Aboutness and negative truths: a modest strategy for truthmaker theorists

Abstract

A central problem for any truthmaker theory is the problem of negative truths (P-NEG). In this paper, I develop a novel, piecemeal strategy for solving this problem. The strategy puts central focus on a truth-relevant notion of aboutness within a metaphysically modest version of truthmaker theory and uses key conceptual tools gained by taking a deeper look at the best attempts to solve the problem of intentionality. I begin this task by critically discussing past proposed solutions to P-NEG in light of Russell’s debate with Demos. This reveals a central difficulty with addressing the problem, specifically that one cannot be committed to incompatibility facts in one’s account of negation and of the truth of negative truths. I then present an aboutness-based version of truthmaker theory. Utilising what I call the strict and full account of aboutness, I extract aboutness-based theories of truth and falsity. I use this machinery to present a promising new strategy for solving P-NEG which does not have the problems of alternative approaches. Finally, I present and respond to some potential objections.

1 Introduction

In this paper, I use the aboutness-machinery of a modest version of truthmaker theory to sketch a novel, piecemeal strategy for solving the central problem for any truthmaker theory, namely the problem of negative truths (P-NEG).

In Sect. 2, I present P-NEG and discuss past proposed solutions in light of Russell’s debate with Demos, which reveals a central difficulty with addressing the problem. In Sect. 3, I discuss Molnar’s (2000) presentation of P-NEG, and explain in what sense there is a real distinction between negative and positive. In Sect. 4, I present the bare-bones of the modest, aboutness-based version of truthmaker theory. In doing so, I focus my attention on key aspects of what I call the strict and full account of aboutness and of the theory of intentionality which help us address the problem of intentionality. This allows me to extract aboutness-based theories of truth and falsity. In Sect. 5, I use this machinery to present an aboutness-based strategy for solving P-NEG. Finally, in Sect. 6, I present and respond to some potential objections.

2 The problem of negative truths and some difficulties for addressing it

P-NEG is the problem of how exactly truthmaker theory (TT) can account for true negative truthbearers¹ such as

T1::

Pegasus does not exist.

T2::

The cat is not on the mat.

T2*::

It is not the case that the cat is on the mat.²

Given their committment to an asymmetric dependence between truths and reality, TT-ists seem beholden to answer the following two questions: “What does the truth of claims such as T1 and T2 depend on?” and, more specifically, “What are the truthmakers for negative truths?” Neither T1 nor T2 seem to describe a way that the world is, but rather purport to describe a way the world is not. And since T1 and T2 are both true, we seem to have a case where there are truths that do not need truthmakers. If this reasoning is correct, the TT-ist seems to be stuck with a dilemma: either reject Truthmaker Maximalism (Maximalism or T-M),³ which states that all truths require truthmakers to make them true, or accept “unsavoury” negative facts, such as Pegasus’s non-existence or the cat’s not being on the mat, into one’s ontology.

This dilemma is very troubling. On the one hand, if one tries to reject T-M, this rejection cannot be arbitrary or ad hoc.⁴ One must have good independent reasons to restrict the scope of truthmaking. And, in the course of one’s rejection-strategy, one must not fall into positing unsavoury negative entities of any sort. On the other hand, philosophers have been very reluctant to accept negative beings (e.g. negative facts or negative properties) into the right ontology. Russell (1918, 1919), notoriously, accepts negative facts into his ontology without any hesitation on his part, but admits that there is “a certain repugnance to negative facts” (1918: p. 211), to such an extent that when he argued that there were negative facts, at a lecture in Harvard in 1914, he reports that “it nearly produced a riot” (ibid.). To explain this, he writes,

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: p. 287; my emphasis]

Besides Barker and Jago (2012) who have recently tried to argue that negative facts can be understood positively, there are hardly any contemporary analytic philosophers⁵ who are willing to accept negative facts, or negative beings of any sort, into their ontology.⁶ Accepting negative beings into one’s ontology is biting the Russellian bullet.

To understand Russell’s strategy, we need to understand the subtle distinction between Meinongianism and Russellian negative facts. Russell tries to avoid what is taken to be an unsavoury Meinongian ontology, in which there are things that do not exist.⁷ By contrast, his view does not commit us to the existence of things that do not exist (e.g. Pegasus), but rather commits us to the existence of the fact that some thing does not exist or the fact that something is not the case.⁸ Thus, instead of existing negative things, we have existing negative facts. However, this still makes negativity part of reality, and thus the taste of unsavouriness remains.

Plenty of others have also tried to find truthmakers for negative truths. For example, Martin posits “absences” (1996: p. 57),⁹ which according to him are “non-abstract, [ ...] localized states of the world or universe, and therefore, though not things or natural properties or relations of things, they can serve as truthmakers for negative existentials” (ibid.: pp. 57–58). Armstrong posits “totality states of affairs” (2004: p. 58; 1997: pp. 137–148) where the-world-as-a-totality is such that there is no cat on the mat.¹⁰ Cameron (2008b: p. 415ff; 2008d: p. 295) says that the essence of the world itself makes true all negative truths. The problem with these views is that each of them still posits some sort of negativity in the world in addition to the positive, though perhaps in a more palatable manner than Russell or Meinong. To accept this, one must be willing to bite the Russellian bullet and leave that “unquenchable desire” (1919: p. 287) unsatisfied.¹¹

Instead, one might attempt to address the dilemma’s first horn by restricting TT’s scope to a subset of primary truths, such as positive truths. For instance, on the so-called “moderate view” (Mellor 2012: p. 96; see also [Heil 2000]):

[O]nly some truths, the primary truths, have truthmakers, while other truths and falsehoods are derivable from the primary truths by means of truth-conditional semantics. [Forrest and Khlentzos 2000: 3]

Similarly, according to the Wittgensteinian version of logical atomism, labeled “optimalism” by Simons (2000: p. 17) and MacBride (2014: §2.2), “[I]t is only atomic propositions that represent the existence of states of affairs” (ibid.). On this view, negation ‘$\lnot$’ is understood purely as a truth-functional connective and truthbearers with negations are understood as molecular truthbearers, mere negations of atomic truthbearers. Negative truths, understood as true truthbearers with negations, get their truth-values, as Mulligan et al. write, “simply in virtue of the fact that the corresponding positive sentences have no truth-maker” (1984: p. 315). Or, as Simons says, they get their “truth by default” (2008: p. 14; also 2005: p. 255). On this account, negative truths do not require truthmakers, for they are not atomic truths, all of which must be positive.

It is an interesting historical fact that by contrast to these philosophers who think that logical atomism (or something similar) can address P-NEG, Russell (1918: p. 211ff) claims that one must posit negative facts for negative truths on the basis of his logical atomism. His basic point is that there is no way to account for negative truths without positing negative facts, even on a logically atomistic theory where only atomic truths are made true and only atomic facts exist. If Russell is right, then any strategy such as the moderate/optimalist view cannot merely assume that negative truths can be accounted for by primary or atomic truths. Let me explain his reasoning.

Purely as an example, take Mellor’s (2012: p. 105) ingenious strategy for accounting for negative truths. Let’s take it (following Mellor’s notation) that ${<}P{>}$ is a primary truthbearer and S is its truthmaker. Mellor (ibid.) explicitly states that ‘${<}\hbox {not-}P{>}$ [which he takes to be a non-primary truthbearer] is true if and only if S does not exist’ is acceptable on the moderate view because ${<}P{>}$ and ${<}\hbox {not-}P{>}$ must satisfy the laws of non-contradiction and excluded middle. Negative truths, according to Mellor, are truth-functions of primary propositions, and can satisfactorily be accounted for by the existence of truthmakers for the primary truths and the laws of logic applied to them to form non-primary propositions.

Russell would argue that this won’t work and is the wrong way to understand negation and falsehood. Mellor’s strategy is similar to Demos’s (1917), to which Russell is responding (1918: p. 211–214). The question Russell presses on Demos is: how should we interpret ‘not- p’? Russell summarises Demos’s proposal thus, “when we assert ‘not- p’ we are really asserting that there is some proposition q which is true and is incompatible with p [...] That is [Demos’s] suggested definition:

‘not- p’ means ‘There is a proposition q which is true and is incompatible with p’.” [Russell 1918: 213]¹²

Mellor’s appeal to the laws of non-contradiction and excluded middle to explain the non-primary status of negative truths is similar to Demos’s proposal; it seems merely to re-describe the incompatibility which is central to Demos’s strategy as a law of logic. Russell responds to Demos in several ways, but the main line of response is to explain that this strategy, as he writes, “makes incompatibility fundamental and an objective fact, which is not so very much simpler than allowing negative facts” (ibid.). According to Russell, if one tries to interpret or define negation, ‘not’, in this way, then one is reducing it to incompatibility. Unless there is a corresponding primary incompatibility-fact to which ‘that p is incompatible with q’ corresponds, then we are left with an unexplained molecular fact, since the fact that p cannot account for the molecular fact that p is incompatible with q and ‘incompatible’ just means ‘not compatible’.¹³ Similarly, appeal to the laws of non-contradiction and excluded middle, as Mellor does, cannot do the job, as the truth of logical laws requires as much explaining as the truth of anything else. And further, I would add, these laws mention negation, so negation cannot be explained in terms of them.

