Earlier this month, MIT Technology Review published an article entitled “A quantum experiment suggests there’s no such thing as objective reality.” It was one of several publications to excitedly report on a recent experiment conducted by Massimiliano Proietti (Heriot-Watt University) and others.The provocative headline drew a lot of attention to the article and the experiment. Given how outlandish it sounded, I—like most people, largely ignorant of cutting-edge physics—thought that the experiment was either earth-shatteringly amazing or that the claims made about it were bunk. Either way, it sounded like the perfect candidate for an intervention from philosophers and philosophy-knowledgeable physicists. This post, the latest entry in the occasional “Philosophers On” series, is the result.
While I am going to leave most of the explanation of the background physics, experiments, and findings to the guest authors, it might be useful to note how the MIT Technology Review article described what happened. It first notes that Proietti’s experiment is based on a thought experiment devised by physicist Eugene Wigner called “Wigner’s Friend.” It continues:
Last year… physicists noticed that recent advances in quantum technologies have made it possible to reproduce the Wigner’s Friend test in a real experiment. In other words, it ought to be possible to create different realities and compare them in the lab to find out whether they can be reconciled. And today, Massimiliano Proietti at Heriot-Watt University in Edinburgh and a few colleagues say they have performed this experiment for the first time: they have created different realities and compared them. Their conclusion is that Wigner was correct—these realities can be made irreconcilable so that it is impossible to agree on objective facts about an experiment.
You can check out the whole article here.
And now let me introduce our guest authors. They are: Sean Carroll (Research Professor of Physics at Caltech), Karen Crowther (Postdoctoral Researcher in Philosophy at the University of Geneva), Dustin Lazarovici (Postdoctoral Fellow in Philosophy, Université de Lausanne), Tim Maudlin (Professor of Philosophy at New York University), and Wayne Myrvold (Professor of Philosophy at Western University).
I am very grateful to them for the time and effort they put into crafting contributions for this post that are informative, fascinating, and, importantly, accessible to non-experts. Thank you, authors!
Thanks also to Michael Dickson (University of South Carolina) and David Wallace (University of Southern California) for some preliminary feedback about this topic.
You can scroll down to the posts or click on the titles in the following list. (Note: while I normally put the contributions in alphabetical order, I am deviating slightly from that and putting Dr. Crowther’s first, as she included a helpful diagram that is relevant to all of the posts).
- “What the Experiment Actually Did and What Is Learned from It” by Karen Crowther
- “Reality Remains Intact” by Sean Carroll
- “Keep Calm, Quantum Mechanics has not Rejected Objective Reality” by Dustin Lazarovici
- “If There Is No Objective Physical World Then There Is No Subject Matter For Physics” by Tim Maudlin
- “Quantum Theory Confirmed Again” by Wayne Myrvold
What the Experiment Actually Did and What Is Learned from It
by Karen Crowther
Quantum mechanics (QM) is supposed to be a universal theory: its domain of applicability is not restricted to the world at very small length scales. In other words, the theory is meant to describe elephants as well as electrons. While we do not, of course, need to use quantum theory to describe elephants, there are increasingly larger and more complex laboratory systems (i.e., tabletop experiments) being built that do display quantum behaviour. There are various proposals for why, in practice, we do not need to use quantum theory to describe the world at the length- and time-scales that are familiar to us as human beings. The central of these is decoherence—the idea that the interference effects that would otherwise reveal our ‘quantum-ness’ get suppressed when a system interacts with other systems around it (‘the environment’). Thus, demonstrating the quantum behaviour of a laboratory system requires the system to be isolated (to a great degree) from outside influences.
Decoherence, however, does not help when it comes to a more problematic disconnect between the quantum-mechanical description of the world and our experience of it. Whenever we take a measurement of a system to determine the value of some property it possesses (e.g., position, charge, spin, mass, polarisation, etc.), we find the system to have a definite value of this property. Yet, before the measurement, QM says that the system does not possess a determinate value of this property, but rather exists in a superposition of different states with different values of this property.
Rectifying these two pictures is known as the measurement problem, and solving it has spawned the development of various interpretations of QM that seek to explain what’s going on. These interpretations are constrained by the violation of a mathematical relation known as the Bell inequality, which makes it particularly difficult to retain the belief that the system possesses a definite state (i.e., one with particular values of its measurable properties) before being observed—as some interpretations known as hidden variable interpretations seek to do.
