Essentialist conceptions of truth-making have proved less influential
in the recent literature than grounding conceptions (1.6 below). This
is surprising in light of the affinities between the notions of ground
and essence, especially given the possibility, favoured by some, of
explaining grounding in terms of essence (Correia 2013). This also
means that at least some of the attractions and some of the objections
to a grounding approach to truth making, discussed below, are liable
to carry over to an essentialist approach. 


### 1.5 Axiomatic Truth-making



The difficulties that have beset the definitions of truth-making
proffered so far have suggested to some philosophers that a
pessimistic induction is in order: that the project of defining
truth-making in more basic terms is misconceived, much as the project
of defining knowledge in more basic terms has come to seem
misconceived because e.g., of the Gettier cases. But there's no
gain to be had from, doing nothing more than declaring the notion of a
truth-maker to be primitive. If it's primitive then we also need
to know how the notion may be fruitfully applied in association with
other concepts we already deploy--entailment, existence, truth
*etc.*--to describe the interplay of truth-bearers and the
world. As Simons remarks, 



> 
> 
> The signs are that truth-making is not analysable in terms of anything
> more primitive, but we need to be able to say more than just that. So
> we ought to consider it as specified by principles of truth-making.
> (2000: 20) 
> 
> 
> 



In other words, the notion needs to be introduced non-reductively but
still informatively and this is to be achieved by appealing to its
systematic liaisons with other concepts.



This is the approach that was originally shared by Mulligan, Simons
and Smith (1984: 312-8). The principal schemata they employed to
convey to us an articulate grasp of what *truth-making* means
in non-reductive terms included:



(i)
(Factive) If *A* makes it true that *p*, then
*p*
(ii)
(Existence) If *A* exists, then *A* makes it true
that *A* exists
(iii)
 (Entailment) If *A* makes it true that *p*, and
that *p* entails that *q*, then *A* makes it true
that *q*


Each of these schemata specifies a definite linkage between the
application of the notion of *truth-making* and some other
condition. *Truth-making* is introduced as the notion that
sustains all of these linkages. Putting the schemata together what it
is to be a truth-maker is then definable intra-theoretically as
follows,



(*Axiomatic-T*) 
A truth-maker is something *x* such that (i) if *x*
makes it true that *p* then *p*, (ii) if *x*
exists then *x* makes it true that *x* exists...
and so on for each of the axiom schemata of our favoured theory of
truth-makers.


It is important to appreciate that adopting this approach to
truth-making doesn't have the benefits of theft over honest
toil. For one thing it doesn't obviate the threat of superfluous
truth-makers for necessary truths. (*Entailment*) is the
principle that truth-making tracks entailment: if *A* makes
*p* true then it makes all the consequences of *p* true
too. It's a principle that recommends itself irrespective of
whether truth-making can be defined. This is because it dovetails
smoothly with the idea that one truth-maker can make many truths true.
For example, suppose that a particular *a* has some absolutely
determinate mass. It is entailed by this description that various
determinable descriptions are also truly predicable of *a*.
Some of these truths say more than others, nonetheless they all have
the same truth-maker. Why so? Because they are entailed by
*a*'s having the mass it does (Armstrong 1997: 130; 2004:
10-11). To answer so is to appeal to (*Entailment*). But
if the entailment that truth-making tracks is classical then we are
back to flouting (*Relevance*). If *q* is necessary then
any contingent *p* classically entails *q.* So if
something at the back of your refrigerator makes it true that
*p* then by (*Entailment*) it makes *q* true too.
To avoid flouting (*Relevance*) in this way
(*Entailment*) had better be a principle that links
truth-making to a more restrictive, non-classical notion of entailment
(Mulligan, Simons, & Smith 1984: 316). So we won't be saved
the logical labour of figuring out which non-classical connective it
is that contributes to capturing what it is to be a truth-maker. Nor
will appealing to (*Axiomatic-T*) save us the hard work of
figuring out what truth-makers and truth-bearers must be like in order
to collectively realise the structure described by the axiom schemata
for truth-makers we favour. But there is nothing about these schemata
that demands truth-bearer and truth-maker be internally related.



It is striking that the Axiomatic approach to truth-making has proved
less popular in the recent literature than other more
metaphysically-loaded conceptions, in terms of necessitation, essence
or grounding. A principal attraction of the approach is its
metaphysical neutrality. By contrast, in more recent debate,
philosophers have preferred approaches which rely upon a distinctive
metaphysical vision.


### 1.6 Truth-Making as Grounding



Many recent approaches define truth-making in terms of
*grounding* or what is sometimes described as *non-causal
metaphysical dependence*. The notion of truth-making is typically
introduced, as we have seen, in terms of the ideology of "in
virtue of". As we have also seen, many philosophers then ask:
but what independent content can be given to this notion? In response
to this challenge, a theory of grounding may be conceived as a general
theory of "in virtue of" in terms of which truth-making
may then be explained. A further consideration which motivates those
already committed to grounding is the general methodological principle
that favours theoretical unification. Their idea is that by conceiving
of truth-making as a kind of grounding, we are able to understand
truth-making better, i.e. not as an isolated phenomenon but as an
instance of a more general pattern, thereby illuminating not only the
nature of truth-making but grounding too. 



Early exponents of grounding within analytic philosophy date from the
1960s (Bergmann 1961: 229, Hochberg 1967: 416-7). Recently,
grounding has been explained in a variety of different ways (Correia
and Schnieder 2012, Raven 2015). But, broadly speaking, we can
distinguish between two conceptions which assign different logical
forms to grounding statements: (1) the "predicate" or
"relational" view whereby grounding statements are
assigned the logical form "*x* grounds *y*"
where "*x*" and "*y*" mark singular
term positions and the verb expresses a relation; (2) the
"operator" view whereby the canonical form of a grounding
statement is characterised by a sentence operator. So statements about
something grounding something else have the logical form
"*p* because *q*" where "*p*"
and "*q*" mark positions for sentences. The predicate
view of grounding is held by, amongst others, Schaffer 2009, Audi
2012, Raven 2012; the operator view is advanced by Fine 2001, 2012,
Schnieder 2006a, Correia 2011 [2014]. (A third approach, owed to Mulligan
2007, recognises a plurality of different forms of grounding
statements.) The choice between (1) and (2) is often made either on
the basis of an assessment of the logical form of typical grounding
claims, or on the basis of ontological commitment, for example, the
claim that the operator approach to grounding is "ontologically
neutral" because (allegedly) operators don't stand for
anything as (allegedly) predicates do (Correia 2010: 254, Fine 2012:
47).



We can now distinguish two broad conceptions of truth-making, defined,
respectively, in terms of the operator and predicate approach to
grounding.



*(Grounding-Predicate-T)*
A truth-maker is an entity *x* which makes a proposition
*y* true iff the fact that *x* exists grounds the fact
that *y* is true. 
*(Grounding-Operator-T)*
 A truth-maker is an entity *x* which makes a proposition
*y* true iff *y* is true because *x* exists.



For the former, see Rodriguez-Pereyra 2005, Schaffer 2009, Jago 2018:
184-202, for the latter, Correia 2005 (sec. 3.2), 2011 [2014],
Schnieder 2006a, Mulligan 2007, Caputo 2007. 



One attraction of conceiving truth-making as based on grounding, aside
from the more general methodological virtues of theoretical
unification mentioned above, arises from taking grounding to be
"hyperintensional" nature. Grounding is intended to be a
notion that's fine-grained enough to distinguish those entities,
e.g., the cardinal numbers, that ground a necessary truth, such as
2+2=4, from those that don't, e.g. a contingent existent such as
the aforementioned ice floe. Because grounding is so fine-grained
neither *Grounding-Predicate-T* or
*Grounding-Operator-T* will give rise to the over-generation
that beset *Entailment-T* and *Necessitation-T* but
without having to appeal, like *Projection-T*, to an
underdeveloped notion of "about " or
"relevance". 



Of course, in light of sec, 1.2 and 1.4 above, we can foresee a
downside to this. Both *Grounding-Predicate-T* and
*Grounding-Operator-T* quantify over propositions that stand
hyperintensionally to their truth-makers. It follows that both
*Grounding-Predicate-T* and *Grounding-Operator-T* share
a commitment with *Necessitarian-T* and
*Essentialist-T*, viz. an ontology of abstract propositions
which have their meanings essentially. But, again, this may be a
commitment many grounding theorists have already made or be willing to
accept if it gives them a good account of truth-making. Another issue
is that there is no consensus upon the formal properties of grounding.
Whilst, for example, Schaffer (2009: 376) has maintained that
grounding is irreflexive, asymmetric and transitive, Rodriguez-Pereyra
(2015) has argued that the relation of truth-making isn't any of
these things. But Rodriguez-Pereyra also argues that grounding
isn't any of those things either. 



So far we have considered efforts to define truth-making in terms of
grounding. But there are other approaches in the literature which seek
to endorse one notion at the expense of the other. One way accepts
grounding as a welcome theoretical innovation but argues that we are
better off without truth-making, at least in the forms which have
become familiar to us. A second way continues to endorse truth-making
whilst rejecting grounding. 