Russell’s problem, for atomist strategies and for strategies similar to Demos’s, is one that everyone in the literature who aims to take the first strategy, of denying T-M, must address. Specifically, they must explain how to account for negation, and for the truth of negative truths, in such a way as to avoid commitment to negative facts or incompatibility facts.

Thus, we need to find a strategy to accept TT, whether in the Maximalist form, which would posit some sort of non-repugnant truthmakers, or in the restricted, moderate non-Maximalist form, which would explain why some truthbearers do not need truthmakers for their truth.¹⁴

3 Addressing Molnar (2000)

Molnar (2000: pp. 84–85) presents P-NEG with four claims, each independently compelling for TT-ists:

(M1) :

The world is everything that exists.

(M2) :

Everything that exists is positive.

(M3) :

Some negative claims about the world are true.

(M4) :

Every true claim about the world is made true by something that exists.

The problem is: (a) given M1–M4, TT-ists are compelled to provide positive truthmakers for negative truths, but (b) non-repugnant, positive truthmakers are not forthcoming.

Broadly, the two main problem-solving strategies are: (1) reject one of M1–M4, or (2) somehow reject Molnar’s picture of the problem altogether.

The proposal of this paper is that the strict-and-full aboutness account of TT (SAC), presented in Sect. 4.2, has the resources to allow us successfully to take strategy (1) by rejecting M4 in a non-arbitrary, intuitive way (Sect. 5).

3.1 Cameron and Parsons’s strategy for addressing Molnar

Before I move on, I want to discuss a strategy that rejects Molnar’s picture of the problem altogether. Cameron (2008b) and Parsons (2006) claim not to understand what the distinction between negative and positive things is; ‘negative’ and ‘positive’ each applies, at best, only to representations and not to things. Cameron writes,

[W]hat is ‘negative ontology’? What is it for a thing to be positive or negative? I have no idea. [...] I don’t believe this is my fault. Being positive or negative seems to apply, in the first case, to representational entities such as propositions. [...] Most things are not representations, so it seems that we can call them ‘positive’ or ‘negative’ in a derivative sense at best. [2008b: 412–413¹⁵]

Parsons (2006: pp. 591–592) claims not to understand what it is for things to be positive:

Just what is it for a chair, a person, or a rock to be positive? I have honestly no idea. Whatever sense of ‘positive’ is meant here, it must be different from the unclear, but not totally opaque, sense in which the proposition ‘there are chairs’ is a ‘positive proposition’. The latter has something to do with the representational properties of the proposition in question; but a chair does not represent anything, so it is not positive in that sense. [ibid.]

I sympathise with their strategy. Let’s assume that the distinction is indeed much clearer as applying to representations, and that negativity and negation are features of representations, not of things.

3.2 The real distinction between negatives and positives

However, even if the distinction does not apply to things, there is an important sense that is compatible with this, in which there is a real distinction between negative and positive,¹⁶ where the distinction applies not just to representations but to reality. For example, there is a real distinction between the sweater I am wearing being yellow and the sweater I am wearing not being yellow.¹⁷ There is a real difference between the sweater being some way and its not being that way, even if this is not a difference between features of things, features which the things have. The sweater not being some way is not a feature of the sweater. The distinction is not, and was never supposed to be, between positive features of things nor between positively existing facts in the world. For the sweater not being some way is not a positively existing fact. Rather, the distinction is between things being some way and things not being some way. When I say that the sweater I am wearing is not yellow, if what I say is to be true, then the sweater must not be yellow. There is a clear distinction between the sweater’s being yellow (in which case what I say would be false) and the sweater’s not being yellow, which is no fact at all.¹⁸ This distinction is not merely representational but real. In the former case, the sweater really is that way, and, in the latter case, the sweater really is not that way.¹⁹

In response to the claim that the sweater’s not being yellow is not a fact at all, one might say, “But, as a matter of fact, my sweater is not yellow, but green.” One might naturally think, on this basis, that the sweater’s not being yellow is a fact, a negative fact that contrasts with another fact, the positive fact that my sweater is green.

In a loose way of speaking about facts, as true truthbearers, this is correct. No one, including Cameron and Parsons, denies that there is a distinction between negative and positive truthbearers, marked at the very least by the presence or absence of a negation. Negative facts of the true-truthbearer sort are not at issue. The problematic, unsavoury sort are negative facts understood as Russellian complex, structured entities. But, Russellian facts are complex, structured entities that are constructed out of properties and the objects in which the properties in question are instantiated. The reason why the sweater’s not being yellow is no fact at all (as I say above) is that not being yellow is not a property. Rather, it is a lack of a property; it is nothing at all. Not even Russellian facts can be constructed out of nothing. So, the sweater’s not being yellow is not a Russellian fact, that is, a structured, complex entity over and above the sweater and how things are with the sweater. Yet, as I have argued, the distinction between the sweater’s being yellow and the sweater’s not being yellow is a real distinction marking real differences not to do merely with representations (or truthbearers) but with reality.

4 The aboutness-based version of truthmaker theory

I shall now articulate the aboutness-based version of truthmaker theory (TAAT). The first, main condition of TAAT is what I shall call the aboutness condition of truthmaking (AC):

(AC)::

truths are made true by the parts (or aspects) of reality which they are about.

According to TAAT, truths are truthbearers that are true and made true by what they are about. Truthbearers are those entities which can be true (or false, i.e. are truth-apt) and which can be about entities and how things are with those entities (i.e. some aspects or modes of that entity’s being) . Truthmakers are those entities and the ways things are with those entities which truths are about. Truths and their truthmakers stand in a relation of truthmaking (T-REL) to each other.

Fraassen (1969) first articulated a version of TAAT, but, since then and until relatively recently, it has been, for the most part, neglected.²⁰ He argued that truthmaking and what he calls “signification” (ibid.: p. 481)²¹ are “dual” (ibid.) relations.²² This is a very powerful insight. The version of TAAT I shall present understands truthmaking and aboutness as dual, or as I like to call them, complementing, relations, whose satisfaction-conditions go hand-in-hand. Thus, an insight into the best truth-relevant account of aboutness will give us an insight into the best version of TAAT.

To this end, I shall introduce and then employ what I take to be the best semantic account of what truthbearers are about (Sect. 4.1), the essentials of which are captured by what I call the strict and full account of aboutness (SAC) (Sect. 4.2). I then use the details of the theory of intentionality as fleshed out by Crane’s solution to the problem of intentionality, to develop a framework wherein p can be about S even if S does not exist (Sect. 4.3). To do this, I shall introduce the notion of aboutness–satisfaction (and -failure) (Sect. 4.4). Since aboutness and truthmaking are dual relations, when there is satisfaction of aboutness at the level of truthbearers, there will be a complementing satisfaction of truthmaking. These details will help to articulate an account of truth (and falsity) in terms of the satisfaction (or failure) of aboutness (and hence truthmaking), and, in turn, to articulate a solution to the problem of negative truths (in Sect. 5).

4.1 What the best semantic account says truthbearers are about

The notion of aboutness involved in TAAT is what I shall call the best semantic account of what truths are about (SEM-TAC). It is more sophisticated than any mere folk²³ notion of aboutness on which, for instance, ‘The average, middle-income family is economically less well off in 2016 than in 2008’ might be taken to be about an entity the average, middle income family. Nor is it some metaphorical sense of aboutness, on which one might say that ‘Ghosts live among us’ is metaphorically about human suffering or mourning. Or, as Max Black reports, when one says, “Nixon is an image surrounding a vacuum” (1993: p. 39), presumably one is not literally talking about Nixon and stating that he is an image surrounding a vacuum, and hence not literally talking about these things. What one might be metaphorically talking about, if there even is a coherent notion of metaphorical aboutness, is anyone’s guess.²⁴

Figuring out what the best SEM-TAC says truths are about is difficult. Consider ‘Brakeless trains are dangerous’.²⁵ At first reading, and presumably this would be the apparent and folk understanding of what this truthbearer is about, one might think that we are referring to all the brakeless trains there are, and saying of them that they are dangerous. However, let’s say that there are no actual instantiations of any of these things: there are no brakeless trains. On the standard analysis, these truthbearers would not be true (and would be either false on a Russellian analysis or neither true nor false on a Strawsonian understanding). The problem with understanding these truthbearers in a folk or unreflective way (and then supplementing it with the standard story of reference failure) is that we get the wrong result. Brakeless trains would be and are indeed dangerous. In fact, it is likely that the reason why there are no brakeless trains is that brakeless trains are dangerous. This truthbearer is true even though the things it is apparently about do not exist. A better semantic analysis would make the truthbearer out not to be about any brakeless trains, which do not exist, but about brakeless trains in general (or if they were to exist). Perhaps this is a law of some sort; a law concerning brakeless trains. Laws hold and statements of laws are true even if nothing is subject to them at some given time.²⁶ Thus, it is clear that the best semantic analysis of truthbearers is not as straightforward as the folk or the unreflective analyser might take them to be.²⁷

4.2 Strict and full aboutness as what the best semantic account says truthbearers are about

What I take to be the best SEM-TAC is what I call strict-and- full-aboutness and it forms what I call the strict-and- full-aboutness-based account of TT (SAC; I shall use this abbreviation both for the notion of aboutness and for the TT-account based on it). I only have space to go into the essentials of SAC in this paper. I shall first say some general things about SAC (Sect. 4.2.1) before introducing it properly (Sect. 4.2.2).