Wigner’s thought-experiment was an attempt to show that conscious observers cannot themselves exist in superpositions because it would lead to situations where a person has an experience of the world that conflicts with the experiences of others: two people would record inconsistent facts about one and the same system (Wigner, 1967). In other words, reality would be observer-dependent.
In the thought-experiment, Wigner has a friend in an isolated lab who measures the polarisation of a photon, and finds it to have a definite value—this is the friend’s ‘fact’. Wigner, however, is outside of the lab, and does not know the outcome of his friend’s measurement. Instead, Wigner uses QM to describe his friend’s entire lab as a quantum system and finds it to be in one giant superposition of the different possible polarisations of the photon, as well as the different possible outcomes of his friend’s measurement—this superposition is Wigner’s ‘fact’. The two ‘facts’ are inconsistent. (See Figure 1).
Different interpretations of QM have different ways of dealing with this scenario. For example, the relational interpretation of QM would embrace the inconsistency of the two ‘facts’, maintaining that facts are observer-dependent. On the other hand, the many worlds interpretation would deny the inconsistency, saying that the universe has branched into multiple universes, and in any one universe, observers will record consistent facts about the state of a given system.
Wigner’s own interpretation was that the scenario described by his thought-experiment was physically impossible: he argued that the conscious experience of his friend as having recorded a definite measurement-outcome would mean that after her measurement, it would not be correct for Wigner on the outside of the lab to describe the system as being in a superposition. This interpretation means believing that a “being with a consciousness must have a different role in quantum mechanics than the inanimate measuring device”, and hence that there must be “a violation of physical laws where consciousness plays a role” (Wigner, 1967, p. 181).
Yet, the laboratory experiment of Proietti et al. (2019) claims to have concretely realised Wigner’s thought-experiment. In this ‘real life’ experiment, the friend, isolated in her lab, measures the polarisation of a photon and records the outcome of her measurement; Wigner, outside of the lab, can then choose to either measure his friend’s record of her measurement-outcome (to attest to the ‘fact’ established by his friend), or to jointly measure both the friend’s record as well as the polarisation of the original photon (to establish his own ‘fact’).
In this ‘real life’ experiment, however, Wigner and his friend are not conscious observers, but pieces of machinery: they are measuring-and-recording devices. Proietti et al. (2019) argue that these devices can act as observers, defining an observer as any physical system that can extract information about another system (by means of an interaction) and can store that information in a physical memory. On this definition, computers and other devices can act as observers, just as humans can.
Now, what the experiment actually did was to use QM to calculate the probabilities of each of the possible measurement outcomes, and then compare these to the probabilities calculated from the experimental data obtained (1794 six-photon coincidence events, using 64 settings, over a total of 360 hours). The experimenters did this in order to test the violation of a Bell-type inequality, and the experiment was indeed successful in confirming its violation. Thus, the significance of the experiment in this sense was to further confirm the violation of Bell-type inequalities by quantum systems (even relatively large, complex ones) and to place stricter constraints on particular hidden variable interpretations of QM. But there are already many other experiments that have confirmed the violation of Bell-type inequalities by quantum systems (although under different conditions, and subject to different ‘loopholes’ and sources of error). And, there are already many other experiments that have confirmed that QM is not restricted in its domain to very small systems.
So, what is the philosophical interest in this particular experiment? The question is what this experiment demonstrates about QM that was not already known from the thought-experiment plus previous experimental results. Plausibly, what it shows is that a scenario analogous to the one imagined by Wigner is in fact physically possible, and in it the observers do record conflicting facts. Thus, the philosophical significance of the experiment is to make Wigner’s own interpretation of his thought-experiment look increasingly implausible: it is difficult to imagine that this experiment would not have been successful if the devices had conscious experiences.
But, on the other hand, the fact remains that these devices are not conscious, and so Wigner could stand resolute in his interpretation. If anything, he could point out that—in the same way that an observation of a non-black, non-raven provides a negligible sliver of confirmation for the claim that ‘all ravens are black’—the success of the experiment even provides inductive support in favour of his interpretation: the ‘observers’ in this experiment are able to record conflicting facts only because they do not experience these facts.
