An Excess of Negatives

0. Introduction

Some correspondence theorists such as Armstrong (2004) and Jago (2018) have argued that every truth has a truthmaker; this view is typically called “truthmaker maximalism” (henceforth “TM”). To account for negative propositions (e.g. ‘there are no wizards’) some defenders of TM treat absences or negative states of affairs as spatiotemporal entities. In this paper, I will argue that Barker and Jago’s (2012) model of TM is false because there is no good reason to think that negative states of affairs actually exist.

In the first section, I describe precisely what negative facts are supposed to be, then I defend an argument against their existence and consider objections to my own account of negative facts before a final conclusion.

1. Negative Facts

Negative facts are supposed to be real entities located in space and time in Jago’s version of TM. Maximalists today typically claim: “Every sentence is such that it is true if and only if it has a truthmaker.” (Rodriguez-Pereyra 2006, p. 2) To say that every truth has a truthmaker is a strong metaphysical claim because it means there always exists some state of affairs in the world which gives sentences their truth value, contingently or necessarily. In other words, some sentences are true because the meanings they express somehow correspond to states of affairs in the world. Existence seems to be a positive property so is tempting to say all facts are somehow positive, as Russell observed:

“You have a feeling that there are only positive facts, and that negative propositions have somehow or other got to be expressions of positive facts.” (2009, p. 41-42)

But there are negative facts and they must be explained, such as the sentence, “Ern Malley does not exist.” The non-maximalist usually explains negative truths such as these by saying that there are some truths with no truthmakers. The sentence is true because of what does not exist, not because of what does; "the absence of Ern Malley" does not refer to anything with properties but to the lack of the existence of a particular thing. In contrast, the maximalist must say that there exists truthmakers even for negative propositions, “there are specific entities such as the absence of Ern Malley.” (Jago 2018, p. 132) The sentence is true because there exists an entity ‘the absence of Ern Malley’ to which it corresponds. These absences are variously called “negative states of affairs” and “negative facts.” (Jago 2018, p. 132) Jago (2018) admits that the non-maximalist explanation should be preferred if it can account for negative truths because TM does carry many metaphysical obligations. Mumford (2007, p. 48) says that TM seems to treat non-existence as though it were existence, and suggests that treating absences as though they were entities is a misuse of language:

“[C]an it really be a fact that 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. Alternatively, could the fact in question be the non-hippopotamus that is in the room?”

Jago and Barker (2012, p. 2) present a model upon which ‘the absence of the hippopotamus in the room would be an entity spatiotemporally located in the room, “we want our negative facts to exist just as much as our positive facts.” This negative fact is supposed to be a fundamental kind of entity, from which properties are abstracted. Negative facts have a kind of non-mereological composition. Jago and Barker (2012, p. 6): 

“As a consequence, we accept negative properties and relations into our ontology, as abstractions from negative facts. If [Fa] — is a negative fact, then λx[Fx]—, the property of non-Fness which is abstracted from it, is a negative one. We then have a corresponding positive fact, [(λx[Fx]−)a]+, the fact that a possesses non-Fness.”

If a is not F and we abstract from this the property of non-Fness, but we must ask whether this is truly a property. Is lacking a property, itself a property? This seems an unnecessary claim. For Jago and Barker (2012, p. 4), absences are also located in time and space—so what about those which are universally true? If there are no fairies, and never will be any fairies, then the entity which is ‘the absence of fairies’ is really omnipresent. It is not located in any particular place, it is at all places and it is true at all times (even timelessly). The fact that there are no fairies would be located in every region there is.

Consider properties like non-Fness again. I would say that this is just the negation of a property, and non-Fness is nothing more than an idea, a way of thinking about our perception of an absence of F. But if it were a property, and nothing possessed Fness, it would then follow that everything has the property of non-Fness. There would be no way to localize non-Fness to any particular space or time.