The first approach, taken by Fine, involves embracing grounding but
rejecting truth-making. It's truth-making, he argues, we can do
without; grounding does a better job (Fine 2012; 43-6). Here
truth-making is conceived as a relation between a worldly entity and a
representation: the existence of the entity guarantees the truth of
the representation. But, Fine argues, it is more theoretically
fruitful to take grounding as the central notion for metaphysics. This
is partly because, Fine maintains, grounding is a less restrictive
notion than truth-making, because grounding does not require that the
ultimate source of what is true should lie in what exists, rather we
can remain open about what form grounding takes. Moreover, whilst
there may be genuine questions about what the ground is for the truth
of the representation that *p* there may be further questions
about what makes it the case that *p* and these questions will
typically have nothing to do with representation as such. Because
truth-making is typically understood in modal terms, i.e.
necessitation is conceived to be sufficient for truth-making, Fine is
also sceptical that there is any way of avoiding the over-generation
of truth-makers we have already discussed (see 1.1 and 1.2 above).
Finally, Fine thinks that we should be able to conceive of the world
hierarchically, whereby (e.g.) the normative is grounded in the
natural, the natural in the physical and the physical in the
micro-physical. But this is difficult to do if we think in terms of
truth-making, because if (e.g.) we conceive of a normative
representation being made true by the existence of something natural,
that natural thing is just the wrong sort of thing to be made true by
something at the physical level because it is not a representation.




Liggins (2012) maintains, like Fine, that the theory of truth-making
is inevitably less general than a theory of grounding. But Liggins
also argues that appealing to grounding obviates the need to appeal to
truth-makers in the sense that (e.g.) Armstrong maintained. This is
because one significant reason for positing truth-makers is that doing
so enables us to explain the asymmetric sense in which truth depends
upon being (see sec. 3.2 below). But, Liggins maintains, this can
already be done in terms of grounding, by saying that the fact that p
grounds the fact that a certain proposition is true, namely the
proposition that p. According to Liggins, this isn't a case of
truth-making because the relation of grounding invoked holds solely
between two facts, albeit one of them a fact about a proposition, that
it is true, rather than, as Liggins reads the requirements of
truth-maker theory, a relation holding between something and a
proposition. 



Fine's critique of truth-making presupposes that we can only avail
ourselves of truth-making if we conceive of truth-making in monolithic
terms, as providing a unique method for metaphysics. But whilst, for
example, Armstrong may have had a tendency to think in such terms,
this doesn't appear to be mandated by the nature of truth-making
itself. One might, as Asay (2017) argues, instead conceive of
grounding and truth-making as complementary projects, whereby a theory
of truth-making doesn't purport to do everything a theory of
grounding does and so reciprocal illumination remains a live
possibility. Indeed one might already think of the aforementioned
definitions or elucidations of truth-making, which are designed in
terms of a hyperintensional notion of grounding in order to avoid
over-generation of truthmakers as one way in which grounding is
already being used to illuminate truth-making. 



The second approach, outlined above, refusing grounding but favouring
truth-making, is advanced by Heil (2016). Heil is generally suspicious
of grounding because, he points out, grounding is often characterized
in different and incompatible ways, so he is sceptical that there is a
univocal concept of grounding to be had. But, more specifically, Heil
has long maintained that hierarchical conceptions of reality spell
trouble because of the difficulties explaining the causal and
nomological relationship between the layers (Heil 2003: 31-9). He
argues that this was the problem identified for supervenience and
realization in the '90s and it's a problem inherited by the
hierarchical conception of reality to which grounding gives rise. So
Heil does a modus tollens where Fine does a modus ponens. Whilst Fine
conceives of the hierarchical styles of explanation grounding provides
as one of the principal virtues of grounding, Heil considers this is
one of the deepest drawbacks of grounding. By contrast with Fine, Heil
instead recommends truth-making as the proper methodology for
metaphysics because it enables us to give a non-hierarchical
description of reality whereby fundamental physics gives us the
truth-makers for truths that have truth-makers. Further and
independent objections to grounding include whether the notion of
grounding is intelligible (Daly 2012), theoretically unified (MacBride
2013b), theoretically illuminating (Wilson 2014) or the result of a
cognitive illusion (Miller and Norton 2017).



Other available positions include: that truth making is a special kind
of grounding which involves a unique form of dependence (Griffith
2013), and that truth making isn't grounding but that grounding
is key to truthmaking (Saenz 2018). 


## 2. Which range of truths are eligible to be made true (if any are)?



Even when truth-maker panegyrists agree about what it is to be a
truth-maker, they often still disagree about the range of truths that
are eligible to be made true. This results in further disagreement
about what kinds of entities truth-makers are. There is potential for
disagreement here because of the appearance that different ranges of
truths require different kinds of truth-makers. Sometimes, discovering
themselves unable to countenance the existence of one or other kind of
truth-maker, panegyrists may find themselves obliged to reconsider
what truths really require truth-makers or to reconsider what it is to
be a truth-maker. We can get a sense of the complex interplay of
forces at work here by starting out from the most simple and general
principle about truth-making (maximalism) and then seeing what
pressures are generated to make us step back from it.


### 2.1 Maximalism



Truth-maker *maximalists* demand that every truth has a
truth-maker--no exceptions granted. So they advance the
completely general principle,



(*Maximalism*) 
For every truth, then there must be something in the world that
makes it true.


The principle lies at one end of the spectrum of positions we can
potentially occupy. At the other end, we find *truth-maker
nihilism*, the idea that no truth needs to be made true because
(roughly) the very idea of a truth-maker is a corrupt one: there is no
such role as making something true for anything to perform.
*Truth-maker optimalism* is the intermediate position that only
some truths stand in need of truth-makers: not so few that truth fails
to be anchored in reality but not so many that we strain credulity
about the kinds of things there are.


#### 2.1.1 The Liar?



Milne (2005) has offered the following knock-down, if not knock-out,
argument against maximalism. Take the sentence,



(*M*)
 This sentence has no truth-maker.


Suppose that (*M*) has a truth-maker. Since it's made
true, *M* must be true. And since it's true, what
(*M*) says must also be the case: that *M* has no
truth-maker. So if (*M*) has a truth-maker then it
doesn't have a truth-maker. By *reductio ad absurdum*
(*M*) therefore has no truth-maker. But this is just what
(*M*) says. So, *contra* (Maximalism), there is at least
one sentence, (*M*), that is true without benefit of a
truth-maker.



Rodriguez-Pereyra (2006c) has responded to this argument by
maintaining that (*M*) is like the Liar sentence



(*L*)
 This sentence is false.


It's a familiar position in the philosophy of logic to respond
to the inconsistency that arises from supposing that (*L*) is
either true or false--if it is, it isn't and if it
isn't, it is--that the *sentence* (*L*)
isn't meaningful, despite superficial appearances (see, for a
useful introduction to these issues, Sainsbury 1995: 111-33).
According to Rodriguez-Pereyra, because (*M*) is akin to the
Liar sentence there's no reason to suppose that (*M*) is
meaningful either. But if (*M*) isn't meaningful then
(*M*) certainly can't be true; in which case (*M*)
can't be a counterexample to maximalism either.



This response is flawed because, as Milne points out, (*M*) is
importantly unlike (*L*): (*L*) gives rise to an
outright inconsistency when only elementary logic rules are applied to
it; whereas (*M*) isn't inconsistent *per se* but
only when combined with a substantive metaphysical principle:
maximalism. If, by contrast, you don't believe in truth-makers
then you have every right to treat (*M*) as just another true
sentence--just as you have every right to think (*P*) is
true if you don't believe in propositions,



(*P*)
 This sentence does not express a proposition


It's only if one was (absurdly) to think that maximalism was a
logical truth that (*M*) could be intelligibly thought to be
"Liar-like". Of course, one person's *modus
ponens* is another's *modus tollens*. So if one
already had very strong independent reasons for being committed to
maximalism, Milne's argument would provide a reason for thinking
that (*M*) is meaningless (even though it isn't
Liar-like). But even if there are such reasons--or appear to
be--we can't claim to have control of our subject matter
until we have established what it is about the constitutive
connections that obtain between truth-making, truth and truth-bearers
that determines (*M*) to be meaningless (if it is); until
we've established the lie of the land, we can't be sure
that we're not kidding ourselves thinking (*M*) to be
meaningless rather than maximalism to be false. The lesson repeats
itself: a convincing theory of truth-makers requires a coeval theory
of truth bearers.



For further discussion of the Liar Paradox in relation to
truth-making, see Milne 2013 and Barrio and Rodriguez-Pereyra
2015.


#### 2.1.2 Could there be nothing rather than something?



Here's another shot across the bows, this time from Lewis. Take
the most encompassing negative existential of all: absolutely nothing
exists. Surely this statement is possibly true. But if it were true
then something would have to exist to make it true if the principle
that every truth has a truth-maker is to be upheld. But then there
would have to be something rather than nothing. So combining
maximalism with the conviction that there could have been nothing
rather than something leads to contradiction (Lewis 1998: 220, 2001:
611). So unless we already have reason to think there must be
something rather than nothing--as both Armstrong (1989b:
24-5) and Lewis (1986: 73-4) think they
do--maximalism is already in trouble.


#### 2.1.3 Maximalism is distinct from 1-1 Correspondence



What is there to be said in defence of maximalism? Even though he
favours it, Armstrong finds himself obliged to admit that "I do
not have any direct argument" for recommending the position
(2004: 7). Instead he expresses the hope that 



> 
> 
> philosophers of realist inclinations will be immediately attracted to
> the idea that a truth, any truth, should depend for its truth for
> something "outside" it, in virtue of which it is true.
> 
> 
> 
> 



Let us follow Armstrong's lead and treat maximalism as a
"hypothesis to be tested". (See Schaffer 2008b: 308 for a
more direct argument that relies upon (*Grounding-T*).)



