Three Boxes Three Ways; illustration by Joy Walker

Joy Walker/MKG127 Gallery, Toronto

Joy Walker: Three Boxes Three Ways, 2009

Bertrand Russell’s 1951 obituary for Ludwig Wittgenstein is only a few paragraphs long, and the second consists largely of a single pointed anecdote:

Quite at first I was in doubt as to whether he was a man of genius or a crank…. He maintained, for example, at one time that all existential propositions are meaningless. This was in a lecture room, and I invited him to consider the proposition: “There is no hippopotamus in this room at present.” When he refused to believe this, I looked under all the desks without finding one; but he remained unconvinced.

The exchange is typical of the two philosophers’ relationship: Russell’s proper British demeanor was frequently ruffled by the Austrian’s dry humor. But it also illustrates two general approaches to philosophy: one that takes pleasure in complexities, absurdities, and ironies, and one that takes pleasure in resolving them. Just as Wittgenstein surely realized that there was no hippopotamus in the room, Russell surely realized that Wittgenstein’s objection could not be dispelled empirically by looking under each desk. At stake was not a fact of perception but the epistemological status of negation—the philosophical meaning and value of assertions about nothing.

Nothing, or nonbeing, belongs to that category of concepts—like being, space, and consciousness—that seem self-evident and self-explanatory to most people most of the time, but that for philosophy have been objects of deepest perplexity and millennia-long dispute. It’s a little like breathing, which happens automatically until we stop to think about it. To most of us, Russell’s statement “There is no hippopotamus in this room” is both easily understood and easily verified. We think we know what it means, and most of us would only need a quick look around to affirm or deny the proposition.

But here our troubles begin. If you look around the room and don’t see a hippopotamus, presumably you do still see something: some kind of perception or sensory data is reaching your consciousness, which allows you to make a judgment. What is it that you do see when you see a hippopotamus not being there? Are you perceiving a nonbeing, seeing a particular thing whose nature is absence, or are you not perceiving any being, seeing no “thing” at all? When you see a hippopotamus not being there, are you also seeing a whale and a lion and a zebra not being there? Is every room full of all the things that aren’t in it?

From an evolutionary perspective, one predator not being there is just as good as any other predator not being there, but dialectics and logic are a little more particular. If every possible animal is not there at the same time, what specific truth-value can the assertion “There is no hippopotamus in this room” possibly have? Hence Wittgenstein’s insistence, facetious or not, that all existential propositions are meaningless. In this manner the complications and implications of nothing spill into every area of philosophical inquiry, and we quickly come to sympathize with Aristophanes’ brutal satire of philosophers in The Clouds:

Socrates: Have you got hold of anything?

Strepsiades: No, nothing whatever.

Socrates: Nothing at all?

Strepsiades: No, nothing except my tool, which I’ve got in my hand.

The earliest Greek philosophers, Thales of Miletus and his immediate successors, were concerned primarily with the study of nature—Aristotle, a few generations later, called them phusiologoi, “those who discourse on nature.” Dissatisfied with mythical and mystical explanations, they sought the causes and meaning of nature in nature itself—that is, in how and what things are. Nothingness or nonbeing (what things aren’t) and possibility (what things can or can’t be) first appear as systematic objects of inquiry a century after Thales, with the Eleatic philosopher Parmenides (born circa 515 BC), the same Parmenides a young Socrates contends with in Plato’s dialogue that bears his name.

In the surviving fragments of Parmenides’ writing, we find the same cluster of speculative problems that concerned Russell some 2,400 years later, including the problem of thinking and talking about things that are not. As Wittgenstein no doubt recognized, to say “There is no hippopotamus in this room” is to predicate being (i.e., to say “there is”) of something that evidently isn’t—the “no hippopotamus.” How can such a statement be meaningful or true, proven or disproven? If we assert that it’s possible to have an idea of something that isn’t, what is it that we have an idea of?