4.2.1 Aboutness apparatuses, pluralism, and context-sensitivity

SAC, as the best SEM-TAC , requires that aboutness is not just a matter of reference, narrowly construed as the relation that relates singular and plural terms to their real-world-correspondents. It is a matter of the aboutness of all the parts of the truthbearer that one can use to be about entities and how things are with those entities. This is an important part of the doctrine of intentionality, which I shall be using to explicate SAC. In my understanding of the doctrine of intentionality, I follow, but also expand on, the construal given by McCulloch (1994: p. 26–31) and Crane (2013), when he says:

I am using the idea of what is ‘talked about’ and ‘thought about’ in a very general way, to apply to any thing that is what we might call the subject-matter of thought or discourse. Recall that I do not understand such ‘aboutness’ as reference. Reference— the relation in which singular terms stand to objects, or plural terms stand to pluralities of objects— is one way in which words can be about things, but it is only one way. Predication, too, is a way in which words can be about things. When I say that some pigs swim what I am saying is about swimming just as much as it is about pigs. ‘All men are mortal’ is about mortality as much as it is about all men. But it is perfectly natural to think of the sentence as being about all men too. [Crane 2013: 39]

The way that Crane uses ‘aboutness’ here captures an important aspect of SAC.²⁸ Predicates as well as singular and plural terms are part of what I shall call our toolbox of “aboutness apparatuses”. These apparatuses help to determine the content of truthbearers (e.g. sentences, beliefs, judgments), especially those aspects that specify what in the world the truthbearers are about, including both which objects (via referring expressions) and how things are with those objects (mainly via predicates). McCulloch (1994: pp. 26–31) sums up this part of the doctrine when he writes, “intentional objects [that is, the objects of aboutness²⁹] have turned out to be properties such as being pretty and individuals such as London, sometimes considered as combined in this or that way. The doctrine of intentionality, on this construal, is the claim that mental acts make reference to such properties and individuals” (ibid.: p. 28).³⁰ He goes so far as to say that this so-called doctrine of intentionality “is one of the glories of analytical philosophy” (ibid.: p. 30).

An important part of SAC, and this will be central to our solution, is that language can represent in intricate ways and that the toolbox of language is very rich. The richness of the toolbox, in turn, allows us to retain a modest commitment to metaphysical tolerance, neutrality, and categorial pluralism concerning the nature of truthbearers and the nature of truthmakers. Ceusters and Smith (2015: p. 2) and Ceusters’ (2012: p. 70) account of aboutness, for instance, is congruous with mine on this matter. They claim that what they call Information Content Entities (ICEs; entities with content and aboutness) “stand in [the] relation of aboutness to some portion of reality rather than just to some entity” (Ceusters and Smith 2015: p. 2). According to them, the domain of the aboutness relation includes properties, universals, relations, other ICEs, objects, their configurations, etc. For example, we can talk not just about Germany and Angela Merkel but also her role as Chancellor of Germany. This notion, that what ICEs are about are “portions of reality”, underlines my point that on a modest account of TT, truthbearers should not just be about entities but how things are with entities and what I shall call a “variety of modes of being”.³¹ Clearly on the most prominent accounts that I have discussed so far, including Crane’s, and Ceusters and Smith’s, aboutness is understood in an inclusive, categorially pluralist way.

The best SEM-TAC must reflect the various, intricate uses of languages.³² And, the best account of TT must respect and accommodate this. It must also incorporate a sensitivity to how context affects aboutness. For example, surface grammar and the normal use of words might mislead us in cases where understanding the context of use is essential to understanding what is talked about. Consider another example, discussed by Bigelow (1996: p. 39):

If you say that Othello loves Desdemona, in a sense which does not require the existence of Othello, then what is said is really not something about Othello at all, but about something else, perhaps we are just saying something about Shakespeare’s play (whatever that is) or about Shakespeare and what he said. [ibid.]

In this case, we are using names in apparently standard ways to talk in an existence-entailing way³³ about things (here, Othello and Desdemona), but in fact the truthbearers are used to talk about completely different things (here, Shakespeare’s play). In this case, plausibly, we are using these names in a different context, to talk indirectly about works of fiction rather than about people. Knowing the context in which the truthbearer is used is sometimes essential for knowing what it is about. The best SEM-TAC must also be sensitive to how context affects aboutness.

4.2.2 SAC and derivative aboutness

Now, I want to make a distinction between what the truthbearer in question is strictly and fully about, and what the truthbearer is derivatively about, given the truth of further truthbearers about the world not mentioned in the truthbearer in question. Consider:

T3::

This table exists.

T3 is strictly about a particular table, while it might derivatively be about what it consists in fundamentally (e.g. the subatomic particles out of which it is constituted, or if trope-fundamentalism about tables is correct, the tropes out of which it is bundled). However, there is nothing in T3 that tells us anything about what the table consists in fundamentally or non-fundamentally,³⁴ nor does it tell us anything about any tropes. These are instances of what Quine calls collateral information (1960: §2, especially pp. 137–138), that is, information that is perhaps important as background information which helps us to understand the truthbearer in question, but that is not the information conveyed in the truthbearer itself.³⁵ The information about tropes and about fundamentality only comes with further information not contained in the truthbearer in question.

To generalise, we might say, then, that what a truthbearer is strictly and fully about is captured by the information that the truthbearer conveys irrespective of its collateral information. And to avoid such a fundamentalist and metaphysically loaded and hence semantically implausible account of what truths in general are about, we might re-formulate the aboutness condition (AC) relevant for TT as one that the fundamentalist clearly rejects, what I shall call the strict and full aboutness condition of truthmaking (SAC):³⁶

(SAC)::

truths are made true by the parts of reality which they are strictly and fully about. ³⁷

SAC is the version AC of TAAT which, I think, minimally captures what we need for a plausible, modest, and useful account of TT. I shall now briefly make clear what strictness and fullness each amounts to.

4.2.3 Strictness

Strictness restricts what the truthbearer is about to just those entities and how things are with those entities that are specified by the truthbearer’s various aboutness apparatuses, which in turn help make the truthbearer about them. It excludes any further entities to which they might be related, and excludes any other properties or relations that the entities described might instantiate other than the ones mentioned. For example, the truthbearer ‘the table is black’ is strictly about the table and that it is black, and not strictly about any of the table’s constituent parts or its shape. As I made clear in the previous sections, specifying exactly what the truthbearers are strictly about is not always straightforward. But, I think that it is safe to say that what the best SEM-TAC says any given truthbearer is strictly about corresponds to important features of the context in which the truthbearer is used to be strictly about certain parts of the world, rather than others. For instance, a competent user of aboutness apparatuses in English may use an English-language truthbearer such as ‘the bank is empty’ to be strictly about the lack of people in the bank in whose lobby he is standing, while another competent user might use the same truthbearer to be about the lack of gold bars in the safe of the bank which he is robbing.³⁸ Neither the normal client who is visiting the bank during his lunch break, nor the unlucky bank robber, are talking about fundamental particles of any sort. Also, in some cases and in some contexts, the surface structure of the truthbearer might not transparently reveal what the truthbearer is strictly about. For instance, when Jack tells Sally that he has left his children in the lurch by opting to go to the pub instead of helping them with their homework, he is not talking about a place the lurch, in which he has left them. As a competent speaker of English, Sally would be able to understand what Jack is strictly talking about, even though they both would most likely need to use collateral information to give a speaker of English unfamiliar with that phrase an understanding of what Jack is strictly talking about.