Reality Remains Intact
by Sean Carroll
Of course there is not a new experiment that suggests there’s no such thing as objective reality. That would be silly. (What would we be experimenting on?)
There is a long tradition in science journalism—and one must admit that the scientists themselves are fully culpable in keeping the tradition alive—of reporting on experiments that (1) verify exactly the predictions of quantum mechanics as they have been understood for decades, and (2) are nevertheless used to claim that a wholesale reimagining of our view of reality is called for. This weird situation comes about because neither journalists nor professional physicists have been taught, nor have they thought deeply about, the foundations of quantum mechanics. We therefore get situations like the present one, where an intrinsically interesting and impressive example of experimental virtuosity is saddled with a woefully misleading sales pitch.
My own preferred version of quantum mechanics is the Everett, or Many-Worlds formulation. It is a thoroughly realist theory, and is completely compatible with the experimental results obtained here. Thus, we have a proof by construction that this result cannot possibly imply that there is no objective reality. I am fairly confident that other realist approaches—hidden-variables models such as Bohmian mechanics, or dynamical-collapse models such as GRW theory—can offer equally satisfactory ways of interpreting this result without sacrificing objective reality, but I’m not confident in my ability to give such an account myself, so I’ll stick to the Everettian story.
Many-Worlds is a simple theory: there are wave functions, and they evolve smoothly according to the Schrödinger equation. Wave functions generally describe superpositions of what we think of as possible measurement outcomes, such as “horizontal” or “vertical” polarizations of a photon. The traditional “collapse of the wave function,” where an observer sees a unique measurement outcome, is replaced by decoherence and branching. That is, once a quantum superposition becomes entangled with a macroscopic system, that entanglement spreads to the environment (effectively irreversibly). If the measurement apparatus included a physical pointer indicating different possible results, that pointer cannot help but interact differently with the photons suffusing the room it’s in, depending on where it’s pointing. The pointer is now entangled with its environment.
That’s decoherence, and it implies that the two parts of the superposition now describe separate, non-interacting worlds, each of which includes observers who see some definite measurement outcome. The separate worlds aren’t put in by hand; they were always there in the space of all possible wave functions, and Schrödinger’s equation naturally brings them to life. If you believe a photon can be in a superposition, it’s not much of a conceptual leap to believe that the universe can be.
The experiment under question here is a version of Wigner’s Friend. The idea is to illustrate the possibility that observers in a quantum world can obtain measurement results, or “facts,” that are seemingly inconsistent with each other. One person, the “friend,” observes the polarization of a photon and obtains a result. But from the perspective of Wigner, both the photon and the friend appear to be in a superposition, and no measurement outcome has been obtained. How can we reconcile the truth of both perspectives while maining a belief in objective reality?
It’s pretty easy, from a Many-Worlds perspective. All we have to do is ask whether the original quantum superposition became entangled with the external environment, leading to decoherence and branching of the wave function. If it did, there are multiple copies of both Wigner and his friend. If it did not, it’s not really accurate to say that a measurement has taken place.
In the experiment being discussed, branching did not occur. Rather than having an actual human friend who observes the photon polarization—which would inevitably lead to decoherence and branching, because humans are gigantic macroscopic objects who can’t help but interact with the environment around them—the “observer” in this case is just a single photon. For an Everettian, this means that there is still just one branch of the wave function all along. The idea that “the observer sees a definite outcome” is replaced by “one photon becomes entangled with another photon,” which is a perfectly reversible process. Reality, which to an Everettian is isomorphic to a wave function, remains perfectly intact.
Recent years have seen an astonishing increase in the precision and cleverness of experiments probing heretofore unobserved quantum phenomena. These experiments have both illustrated the counterintuitive nature of the quantum world, and begun to blaze a trail to a new generation of quantum technologies, from computers to cryptography. What they have not done is to call into question the existence of an objective reality. Such a reality may or may not exist (I think it does), but experiments that return results compatible with the standard predictions of quantum mechanics cannot possibly overturn it.
Keep Calm, Quantum Mechanics has not Rejected Objective Reality
by Dustin Lazarovici
A group of physicists claims to have found experimental evidence that there are no objective facts observed in quantum experiments. For some reason, they have still chosen to share the observations from their quantum experiment with the outside world.