The philosophical fortunes of nothing have undergone several reversals in the subsequent centuries. Aristotle thought nothingness was impossible, but by the late Roman Republic, Epicureanism, which held that all existence was a mixture of atoms and the nothingness of the void, was the more popular philosophy. The Middle Ages restored Aristotle to dominance and rejected any concept of nonbeing, leading to the infamous horror vacui that is a running gag in Umberto Eco’s Baudolino. Since the early modern period, resurgent atomic theory, Newtonian and later quantum physics, and advances in mathematics have all made nonbeing, void, and hypothetical entities relevant as objects of inquiry. In June NASA confirmed the existence of a supermassive black hole within the Milky Way galaxy, a vast blob of nothingness floating among the stars.


The work of Parmenides and the problems that emerge from it, including Russell’s hippopotamus, are the subject of Stephen Mumford’s Absence and Nothing: The Philosophy of What There Is Not. Mumford, a metaphysician and the deputy head of the philosophy department at Durham University in the UK, begins by extracting a set of seven propositions from the fragments of Parmenides, presented as the ancient philosopher’s core tenets. He tells us that he accepts two, rejects two, and is willing to negotiate three (hence A, R, and A/R in the list):

Pi. Nothing is not (A)

Pii. There are no degrees of being (A)

Piii. Nothing comes from nothing (A/R)

Piv. Non-being is unknowable (A/R)

Pv. Reality is a single plenum (A/R)

Pvi. Non-being is unthinkable and unnameable (R)

Pvii. Neither motion nor change is possible (R)

Mumford describes his book as a “soft Parmenidean project” because he does not accept all of Parmenides’ tenets. “Not all of Pi to Pvii carry equal weight,” he writes. “Indeed, I have arranged Pi to Pvii in an order where they become progressively less and less essential to Parmenideanism, as I am conceiving it.” That last bit is important; by many testimonies, including Plato’s and Aristotle’s, the impossibility of motion and change was central to Eleatic philosophy.

The book’s hard line is Pi and Pii: Mumford follows the ancient philosopher in the domain of ontology, the study of what is and what it means to say that something “is.” For Parmenides and for Mumford, when we say, “There’s nothing there,” we’re saying there’s no thing or being; many other philosophers would say instead that there is a thing there, a nonbeing.

But Mumford diverges from Parmenides when it comes to thinking and talking about nothing (Piv and Pvi). Whereas Parmenides seems to say that we can’t talk about or adequately conceive of nothing in any way, Mumford allows that we can have an idea of nothing, and maybe even talk about it meaningfully. Ontologically, there is no way we can say of an entity like Russell’s non-hippopotamus that it is, as the sentence “There is no hippopotamus in this room” seems to assert; nonetheless, the sentence might have some meaningful referent or some other value, even if it doesn’t turn out to be “true” in the metaphysical sense. It’s probably useful to know whether or not there’s a dangerous animal charging at you even if you can’t objectively evaluate the assertion’s truth-value. From another perspective, we might ask whether “There is no hippopotamus in this room” is the same kind of nothing as “There is no unicorn in this room,” since only one of those animals could be in the room. But what if hippopotamuses go extinct?

“In holding any position,” Mumford reasonably argues, “you ought to be able to say in what circumstances you would be prepared to relinquish it.” In the rest of the book, he gamely runs his core propositions through a series of conceptual tests to see if they will hold—that is, to see if, without violating them, we can give a sufficient account of the world and all the negative phenomena we seem to encounter in it. With a good amount of softening and some gentle massaging, Mumford’s account forecloses the existence of negative entities while leaving open the possibility that some phenomena might not be explicable without admitting negative ideas. In the process he ranges, but not too far. As he notes in the introduction, “Only the first half of this book is metaphysics. The second half is epistemology, philosophy of language, and logic.”

Absence and Nothing gives an admirable survey of nothing and its attendant problems, including perception (what do we see when we see that something isn’t there?), existence (does nothing have being or not?), conception (when I think about nothing, what am I thinking about?), and reference (when I say, “It’s not there,” what entity is the referent of the pronoun?). The writing is clear and effective, even in addressing the most complex difficulties—chapter 3, for example, offers a useful and necessary typology of nothings and absences, which include “non-beings, limits, privations, omissions, negative epistemic states, normative negatives, and logical/mathematical constructs”—but not shy about eschewing a full explanation when an adequate one will suffice.