The strictness constraint is similar to Yablo’s proportionality requirement on aboutness (2014: pp. 75–76). In explaining this requirement, he writes:

Truthmakers should on the one hand not incorporate irrelevant extras, in whose absence we’d still have a guarantee of truth. What makes it true that there are dogs? Proportionality favors the fact that Sparky is a dog over the fact that Sparky is a black-and-white cockapoo; the extra detail is unneeded. [ibid.: p. 75]

Proportionality and strictness yield the result, and capture the intuition, that not just is it unneeded, but it is not strictly relevant that Sparky is a black-and-white cockapoo. What is relevant is that there are dogs. And Sparky is a truthmaker only in virtue of his being one of the dogs that exist. See also (ibid.: p. 13–14) for a discussion of other examples relevant to this. In particular, strict aboutness as a requirement on the relation between truth and truthmakers has a parallel in Confirmation Theory (ibid.: p. 13). Consider a problem called “tacking by disjunction” (ibid.: p. 13; see also Moretti 2006). Take the truthbearer ‘all ravens are black’. The truthbearer is confirmed by its true consequences. But, some true consequences better confirm it than others. For example, ‘this raven is black’ better confirms the truthbearer than ‘this raven is black or the sky is pink or Sally loves sauerkraut’. Similarly, the truthbearer is not strictly about any of the things tacked on as a disjunct (in the latter), while it is strictly about this raven, as well as all other ravens. Though, as we’ll see in my next point, it is not fully about this raven; it is fully about all ravens.

4.2.4 Fullness (and partiality)

Fullness indicates that what the truthbearer is about is everything that the aboutness apparatuses make the truthbearer about, including all the entities and how things are with those entities, and not just any single thing mentioned or described. For example, the truthbearer ‘the table is black’ is fully about both the table and that it is black and not just the table or blackness-in-general or even its blackness. It may be partially about these latter things, but not fully (or wholly) about them. The truthbearer ‘all ravens are black’ is strictly about each and every raven but it is also fully about all of them, and their being black.

As with strict aboutness, sometimes it is not straightforward to give an account of what exactly a truthbearer is fully about. For instance, how partial and strict aboutness and further non-aboutness apparatuses, perhaps such as truth-functional connectives, affect full aboutness, can be complicated. A fully developed theory of these matters cannot be given in this paper. However, with regard to partial aboutness, I am inclined to claim that truthbearers are partially about the various things (and how things are with those things) that the various aboutness apparatuses that make up the truthbearer refer to.³⁹ For instance, that the table is black refers to a specific table. So, it is partially about that table. Yablo (2014: p. 14) talks in terms of truthbearers being wholly true, which I think is related to my notion of fully about. Take the conjunction ‘the table is black and the table is round’. This truth is made true in part by the table’s being black, and in part by the table’s being round. As Yablo puts it “True parts confer partial truth on their wholes” (ibid.). As should be clear, the true parts confer partial truth on their wholes, because the whole truthbearer is in part about what the parts are about. But, for the whole to be true, all the truthbearer-parts that it is a conjunction of need to be true. And, for the truthbearer to be wholly true, all the various things it is wholly or fully about, via the aboutness apparatuses and truthbearer-parts out of which it is composed, need to make it true.

In the case of disjunctions, I think the right account formulated in these terms should say that the disjunction is fully about each of its disjuncts. Thus, the truthmakers for any of the disjuncts will make true the whole truthbearer, which is constructed out of the disjuncts and the disjunction connective. Although such truthbearers are strictly about many more things than each of the things it is fully about, the truthbearer can be made true by any of the disjuncts, each of which it is fully about. Fine (2015b) treats the truthmakers of disjunctions in a similar way, when he discusses what he calls “the notion of being partly about” (ibid.: p. 3; see also 1).

4.3 SAC and the problem of intentionality

I shall now, in Sects. 4.3 and 4.4, present the aspects of SAC which allow us to answer P-NEG. According to TAAT, when some truthbearer is about some particular truthmakers, then that truthbearer is made true when those truthmakers have being. Of course, on the standard understanding of the aboutness relation (A-REL), a truthbearer can be about some truthmaker, even if the truthmaker does not have being. A-REL does not seem to require the existence of the entity which it is about. A truthbearer, or some term which helps constitute a truthbearer, can be about things which do not exist. According to Crane (2001: p. 23), this is “undeniable” (ibid.) and a “manifest fact” (ibid.). Consider:

T4::

Pegasus exists.

T4 is about Pegasus. So there seems to be an A-REL between T4 and Pegasus. But Pegasus does not exist. For T4 to be true, according to TAAT, the truthmaker, namely Pegasus, would have to exist. But since Pegasus does not exist, there is no truthmaker for T4. So, T4 is false. There seems to be a disanalogy here between A-REL and T-REL. However, a complication arises from this supposed disanalogy. Specifically, it is also an undeniable fact about relations that no relation can exist without its relata existing.⁴⁰ By analogy, if Jon is shorter than Wendy, then the relation shorter than exists or holds between Jon and Wendy. And for this to be the case, Jon and Wendy need to exist. Thus, T4 cannot be about Pegasus if the thing that it is about does not exist. But, Pegasus does not exist! What gives?

Broadly, this is what Crane (2001: p. 22ff) calls “the problem of intentionality” (P-INT). The problem is that there is a conflict between these three claims:⁴¹

C1::

All truthbearers are related to the things they are about.

C2::

Relations entail the existence of their relata.

C3::

Some truthbearers are about things which do not exist.

The question is: How can C3 be true, given C1 and C2? C3 is clearly true given truthbearers such as T4. Since C2 and C3 are plausibly undeniable truths, the way to resolve P-INT is to reject C1.

To do this, I now introduce the notion of an intentional object.⁴² These are just the schematic objects of attention; the things thought about. Such things are not restricted to objects in the ordinary sense (ibid.: 16);⁴³ they are objects in the broader sense that they can be objects, particulars, properties, events, states, processes, etc. So, unlike the ordinary, substantial sense of ‘object’, according to Crane (ibid.: p. 15), the schematic, intentional objects of attention clearly do not need to have anything in common with each other, except that they are objects of thought. Further, that there is no essential nature to truthmakers fits nicely with the truthmaker-pluralism of Sect. 4.2, and is something I take to be a virtue of the account.

Importantly, they are not what Searle calls “shadowy intermediaries” (1983: p. 17). They are just the entities that the truthbearers are about. They are not further “representation in our heads” or “ideas in our minds” (Crane ibid.: p. 16) which we need to be thinking about when we are thinking about other entities such as tables. There is no reason to think that one is thinking about some idea to be thinking about a table ([ibid.], though the existence of such ideas might be part of the story about how intentional states such as truthbearers can be about tables and other things [ibid.: pp. 28–33]). Sometimes our thoughts and truthbearers are about ideas and representations, sometimes they are about tables. Thus, the intentional objects are just those objects that the truthbearers are about.

Crane (ibid.: pp. 15, 17) tries to explain how intentional objects are not “shadowy intermediaries” by drawing a parallel between the schematic idea of object and the grammatical idea.⁴⁴ He illustrates this with the example of transitive verbs such as ‘kicked’, ‘played’, or ‘called’. They take objects. (For example, ‘Ernest kicked the ball’, ‘Emily played the piano’, and ‘Emily called Ernest’ each have a direct object.) We understand this when we learn grammar. But, we do not need to have a substantial conception of object to understand this. Crane writes, “All we need to know is that the object is something which plays a certain role in the sentence” (ibid.: p. 15). Analogously, when our truthbearers (and thoughts, desires, etc.) are about things, those things are intentional objects which merely play a certain role in our truth-apt constructions (or thoughts) but do not have substantial natures; they are not objects in the ordinary, substantial sense. Just as we have a good grasp of objects in the grammatical sense (illustrated by our linguistic mastery and understanding of the examples above), we have a good grasp of objects in the schematic sense of (intentional) objects of concern.⁴⁵

This strategy lets us accept C3: some truthbearers are about things that do not exist, or in other words “there are intentional objects which do not exist” (ibid.: pp. 22 and 25). When we answer ‘Pegasus’ when we are asked what T4 is about, we are talking about Pegasus, the intentional object of T4. But we are not, in this case, referring to anything, since “Pegasus [is] nothing” (ibid.: p. 25). Now consider T5:

T5::

Zeus exists.

According to Crane, “neither Zeus nor Pegasus exists; both Zeus and Pegasus are nothing” (ibid.), but what distinguishes T4 and T5 from each other as intentional states (thoughts or truthbearers) is the fact that T4 is about the intentional object Pegasus while T5 is about the intentional object Zeus. According to Crane, this allows one to accept both C2 and C3 as undeniable, while rejecting C1. The way I think that we should understand Crane, then, is to see him as denying that all truthbearers are related (or “involve relations” [Crane ibid.: p. 26]) to the things they are about. Sometimes the things they are about do not exist and are not real, as with T4 and T5. In these cases, the truthbearers have intentional objects which they are about, but they are not related to any existing, real intentional objects. This is not to posit some shadowy entity, and this is not to deny either C2 or C3. It is just to deny C1: that all truthbearers are related to the things they are about.

