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.

What is Metaphysics?

Metaphysics is the study of the most basic principles of reality, the ultimate structure of things, or as the ancient Greeks would say “first principles.” The goal of metaphysics is to find out the truth about the basic nature of reality, to determine what kinds of things exist and what things do not exist and how they relate to each other. Generally, the kind of stuff that Aristotle was concerned about when the wrote his Metaphysics. (Thomson, 265)

One way to conceptualize metaphysics is to say that science typically seeks to describe “how” things work, but metaphysics focuses upon “what” kinds of things exist, what it means for them to exist, and the “why” questions concerning these things. (Ney, 31-36).

A primary concern of metaphysicians is what it means for something to “exist” and what kinds of things exist. Ancient metaphysicians often relied upon reason, intuition, trances, dreams, and the study of nature to draw conclusions about how reality is structured. Plotinus practiced divination and an entire section of his Enneads (3.4) is dedicated to Tutelary Spirits.

Nowadays, metaphysicians rely primarily upon the tools of logic and insights gained from scientific discovery to go about their research. In the past century great discoveries have been made by physicists concerning the nature of space, time, causation and the nature of reality at the microscopic scale. These are of great interest to metaphysicians, who are often concerned with the nature of physical things, free will, time, and how they relate with one another.

A great deal of modern metaphysics is about whether anything exists beyond the natural or physical world. Some philosophers think there are abstract objects (such as mathematical objects) in addition to physical things. An abstract object, would be one which exists but is not extended in space, something which has properties but does not have any physical properties like location, weight, or mass. Some philosophers think that the mind is an immaterial substance (substance dualism) or that there is a God of some sort. If real, such things would exist beyond the physical world in some sense.

In metaphysics, claims about reality are supported by arguments because no direct proof is often available. The premises of these arguments are usually supported by claims about possibility, impossibility and necessity (i.e. modality). Claims about the way things could possibly be, how they could not possibly be, and what things must always be the case. Also scientific evidence is sometimes used to support premises and metaphysical arguments or appeals to intuition. Modern philosophers do not usually make appeals to dreams, mystical experiences, or visions (like Socrates, etc.). (Apology, 21b-d, et al) 

A Basic Introduction to Logic

The primary tool of philosophers is logic, essential to construct arguments and analyze concepts. The field of logic is the systematic study of the principle of valid reasoning. If philosophy is going to arrive at the truth of anything, it requires methods to arrive at the truth. There is nothing more fundamental.

An argument in philosophy is a series of statements or claims which are presented in support of a particular conclusion. A premise is a statement in the argument that leads to the conclusion. There are two basic kinds of arguments, deductive arguments and inductive arguments. The most common example of a valid argument is:

1. All men are mortal.

2. Socrates is a man.

C. Socrates is mortal.

This is an example of a deductive argument. Deductive arguments are arguments which are intended to reason from general principles to specific conclusions. In a valid deductive argument, if the premises are true, then the conclusion must also be true. An argument is sound if and only if, it has true premises and a valid form. It is possible for an argument to be valid and yet unsound.

It is impossible for the premises of a deductive argument to be true, yet for the conclusion to be false. If the first two premises of this example argument are true then the conclusion is entailed by logical necessity. If all men are mortal and Socrates is a man, then it cannot be the case that “Socrates is not mortal.”

This example argument is also a kind of Categorical Syllogism. A syllogism is a formal argument with numbered or otherwise ordered steps and a conclusion. It is called a categorical syllogism because it reasons about categorical claims, i.e. about the category “men.”

Inductive arguments differ in that they argue from specific observations to a more general conclusion. They include probabilistic arguments, and they seek to make probable conclusions about the world from some set of data which seems to favor the conclusion.

1. About 99% of all species that have ever lived on earth are now extinct.

2. Canis familiaris is a species that has lived on Earth.

C. Therefore, the species canis familiaris is extinct.

The conclusion of this inductive argument is factually wrong, canis familiaris refers to dogs, which are quite common nowadays. Hence, this is an unsound argument. But, it is not an invalid argument. Both of the premises are true and yet the conclusion is false. This illustrates that inductive arguments do not lead to certain conclusions. It is possible for all the premises of an inductive argument to be true and yet for the conclusion to be false—this is unlike deductive arguments, where, if the premises are true then the conclusion cannot be false.