As with all pre-Socratic philosophy and most post-Socratic ancient philosophy, no complete text by Parmenides survives. What we have are bits of his own writing preserved as quotations by later authors (“fragments”) and later writers’ descriptions and summaries of his ideas (“testimonia”). From what we can tell, which is not nearly enough to be certain of anything, it seems that Parmenides wrote a single work, a philosophical poem in hexameter, divided into two parts. The first, large chunks of which have survived, is sometimes called “The Way of Truth” but its Greek title can be more literally translated as simply “What Is.” It seems to have described a deductive metaphysics. This part of the poem contains the arguments most widely associated with Parmenides today: that both motion and change are impossible and that being is absolutely one, purely positive (a “plenum”), without negation, coming-to-being, or passing away. Mumford’s very brief quotations are drawn entirely from this first part. In the testimonia of Plato and Aristotle, Parmenides’ philosophy consists of the arguments in this part of the poem.

But the poem’s second half, much of which is missing, seems to have resembled the philosophies of the early phusiologoi, with a typology of elements and a cosmology. Diogenes Laërtius, author of the third-century AD Lives and Opinions of the Eminent Philosophers, who knew and makes references to Plato’s Parmenides, does not mention motion, change, or being at all, instead attributing to Parmenides the belief that “there were two elements, fire and earth, and that…the generation of man proceeded from the sun as first cause.” These ideas make Parmenides resemble his predecessors but are entirely incompatible with the metaphysics of the poem’s first half. They must have been the subject of its second, largely absent portion.

A fragment of Parmenides describes the distinction between the poem’s parts and illustrates the difficulty of the material:

Come now, and I will tell you (and you must carry my account away with you when you have heard it) the only ways of enquiry that are to be thought of. The one, that [it] is and that it is impossible for [it] not to be, is the path of Persuasion (for she attends upon Truth); the other, that [it] is not and that it is needful that it not be, that I declare to you is an altogether indiscernible track: for you could not know what is not—that cannot be done—nor indicate it.

Obscure as it is, the fragment seems to summarize the core tenets that both Aristotle and most modern scholars, Mumford among them, ascribe to Parmenides as his real philosophy, including one of the most vexed and vexing positions attributed to him, Mumford’s Pvi: that it is impossible to think or talk about nothing; that nothingness cannot be known or even “indicated” (phrasais). The most obvious question—how and why Parmenides wrote half of his poem about things he knew were not the case, which by his own account should be impossible to conceive or write about—remains a point of some dispute.

“It is quite a philosophical irony that there are parts of Parmenides’ poem that no longer exist,” Mumford writes, but beyond this joke and a few scattered references in chapter 1, he offers no consideration of the text’s fragmentary state, its poetic form, or its division of contents, and hence no mention of that last problem—how Parmenides managed to write, apparently at length, about something that wasn’t. Instead, Mumford presents the ancient philosopher as clear and uncompromising on the topic: “If we had a way of overcoming Parmenides’ Pvi claim that we cannot name or think about nothing, then it would allow us to name something that did not exist.”

The epistemological status of negatives and of nonbeing takes up most of Mumford’s book and offers the most difficult perplexities. Excluding nonentities ontologically—denying that nonbeings can be said in any way to actually exist—is relatively easy; that issue is mostly laid to rest by the third chapter. Aristophanes’ satire notwithstanding, metaphysics offers at least the possibility of clear and distinct lines. Demonstrating the status of negative ideas and assertions in the mind is a much messier project, relying as it does on irreducibly subjective processes like perception and association. As we move through the book, Mumford relies increasingly on what “seems reasonable” to select from competing theories: “What would it matter if there was another theory…if it was not the best theory?” Beyond conforming to or rejecting the precepts of soft Parmenideanism, though, it’s not fully clear what the criteria for “best” are.