Maximalism needs to be distinguished from the even stronger claim,



(*Correspondence*) 
For each truth there is exactly one thing that makes it true and
for each truth-maker there is exactly one truth made true by it.


But that there's clear blue water between these claims is
evident if we combine maximalism with (*Entailment*)--that
whatever makes a truth *p* true makes what *p* entails
true too. So *p* and all of its consequences are not only all
made true (as maximalism demands) but they also share a truth-maker
(as *Correspondence* denies). This takes us halfway to
appreciating that so far from being an inevitably profligate
doctrine--as its name suggests--maximalism is compatible
with denying that some logically complex claims have their own bespoke
truth-makers. (The inspiration for thinking this way comes from the
logical atomism of Russell (1918-19) that admitted some
logically complex facts but not others--it is to be contrasted
with Wittgenstein's version of the doctrine (1921) which
admitted only atomic facts.)



Suppose, for the sake of expounding the view, that some truth-bearers
are atomic. Also suppose that *P* and *Q* are atomic and
*t* makes *P* true. Then, by *Entailment*,
*t* makes *P* [?] *Q* true too. Similarly, if
*s* makes *P* true and *s*\* makes *Q* true
then, by *Entailment*, *s* and *s\** together make
*P* & *Q* true. Since the task of making *P*
[?] *Q* and *P* & *Q* true has already been
discharged by the truth-makers for the atomic truth bearers, there is
no need to posit additional truth-makers for making these disjunctive
and conjunctive truths true. Similar reasoning suggests that there is
no need to posit bespoke truth-makers for existential generalisations
or truths of identity either (Mulligan, Simons, & Smith 1984: 313;
Simons 1992: 161-3; Armstrong 2004: 54-5). But maximalism
is not thereby compromised: even though disjunctive and conjunctive
truths lack specific truth-makers of their own, they're still
made true by the truth-makers of the basic claims from which
they're compounded by the logical operations of disjunction and
conjunction.


#### 2.1.4 The need for bespoke truth-makers



But positing truth-makers for atomic truths doesn't obviate the
need--supposing maximalism--to posit additional truth-makers
for negative and universal truths. This becomes apparent in the case
of negative truths when we compare the truth-tables for conjunction
and disjunction with the truth-table for negation. The former tell us
that the truth of a disjunctive formula is determined by the truth of
one or other of its disjuncts, whilst the truth of a conjunctive
formula is determined by the truth of both its conjuncts. But the
truth-table for negation doesn't tell us how the truth of
~*P* is determined by the truth of some other atomic formula
*Q* from which ~*P* follows; it only tells us that
~*P* is true iff *P* is *false*. The strategy for
avoiding bespoke truth-makers for logically complex truths can't
get a grip in this case: there's no *Q* such that
supplying a truth-maker for it obviates the necessity of positing an
additional truth-maker for ~*P* (Russell 1918-19:
209-11; Hochberg 1969: 325-7).



The problem is even starker for universal truths: there's no
truth-table for them because there is no set of atomic formulae whose
truth determines that a universally quantified formula is true too.
Why so? Because whatever true atomic formulae we light upon
(*Fa*, *Fb*... *Fn*), it doesn't
follow from them that [?]*xFx* is true. To extract the
general conclusion one would need to add to the premises that
*a*, *b*... *n* are *all* the things
there are; that there's no extra thing waiting in the wings to
appear on stage that isn't *F*. But this extra premise is
itself universally quantified, not atomic. So it can't be argued
that the truth-makers for *Fa*, *Fb*... *Fn*
put together already discharge the task of making [?]*xFx*
true because they entail it (Russell 1918-9: 236-7;
Hochberg 1969: 335-7).


##### 2.1.4.1 Truth-makers for Negative Truths



The most straightforward response--since we are treating
maximalism as a working hypothesis--is to find more fitting
truth-makers for those truths that aren't already made true by
the truth-makers for the atomic truths that entail them. Whilst
looking around for truth-makers for negative truths Russell reflected,




> 
> 
> There is implanted in the human breast an almost unquenchable desire
> to find some way of avoiding the admission that negative facts are as
> ultimate as those that are positive. (1919: 287)
> 
> 
> 



He was right that our desire for positive facts and things makes us
awkward about acknowledging that negative facts or things are the
truth-makers of negative truths. Nonetheless, discussions about
whether there are truth-makers for a given range of truth bearers on
one or the other side of the positive-negative divide are apt to
appear nebulous. This is because, as Russell had himself previously
noted, there is "no formal test" or "general
definition" for being a negative fact; we "must go into
the meanings of words" (1918-19: 215-6). Statements
of the form "*a* is *F*" aren't
invariably positive ("so-and-so is dead"), nor are
statements of the form "*a* isn't *F*"
("so-and-so isn't blind") always negative. But it
doesn't follow from the fact that a syntactic test cannot be
given that there is nothing to the contrast between positive and
negative. Molnar suggests that the contrast can be put on a sound
scientific footing. For Molnar, natural kinds are paradigm instances
of the positive, to be identified on *a posteriori* grounds
(2000: 73). To say that a thing belongs to a natural kind identified
in this way is to state a positive fact. To state a negative fact is
to negate a statement of a positive fact.



It's a very natural suggestion that if the negative claim that
*a* isn't *F* is true it's made true by the
existence of something positive that's *incompatible*
with *a*'s being *F* (Demos 1917). For example,
the truth-maker for the claim that kingfishers aren't yellow is
the fact that they're blue because their being blue is
incompatible with their being yellow. But what makes it true that
these colours are incompatible? The notion of *incompatibility*
appears itself to be negative--a relation that obtains between
two states when it's *not* possible for them to obtain
together. So this proposal threatens to become regressive: we'll
need to find another positive truth-maker for the further negative
claim that yellow and blue are incompatible, something whose obtaining
is incompatible with the state of yellow and blue's being
compatible, and so on (Russell 1918-9: 213-5, 1919:
287-9; Taylor 1952: 438-40; Hochberg 1969: 330-1;
Grossman 1992: 130-1; Molnar 2000: 74-5; Simons 2008).
There's another worry: it's not obvious that there are
enough positive states out there to underwrite all the negative truths
there are. Even though it may be true that this liquid is odourless
this needn't be because there's something further about it
that excludes its being odorous (Taylor 1952: 447; Mulligan, Simons,
& Smith 1984: 314; Molnar 2000: 75; Armstrong 2004: 62-3;
Dodd 2007: 387).



One could circumvent the threatened regress by denying that the
incompatibilities in question require truth-makers of their own
because they're necessary truths and such truths are a
legitimate exception to maximalism--because "they are true
come (or exist) what may" (Simons 2005: 254; Mellor 2003: 213).
There is some plausibility to the idea that formal truths
(tautologies) don't stand in need of truth-makers; their truth
is settled by the truth-tables of the logical constants. But material
necessary truths--such as that expressed by "yellow is
incompatible with blue"--appear to make just as substantive
demands upon the world as contingent truths do (Molnar 2000: 74). In a
sense they appear to make even more of a demand since the world must
be so endowed that it could not in any circumstances have failed to
live up to the expectations of material necessary truths. It's a
peculiar feature of our philosophical culture that even though
it's almost universally acknowledged that Wittgenstein's
plan (1921: 6.37) to show all necessity is logical necessity ended in
failure--indeed foundered upon the very problem of explaining
colour incompatibilities--that so many philosophers continue to
think and talk as though the only necessities were formal ones so that
necessary truths don't need truth-makers (MacBride 2011:
176-7).



Russell reluctantly chose to acknowledge negative facts as
truth-makers for negative truths. He just couldn't see any way
of living without them. But negative facts are an unruly bunch. Try to
think of all the ways you are. Contrast that with the even harder task
of thinking of all the ways you aren't! If negative truths are
acknowledged as truth-makers they will have to be indefinitely
numerous, unbounded in their variety; choosing to live with them is a
heavy commitment to make (Armstrong 2004: 55). What's worse, if
negative facts are akin to positive facts--as their name
suggests--then they must be made up out of things, properties and
relations arranged together. But, *prima facie*, many of these
things, properties and relations aren't existing elements of
reality. So unless, like Meinong, we believe in the non-existent,
we'll have to admit that negative facts aren't
configurations of their constituents and so an entirely different kind
of entity from positive facts altogether (Molnar 2000: 77; Dodd 2007:
388).



It is for such reasons that Armstrong counsels us to adopt a more
parsimonious account of what makes negative truths true (2004:
56-9). Armstrong's own account lies at the opposite
extreme to Russell's. Whereas Russell posited indefinitely
*many* negative facts to make negative truths true, Armstrong
posits just *one* thing that's responsible for making
them *all* true, *viz*. a totality fact.



We should register C.B. Martin's doubt that this is throwing out
the baby with the bath water (1996: 59). According to Martin, we
already recognise in ordinary discourse that different negative truths
have different truth-makers--not just one as Armstrong proposes.
For example, we recognise that what makes it true that there is no oil
in this engine is different from what makes it true that there are no
dodos left. What makes claims like these true are absences, lacks,
limits, holes and voids, where these are conceived not as things but
as "*localised* states of the world", robustly
first-order and "causally relevant" to what goes on
(Martin 1996: 58, 65-6; Taylor 1952: 443-5). But, as many
philosophers have argued, when we talk about an absence having causal
effects what we're really saying can be understood without
reifying negative states and appealing instead to the actual effects,
or the counterfactual effects, of a positive state (Molnar 2000:
77-80; Armstrong 2004: 64-7; Lewis 2004; Beebee 2004).