A consequence of this is that aboutness is not always a relation. Sometimes truthbearers are not related to the things they are about. “But,” as Crane states, “to say this is not to say that no thoughts [and no truthbearers] involve relations to real existing things; it is just to say that not all of them do” (ibid.: p. 26). Often our thoughts and truthbearers are about things that exist, such as Barack Obama or this very sentence. In such cases, the truthbearers are related to the things they are about. In other cases, the intentional objects that they are about do not exist, such as Pegasus or Zeus. Thus, sometimes truthbearers stand in A-REL to their intentional objects, that is, when they exist and are real; sometimes truthbearers do not stand in A-REL to their intentional objects.

4.4 SAC and the explanation of falsity and truth as the failure and satisfaction of aboutness (respectively)

One way to understand this more clearly is by using an important notion: the notion of aboutness–satisfaction ⁴⁶ or aboutness–success.⁴⁷ I think that we can understand the existence or presence of the relation between truthbearer and truthmaker as a satisfaction (or success) of aboutness. In the cases where the intentional objects of the truthbearers exist and are real, the truthbearers are related to the things they are about. Here, there is a satisfaction of the aboutness of these truthbearers. If none of the putative intentional objects of the truthbearer in fact exist and are real, then the truthbearers are not related to those putative objects. In this case, there is no satisfaction of aboutness. Searle, who also employs the notion of satisfaction, would say that in that case, the truthbearers are not about anything at all, even though they might seem to be about something (see [1983: p. 17]). For our purposes, it is enough to think that truthbearers can be about their intentional objects even if those objects do not exist, but when what they are about exists, then the truthbearers are satisfied (or successful) in regard to their aboutness. Aboutness–satisfaction marks the presence of an A-REL.

One should understand T-REL in the same way. When the intentional objects of the truthbearer exist and are real and the truthbearer is about ways that these objects really are, then there is not just an A-REL going in the direction from the truthbearer to the truthmaker, but there is a T-REL going in the direction from the truthmaker to the truthbearer.

To make the connection between T-REL and A-REL via aboutness–satisfaction clearer, it’s useful to contrast it with what I’ll call partial aboutness–satisfaction. It is an important detail that a truthbearer is often not just about real and existing objects, but also about (putatively) real ways these objects are (how things are with the object). A truthbearer which is about an existing and real object can also be false of that object in some way. But, in so far as it is also about how things really are with the object, the truthbearer is at least partially true of that object. For instance, ‘Quacky is a small duck’ is false but partially true in that she’s a duck, albeit a decidedly large one. In Sect. 4.2.4, I explained that partial aboutness is not satisfactory for T-REL and argued that fullness in regard to aboutness is important for T-REL; in the example, for the truthbearer to be true, Quacky must be a small duck, not just either a duck or small. Here, we can make clear that what we need is not partial aboutness–satisfaction but ( strict and full) aboutness–satisfaction.

The parallel between T-REL and A-REL extends to cases where there is no aboutness–satisfaction, or to put it another way, there is a failure of aboutness–satisfaction. When there is no relation, and the truthbearer in question is not about anything real or existing, while at the same time it is committed to the existence and reality of some thing, then the truthbearer is, strictly speaking, false.⁴⁸ The truthbearer is neither satisfied in terms of aboutness nor is it satisfied in terms of truthmaking. ⁴⁹

Now that we have introduced the notions of aboutness–satisfaction and -failure, and tied them to truth and truthmaking, we can formulate an understanding of truth and falsity in SAC-ist terms. Falsehood on the SAC-account is the non-satisfaction or failure of strict and full aboutness:

FALSEHOOD-SAC :

                                  (F-SAC) : A truthbearer which positively describes things to be a certain way is false iff the truthbearer fails to be strictly and fully about anything that is really the way(s) it is described to be.⁵⁰

What the truthbearer is about, when what it is about exists and is real, is (or are) its truthmaker(s). Conversely, if instead of failure there is aboutness– satisfaction, then there is truth:

TRUTH-SAC :

                      (TR-SAC) : A truthbearer is true if it is strictly and fully about things that exist and are real, and it is about how things actually are with those things.⁵¹

5 The SAC-ist solution to the problem of negative truths

Now that we have the SAC-machinery in place, we can address P-NEG. As Russell implies in his criticism of Demos (Russell 1918: p. 213), a theory of negative truths is also a theory of falsehood. As we saw in Sect. 4.4, SAC can give us a theory of falsehood in terms of aboutness–satisfaction failure, namely F-SAC. With F-SAC, we get an answer to the problem of intentionality. We can explain the falsity of T4 (Pegasus exists) and T5 (Zeus exists) in terms of their failure to be about anything that exists or is real. T4 and T5 are positive falsehoods. There are also converse truthbearers which are not positive falsehoods but are, rather, negative truths:

T1 :

(Not- T4 ): Pegasus does not exist; or equivalently, Not-(Pegasus exists).

T6 :

(Not- T5 ): Zeus does not exist; or equivalently, Not-(Zeus exists).

T1 and T6 are negative existentials. By contrast, T2 is a negative truth since, as it says, the cat is not on the mat. It is what we might call “a negative predicative truth”.

Recall TR-SAC. The reason why I did not put this in terms of a bi-conditional is because sometimes truths, such as T1 and T6, are also not about anything that is real, but they are still true. So, one cannot insert ‘only if’ into TR-SAC to make it a bi-conditional, because it is possible for a truthbearer to be true, and for it to be the case that what the truthbearer is about does not exist and is not real. In short, some truths are negative truths. We can clearly distinguish them from positive truths on the basis of what they are about. And they are true for other reasons than that they are related to existing and real beings. Specifically, they are true on the basis that they are not related to those beings! Let me explain.

In the case of T1 and T6, the truthbearers are about things that do not exist and are not real, but the truthbearers are also true. But it would seem that according to F-SAC, if they do not exist and are not real, then the truthbearers should be false. However, T1 and T6, and T2, are not fully about things that do not exist and are not real. Rather, T1 and T6 are fully about these things not existing. What should make these truthbearers true is not the positive existence or reality of anything at all, and especially not something negative. Instead, the reason they are true, when they are true, is that what they are in part about does not exist. In SAC terms, they are strictly and fully about certain putative entities not existing. In particular, even if T1 is strictly about Pegasus, it is only partially about Pegasus. It is fully about Pegasus not existing. For T1 and T6 to be true, the things that they are strictly and partially about need to be how they are described; in these cases, they should not be any way. That is, there should not be a relation between the truthbearers T1 and T6 on one side, and Pegasus and Zeus on the other, or else things would not be how they are described to be. For T2 to be true, what it is strictly and partially about, that is, the cat, should not be some way. It is strictly and fully about the cat not being some way. To think otherwise, and to think that what they are about must be positive, is to misunderstand what these truthbearers are strictly and fully about.

What I shall call the Representationalist would have a hard time expressing this. Her account differs from mine most centrally in her understanding of the consequences drawn from talk about satisfaction.⁵² Searle, who the theorist I am calling “the Representationalist” follows, writes,

In such cases, just as there is no “referred-to object” of the speech act, so there is no “Intentional object” of the Intentional state: if nothing satisfies the referential portion of the representative content then the Intentional state does not have an Intentional object. [1983: 17]

Ceusters and Smith (2015) are also Representationalists and capture the core of the view well when they say: “an ICE must in every case be about some portion of reality, where the aboutness in question must always be veridical, so that ‘being about’ is a success verb” (ibid.: p. 3). They contrast ICEs with representations, which “in contrast, [are] required merely to intend to be about something, and this intention might fail (as when a child draws what she thinks of as a unicorn)” (ibid.).⁵³ Strictly speaking, according to the Representationalist, T4 and T5 are not about anything, and thus their falsity is explained by their aboutness failure. However, one cannot merely claim that T1 and T6 are not about anything in the same way, since they are also true. T1 and T6 are about some putative entities not existing. If the Representationalist claims that they are true because T1 and T6 are satisfied in terms of aboutness, this seems to be committing her, paradoxically, to the (positive) reality of non-existence. Alternatively, the Representationalist seems forced to say that some truthbearers which are not about anything are nonetheless true. This is counterintuitive and at best awkward.