2. An Argument

Non-Fness is not a property unless lacking a property is itself a property. But the lack of property ought not to be considered a property because this would result in a very bloated ontology. It is also difficult to see what distinguishes one negative property from another aside from appeals to a kind of thisness. The argument might be summarized this way:

1. If absences (or negative states of affairs) are entities, then there are an infinite number of them. (Premise)

2. For there to be an infinite number of absences, they must be distinguished by individuating properties. (Premise)

3. But absences could not have such individuating properties. (Premise)

4. Hence, there are not an infinite number of absences. (From 2 and 3)

5. Hence, absences are not entities. (From 1 and 4)

The truth of the first premise is shown by the fact that there are an infinite number of properties which nothing has. If negative properties exist, TM would commit us to saying that every object has an infinite number of negative properties which are just as existent as their positive properties, e.g. an apple has the negative properties of ‘not-humanness,’ ‘not-numberness,’ ‘not-planetness,’ and so on. An apple would have an infinite number of such negative properties because there are innumerable properties which the apple does not have and will never have.

With regard to the second premise, the sentence “Ern Malley does not exist” would be true according to TM because of an entity which is ‘the absence of Ern Malley.’ But the defining property of this entity is that it is not something. But what other properties does this absence have, other than it is not Ern Malley? Consider also the entity, ‘the absence of fairies’; any other properties it might have are abstracted only from its being an ‘absence of fairies.’ Both absences are universally located and true at all times. Why not say there is a single entity which is both the absence of fairies and the absence of Ern Malley? There must be some individuating properties which distinguish the two entities.

“We’ve presented our theory of facts. However, let’s admit it: our clarification of negative facts is achieved through the notion of anti-instantiation. And what kind of clarification can that be, given that anti-instantiation is opaque? We admit the opacity.” (Jago and Barker, 2012, p. 9)

The third premise states that there are no such individuating properties because there does not seem to be any way to determine whether ‘the absence of Ern Malley’ is a distinct entity from ‘the absence of fairies’; or whether there is actually a single entity which is ‘the absence of Ern Malley and the absence of fairies.’ The defender of TM might make an appeal to a kind of thisness, and argue it is a brute fact that ‘the absence of Ern Malley’ is not ‘the absence of fairies.’ But it is a dubious thing to say that there is nothing that does the metaphysical work of distinguishing these two entities. For TM to be true, there must be an infinite number of such entities which are likewise distinguished by brute facts of identity. At this stage TM becomes more opaque and difficult than any problems it seeks to solve.

In short, I have argued that there does not seem to be any good way to distinguish one negative fact from another and this is especially the case with universal negatives. This problem can be avoided entirely by simply denying the privilege of existence to negative facts.

3. Conceptual Existence and Negative Facts

It is better to regard negative facts as having only a conceptual existence which avoids the costly metaphysical commitments of TM. I shall give my own non-maximalist account of true negative propositions of the sort “Ern Malley does not exist,” and then see if it survives the objections Jago (2018) levies. If it is even possible that my account is true, then it should be preferred because it is simple and does not require postulating an infinite number of entities. In my view, negative facts have only a conceptual existence. When I say “Ern Malley does not exist” I mean only that I have a concept of what it would mean for Ern Malley to exist, but there is no state of affairs in the world which corresponds to this concept. The sentence is true precisely because the opposite sentence “Ern Malley exists” does not have a truthmaker, there is not an entity (e.g. the absence of Ern Malley) that exists which ensures the truth of the sentence because it is not the kind of sentence that would require one. There is no such person as Ern Malley in the furniture of the world, and this is what makes the sentence true.

Jago (2015) responds to this kind of view firstly by saying that it implies that there are three differing types of true propositions, positive (e.g. ‘the sun exists’), negative (e.g. ‘Ern Malley does not exist’) and derivative (either ‘Mark is pacing or Ern Malley does not exist’). I think this threefold distinction is correct. Only the first sort of propositions always require truthmakers. The second sort, as we have seen, do not, and the third sort does if one of the disjuncts is a positive proposition. Jago argues that this categorization fails because of certain true epistemic propositions that do not fall into any of the three categories just spelled out. Hence, the non-maximalist position is implicitly committed to TM or has more fundamental problems, Jago (2015):

“I still think this theory won't work. Here's why: take this proposition—”Max knows there are no daleks.” We've got to work out what kind of proposition that is, according to the non-maximalist lines… it better not be the positive kind; if it is, then it has a truth-maker… Knowledge is factive, so the truth-making must be some entity in the world that guarantees that there are no daleks. And that's just the kind of entity the non-maximalist wanted to avoid—some weirdo absence that somehow guarantees that such and such won't exist.”