##### 2.1.4.2 Truth-makers for general truths



Armstrong's grand design is to sweep away the difficulties that
attend the admission of negative facts by positing a special kind of
general fact that also serves as the truth-maker for general truths.
Russell admitted general facts too but he acknowledged that, "I
do not profess to know what the right analysis of general facts
is" (Russell 1918-9: 236-7). But Armstrong has gone
further and assigned to general facts the following structure: a
general, or totality fact consists in a binary relation *T* of
*totality* that holds between an aggregate on the one hand and
a property on the other when the aggregate comprises *all* the
items that fall under the property in question (Armstrong 1989b:
93-4, 1997: 199-200, 2004: 72-5).



For example, China, France, the Russian Federation, the U.K. and the
U.S.A. comprise the permanent membership of the UN Security Council.
So the aggregate (*A*) of them bears the *T* relation to
the property (*P*) of being a permanent member of the Council
(*T*(*A*, *P*)). Since the aggregate bears that
relation to that property, there can be other permanent members of the
Council who aren't already included in it. So the totality fact
*T*(*A*, *P*) suffices for the general truth that
China, France, the Russian Federation, the U.K. and the U.S.A are
*all* its members. It also suffices for the truth of the
negative existential that there are *no* other members of the
Council. So once we've recognised that *T*(*A, P*)
exists, there's no need to recognise additional bespoke
truth-makers for these negative truths.



In a similar way Armstrong endeavours to sweep away the need for
negative facts by affirming "the biggest totality state of all,
the one embracing all lower-order states of affairs", i.e., the
existence of a totality state that consists in an aggregate of all the
(1st order) states of affairs there are related by
*T* to the property of *being a (1st order)
states of affairs* (2004: 75). It's one of Armstrong's
abiding contentions that the world is "a world of states of
affairs, with particulars and universals only having existence within
states of affairs" (1989: 94). Consequently this totality state
comprises a vast swathe of what exists--whether particulars,
universals or states of affairs that consist in particulars having
universals. So it follows from the existence of this totality fact
that there are no more (1st order) states of affairs that
are not already included in the aggregate of states that *T*
relates to the property of *being a (1st order) states
of affairs*. Nor are there any particulars or (1st
order) universals had by those particulars that are not constituents
of the state of affairs included in that aggregate. It also follows
that there are no more particulars or (1st order)
universals. So this totality fact serves as truth-maker for all these
negative truths.



It is sometimes objected that such totality facts are just negative
facts in disguise: "Totality statements state the non-existence
of certain entities, they state 'no more facts'"; so
we should reject totality facts if we are dissatisfied with negative
ones (Molnar 2000: 81-2; Dodd 2007: 389). Armstrong responds to
this charge with equanimity: "It is not denied, of course, that
the totalling or alling relation involves negation. It sets a limit to
the things of that sort" (2004: 73). But if negation has indeed
been smuggled into the description of the role that *T*
performs in comprising a totality state then it is difficult to avoid
the suspicion that Armstrong has simply exchanged many negative facts
for one big one. But we may think of Armstrong's contribution in
a different way. There are two ostensible concerns that negative
states of affairs present. First, there is a concern about their
number. Second, there is a concern about, so to speak, their
*negativity*. Armstrong has addressed the first concern by
showing how we may reduce the number of negative states of affairs.
But the second concern neither cannot be met--because, as
Armstrong reflects, we cannot eliminate negation from our description
of the world.



It has also been objected that Armstrong's position gives rise
to a "paradox of totality" (Armstrong 1989: 94, 1997:
198-9, 2004: 78-9; Cox 1997: 53-60; Molnar 2000:
81). Take the totality state of affairs that comprises all the
(1st order) state of affairs. Since this (2nd
order) state is itself a state of affairs it follows that the initial
aggregate of (1st order) states of affairs failed to
comprise all the states of affairs there are. So there must be a
further totality state that comprised the aggregate of all of them.
But this (3rd order) state is also a state of affairs so it
will need to be added to the mix too, and so *ad
infinitum*.



Armstrong responds to this objection with equanimity too: 



> 
> 
> we can afford to be casual about this infinite series. For after the
> first fact of totality these "extra" states of affairs are
> all supervenient. As such, we do not have to take them with
> ontological seriousness. (1989b: 94)
> 
> 
> 



To understand this we need to appreciate that Armstrong's notion
of *supervenience* is non-standard: "an entity *Q*
supervenes upon entity *P* if and only if it is impossible that
P should exist and *Q* not exist" or, in other words that
the existence of *P* entails the existence of *Q*.
(Armstrong 1997: 11). He also holds a non-standard conception of
ontological commitment, *viz*. that "What supervenes is
no addition of being" (Armstrong 1997: 12, 2004: 23-4).
Armstrong's idea is (roughly) that to be a genuine addition to
being is to be a net (indispensable) contributor to the schedule of
truth-makers for all the truths. But supervenient entities are
superfluous as truth-makers. If the existence of an *R* entails
the existence of a certain *S* which in turn entails the truth
of *P*, then *R* already makes *P* true so there
is no need to include *S* in the inventory of truth-makers. It
follows that supervenient entities, like *S,* are no addition
of being (Lewis 1992: 202-3).



Now bring this non-standard conception of ontological commitment to
bear upon the envisaged infinite series of totality facts. It is
impossible that the 2nd order totality fact comprising all
the 1st order states of affairs exist and the 3rd order
totality fact comprising all the 1st and 2nd
order states not exist. So the 3rd totality fact--or
any other state higher-order than it--is entailed by the
existence of the 2nd order totality state. So all of these
*n* > 2 higher-order totality states supervene on it.
That's why Armstrong doesn't think we need to take any of
them with ontological seriousness.



What should we make of this non-standard conception of ontological
commitment in terms of truth-making: that to be is to be a
truth-maker? Cameron (2008c) has proposed that this conception should
*replace* the standard one that to be is to be the value of a
variable. But this threatens to cut off the branch the advocates of
truth-maker theory are sitting on: if they disavow that existential
quantification is ontologically committing then they will be left
without a means of determining the ontological commitments of
truth-maker theory itself, i.e., the theory that gives the inventory,
using existential quantification, of what makes all the truths true
(Schaffer 2010: 16-7).



Of course, if someone grants that existential quantification is
ontologically committing *in* the context of a theory of
truth-makers then they won't stultify themselves in this way
(Heil 2003: 9, 2009: 316-7, Simons 2010: 200). But this just
seems like special pleading. An argument is owed that we can't
legitimately commit ourselves to the existence of things that perform
theoretical roles outside the theory of truth-makers (MacBride 2011:
169). Why should there be only one theoretical dance allowed in town?
Why shouldn't we allow that there are other theoretical roles
for existing things to perform? Indeed it's a very real
possibility that when we come to understand the capacity of the
truth-makers to make truth-bearers true we will find ourselves
embroiled in commitment to the existence of other things in their
explanatory wake that aren't truth-makers themselves. In fact
Armstrong himself should have been one of the first to recognise this.
For it has been an abiding feature of Armstrong's world view
that we are obliged to acknowledge not only states affairs, which are
truth makers, but also properties and relations, constituents of
states of affairs, which aren't.



More generally, can we make any sense of the idea of "an
ontological free lunch"? Why is something supervenient no
addition to being? Even if we only ever came to recognise the
existence of one supervening entity would we not thereby have
*added* at least one extra item to our inventory of things that
exist? Of course in the special case where the supervening entity is
*constituted* by the entities it supervenes upon--i.e.,
the things that are already there--it makes some sense to say
that it's not adding anything new; but it's not at all
obvious that what Armstrong et al. declare to be ontological free
lunches are constituted from the entities upon which they supervene
(Melia 2005: 74-5). Accordingly Schulte (2011a, 2011b) argues
that no necessitarian or grounding account of truth-making can make
sense of the notion of an ontological free lunch, maintaining instead
that truthmaker theory needs to be augmented with the idea that we are
offering a reductive explanation when we make an explanation in terms
of truthmakers



Where does this leave us? So long as Armstrong's non-standard
conception of ontological commitment remains controversial, it also
remains controversial whether the infinite series of totality facts to
which Armstrong is "committed" may be dismissed as mere
ontological frippery.


### 2.2 Optimalism



One way to respond to these difficulties is to abandon maximalism in
favour of optimalism, to deny that universal and negative statements
need truth-makers. But Merricks argues the optimalist "way
out" is blocked. Negative truths need truth-makers if any truths
do, but they can't have them. So we must give up thinking that
truths need truth-makers in the first place (2007: 39-67).



Here's why Merricks thinks so. In order to avoid the
over-generation of truth-makers for necessary truths (*etc*.)
Merricks imposes a relevance constraint: "a truth-maker must be
that which its truth is about" (2007: 28). But can this
constraint be satisfied in the case of negative existentials, such as
the statement there are no hobbits? This statement isn't about
hobbits, because there aren't any, and other apparent
candidates, such as the universe's exhibiting the global
property of *being such that there are no hobbits in it*,
appear hoaxed up and artificial (2007: 43-55). Even if one
follows Merricks this far, one may still think that negative
existentials are the principled exception that proves the rule that a
truth-maker for a positive truth must be what its truth is about. But,
so far as Merricks is concerned, this is throwing the baby out with
the bathwater: 



> 
> 
> I deny that if we set aside the intuition that "a truth, any
> truth" depends on being we are left with the equally compelling
> intuition that all truths *except negative existentials* depend
> on being. (2007: 41) 
> 
> 
> 



He also suggests that this position is theoretically disingenuous
because no one would consider retreating to it from full-blown
maximalism unless he or she had already been "spooked" by
his or her failure to find truth-makers for negative truths; or if
they held onto the view that truth is correspondence (Merricks 2007:
40-1; Dodd 2007: 394; Cameron 2008a: 411). Merricks surmises
that if we have any reason to commit to truth-makers, we have only
reason to commit outright to a truth-maker for every truth
(maximalism). But since maximalism cannot be sustained because of the
lack of things for negative existentials to be about, Merricks
recommends the rejection of truth-makers altogether.