Abductive arguments are sometimes set as a third class of argument (some authors include them as a subset of inductive argument). These are inferences to the best explanation. Most of our daily reasoning may be considered abductive. Consider, when someone sits down in their favorite chair it is because they trust that the chair will be stable when they sit in it. Very rarely do people first test the stability of the chair. It is often possible that someone filed down the legs of the chair or otherwise rigged the chair to collapse when anyone attempted to sit in it. But the chair was stable in the past, and the chair looked fine upon cursory glance, so people tend to sit in their chair and often are right in their belief that the chair will be stable when they sit in it. They make an abductive inference that the chair will not collapse once they sit in it. An example of an abductive argument would be:

1. There are cell phones in the world.

2. Humans tend to make cell phones.

C. All cell phones are made by humans.

It is possible that there is a cell phone made by an artificial intelligence, or an alien or by some unknown process. But the best explanation for all the cell phones in the world is that humans have made them. This is the simplest explanation, consistent with what is usually true about cell phones, as stated in premise 2. Many would even think it “crazy” to deny the conclusion of the argument without some strong evidence of non-human cell phone makers. Why is this the “best explanation”? What constitutes a “best explanation?” This depends upon the standards of explanation, justification, and other criteria that the reasoner has in place. But generally, and in our everyday life, explanations are good insofar as they are simpler than rival explanations, explain the data under consideration, and are consistent with our background knowledge.

Symbolic logic is a way of talking about logical expressions and structures without using traditional language. It allows for more precise expressions of logical formulas than vernacular speech. Consider again the following example:

1. All men are mortal.

2. Socrates is a man.

C. Socrates is mortal.

It is possible to symbolize this argument in the following way, if we let M(x) = “x is mortal” and H(x) = “x is a man” and s = “Socrates”

1. ∀x(H(x) ⊃ M(x))

2. H(s)

C. M(s)

The subjects are substituted with variables or letters and operators or adjectival expressions are substituted for symbols. For example, ⊃ means “then” or “entails.” The symbol ∀ means “all” or “for every.” To say “∀x” is then, to make a claim about all x’s i.e. about anything which is an x. The parentheses are used to divide up the expressions and organize them, so we know the full range of applications for the expressions given i.e. it groups things together for us.

What is Philosophy?

The English word philosophy is derived from the Greek φιλοσοφία (filosofia) which means love of wisdom. Webster’s dictionary gives a definition of philosophy which is too broad to apply to the academic study of philosophy, “all learning exclusive of technical precepts and practical arts.”

The Platonic dialogue, the Euthydemus says “philosophy is the possession of knowledge; and knowledge must be of a kind which is profitable and may be used.” In the early days of the scientific era, the now separate fields of chemistry, biology, and physics were together labeled as “natural philosophy” because they sought to gain wisdom about the natural world. Nowadays, we make a distinction between “science” and “philosophy.” Bertrand Russell considered philosophy to be the study of the uncertain, an attempt to gain clarity on those facts which are outside the reach of science. On one occasion, Russell said “science is what we know and philosophy is what we don't know.”

Nowadays, modern philosophers generally like to think that their work leads to knowledge of something and is practically useful. Academic philosophers often wish their work to be practical rather than abstract, and their theories to be natural rather than spiritual. Since Karl Popper, it is especially fashionable for philosophers to desire their work to be beneficial to science. Modern philosophy refers to an academic study of the nature of reality, existence, the mind and knowledge—it is a quest to understand the truth about the most general features of the world. It considers questions like “What is existence?” “Is there a God?” “What is consciousness?” “What is the nature of moral values?”

Introductory Philosophical Resources:

Stanford Encyclopedia of Philosophy 

Routledge Encyclopedia of Philosophy 

Internet Encyclopedia of Philosophy 

Perseus Digital Library (Tufts University)

The Internet Classics Archive (MIT)