So then, the proposition “Max knows there are no daleks” isn’t negative because it involves a claim about what Max knows. It is not positive because it would require a truthmaker ensuring what Max knows. The third option is that the proposition is a derivative proposition. But Jago (2015) objects that this would require a reductive theory of knowledge to which he says, “people have been trying to work out what knowledge is trying to give a reductive definition of knowledge for absolutely honest that hasn't worked out good.” But if a reductive theory of knowledge is at least possible, then this is problematic for TM. The existence of any negative facts or absences is already controversial and is at least as controversial as reductive theories of knowledge, Jago and Barker (2012, p. 1) describe an "enmity to negative facts” among their peers.

Further I would say that modern physics has had much benefit in describing the world in terms of laws and initial conditions, but has had no use for positing negative states of affairs or negative initial conditions. Our scientific theories are useful because they describe reality accurately to some extent. Godfrey-Smith (2003, p. 91-92) gives the example of building a bridge which people will use to cross. If the principles of physics and engineering underlying this project were faulty we ought not to expect success in our project. But physics has been very successful without positing these negative entities. This objection of mine assumes a modest scientific realism, that our theories, to some extent actually describe “what the world is like” and that this issue does not involve metaphysical truths that do not hide beyond the edges of physics. (Godfrey-Smith, 2003, p. 347) But this is a reasonable assumption, if something is metaphysically necessary then it should reflect in our physics in some way. In the case of negative facts or absences, Jago and Barker (2012, p. 1) address concerns they are “causally inert" by suggesting that they might be regarded as having causal powers. If absences are really existent entities which have causal powers, then they should be detectable in physics or at least useful to the physicist in her theorizing.

If their existence would make no difference to physics, then I would say that TM is guilty of causal overdetermination. In contrast, it is better to treat positive states of affairs as synonymous to an extent with initial conditions and negative facts as the lack of any such conditions. The non-maximalist explanation fits in well with modern physics. Our physics should inform our metaphysics whenever possible to avoid unfalsifiable theory crafting when we can.

It seems to me that the central problem which might be faced by the non-maximalist solution which I have given is how well it fits with the English language. When we talk about absences or negative facts, it is common to talk about them as though one is referring to entities that exist. But I would say that most people do not believe negative facts are real entities and so even when they use language that seems to imply that they are the sentences or unintended to express that proposition. Negative facts should be regarded as statements about properties that nothing has or things that do not exist in the world. Such statements could only be false if those things or properties actually did exist in the world.

4. Conclusion

Non-maximalist explanations are less problematic than TM because they require less ontological commitments. There are also significant challenges to distinguishing one universal negative fact from another on TM, and solving this problem (if possible) would require further costly metaphysical commitments. The primary objection to non-maximalism raised by Jago regarding reductive theories of knowledge, even if true, is less costly than what TM requires.

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Armstrong, D. (2004). Truth and Truthmakers. Cambridge University Press, Cambridge. 

Godfrey-Smith, Peter (2003). Theory and reality: an introduction to the philosophy of science. Chicago: University of Chicago Press.

Jago, Mark (2018). What Truth Is. Oxford: Oxford University Press.

Jago, Mark & Barker, Stephen (2012). Being Positive About Negative Facts. Philosophy and Phenomenological Research 85 (1):117-138.

Jago, Mark, (Jan 30, 2015). Lecture: “What Truth is” at the University of Edinburgh https://www.youtube.com/watch?v=jyOGlrIiWR

Mumford, S. (2007). Negative truth and falsehood. Proceedings of the Aristotelian Society 107(1): 45–71. 

Rodriguez-Pereyra, Gonzalo (2006). Truthmaker Maximalism Defended. Analysis 66 (3):260–264.

Russell, B. (2009). The Philosophy of Logical Atomism. Routledge, Oxford.