But optimalists aren't just "spooked" or
"timid" maximalists. They stand on their two feet with a
principled position of their own that need neither be based upon
"gerrymandered intuition" nor adopted as a consequence of
a forced retreat from maximalism. If maximalism is intellectual heir
to Russell's logical atomism, then optimalism (at least in the
form under consideration) is heir to Wittgenstein's version of
the doctrine according to which it is only atomic propositions that
represent the existence of states of affairs. The optimalists'
idea is that once truth-makers have been supplied for the atomic
truths there is simply *no need* to posit further truth-makers
for the molecular ones. All we need to recognise is that an atomic
statement *P* is true whenever a truth-maker for *P*
exists, that *P* is false if and only if no truth-maker for
*P* exists. Once the existence and non-existence of the
truth-makers has settled the truth-values of all the atomic
statements, the logical operations described by the truth-tables then
settle the truth and falsity of all the molecular statements (another
story must be told about what the truth-makers are for the
non-extensional constructions--another elephant in the room). In
particular, the truth-table for negation--that tells us what
"~" means--assures us that if *P* is false
then ~*P* is true. So all it takes to make ~*P* true is
that no truth-maker for *P* exists. Thus Mulligan, Simons, and
Smith: 



> 
> 
> it seems more adequate to regard sentences of the given kind as true
> not in virtue of any truth-maker of their own, but simply in virtue of
> the fact that the corresponding positive sentences have no
> truth-maker. (1984: 315; see also Mellor 2003: 213-4, 2009;
> Simons 2000:7-8, 2005: 255-6)
> 
> 
> 



Simons offers the illuminating reflection: 



> 
> 
> This is the truth-maker end of Wittgenstein's insight that
> propositions are bi-polar: if a proposition has one truth-value,
> however it gets it, its contradictory opposite has the opposite
> truth-value without further ado; 
> 
> 
> 



Simons dubs the truth functional mechanism whereby the negation of an
atomic statement gets the value true, "truth by default"
(2008: 14).



Optimalists also think that general truths are true by default so
there is no need for bespoke truth-makers for them (like totality
facts). Universal quantifications [?]*xFx* are logically
equivalent to negative statements of the form
[?][?]*x*[?]*Fx*. Since the latter are negative,
they're true, if they are, only by default. Then because the
former statements are logically equivalent to them, the optimalists
surmise that universal quantifications are true by default too (Mellor
2003: 214; Simons 2008: 14-5).



Further challenges for the optimalist or non-maximalist are discussed
in Jago 2012, Simpson 2014, Jago 2018 (81-102). 


### 2.3 Truth Supervenes Upon Being



Optimalism retains the original demand for truth-makers but restricts
it to atomic statements. Optimalism accordingly disavows a commitment
to truth-makers for negative statements and statements of generality.
But Bigelow[?]also wary of the commitments that maximalism
engenders to negative and totality facts[?] weakens what
truth-making means to a point where negative and general statements
don't require bespoke truth-makers of their own (1988:
131-3). He offers the following principle to capture the kernel
of truth in truth-making worth saving.



(*Truth Supervenes on Being*) 
If something is true then it would not be possible for it to be
false unless either certain things were to exist which don't, or
else certain things had not existed which do (1988: 133).


This principle allows atomic truths to have truth-makers[?]because
it would only be possible for them to be false if certain things had
not existed: their truth-makers. But it also allows negative truths to
be true without them. The statement that there are no dragons gets to
be true because it would only be possible for that statement to be
false if something which hadn't existed (dragons) did exist.
Such statements are true not because they have truth-makers but
because they have no counterexamples, "they lack
false-makers" (Lewis 1992: 216, 2001: 610).



General truths are also true for lack of false-makers. The statement
that everything is physical (if true) is true because it would only be
possible for the statement to be false if something that hadn't
existed did, *viz*. something that wasn't physical. So
when truth-making is understood in this weakened sense there is no
need to acknowledge, e.g., an additional totality fact to make it true
that there are only five coins in my pocket; it's enough that if
I hadn't stopped adding coins that statement would have been
false because then there would have been at least one other coin in my
pocket (Heil 2000: 236-240, 2003: 68-72, 2006:
238-40; Bricker 2006).



Despite their differences, optimalism and (*Truth Supervenes Upon
Being*) share a key idea in common--that a negative
existential truth isn't true because something exists, but
because something doesn't, *viz*. a truth-maker for its
contradictory, a false-maker for it. C.B. Martin has objected that
this doesn't obviate the need to posit truth-makers for negative
existentials. This is because a statement that there are no
false-makers for a negative existential truth is itself a negative
existential truth. So this statement "can't be used to
explain or show how the latter needs no truth-making state of the
world for it to be true" (1996: 61). Lewis takes Martin's
objection to be that this account of the truth of negative truths
isn't informative. Take the statement that there are no
unicorns. Why is it true? Well because there are no
unicorns. That's not much of an explanation! But, Lewis retorts,
the positive existential statement that there is a cat is true because
there is a cat. That's "No explanation at all, and none
the worse for that" (Lewis 2001: 611-12). Fair enough; but
perhaps Martin meant that optimalists and their fellow-travellers were
presupposing what they set out to show--because they assumed
without argument that a special class of negative claims stood in no
need of truth-makers, those according to which other negative
statements lacked false makers.


### 2.4 Humean Scepticism



Lewis has anyway argued that the doctrine that truth supervenes upon
being--and, by implication, optimalism--are an uncomfortable
halfway house. He began by trying to persuade us that the retreat from
maximalism was already mandated. He pointed out how deeply
counterintuitive it is to suppose that negative existentials are true
because their truth-makers exist. It seems, offhand, that they are
true not because some things do exist but because some don't.
"Why defy this first impression?" (1992: 204). But, more
importantly, Lewis pointed out that maximalism was incompatible with
what he took to be the master principle governing our thought about
modality: Hume's denial of necessary connection between distinct
existences. It is a consequence of this principle that anything can
co-exist with anything else that's distinct. But it is the
*raison d'etre* of any truth-maker for the negative
existential truth that there are no unicorns--if there is one and
whatever else it is like--that even though it is distinct from
all unicorns it cannot co-exist with any of them, else it would make
it true that there are no unicorns even in circumstances where
unicorns existed. Similarly it is the *raison
d'etre* of any truth-maker for a general truth that
such-and-such are all the facts there are that it refuses to co-exist
with any other facts even though it is distinct from them. So if
we're to hang onto Hume's denial of necessary connexions,
we'd better give up the demand for truth-makers for negative and
general truths, i.e., maximalism (Lewis 1992: 205, 2001:
610-11).



Lewis also argues that we can't stop here--just giving up
maximalism for optimalism--because even the truth-makers for
atomic statements conflict with Humeanism. Suppose that the statement
that Dog Harry is golden is atomic. Also suppose that Harry is only
accidentally golden, so the statement is contingent. What is its
truth-maker? It can't be Harry because it's possible for
him to exist even in circumstances where the statement is false, i.e.,
when he has a different coloured coat. But it can't be the
property of *being golden* either since there are possible
circumstances in which plenty of things are golden but not Harry. It
can't even be the mereological fusion Harry + *being
golden* because it's a feature of fusions that they exist
even in circumstances where their parts are otherwise
unrelated--e.g., when Harry is black whilst Harriet is golden.
For this reason, many maximalists make common cause with optimalists
to posit another fundamental kind of thing to perform the truth-making
role in the case of contingent (atomic) predications: facts that
consist in objects, properties and relations bound together; in this
case the fact *Harry's being golden* (Armstrong 1989a:
41-2, 1997: 115-6; Mellor 1995: 24). Now facts in general
and *Harry's being golden* in particular cannot be built
up mereologically from Harry and *being golden*; otherwise
*Harry's being golden* would be no more fit a candidate
for making the statement that Harry is golden true than the fusion
Harry + *being golden*. Since *Harry's being
golden* isn't built up mereologically from Harry and
*being golden*, they cannot be parts of it. But if they
aren't parts of it they must be entirely distinct from this
state of affairs. This is where Lewis pounced. Even though
*Harry's being golden* is entirely distinct from its
"constituents" it cannot obtain without Harry and
*being golden* existing. More generally, the obtaining of a
fact necessitates the existence of its constituents even though the
fact and its constituents are entirely distinct. So we cannot posit
facts as truth-makers for contingent (atomic) statements without going
against Humeanism (Lewis 1992: 200, 1998: 215-6, 2001: 611).