We can better express ourselves with the broadly Cranean⁵⁴ way of understanding aboutness and intentional objects that I have been sketching so far. T1 and T6 are in part about Pegasus and Zeus (as T4 and T5 are fully about Pegasus and Zeus); Pegasus and Zeus are the intentional objects of T1 and T6 (and T4 and T5). But Pegasus and Zeus do not exist and are not real. They are just intentional objects, in the schematic sense of being what the truthbearers are about. And sometimes the intentional objects of the truthbearers do not exist and are not real. This, I think, fits neatly with a good semantic account of true negative existentials and other negative truths. They are in part about things that do not exist and are not real; they just differ from true positive existentials such as ‘Barack Obama exists’, in that they are negative existentials and hence claim about those things that they do not exist or that they are not real. Surely, nothing positively existing needs to exist for those kinds of claims to be true. In fact, for those claims to remain true, the things they are about must remain nothings. I take it that this is consistent with what Mumford (2007) says when he tries to persuade his readers of the non-existence of negative facts:

A fact [...] is taken to be some kind of existent in the world. [...] But [...] can it really be a fact in the world that there is no hippopotamus in the room? This sounds like an absence of a fact, and an absence is nothing at all. [ibid.: p. 46]

Even though this might disappoint those, such as Russell or Barker and Jago, who believe in negative facts and negative entities, there is no need to understand these nothings as non-existent entities, or any entities or objects in a substantial sense. Rather, they are, in the case of the false truthbearers and the negative truths, nothing except the schematic, intentional objects of our thought, of our attention, and of truthbearers. In general, intentional objects are not always real, for instance when aboutness is not satisified, nor do they need to be posited as real existing entities. In fact, especially in the case of negative existentials, they should not be real, existing entities at all. Under the Cranean understanding of ‘about’, unlike the Representationalist, one does not need to posit the reality of non-existence. Instead, one gets the right result: for their truth, negative truths require things not to be some way; they do not require things to be any way, least of all some mysterious negative way.

SAC shows us how to reject T-M (and Molnar’s M4 above) in a way that is not arbitrary. The right SEM-TAC, if the Cranean framework for thinking about intentionality is right, requires merely that we make a distinction between cases where the intentional objects exist and are real, and the cases where they do not exist and are not real. And, it is clear that we can easily distinguish between positive and negative truthbearers in general. The former are used to claim that some thing exists or is some way. The latter are used to claim that some thing does not exist or is not some way.

Further, with this strategy we do not need to posit underlying or fundamental incompatibility facts, as Demos’s strategy does according to Russell and as many recent strategies would need to do. For instance, negative truths do not need to be explained in terms of entailments from primary or atomistic truths (in Mellor’s moderate case) nor by an ontology of totality facts or essence-facts (in Armstrong and Cameron’s ontological strategy). With the alternative strategies, we were left with the dilemma of accepting incompatibility facts or rejecting T-M in a rather arbitrary or unexplained way. The SAC-strategy gives us the resources not to have to accept incompatibility facts, and to draw our rejection of T-M along non-arbitrary, aboutness lines. Non-negative, positive truths are about things that exist and are real, and about how things really are with those things. Negative truths and falsehoods are about things that do not exist or are not real, or they are about real and existing things but claim that they are not some way. It is clear that a negative truthbearer does not require a negative entity to make it true, if we are clear about what we are talking about.

6 Responses to potential objections

I now respond to some potential objections. Especially my responses in Sects. 6.1, 6.2.5, and 6.4 are meant to address the worry that negative facts of some unsavoury sort might be being smuggled in under a false passport.⁵⁵

6.1 Objection #1: Higher-order incompatibility?

One might object that the account of falsehood in terms of the failure of aboutness–satisfaction, and the account of negative truths being about things not being some way, posit some sort of higher-level incompatibility fact. This, I think, would be to misunderstand what it is to fail in terms of aboutness–satisfaction.

Failing is indeed incompatible with succeeding. But this incompatibility is not what makes anything true (except perhaps truthbearers about their incompatibility). When I claim, for instance, that in the case of T4, we have a falsehood because of a failure of aboutness–satisfaction, I am not saying that there is something, a failure, which is incompatible with a success of aboutness–satisfaction. When we talk about failings or failures of something, we are saying that something is missing, not that there is a missing. In the same way that T1 does not require anything to exist (and especially not Pegasus) to be true, but instead relies on some putative thing (namely Pegasus) not existing, truths about failings and failures of something do not require anything to exist to be true. Rather, they require there not to be something. In the case of truthbearers about failures of about-satisfaction such as ‘T4 fails to be about anything that exists’, there must not be a relation between T4 and what it is about. To think that this failure requires some incompatibility fact, or some further, higher-level negative fact, would be to misunderstand the account and to misunderstand what truthbearers about failures of aboutness–satisfaction (or about failures of anything) are about.

6.2 Objection #2: Does the account make truth and truthmaking disunified?

One might worry that the accounts that I gave of truth and falsity, and the subsequent strategy for responding to P-NEG, make truth and truthmaking disunified in a way that is both arbitrary and radical. What results, as the objection might go, are different stories about positive falsehoods, negative truths, and positive truths, with nothing unifying them. This seems, further, to go against the aims of any account of truth (or falsity) and of truthmaking. I shall respond to these potential objections in turn.

6.2.1 Response #1: the account is not arbitrary, but piecemeal

First, the account is not arbitrary. In fact, I see no good basis for thinking that a theory of truth must account for all truths in exactly the same way or that a theory of truthmaking must account for all truths in the same way. A unified theory which does this without any costs, would perhaps be more attractive than a disunified theory. However, as the recalcitrance of P-NEG indicates, such a unified theory is not forthcoming.

Any theory which is disunified, of course, must not make arbitrary distinctions. The proposed approach is piecemeal ⁵⁶ and allows us to make non-arbitrary distinctions, based on what I take to be plausible grounds, and in a plausible, intuitive way, consisting broadly of two steps:

(Step One)::

               look closely at what the words in a truthbearer mean, and how they contribute to its meaning and what it is about (e.g. via their word order and their cases, which reveal whether the nouns, pronouns, adjectives, etc., in question take, for instance, the nominative or accusative), and

(Step Two)::

               only on the basis of what the truthbearer says about how things are should we accept an account of what makes it true.

If what the truthbearer says and is about does not make any claims or demands on what exists, and/or how things are with what exists, then it seems perfectly reasonable that things do not need to be any way, and, in fact, things should not be the way they are described not to be for those truthbearers to be true.

Thus, it seems perfectly reasonable that there are no truthmakers for those truths. As we have seen, positive and negative claims clearly differ in what they say about how things are or how things are not. It is, therefore, to be expected, that their truth and falsity should also differ according to what they say about how things are and are not. Not only does what makes them true, when they are true, differ depending on what they are about, but whether or not they are made true, or should be made true, by anything at all can differ depending on what they are about. This can be approached in a piecemeal manner by looking closely at what the truthbearers or the parts of the truthbearers are about.

6.2.2 Response #2: the strategy is not radical, but conservative

Second, the strategy is not radical either. This piecemeal or contextual approach to whether or not truthbearers require truthmakers is much more modest and conservative, and hence less radical, than a unified approach that makes the bolder and more extravagant claim that all truths are true in exactly the same way and that all truths must be made true in exactly the same way. The latter approach tries to fit all truths into the same mould and must explain, despite difficulties and despite appearances to the contrary, how this is the case. P-NEG, as I see it, is one of those major difficulties that make it appear that truth is disunified. The more radical approach is one that explains that the appearances are faulty. The more modest, and less radical, approach is one that accepts that the appearances are correct, but explains how TT can accommodate the appearances.

6.2.3 ‘Truth’ is a success term

Further, ‘truth’ is a success term. The property being true is what one might call a “success-property”. In this way, one might think of truth as similar to other success terms and properties, such as those involved in the winning of games. Just as there is no unity with regard to winning games, there is no reason to think that truth and truthmaking should have any unity either. It is highly contextual and depends from game to game what the criteria are for winning any particular game. Even within games, there are sometimes many different ways that one can win. For instance, one can win at chess either by putting one’s opponent in a checkmate position or by putting one’s opponent in an impossibly difficult position, not quite checkmate, but one which makes her forfeit the game. Also in backgammon, one can win in different ways. Most standardly one wins by getting one’s pieces off the board before one’s opponent. But one can also win if one’s opponent “drops the stakes,” that is, resigns after one has doubled the stakes of the game. In some games, there are no ways to win at all, such as with games that have no criteria for winning (for example, continuous play games such as the game of LIFE or non-competitive Frisbee; they have rules for game-play but no rules for winning). Also, some card games are such that one can win by winning all the chips or tokens in play while others are such that one wins by losing all one’s chips or tokens. In the same way as the rules for successfully winning may vary greatly from game to game, it seems that the rules for a truthbearer to succeed at being true might also vary greatly from truthbearer to truthbearer. And it seems perfectly modest and plausible to think that the criteria for truth vary according to what the truthbearers are strictly and fully about. Such disunity is far from radical and seems plausibly commonplace.