There is a lot wrong with the paper, so let me focus on the most critical points. First of all: what the experiment actually tested has little to do with the existence or non-existence of objective facts. It rather shows that the outcomes of different possible “Wigner’s friend-type” measurements cannot be predetermined, independent of what measurements are actually performed. This should come as no surprise to anyone familiar with quantum foundations as similar results have been established many times before (by various so-called “no hidden variables theorems”). In particular, it doesn’t mean that measurement outcomes, once obtained, are not objective. It rather reminds us that a measurement is not a purely passive perception but an active interaction that “brings about” a particular outcome and can affect the state of the measured system in the process.
Even from a logical point of view, the argument in the paper doesn’t hold water. Proietti et al. test a version of the Bell inequality whose violation, in different settings, has already been confirmed by various other experiments. They claim (but never prove) that their inequality follows from three assumptions: Locality (simply put: distant simultaneous measurements cannot affect each other), “free choice” (simply put: the experimentalists can freely choose what they measure) and “observer-independent facts” (whatever this means). Now, the original Bell inequality is derived from only the first two assumptions, locality and free choice. Hence, it’s already well-established that at least one of these assumptions is violated by quantum phenomena. (Indeed, the extended Wigner’s friend experiment does involve nonlocality; it is carried out on entangled systems, and the measurement of Alice’s friend can instantaneously affect the outcome obtained by Bob’s friend and/or vice versa.) So how could the violation of the Bell inequality in the extended Wigner’s friend scenario challenge the assumption of “observer-independent facts”? Well, it can’t, and it doesn’t. Not any more than the experimental falsification of an inequality derived from the assumption that 2+2=5 and the existence of observer-independent facts.
On a more general note, the entire Wigner’s friend craze is a bit silly. In effect, Wigner’s friend is little more than a rendition of the famous Schrödinger cat paradox, and any precise quantum theory that solves the Schrödinger cat paradox (also known as the “measurement problem” of quantum mechanics) has no difficulties providing a precise and objective description of “extended Wigner’s friend experiments”. My colleague Mario Hubert and I have discussed this in detail for the example of Bohmian mechanics, a quantum theory that grounds the prediction of standard quantum mechanics in an ontology of point particles and precise mathematical equations. In particular, in Bohmian mechanics, the state of a system is not described by the wave function alone but has a definite configuration even if its wave function is in a superposition. This provides a clear and simple solution to both Schrödinger’s cat and the Wigner’s friend “paradox.”
To their credit, the authors are more or less acknowledging this in their discussion, writing:
[O]ne way to accommodate our result is by proclaiming that “facts of the world” can only be established by a privileged observe — e.g., one that would have access to the “global wavefunction” in the many worlds interpretation or Bohmian mechanics.
But Bohmian mechanics and Many-Worlds theories have nothing to do with “privileged observers.” The whole point of these theories is to provide an objective description of the quantum world in which observers have no distinguished role in the first place but are treated just like any other physical system (that’s why John Bell called them “quantum theories without observer”). In doing so, both Bohmian mechanics and the Many-Worlds theory use, of course, an objective wave function that describes the experiment in its entirety. If the authors assume, instead, that wave functions describing the state of quantum systems are subjective, defined relative to different observers, (and mind you, some of the “observers” are just photons in this case!) it is not at all surprising that they end up with inconsistent or observer-dependent facts. They should just not suggest that their experiment provides corroboration for this bizarre and ultimately solipsistic view.
In my opinion, the paper does indeed raise some important questions, though they are mostly sociological ones. For instance: Why does physics tend to get exposure and attention merely for making outlandish claims, regardless of their scientific substance? And why do even many experts tend to abandon rational and critical standards when it comes to quantum mechanics? Why, in other words, have we gotten so used to quantum physics being crazy that even the most outlandish claims come with a presupposition of plausibility and relevance?
As a matter of fact, quantum mechanics can be as clear and rational as any respectable theory that came before it. You just have to do it right.
If There Is No Objective Physical World Then There Is No Subject Matter For Physics
by Tim Maudlin
The MIT Technology Review article that occasions this discussion has the rather astounding title “A quantum experiment suggests there’s no such thing as objective reality”. One could be rightly puzzled about how any experiment could suggest any such thing, since the existence of “objective reality” seems to be a pre-condition for the existence of experiments in the first place.