The difficulty of establishing Parmenides’ actual position on this set of problems is not incidental. In the fragment above, Parmenides seems to say that the second way, while not true, is still one of two valid modes of inquiry. If we take him at his word, we might not have to “soften” his epistemology as much as Mumford assumes in order to demonstrate, for example, that when I come back to where I parked and see that someone stole my car, I am in fact perceiving that my car isn’t there. (Contemporary philosophy has a harder time with this question than you might imagine.) If the second half of the poem described things that are not the case but nonetheless represent a valid mode of inquiry, it seems reasonable to accept a middle ground of some kind, where what makes sense but cannot deductively be the case has some kind of explanatory power. Recognizing that fact wouldn’t make the epistemological problems magically disappear, but it would potentially allow solutions from within Parmenides’ philosophy, such as we have it, removing the need to hunt for alternatives.

There’s a slight tension throughout Mumford’s book between the amiable, teacherly way in which he explores various recent theories and the demand for a “best” or ultimate outcome. “Philosophy is at its most satisfying,” he writes, “when it articulates a problem clearly and then provides a neat solution: one that is demonstrably better than its rivals and ties up all the loose ends.” Is it, though? As with the choice of best theory, a lot depends here on what you see as the purpose of philosophical inquiry. Is the point to reflect on the complexities and savor the impossibilities, or is it to produce solutions in every case? It’s the difference, I suppose, between a building inspection and an architectural tour.

Red Grid (with void); illustration by Joy Walker

Joy Walker/MKG127 Gallery, Toronto

Joy Walker: Red Grid (with void), 2009

Beyond Parmenides himself, the book’s points of reference are mostly other recent (analytic) academic philosophy, and we get the impression that nobody had anything relevant to say about nothing between Parmenides and Gottlob Frege in the late nineteenth century. This is a general issue with contemporary academic philosophy, of which Mumford is hardly an egregious example: to pretend, after 2,400 years, that the questions are new would be a little absurd, so scholars tend to take the more polite route of pretending that the only possible solutions are.

In fact, Mumford seems to reject historical considerations entirely: “I hold no particular brief for Eleatic or other ancient philosophy. Unless we are historians of philosophy, such ideas deserve our attention only insofar as they are relevant to our present concerns.” Fair enough. Mumford’s book is an excellent survey of problems and of approaches to solving them. It also offers a range of solutions, some of them Mumford’s own. Whether these are “demonstrably” the best and most satisfying theories is arguable, but I’m not sure that’s the point.

As it happens, I find few of Mumford’s solutions best or most satisfying, not because he argues badly or wrongly, but simply because I disagree on the axioms from which he departs: for example, I reject the Fregean equivalence thesis, which holds that “for every thought there is a contradictory thought; we acknowledge the falsity of a thought by admitting the truth of its contradictory”; Mumford spends a considerable amount of time on the thesis and its implications for his project. To me the entire problem seems moot because I think assertions can be true and valid but have only contraries and no contradiction: I’m Freudian enough to think that the assertion “I love you” doesn’t automatically make the assertion “I hate you” untrue: the two are opposites but do not negate each other; the truth of one doesn’t necessitate the falsehood of its contrary. Nonetheless, I appreciate Mumford’s rigor in subjecting his own conclusions to the guiding rules of his inquiry.

Once you accept that conclusions drawn from different first principles will never agree, no matter how elegant or airtight the solution, you can just appreciate the process of argumentation. That the recent theories Mumford cites sometimes resemble less succinct versions of Bergson’s theory of perception in Matter and Memory or take a long conceptual journey only to reaffirm Hume’s guillotine; that all the theories cited seem to take inference as an act of will and lack a concept, like Freud’s unconscious or Spinoza’s conatus, that would allow for inferences dependent on perception but independent of volition or consciousness—these are only problems if we agree with the book that theories are meant to compete and not merely to describe.