Other maximalists and optimalists, often those wary of facts, posit
(non-transferrable) tropes as truth-makers for contingent predications
(Martin 1980; Mulligan, Simons, & Smith 1984: 295-304, Lowe
2006: 186-7, 204-5) Tropes, in the non-transferrable
sense, are particular instances of properties that are existentially
dependent upon their bearers. For example, the particular golden
colour *g* of Harry's coat is a non-transferrable trope
because *g* could not have existed except as the colour of
*his* coat. Since *g* is non-transferrable, this trope
only exists in circumstances where Harry's coat is golden; hence
*g*'s eligibility to be a truth-maker for the statement
that Harry is golden. (If *g* was transferrable, then
*g* could have existed in circumstances where whilst borne by
Harriet, Harry bore another black trope *d*; so if *g*
is transferrable it isn't eligible to be a truth-maker for the
statement that Harry is golden.) But Lewis' reasoning can be
easily extended to show that non-transferrable tropes cannot serve as
the truth-makers for contingent statements without contradicting
Humeanism. If trope *g* is a property that Harry bears rather
than a part of him, then *g* is wholly distinct from Harry.
Nevertheless, the existence of *g* necessitates the existence
of Harry even though they are distinct (MacBride 2005: 121).
Alternatively if *g* is a part of the bundle of tropes that
constitute Harry, if *g* is non-transferrable, then the
existence of *g* necessitates the existence of some other
distinct tropes that are also parts of this bundle. So Humeanism is
violated either way.


#### 2.4.1 Subject Matter



In order to avoid contradicting Humeanism, Lewis recommended a further
weakening of (*Truth Supervenes upon Being*). According to
Lewis, the kernel of truth in truth-making is the idea that
propositions have a *subject matter*. They are *about*
things so whether they are true or false depends on how those things
stand. This led Lewis to endorse (2003: 25):



(*Subject matter*) 
Any proposition has a subject matter, on which its truth value
supervenes.


Equivalently, *there cannot be a difference in the truth-value of a
proposition without a difference in its subject matter*. This
might consist in (1) an increase or decrease in the population of
things that fall within the subject matter; or (2) a shift in the
pattern of fundamental properties and relations those things exhibit
(Lewis 2001: 612). Now the truth value of "Harry is
golden" supervenes upon its subject matter without there needing
to be any existing thing distinct from Harry or *being golden*
that necessitates their existence; it is enough that the statement
would have been false if Harry had lost his hair or been dyed. So we
can avoid contradicting Humeanism by abandoning optimalism in favour
of (*Subject matter*).



In an intriguing twist to the plot, Lewis subsequently appeared to
withdraw his doubts about truth-makers (2003: 30, Lewis & Rosen
2003: 39). When building the case for (*Subject Matter*) Lewis
had deliberately remained neutral about the metaphysics of modality
(2001: 605). But Lewis recognised that if he gave up his neutrality
and availed himself of counterpart theory then he could supply
truth-makers aplenty whilst still adhering to his Humeanism.



According to Lewis's counterpart theory, "*a* is
essentially *F* just in case all of *a*'s
counterparts (including *a* itself) are *F*"
(2003: 27). Counterparts of *x* are objects that are similar to
*x* in certain salient respects. Different conversational
contexts make different respects salient. This means that the truth
(or falsity) of essentialist judgements is always relative to the
counterpart relation conversational cues select; so it will often be
the case that whilst something is essentially *F* with respect
to one counterpart relation it won't be with respect to another
(Lewis 1968). In a conversation that makes it salient to think about
Harry under the counterpart relation of *being a golden
Labrador* then every relevant counterpart of him will be golden.
So relative to this counterpart relation he is essentially golden. But
in a different conversation that selects the counterpart relation of
*being a dog* because then whilst all of his counterparts will
be dogs Harry won't be essentially golden because some of his
counterparts will be other colours. What's important is that
it's one and the same thing, our beloved Harry, that's
essentially golden with respect to the former counterpart relation but
only accidentally so with respect to the latter. To make these
essentialist judgements count as true in the right contexts we
don't need one dog that's essentially golden, and another
that's only accidentally so; we just need to think about Harry
in two different (but compatible) ways.



According to (*Necessitarian-T*) and other related views, the
property a truth-maker *x* has of making a given proposition
*P* true is an essential feature of it. Why so? Because
*x* is supposed to be something the mere existence of which
suffices for the truth of *P*; it couldn't have existed
without *P* being true (Armstrong 1997: 115). But Lewis'
proposal is to treat essentialist attributions about truth-making in
the same relativistic spirit that counterpart theory treats every
other modal attribution (2003: 27-32). Think of Harry
*qua* golden Labrador, i.e., under the counterpart relation of
being a golden Labrador. All his counterparts selected by this
relation are golden. So every world in which Harry or one of the
counterparts exists is a world in which "Harry is golden"
is true. In other words, Harry *qua* golden is truth-maker for
the proposition that Harry is golden. But this doesn't commit us
to necessary connexions between distinct existences--to a dog
that couldn't have failed to be golden. In another context it
will be just as legitimate to talk about Harry in a different way, as
Harry *qua* dog. In that context his counterparts will include
dogs that aren't golden. So Harry *qua* dog will be the
truth-maker for the statement that Harry is a dog, but not the
statement that he is golden.



In the same way that ordinary objects like Harry can serve as
truth-makers for contingent predications, Lewis & Rosen (2003)
suggest that the entire world--"the totality of everything
there actually is"--can serve as the truth-maker for
negative existentials. Take the world *qua* unaccompanied by
unicorns. In the conversational context just set up, the world has no
counterparts that are inhabited by unicorns. So the world *qua*
unaccompanied by unicorns is essentially lacking in unicorns and
therefore qualifies as a truth-maker for the statement that there are
no unicorns.



Has Lewis shown how it is possible to garner truth-makers for
contingent predications and negative existentials without positing
totality facts or tropes that ensnare us in a web of necessary
connections? Indeed has he shown how we can get by using only ordinary
objects and collections of them to serve as truth-makers? We need to
be clear about what Lewis is trying to do in this paper. He
isn't reporting upon a damascene conversion, belatedly
recognising what he had previously denied, that the truth-making role
is genuine, but then ingeniously coming up with the idea that
*qua*-versions of things perform this role just as effectively
as states of affairs, only without necessary connections between
distinct existences. Rather, Lewis' aim in this paper is to damn
the very idea of truth-makers with faint praise. By showing how
*qua* versions of things performed the truth-making role just
as effectively as facts or tropes Lewis aimed to show how
explanatorily bankrupt the truth-making role truly was (MacBride 2005:
134-6, Bricker 2015: 180-3).



There are various criticisms of detail that might be made. MacBride
(2005: 130-2) points out that Lewis failed to provide any
account of the truthmakers for relational predications and argues that
it is very difficult to see how the lacuna can be filled when the
class of eligible truthmakers is restricted by Lewis to the class of
ordinary things and only intrinsic counterpart relations can be
evoked. Lewis considers a relaxation of the latter requirement when it
came to negative existentials (*qua unaccompanied by unicorns*
does not express an intrinsic counterpart relation). But MacBride
argues removing the latter requirement risks trivialising
Lewis's account because for any object *a* such that
*p* is true, for any true *p*, *a* satisfies the
description *F*: "inhabiting a world where *p* is
true", hence *a qua F* makes it true that *p*.
Bricker (2015: 179-80) argues that Lewis can provide for
relational predications by allowing sequences to be truthmakers, i.e.
not just ordinary things as Lewis required. But Bricker finds this
solution ultimately unattractive because it conflicts with another
truthmaking principle he finds plausible: that distinct atomic truths
have distinct truthmakers.



One might also object to Lewis' controversial modal metaphysical
assumptions of counterpart theory more generally (Rodriguez-Pereyra
2006b: 193; Dodd 2007: 385). More broadly, one might question whether
Lewis was right to place so much weight upon Hume's denial of
necessary connections between distinct existences or question whether
Lewis had interpreted it correctly (Daly 2000: 97-8; MacBride
2005: 123-7; Hoffman 2006; Cameron 2008b). It's one thing
to say that we shouldn't multiply necessities without necessity
but it's another thing to demand that we purge our world-view of
them altogether. What about dispositions, chances, laws *etc*?
Hume relied upon an empiricist theory of content to underpin his
rejection of necessary connections. But Lewis certainly didn't
advocate such a view. One is left wondering therefore whether
Hume's denial of necessary connexions should be abandoned along
with the theory of content that inspired it, an antiquated relic. If
so, then we have yet to be given a reason to retreat from either
optimalism or (*Truth Supervenes Upon Being*) to (*Subject
Matter*)(MacBride 2005: 126-7).


## 3. What Motivates the Doctrine of Truth-makers?


### 3.1 To catch a cheater



What is the motivation for adopting a theory of truth-makers, whether
maximalist or optimalist? Following Sider, it has become customary to
describe the "whole point" of adopting a theory of
truth-makers thus: to "Catch the cheaters" who don't
believe in truth-makers (Sider 2001: 40-1; see also Merricks
2007: 2-3). But this is a bit like saying that the point of a
benefit system is to catch out benefit frauds. It's only if
there is some antecedent point in favour of truth-makers that there
can be anything wrong with leaving them out. Nonetheless, it is
possible that we can come to appreciate the need for truth-makers by
appreciating what is lacking in theories that neglect them. This is
how C.B. Martin and Armstrong came to recognise the necessity for
admitting truth-makers (Armstrong 1989b: 8-11, 2004: 1-3).
Consider phenomenalism: the view that the physical world is a
construction out of sense-impressions. One obstacle for this view is
the need to make sense in sense-impression terms of true claims we
make about the unobserved world. Martin noticed that the phenomenalist
could only appeal to brute, ungrounded counterfactuals about possible
experience to do so. But counterfactuals do not float free in a void.
They must be responsive to an underlying reality, the reality that
makes them true. For Martin this was the phenomenalists' fatal
error: their inability to supply credible truth-makers for truths
about unobserved objects. The same error afflicted Ryle's
behaviourism with its brute counterfactuals about non-existent
behaviour and Prior's presentism according to which there is
nothing outside the present and so there is nothing for past-tensed
and future-tensed truths to be held responsible to. We come to
appreciate the need for truth-makers as the common need these
different theories fail to fulfil.