6.2.4 The strategy lets us conserve classical logic

The SAC-proposal is also less radical than other proposals in other ways. Let me briefly illustrate this with a comparison. Mumford (2007) rejects Molnar’s M3 on the basis of giving a “philosophical account” (ibid.: p. 53) of negative truths in terms of equivalent falsehoods, reducing the former to the corresponding instances of the latter. For example, the “correct philosophical account” (ibid.) of ‘It is not raining’, when true, is nothing more than that ‘It is raining’ is false. So, he rejects the claim that some negative truths about the world are true by “eliminating all negative truths” (ibid.: p. 51). Mumford (ibid.: §7, pp. 57–58) admits, however, that this solution requires us to revise classical logic, or at least to “reinterpret certain claims in the light of the new equivalences” (ibid.: p. 57). In particular, he thinks that all that we need to do is to understand the law of excluded middle (LEM) in terms of bivalence (BIV). The law is:

LEM::

$\forall {p} ({p} {{\vee }} \lnot$ p)

If understood in the following way, we are committed to the possibility of negative truths:

LEM*::

$\forall {p} ({true}{{<}}{p}{{>}} {{\vee }} {true}{{<}}\lnot {p}{{>}})$

This is not acceptable to a view that attempts to eliminate negative truths. Mumford claims he has a principled reason for understanding LEM in terms of BIV, which is:

BIV::

$\forall p ( {true}{{<}}{p}{{>}}{{\vee }} {false}{{<}}{p}{{>}})$

However, this seems to me to be a rather radical interpretation, since LEM and BIV are not the same principle and should be understood independently, even if they are equivalent. First, whatever the merits of classical logic, understanding LEM in terms of BIV rules out being able even to express other logics which are not bivalent, but which accept LEM. Second, it is radical because, by contrast, the new, rival strategy will allow us to understand LEM in terms of LEM*, rather than BIV. Mumford (ibid.: 58) argues that his interpretation will be able to account for truthbearers about the future better than LEM*. Consider the truthbearer:

P1::

There will be a sea battle tomorrow.

Let’s say that P1 is neither true nor not true now. According to Mumford, if one accepts LEM*, then “when [one] thought $\lnot {t}{[} {rue}{]}{<}{p}{>}$, then [one] would have to accept ${t}{[} {rue}{]}{<}\lnot p{>}$” (ibid.). The problem according to him is that there is no truthmaker for ${<}{p}{>}$ nor one for ${<}\lnot {p}{>}$. His suggestion is to understand LEM as BIV, on which $\lnot true {<}{p}{>}$ is understood as ${false}{<}{p}{>}$, which, according to him, doesn’t require a truthmaker. The SAC-strategy allows us to avoid the problem he raises for accepting the equivalence of $\lnot true{<}{p}{>}$ with ${true}{<}\lnot {p}{>}$, remaining conservative by not having to radically reinterpret LEM as BIV. It does not matter that ${<}\lnot {p}{>}$ does not have a truthmaker according to SAC, because ${<}\lnot {p}{>}$ is not a positive claim, and hence does not need one; in fact, one will realise that it should not have a truthmaker, if one understands what it is about. Thus, the SAC account is at least less radical than Mumford’s and allows us to interpret laws such as LEM in the standard way.

6.2.5 Knowing which terms are existence-entailing is essential to understanding what the truthbearers are fully about

There is also another reason why it is not radical. The distinction between negative truths and positive truths is not the only distinction that can be made on the basis of aboutness and being careful about what exactly truthbearers are strictly and fully about. Consider:

T7::

Pegasus is a mythological animal.

and

T7*: :

Vulcan is a hypothetical planet.

Both T7 and T7* are true. However, neither Pegasus nor Vulcan exist. Some predicates such as ‘...is material’, ‘...is an animal’, and ‘...is a planet’ are existence-entailing⁵⁷ and others such as ‘...is mythological’, ‘...is a mythological animal’, and ‘...is a hypothetical planet’ are not. Plausibly, predicates made up of adjectives such as ‘potential’, ‘putative’, ‘hypothetical’, ‘mythological’, and ‘imaginary’ are not existence-entailing; this is why one speaks the truth when one says that the hypothetical object Vulcan does not exist but that the hypothetical and confirmed-to-exist object Neptune does exist. We understand this on the basis of thinking about what kinds of predicates these are, what they mean and are about. Understanding that these predicates are not existence-entailing, and understanding what they say about the things that they are used to talk about, is essential for understanding that these kinds of claims, while positive, also do not require truthmakers.

Knowing which expressions are referential and existence-entailing and which ones are not is an important part of mastering the vocabulary of a language and is important for non-philosophical contexts as much as for philosophical contexts. This is an important part of understanding how varied and rich is the toolbox of aboutness apparatuses, which I talked about in Sect. 4.2.1. If Alfred tells little Erik that the Kraken is a mythological, imaginary creature invented to frighten children when they think of the sea, then Erik would be making a mistake if, trusting that Alfred is telling the truth, he were to think, as a result, that the Kraken exists. Specifically, he misunderstands what Alfred is saying, what he is talking about. He does not understand yet that ‘mythological, imaginary creature’ is not existence-entailing. And knowing this is essential for Erik’s understanding of what Alfred is talking about here. Unless Erik comes to understand which terms are existence-entailing and which are not, Erik will not understand either what is said or what is being talked about. The best SEM-TAC and, hence, the best account of TT must respect and accommodate this.

Thus, understanding what we are strictly and fully talking about also helps us to understand which positive truths require truthmakers, and which do not require truthmakers, not just that negative truths do not require truthmakers. This, I think, is a perfectly reasonable way of understanding the connection between what these kinds of truths are about and whether they require truthmakers. Negative truths use the negation connective, ‘it is not the case that $\phi$’, and can be understood in a similar, non-existence-entailing way. Thus, the SAC-strategy for addressing negative truths is just as non-radical as the strategy for understanding other truthbearers, constructed out of such predicates, which are not existence-entailing. For truthbearers that are not existence-entailing, such as negative truths, it would be unreasonable to require that they are made true by things that exist. That would be to misunderstand what they are about. And, this is also why we are not smuggling in negative facts under a false passport. Understanding what ‘Pegasus does not exist’ is strictly and fully about means understanding that Pegasus must not exist, not that there must be a non-existence of Pegasus. To think otherwise is to misunderstand what we are strictly and fully talking about when we are using ‘not’ to deny that some putative thing exists.

6.2.6 Is the strategy Meinongian?

It is an interesting question to what extent there are similarities between the approach I have sketched and Meinong’s.⁵⁸ An in depth discussion of this will, however, have to be left for another time, as it goes beyond the scope of this paper to address this issue properly. Thus, I remain neutral here about whether or not the approach I have sketched is Meinongian and to what degree there are similarities or overlap with the subtle and important distinctions Meinong made between the various categories of object in especially his mature Gegenstandstheorie, the theory of intentional objects.⁵⁹

However, it is worthwhile to say something about the similarities and differences. There are interesting similarities, for instance, between Meinong’s mature doctrine of the Außersein of “pure objects” and my treatment of talk about mythological creatures.⁶⁰ In particular, it is their Außersein, their essential constitutive properties which they have whether or not they exist, which distinguishes nonexistent intentional objects such as the golden mountain from similarly nonexistent intentional objects such as the largest six-winged, peach-coloured horse and from existent intentional objects such as Big Ben. The Außersein of an object is its indifference to being and non-being, and underlies the famous Meinongian principle of the independence of Sosein from Sein: in short, that an object can have properties ( Sosein) without having being ( Sein).⁶¹ Because an object need not have being to have properties and what Meinong calls a “proper essence” (ibid.),⁶² we can, for instance, distinguish between the golden mountain and the largest six-winged, peach-coloured horse. For one, the latter is six-winged while the former is not. In this way, Meinong gives a detailed and important account of the way in which we can distinguish between nonexistent intentional objects.

Although it is, as I have pointed out earlier, important to be able to distinguish between nonexistent intentional objects, it is unclear that I would have to subscribe to the Meinongian distinctions and categories to do so. First, nothing that I have said so far commits me to the claim that objects do not have to exist to be certain ways. In fact, the strategy sketched in the paper is consistent with thinking that objects cannot be any way, if those objects do not exist. Talking about the Kraken is different from talking about Pegasus. However, talking about something does not carry any ontological commitments, that is, something does not have to be real to be the object of conversation, talk, or thought. Rather, talking truly about things while using existence-entailing predicates does. Given that ‘...has wings’ is an existence-entailing predicate, one cannot truly claim, for instance, that one way to draw a distinction between Pegasus and the Kraken is that the former has wings while the latter does not. Since Pegasus is a mythological creature, he, just like the Kraken, cannot have wings. For being winged requires a body to which the wings are connected. And since having a body requires existence, being winged also requires existence.⁶³ According to Meinong, however, Außerseiende objects such as Pegasus, the Kraken, and the King of France do have properties such as, respectively, being winged, being a sea dragon, and being a king. In fact, they have these properties essentially and constitutively. The account that I have sketched does not require this.