The abstract is perhaps slightly more promising: “Physicists have long suspected that quantum mechanics allows two observers to experience different, conflicting realities. Now they’ve performed the first experiment that proves it.” After all, familiar optical illusions permit different observers to “experience different, conflicting realities” in the sense of conflicting apparent realities. Of course, in such a case at least one of the “perceived realities” is indeed illusory, since they cannot both be veridical and also conflicting on pain of violating the Law of Non-Contradiction.
But further perusal of the article dashes any hope of anything comprehensible in this way. The experiments in question are done on a system composed of only six photons. Obviously the photons do not experience anything at all, much less conflicting realities. What in the world is going on?
In short, the way that this experiment is described—in terms of its significance—is complete nonsense. Physicists have become accustomed to spouting nonsense when quantum mechanics is the subject of discussion, which often takes the form of mind-blowing assertions about the loss of “classical reality” or even “classical logic”. The reason we know that all of this is nonsense right off the bat is that the experimental predictions of standard quantum mechanics can be accounted for—in several different ways—by theories that postulate an objective, unique physical reality governed by definite laws and using only classical logic and mathematics. So when the sorts of claims made in the title and abstract of the article are made, one knows immediately that they are unjustified hype.
But surely some sort of interesting experiment was done! Yes, indeed. The experiment is of the same general sort as has been done for the last half-century, beginning with John Clauser and Alain Aspect, and continued by many other experimentalists including Anton Zeilinger. All of these are usually, and accurately, described as tests of violations of Bell’s Inequality, the epochal discovery of John Stewart Bell. What Bell showed is that certain correlations between the outcomes of distant experiment cannot be predicted or explained by any theory that satisfies a certain precise locality condition—a condition one would expect any fundamentally Relativistic theory to obey. The fact that quantum theory predicts violations of Bell’s Inequality has been called quantum non-locality, and the increasingly precise and exacting experiments done over the past half-century have all confirmed the quantum predictions, as does this experiment.
All of this is even spelled out in the article itself: “But there are other assumptions too. One is that observers have the freedom to make whatever observations they want. And another is that the choices one observer makes do not influence the choices other observers make—an assumption that physicists call locality.” That is, in order to account for the outcome of this experiment, one has to deny that physical reality is local in Bell’s sense. (This gloss on the locality condition is not accurate, but leave that aside.) That is something we have known for 50 years.
What about “objective reality” and “Wigner’s friend” and what-not? Well, the non-local theories that we have—pilot wave theories such as Bohm’s theory, objective collapse theories such as the Ghirardi-Rimini-Weber theory, and the Many Worlds theory of Hugh Everett—all postulate a single objective reality. In the proper sense of “conflicting”, none of them allow for observers to observe “conflicting realities” (although in the Many Worlds theory observers have experimental access only to a small part of the objective reality). And of course, all of these theories are non-local, as Bell requires.
Now suppose that, for some obscure reason, one were dead-set against accepting Bell’s theoretical work and all of the experiments that have been done. Suppose, in other words, one were dead-set on maintaining that the physical world is local in the face of all the experimental evidence that it isn’t. How might that be done?
It seems rather desperate but I suppose one might go so far as denying the very existence of any objective physical reality at all. Or, as I sometimes put it, “Nothing really exists, but thank God it is local”. But as should be obvious, this accomplishes nothing. If there is no objective physical world then there is no subject matter for physics, and no resources to account for the outcomes of experiments.
There are many good books that correctly and clearly exposit the situation, including David Albert’s Quantum Mechanics and Experience, Travis Norson’s Foundations of Quantum Mechanics, Peter Lewis’s Quantum Ontology, Jean Bricmont’s Understanding Quantum Mechanics and Quantum Sense and Nonsense, and (co-incidentally) my own Philosophy of Physics Quantum Theory which happens to go on sale on March 19.
Quantum Theory Confirmed Again
by Wayne Myrvold
Headline news! Stop the presses! A group of experimenters did an experiment, and the results came out exactly the way that our best physical theory of such things says it should, just as everyone expected. Quantum Theory Confirmed Again.
That’s what actually happened, though you’d never know it from the clickbait headline: A quantum experiment suggests there’s no such thing as objective reality .