As Lewis points out, this demand for truth-makers represented an
overreaction to what was undoubtedly a flaw in phenomenalism (1992:
217). We can already understand what's wrong with phenomenalism
when we appreciate that it fails to provide an account of the things
upon which the truth of counterfactuals about sense impressions
supervene, i.e., when we see that it fails to satisfy (*Subject
Matter*). This leaves under-motivated the claim that phenomenalism
should also be faulted for failing to supply truth-makers to ground
counterfactuals about sense-impressions. The same reasoning applies to
behaviourism and presentism; they also fail to satisfy (*Subject
Matter*). So there's no need to adopt truth makers to catch
cheats. All we need to do is to recognise the strictures (*Subject
Matter*) places upon us.



It's a further flaw of Martin and Armstrong's reasoning
that even if we accede to the demand for truth-makers it doesn't
follow that even idealism is ruled out. According to Armstrong if we
forsake the demand for truth-makers we thereby challenge "the
realistic insight that there is a world that exists independently of
our thoughts and statements, making the latter true or false"
(1997: 128). But even an idealist could accept that there are
truth-makers whilst thinking of them as mind-dependent entities. So
acceding to the demand for truth-makers doesn't tell us
what's wrong with idealism (Daly 2005: 95-7). Bergmann,
the grandfather of the contemporary truth-maker movement, was explicit
about this: "the truth of *S* must be grounded
ontologically. On this first move idealists and realists agree"
(Bergmann 1961: 229). The realist-idealist distinction cuts across the
distinction between philosophers who admit truth-makers and those that
don't (Dodd 2002: 83-4).



The demand for truth-makers doesn't help "catch
cheaters" at all. Just acknowledge, e.g., some brute
counterfactual facts about sense data, or brute dispositions to behave
in one way or another, or brute facts about what happened in the past
or will happen in the future. What's unsatisfactory about these
posits isn't that if they existed they'd fail to make true
statements about unobserved objects or statements about mental states
that failed to manifest themselves in actual behaviour or statements
about the past or future. The problem is that we have difficulty in
understanding how such facts or dispositions could be explanatorily
sound (Horwich 2009: 195-7). Whatever we find lacking in
theories that posit such items, it isn't that they fail to
provide truth-makers, because they do. Of course if we are already
committed to the need for truth makers then we will likely conceive of
the demand for them as, e.g., drawing the phenomenalist out into the
open to reveal the unfitness of their explanatory posits. But unless
we already have independent reasons for recognising the demand for
truth makers, catching cheaters cannot provide a motivation for
positing them.


### 3.2 Truth Depends on Being



Does this mean that we should join Bigelow in his retreat to
(*Truth Supervenes Upon Being*) or step back with Lewis to
(*Subject Matter*)? The problem is that these supervenience
principles don't seem a satisfactory resting place either, not
if our concern is to understand how true representations can touch
upon an independent reality, i.e., something non-representational.
First, it is familiar point that just appealing to a systematic
pattern of modal co-variation between truths and their subject
matters--so that there is no difference in the former without a
difference in the latter--doesn't provide us within any
insight into the underlying mechanism or mechanisms that sustains this
dependency (Molnar 2000: 82-3; Heil 2003: 67; Daly 2005:
97-8; Melia 2005: 82-3). Second, if possible worlds are
conceived as maximal representations then these supervenience
principles (understood in the idiom of possible worlds) fail to
articulate what it is for a representation to touch upon being,
something non-representational: "For the idea that every truth
*depends on being* is not the idea that every truth is
*entailed by propositions of a certain sort*" (Merricks
2007: 86).



A third reason for being unsatisfied with Lewis' (*Subject
Matter*) is based upon the observation that the supervenience
involved is symmetric. Just as there is no difference in the
distribution of truth-values amongst the body of propositions without
a reciprocating difference in their subject matter, there is no
difference in their subject matter without a difference in the
distribution of their truth-values (Armstrong 2004: 7-8). But we
also have the firm intuition that the truth or falsity of a
proposition depends upon the state of the world in a way in which the
state of the world doesn't depend upon the proposition's
truth or falsity. This means that a supervenience principle like
(*Subject Matter*) cannot be used to articulate the asymmetric
way in which truth so depends upon being; for this, it is argued, we
need to rely upon a robust asymmetric notion of truth-making
(Rodriguez-Pereyra 2005: 18-19). Bricker (2015: 180-183)
replies on Lewis's behalf that the oft-heard complaint that
supervenience by itself is not a dependence or ontological priority
relation is besides the point. Rather, Bricker argues, the
metaphysical punch of Lewis's doctrine that truth supervenes
upon being "has little to do with the 'supervenience
part' and everything to do with the 'being' part and
the conception of fundamentality that informs it", where by
'fundamental' Bricker means Lewis's theory of
natural properties and relations.



But is there really anything so problematic or mysterious about the
asymmetric dependence of truth upon being that we need anything as
heavy duty as truth-making or supervenience+naturalness to explain it?
A number of proposals have been made for explaining the felt asymmetry
in other terms. Horwich (1998: 105; 2008: 265-66) argues that
asymmetric dependence of truth upon being arises from the fact that we
can deduce *p* from the proposition that *p is true*. But we
can equally deduce *p* from *p is true* so this fails to
establish an asymmetric dependence (Kunne 2003: 151-52;
Rodriguez-Pereyra 2005: 27). 



Hornsby argues instead that there is explanatory asymmetry between its
being the case that *p* and the proposition that *p is
true*, because the latter requires more to be the case than the
former, (e.g.) that there are propositions (Hornsby 2005: 44). Dodd
suggests a cognate alternative: that the felt asymmetry of truth upon
being arises from the fact that the identity of the proposition that p
is partially determined by the worldly items it's about, so we
can't understand what is required for the proposition that *p*
to be true without already having an understanding of what it is for
*p* to be the case (Dodd 2007: 398-400).



MacBride (2014) offers a purely semantic account of the felt asymmetry
in terms of the interlocking mechanism of reference and satisfaction
that explains the truth of a proposition. Whilst we can deduce from
the truth of the proposition that *p* that *p* is the case,
MacBride argues that we can't (ultimately) explain its being the
case that *p* in terms of the truth of the proposition that
*p* because its being the case that *p* is already assumed
by the truth of that proposition, that is, has already performed a
role in the semantic mechanism whereby the truth-value is determined.
By contrast, MacBride continues, its being the case that *p*
isn't determined by a semantic mechanism but by whatever worldly
factors, if any, that gave rise to *p*'s being the case. Saenz
(2018) replies that whilst reference and satisfaction may be used to
explain that propositions are true, they still "do not, in any
sense, account for the world 'making it' [*sic*] that
propositions are some way" (a similar point is made by Mulligan
et al 1984: 288, see sec. 3.5 below for further discussion). But Saenz
risks begging the question by making the additional demand on the
character of the felt asymmetry of truth and being that it consists in
more than an asymmetric relationship between truth and being. Saenz
holds that the felt asymmetry consists in the requirement that the
world makes propositions true but whether we need to appeal to the
idea of the world making propositions true in the first place is the
point at issue. Finally, Liggins (2012) argues that the felt asymmetry
between truth and being is best explained in terms of the asymmetry of
grounding, although, as we have seen, the asymmetry of grounding is
contested (see sec. 1.6 above for further discussion). 


### 3.3 Correspondence



"Catching cheats" doesn't supply a motivation for
adopting truth-makers. Are there other motivations for so doing? One
such motivation is that truth-making falls out naturally from the
correspondence theory of truth. 



> 
> 
> Anybody who is attracted to the correspondence theory of truth should
> be drawn to the truth-maker [*sic*]. Correspondence demands a
> correspondent, and a correspondent for a truth is a truth-maker.
> (Armstrong 1997: 14; see also 1997: 128-9, 2004: 16-7)
> 
> 
> 
> 



According to Armstrong, the "truth-maker principle" (aka
maximalism) just is what we are left with once we drop the assumption
from the correspondence theory that the relation between truth bearers
and truth-makers is one-one. Of course, the truth-making relation,
however it is explicated, cannot be the relation of correspondence in
terms of which *truth* is defined--for whereas the latter
is symmetric, the former isn't (Beebee & Dodd 2005b:
13-4). But this doesn't prevent truth being defined using
the *truth-making* relation, albeit in a more roundabout way
according to the following pattern,



(C)
 *S* is true = ([?]*x*)(*S*
is-made-true-by *x*).


Of course such a definition will only succeed if the relation
expressed by "is-made-true-by" can itself be explicated
without relying upon the notion of *truth* itself or other
notions that implicitly presuppose it, e.g., entailment (Merricks
2007: 15). This is no doubt one of the reasons that principles of
truth-making are typically not put forward as definitions of truth
(David 2009: 144). Another objection made by Horwich is that it is
implausible to suppose that an ordinary person understands the notion
of truth *via* the heterogeneous principles that govern the
provision of truth-makers for different types of propositions.
It's more plausible to suppose that we first grasp what truth
is, and only subsequently figure out what truth-makers are required
for the various kinds of propositions there are (Horwich 2009:
188).