Roy Sorensen’s Nothing: A Philosophical History seems to offer a deeper exploration of nothing’s past, but it drifts from topic to topic, often without prompting or explanation. The range of disciplines and historical figures cited is impressive in its breadth, yet the book rarely stops to explain ideas or their backgrounds, leaving its movements less a connecting of dots than a display of erudition. Though the chapters are arranged roughly chronologically, within individual chapters Sorensen jumps back and forth in time and among subjects. In the chapter on Buddhism, for example, there are long digressions on Kant’s conception of the self and on the British utilitarianism of the nineteenth century. At its best, this approach offers brief, engaging summaries of complex topics like the shadows in Plato’s cave or Newton’s theories of space. At its worst, Nothing’s brisk style makes its treatment of serious topics awkwardly blasé, as in its discussion of suicide.

The book’s greatest weakness is a failure to define or clarify terms. It’s hard to imagine a reader who needs an introduction to Plato’s theory of forms but no explanation of the difference between “relative nothing” and “absolute nothing”; there are section headings with no explanation in the body of the text, and no glosses for statements like “The key incompleteness of the ontological argument is the absence of a consistency proof for the definition,” a passing assertion in the discussion of Leibniz. In the first few chapters, Neanderthals living in caves, an Egyptian dialogue about suicide, and the Daoist ethics of inaction are all given as examples of nothing, but do all of those things really describe a “nothing,” much less in the same way? A cave isn’t a nothing; it’s the interior of a clearly recognizable thing; it’s not a vacuum but a hollow in the rock around it, with defined limits, full of air and maybe bats.

Nor is willed inactivity the same as nothing. Willed inactivity isn’t even the same as the total absence of activity, which itself is still only an absence and not an assertion of the existence of nonbeing: you are consciously deciding to do nothing. In a philosophy in which the will is active and undetermined, as in Epicureanism or in the picture offered here of Daoism, deciding not to act is a positive choice, an act of willing. Of these three examples early in the book—caves, suicide, and inaction—only the nonbeing of the soul after suicide qualifies as the predication of nonbeing in any clear sense.

It’s true that many historians of philosophy are first and foremost historians and not philosophers, but to subtitle Nothing “A History” is a reach. The book offers a strong thesis question right at the start:

About the fifth century BC, three civilizations independently and simultaneously began to philosophize about nothing: China, India, and Greece. Their luminaries had previously focused on what is the case….

Why were the riddles first posed 2,600 years ago? Why all at once?

But neither question is addressed in the body of the text beyond a few vague assertions about grammar. Nor does any other through line of inquiry emerge.

A historical work should clear the low bar of accurate chronology. On page 108 and again on page 153 Sorensen puts Lucretius, philosopher-poet of the late Roman Republic, in the fourth century AD. More egregiously, Hermes Trismegistus, the fictitious author of a group of works written mostly in the second and third centuries AD, is placed after hominids and before Lao-Tzu as evidence of pre-Hellenic Egyptian philosophy, an extremely dubious choice not supported by the sources.

No less egregious is the calumnious treatment of Moses Maimonides. Sorensen falsely claims that

Maimonides himself lived the life of [a] crypto-Jew. He took the religious oath making him a Muslim. He prayed at mosques. He studied the Koran. Maimonides chose to lie about sacred matters. He suborned his fellow Jews to do the same.

Maimonides, the most prominent (and prominently) Jewish intellectual of his time, studied the Koran because he was a widely read scholar in a cosmopolitan Muslim milieu; he wrote in Arabic and was well versed in contemporary Islamic learning. Some scholars believe that he and his family had to formally convert to Islam in order to escape the increasingly hostile climate of Almohad Andalusia, but once settled in Cairo, he famously lived as a shining example of Jewish piety.

Sorensen treats Maimonides’ negative theology as a peculiar Jewish outgrowth; oddly for a historical account, there’s no mention of how Maimonides’ distinctive philosophy soon passed into Christian orthodoxy by way of Thomas Aquinas, who frequently cites “Rabbi Moses.” Also largely absent from the account are Hegel and Heidegger, two enormously influential philosophers for whom nonbeing is a central concept. It’s hard to fault Mumford too severely for failing to historicize his subject, a task he explicitly rejects, but the improbable gaps in Sorensen’s account leave it feeling less like a work of history and more like an accidental triumph of irony.