Second, although it is true that being an intentional object (and hence being the object of talk and thought) is ontologically neutral (see Sect. 4.3), and in that sense outside of being and non-being, it is unclear that we need to subscribe to Meinong’s sense of Außersein. As Lambert explains, Außersein is a metaphysical notion and captures the claim that “what an object is [is] a function solely of its nature. It is in virtue of their natures that camels have humps, the number one is prime, and Mill’s round square is round” (1983: p. 17). The approach that I have sketched can remain modest and be ontologically neutral about there being essences or natures of things. Even though we can talk about Pegasus and also talk about something else, the Kraken, that we’re talking about these different things does not require us to have any commitments about their essences or natures. When asked to say more about the differences between the Kraken and Pegasus, one may say further true things such as ‘The Kraken is a mythological sea dragon while Pegasus is a mythological winged horse and not the other way around’. What one has said is true, and since it is not existence-entailing (for neither the predicates ‘...is a mythological sea dragon’ nor ‘...is a mythological winged horse’ is existence-entailing), it carries no commitments to what exists. Most importantly for our current discussion, it carries no consequences for what the natures of these intentional objects are. In fact, as I have explained (Sect. 6.2.5), the Kraken and Pegasus, being mythological creatures, are importantly not real. And it is plausible that things that are not real do not have essences or natures. Meinong’s account of Außersein attempts to give us the deep story about what is going on with intentional objects and their natures. But, the modest strategy that I have sketched takes part of its modesty from the fact that intentional objects are just the schematic objects of attention (see Sect. 4.3). There is no need for a deeper story about the nature of intentional objects, neither when they are merely intentional objects nor when they are truthmakers. Even if Meinong’s Außersein gives us the correct deep, metaphysical story of the nature both of intentional objects and truthmakers, it will be the task of further inquiry to convince me of this, as I see no reason to think that the current strategy requires any such metaphysically rich notions.

Of course, there is much else to say about Meinong, Meinongians, and both how the current strategy I have sketched differs from and overlaps with other strategies and accounts. However, I feel that I have, for now, said enough to present some potential differences between the current strategy and what Meinong and Meinongians have claimed.

6.3 Objection #3: Does the SAC understanding of TT reject everything the TT -ist holds dear?

The third objection is that understanding TT in this piecemeal and disunified way rejects everything that TT-ists hold dear. The worry might be that the SAC account is no longer a version of TT, if it allows that so many truths, all negative truths and even some positive truths, do not have truthmakers.

My response is that a modest version of TT, which respects what we say and what we are talking about when using truthbearers, is a more plausible version of TT, whose main aim is to elucidate and say true things about the relation between truths and reality. If it turns out that many truths do not have a relation to reality, and in fact, given what they say and are about, require there not to be a relation with reality, then the version of TT which identifies and captures this is a better version of TT than the alternatives, which claim that there is a relation when there is not. SAC identifies when there is indeed a relation between truths and reality, and modestly and correctly, refuses to claim that there is such a relation when there should not be. The way that SAC does this is by telling us to look closely at what our truthbearers are strictly and fully about. And, we are clearly still TT-ists, because we claim that there is a large subset of truths that require there to be truthmakers for them to be true, even though there are many truthbearers which do not require truthmakers to make them true. Happily, we restrict the need for truthmakers and reject Maximalism in a non-arbitrary way.

6.4 Objection #4: Does the truth of logical laws and analytic truths go against SAC ?

A fourth general objection might go thus. Recall my point in response to Mellor’s strategy of appealing to the laws of non-contradition and excluded middle, which I considered to be re-describing Demos’s incompatibilities as laws of logic. I wrote, following Russell, that the truth of logical laws requires as much explaining as the truth of anything else. However, one might take logical truths and also broadly analytic truths to be counterexamples to SAC. One might think, for instance, that truths concerning logical laws are true in virtue of the meanings of the logical constants, and, likewise, that broadly analytical truths are true in virtue of the meanings of the non-logical terms in them. Thus, what explains these truths is not what they are about, but something else. For instance, LEM seems to be true merely because of the meaning of the logical constants and independently of any assignments given to the variable. And, ‘bachelors are unmarried men’ is true merely because of the underlying complex linguistic behaviours and conventions which fix the meanings of ‘bachelors’ and ‘unmarried men’ and ‘are’, rather than what they are about.

First, a general response. The piecemeal aspect of the SAC-strategy does not rule out that there are possible exceptions to the claim that truths are made true by what they are strictly and fully about. Perhaps the nature of such truths can explain why they are exceptions. However, one of the reasons why the approach to negative truths wasn’t arbitrary was because there was a non-arbitrary fact about truthbearers, which are semantic constructions: negative truths have aboutness features which can explain why they don’t need truthmakers to be true. The aboutness features of logical and analytical truths don’t seem to be similarly explanatory. Or are they?

Let’s first look at analytic truths, such as ‘bachelors are unmarried men’. Indeed, one explanation for why such analytic truths are true is that there is something about the conventions which fix their meanings in virtue of which they are true. However, another explanation for their truth is that things are the way they are described to be. Bachelors are, indeed, unmarried men. Knowing linguistic usage and conventions is perhaps sufficient for knowing the truth of such analytic claims, but they do not determine the truth in the way that their truthmakers do. Whether things are the way they are described, whether what they are strictly and fully about is how things are, determines the truth of these claims in the appropriate truthmaking way.

The truths of logical laws are a bit more tricky and the correct response will inevitably depend on what the best SEM-TAC says about them. Perhaps these truths are just truths about logical laws, that is, the best SEM-TAC might give an account of statements of logical laws, such as LEM above, as statements about the relevant logical laws. If this is the case, then the logical laws, as what such truthbearers are about, would make true such statements, in the same way as perhaps the laws about brakeless trains make true the truthbearers in Sect. 4.1. These logical laws and brakeless train laws are just what the best SEM-TAC will say that the corresponding truthbearers are about. The truthmakers for such laws will not be the meanings of logical constants. Rather, the meanings of the logical constants will reflect the reality concerning logical laws which they are used to talk about. This reality is both what these truthbearers are about and what makes them true.⁶⁴

6.5 Objection #5: Does SAC rule out alien truthmakers?

The final objection which I would like to consider is this. Armstrong (2004: p. 88) argues that alien truthmakers must be not just epistemically but metaphysically possible. That is, it must be possible for there to be alien truthmakers, properties and relations which are not actually instantiated nor combinatorially constructible out of actually instantiated properties or relations. He argues there that the existence of such aliens is a “genuine possibility, although, of course, a mere possibility” (ibid.). One might argue that SAC rules out the very possibility of alien truthmakers. And, then, on the assumption that Armstrong is right about aliens, one might conclude that SAC gets us the wrong result about them, and thus must be rejected.⁶⁵

My response is that I don’t see how this argument would go. SAC doesn’t rule out alien truthmakers. As with negative truths, we would have to address modal truths in a piecemeal way. Nothing I have said about SAC in this paper addresses what the right account of modal truths is. My general answer to anyone who demands that I give an account of the truthmakers of modal truths would be: let’s see what SAC and the best SEM-TAC say modal truths are about. Once we have the best account of what they are about, we also have an account of their truthmakers. Consider ‘It is possible that I raise my left arm after I finish typing this sentence’. The truthbearer is about the possibility that I raise my left arm after I finished typing that sentence. Let’s say that a combinatorialist [such as Armstrong (1989)] is right. Then, what that possibility amounts to is a combination of various properties which are actually instantiated. If a dispositionalist about possibilities is right (see, for instance, Martin 2008: pp. 29–33), then the truthbearer is about the disposition I had of raising my left arm in that circumstance.

But what about alien properties? Consider ‘Alien properties are merely possible’ or ‘It is possible that I may instantiate some alien property’. Both of these truthbearers are strictly about alien properties and fully about alien properties and their being possible in the first case, and my possibly instantiating them, in the second. If alien properties are indeed possible, and if it is indeed possible that I instantiate an alien property, then these facts, whatever they are fundamentally or whatever metaphysical account of modal facts is the correct one, will be the truthmakers for these modal truths about aliens. Therefore, SAC does not rule out alien truthmakers.

7 Conclusion

Finally, it should be clear that we are able to avoid positing any sort of ontologically repugnant things which must exist to make negative claims true. There are no entities that are smuggled in through a false passport—in fact there are no entities at all that make true negative truths, and given SAC, that’s exactly how it should be. For it would be to misunderstand what these negative truths are about to think otherwise.

In conclusion, the version of TT which respects and incorporates strict and full aboutness can give us a strategy for addressing the problem of negative truths in a non-arbitrary, intuitive, and modest way.