### 3.4 Deflationism



Several philosophers have argued that so far from presupposing the
notion of *truth*, the various truth-making principles we have
discussed operate at a far more subterranean level. Bigelow writes,
"The force behind Truth-maker lies deeper than worries about the
nature of truth and of truth-bearers" (Bigelow 1988: 127, 2009:
396-7; Robinson 2000: 152; Lewis 2001: 605-6; Horwich
2009: 188-9, Bricker 2015: 169). Suppose we understand what it
is to be truth-maker in terms of entailment. Then whatever the range
of truths we think are capable of being rendered true, the
"guts" of our truth-maker principle can be stated using
the schema,



(*Schema*) 
If *P*, then there must be something in the world whose
existence entails that *P*.


This schema is equivalent to the infinitely many conditionals that
fall under it:



(*i*1)
 If the donkey is brown, then there must be something in the world
whose existence entails that the donkey is brown;
(*i*2)
 if the Parthenon is on the Acropolis then there must be something
in the world whose existence entails that the Parthenon is on the
Acropolis; and so on.


Note that neither "true" nor "truth" shows up
anywhere in the schema or its instances. Arguably the only role that
the notion of *truth* perform*s* is the one that
minimalist or deflationary theories of truth emphasize, that of
enabling us to capture all of that unending string of conditionals in
a single slogan,



(*Slogan*) 
For *any truth*, there must be something in the world whose
existence entails *that truth*.


But since truth is serving here *only* as a device of
generalization, the real subject matter of (*Slogan*) is
already expressed by the conditionals (*i*1), (*i2*)
*etc*. Since they make no explicit mention of either
propositions or truth, a theory of truth-makers is neither a theory
about propositions nor a theory about truth. If so, then the theory of
truth-makers can neither gain inspiration from, nor be tarred by the
same brush as the correspondence theory of truth. Nor need the theory
of truth-makers be bedeviled by concerns about the nature of truth
bearers.



One may nevertheless wonder whether Bigelow and Lewis have thrown the
baby out with the bathwater. MacBride (2013a) argues that if we do not
allow ourselves the general thought that truth-bearers are true or
false depending upon how things stand in the world then it is unclear
what, if any, credibility (*i1*), (*i2*) etc. have. For
why should there be something in the world whose existence
necessitates that (e.g.) cats purr? Why can't cats purr, even though
there is nothing whose existence entails that truth? Since
*Slogan* is intended to be just shorthand for its instances,
(*i* 1), (*i* 2) etc. it follows *Slogan* can't
be any more credible or motivated than its instances. If, however, we
allow ourselves a conception of truth which isn't deflationary, i.e.
a substantial conception whereby truth is conceived as a relation
borne by a truth-bearer to something worldly that exists independently
of us, then, MacBride argues, we will have an independent reason for
positing something worldly the existence of which necessitates the
truth that cats purr etc. (see also Armstrong 1997: 128). For further
discussion of deflationism in connection with truth-making see McGrath
2003, Vision 2005 and Thomas 2011. 


### 3.5 Truth-making and Conceptual Explanation



Other philosophers appeal to the idea that when we say that a
statement is true *because* a truth-maker for it exists, the
"because" we employ is a connective (Kunne 2003:
150-6; Hornsby 2005: 35-7; Melia 2005: 78-9;
Schnieder 2006a: 29-37; Mulligan 2007). They think of this
connective on the model of logical operators ("&",
"[?]" etc.) i.e., expressions that link sentences but
without expressing a relation that holds between the states of
affairs, facts or tropes that these sentences denote; but unlike
"&", "[?]" etc., "because"
is not truth-functional. According to these philosophers, the
truth-maker panegyrists have misconstrued the logical form of
"makes true". They have taken it to be a verb like
"*x* hits *y*" when really it is akin to the
connective "-" or "because" (Melia 2005:
78). There's no need to introduce truth-makers as the special
things that stand at one end of the *truth-making* relation
with true statements at the other, no need to because it's only
superficial features of the grammar of our language that suggest there
is a truth-making relation to stand at the ends of.



Typically philosophers who maintain that "makes true" is a
connective do not argue for this conclusion directly but encourage us
to dwell upon the fact that it natural to hear the
"because" that occurs in equivalent constructions as a
connective. When we hear, e.g., "It is true that the rose is red
because the rose is red" we don't naturally hear it as
expressing a binary relation between two things. So we shouldn't
hear, or at least don't have to hear, "It's true
that the rose is red in virtue of the rose's being red" or
"the rose's being red makes it true that the rose is
red" as a expressing a binary relation between a truth and
truth-maker either.



Kunne has gone further and suggested that the truth-making
connective is really the "because" of conceptual
explanation (2003: 154-5; see also Schnieder 2006a: 36-7).
He encourages us to hear the equivalence between,



(*R*)
 He is a child of a sibling of one of your parents, which makes
him your first cousin


and,



(*R\**)
 He is your first cousin because he is a child of a sibling of one
of your parents.


He tells us that the "because" in (*R\**) is the
"because" of "conceptual explanation". Since
(*R*) and (*R\**) are equivalent, he concludes that the
"makes" construction in (*R*) is just a cumbersome
way of expressing the "because" of conceptual explanation
in (*R\*)*. Kunne then invites us take the use of
"makes" in (*R*) as a model for understanding the
truth-making construction,



(*S*)
 The fact that snow is white makes the statement that snow is
white true.


This enables us to see that (*S*) does "not affirm a
relation of any kind between a truth vehicle and something in the
world" (Kunne 2003: 155). Why? Because it is equivalent
to,



(*S\**)
 The statement that snow is white is true because snow is
white.


a claim that makes no (explicit) mention of facts. Moreover, the
second clause of (*S*\*), like the second clause of
(*R\**), tells us when it is correct to affirm its first clause.
In both cases we have an explanation that draws respectively upon our
understanding of the concepts *cousin* and *truth.*
Drawing upon these materials, we are then able to construct an
explanation of the felt asymmetry whereby the truth of what we say
about the world depends upon what the world is like, but not the other
way around. What is written on the left-hand-side of (*S*\*) is
conceptually more sophisticated than what is written upon the
right-hand-side because the former requires us to be able to grasp the
concepts of *statement* and *truth* to understand it
whereas the latter does not. Accordingly the latter requires less of
both the world and us than the former to be both understood and true.
That's why it makes sense to deploy the right-hand-side (a claim
about reality) to explain the left-hand-side (a claim about a truth
bearer) but not the other way around (Hornsby 2005: 44; Dodd 2007:
399-400). It may still be that this is just wishful thinking,
until it has been established that the "because" of truth
making is a connective rather than a relational expression--i.e.,
not just because it would be technically convenient for us to believe
it to be so or because it sounds like a connective to someone with the
ears of a naive grammarian. As we saw in section 1.6, some advocates
of truth-making as grounding also consider "because" to be
a connective, although there is much disagreement about its
implications. Some early exponents of the connective view of
truth-making have embraced grounding (e.g. Schnieder), while others
have not (e.g. Hornsby and Dodd). 


### 3.6 Truth Making and Quantification



A final supporting suggestion: that the grand truth-maker projects of
the late twentieth century arose (partly) out of a failure to
appreciate the logical variety of natural language quantifiers that we
unreflectively employ when expressing the intuitions that speak in
favour of truth- makers.



Consider how Armstrong expressed himself when he started out: 



> 
> 
> It seems obvious that for every true contingent proposition there must
> be something in the world (in the largest sense of
> "something") which makes the proposition true. For
> consider any true contingent proposition and imagine that it is false.
> We must automatically imagine some difference in the world. (Armstrong
> 1973: 11) 
> 
> 
> 



Bigelow asks us to compare two worlds, one in which *A* is
true, the other in which it is false. According to Bigelow, 



> 
> 
> There must surely be some difference between these two possible
> worlds! They are clearly different in that *A* is true in one
> but not the other. So there must be something in one of these worlds
> which is lacking in the other and which accounts for the difference in
> truth. (1988: 126) 
> 
> 
> 



Armstrong and Bigelow make the same assumption about the
"some" they employ in their expression of what makes the
difference between the world in which *A* is true and the world
in which *A* is false; they assume it is an objectual
quantifier in name position.



With this assumption in place it is an easy move to make to think that
there must be some thing that we quantify over that
*constitutes* the difference between these circumstances,
*viz.* the truth-maker for *A*. But as Williamson
remarks "We should not assume that all quantification is either
objectual or substitutional" (1999: 262-3; *cf*.
Prior 1971: 31-4). Williamson argues that that the truth maker
principle in fact 



> 
> 
> involves irreducible non-substitutional quantification into sentence
> position... We should not even assume that all non-substitutional
> quantification is interpreted in terms of assignments of values to the
> variables. For "value" is a noun, not a sentence. (1999:
> 263)
> 
> 
> 



But suppose the "some" Armstrong and Bigelow employ is
understood not as an objectual quantifier that comes equipped with a
domain of entities over which it ranges but is understood in some
other way. Then it would be open to us to acknowledge the force of
Armstrong and Bigelow's intuition that the circumstances in
which *A* is true are somehow different from those in which it
isn't, but without our having to think that there exists
something that we've quantified over than makes it so. Evidently
it will not be until we have arrived at a settled view of the
admissible interpretations our quantifiers may bear that this issue
can be settled in a principled rather than dogmatic manner.