The experiment  was inspired by a recent paper by Časlav Brukner, entitled “A No-Go Theorem for Observer-Independent Facts” . The abstract of the paper reporting on the experiment proclaims, “This result lends considerable strength to interpretations of quantum theory already set in an observer-dependent framework and demands for revision of those which are not.”
Here’s a nice fact about claims of this sort: when you see one, you can be sure, without even going through the details of the argument, that any conclusion to the effect that the predictions of quantum mechanics are incompatible with an objective, observer-independent reality, is simply and plainly false. That is because we have a theory that yields all of the predictions of standard quantum mechanics and coherently describes a single, observer-independent world. This is the theory that was presented already in 1927 by Louis de Broglie, and was rediscovered in 1952 by David Bohm, and is either called the de Broglie-Bohm pilot wave theory, or Bohmian mechanics, depending on who you’re talking to. You can be confident that, if you went through the details of any real or imagined experiment, then you would find that the de Broglie-Bohm theory gives a consistent, observer-independent, one-world account of what happens in the experiment, an account that is in complete accord with standard quantum mechanics with regards to predictions of experimental outcomes.
There are other theories, known as dynamical collapse theories, that also yield accounts of a single, observer-independent reality. These theories yield virtually the same predictions as standard quantum mechanics for all experiments that are currently feasible, but differ from the predictions of quantum mechanics for some experiments involving macroscopic objects.
Much of the confusion surrounding quantum mechanics, which leads smart people to say foolish things, stems from the fact that, in the usual textbook presentations, we are not presented with a coherent physical theory. Typical textbook presentations incorporate something that is called the “collapse postulate.” This postulate tells you that, at the end of an experiment, you dispense with the usual rule for evolving quantum states, and replace the quantum state by one corresponding to the actual outcome of the experiment (which, typically, could not have been predicted from the quantum state).
If we want to apply the collapse postulate, we need guidance as to when to apply it, and when to use the usual quantum dynamics. Standard textbooks are invariably vague on this. In practice, this vagueness tends not to matter much. But a thought-experiment devised by Eugene Wigner  imagines a situation in which it does matter. Brukner’s thought-experiment is a combination of Wigner’s thought-experiment and tests of Bell inequalities.
Brukner’s version of the thought-experiment involves a pair of hermetically sealed labs, each containing an observer playing the role of Wigner’s friend, and an observer outside each of these labs. Each outside observer has a choice of experiments to do. One choice of experiment amounts to asking the friend what result was obtained, the other, to the sort of experiment Wigner is imagined to do. Brukner considers a situation in which an assumption of locality would entail the existence of pre-existing values for the results of both experiments, which are merely revealed if the experiment is done. His thought-experiment involves an entangled state of the labs for which this is in conflict with the quantum-mechanical statistical predictions. But we already know that any theory that reproduces the probabilistic predictions of quantum mechanics is going to have to reject any locality assumption that leads to Brukner’s conclusion; this is Bell’s theorem (see ). Moreover, in spite of the title of his paper, “A No-Go Theorem for Observer-Independent Facts,” Brukner explicitly mentions both of the ways that we’ve discussed—the de Broglie-Bohn theory, and collapse theories—for there to be observer-independent facts.
If we have a theory that tells us whether the quantum state collapses, and, if so, when it does, then that theory can be applied both to the Wigner-Brukner thought-experiment and to the actual experiment of Proietti et al.. The de Broglie-Bohm theory will predict the same thing as standard quantum mechanics for both. Collapse theories predict the result of the Proietti et al.experiment, but predict a departure from the predictions of any no-collapse theory for the full-blown Wigner-Brukner thought-experiment, if it could be realized.
There’s nothing new here, and nothing that prompts revision of any existing theory of quantum phenomena set in an observer-independent framework.
Notes: “A quantum experiment suggests there’s no such thing as objective reality.” MIT Technology Review, March 12, 2019.
 Proietti, Massimo, et al., “Experimental rejection of observer-independence in the quantum world.” arXiv:1902.05080v1 [quant-ph].
 Brukner, Časlav, “A No-Go Theorem for Observer-Independent Facts,” Entropy 2018, 20(5), 350.
 Wigner, Eugene, “Remarks on the mind-body question,” in The Scientist Speculates, I. J. Good (ed.). London, Heinemann, 1961: 284–302.
 Myrvold, Wayne, Marco Genovese, and Abner Shimony, “Bell’s Theorem.” The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.).