How can a particle be in two places at once? (Superposition, Again)

Image of atom

A common question for lay people confronted with counterintuitive popular narrative accounts of quantum physics is:

 

How can a particle be in two places at once?

The idea that a particle can be in two places at once is a common enough interpretation of the idea of quantum superposition, but this is not the only possible interpretation. Some physicists suggest that superposition means that we simply don't know the position, and some say that it means that the "position" is in fact smeared out into a kind of "cloud" (not an objective cloud). However, being in two places at once is an interpretation that lay people routinely encounter, and it has become firmly established in the popular imagination.

Note that while the idea is profoundly counterintuitive, physicists often scoff at intuition. Richard Feynman once said, "The universe is under no obligation to make sense to you." I suppose this is true enough, but it lets scientists off the hook to easily. The universe might be obligation-free, but science is not. I would argue precisely that science is obligated to make sense. For the first 350 years or so, science was all about making sense of empirical data. This approach was consciously rejected by people like Werner Heisenberg, Max Born, and Niels Bohr before arriving at their anti-realist conclusions.

But here's the thing. Atoms are unambiguously and unequivocally objective (their existence and properties are independent of the observer). We even have images of individual atoms now (above right). Electrons, protons, neutrons, and neutrinos are all objective entities. They exist, they persist, they take part in causal relations, and we can measure their physical properties such as mass, spin, and charge. The spectral absorption/emission lines associated with each atom are also objective.

It was the existence of emission lines, along with the photoelectric effect, that led Planck and Einstein to propose the first quantum theory of the atom. And if these lines are objective, then we expect them to have an objective cause. And since they obviously form a harmonic series we ought to associate the lines with objective standing waves. The mathematics used to describe and predict the lines does describe a standing wave, but for reasons that are still not clear to me, physicists deny that an objective standing wave is involved. The standing wave is merely a mathematical calculation tool. Quantum mechanics is an antirealist scientific theory, which is an oxymoron. 

However, we may say that if an entity like the atom in the image above has mass, then that mass has to be somewhere at all times It may be relatively concentrated or distributed with respect to the centre of mass, but it is always somewhere. Mass is not abstract. Mass is physical and objective. Mass can definitely not be in two places at once. Similarly, electrical charge is a fundamental physical property. It also has to be somewhere. If we deny these objective facts then all of physics goes down the toilet. 

Moreover, if that entity with mass and charge is not at absolute zero, then it has kinetic energy: it is moving. If it is moving, that movement has a speed and a direction (i.e. velocity). At the nanoscale, there is built-in uncertainty regarding knowing both position and velocity at the same time, but we can, for example, know precisely where an electron is when it hits a detector (at the cost of not knowing its speed and direction at that moment).

Quantum theory treats such objective physical entities as abstractions. Bohr convinced his colleagues that we cannot have a realist theory of the subatomic. It's not something anyone can describe because it's beyond our ability to sense. This was long before images of atoms were available. 

The story of how we came to have an anti-realist theory of these objective entities and their objective behaviour would take me too far from my purpose in this essay, but it's something to contemplate. Mara Beller's book Quantum Dialogue goes into this issue in detail. Specifically, she points to the covert influence of logical positivism on the entire Copenhagen group.

The proposition that a particle can be in two places at once is not only wildly counterintuitive, but it breaks one of Aristotle's principles of reasoning: the principle of noncontradiction. Which leaves logic in tatters and reduces knowledge to trivia. Lay people can only be confused by this, but I think that, secretly, many physicists are also confused.

To be clear:

• No particle has ever been observed to be in different locations at the same time. When we observe particles, they are always in one place and (for example, in a cloud chamber) appear to follow a trajectory. Neither the location nor the trajectory is described by quantum physics.
• No particle has ever been predicted to be in different locations at the same time. The Schrödinger equation simply cannot give us information about where a particle is.

So the question is, why do scientists like to say that quantum physics means that a particle can be in two places, or in two "states"*, at one time? To answer this, we need to look at the procedures that are employed in quantum mechanics and note a rather strange conclusion.

* One has to be cautious of the word "state" in this context, since it refers only to the mathematical description, not to the physical state of a system. And the distinction is seldom, if ever, noted in popular accounts.

What follows will involve some high school-level maths and physics.

The Schrödinger Equation

Heisenberg and Schrödinger developed their mathematical models to try to explain why the photons emitted by atoms have a specific quantum of energy (the spectral emission lines) rather than an arbitrary energy. Heisenberg used matrices and Schrödinger used differential equations, but the two approaches amount to the same thing. Even when discussing Schrödinger's differential equation, physicists still use matrix jargon like "eigenfunctions" indiscriminately.

The Schrödinger equation can take many forms, which does not help the layperson. However, the exact form doesn't matter for my purposes. What does matter is that they all include a Greek letter psi 𝜓. Here, 𝜓 is not a variable of the type we encounter in classical physics; it is a mathematical function. Physicists call 𝜓 the wavefunction. Let's dig into what this means.

Functions

A function, often denoted by f, is a mathematical rule. In high school mathematics, we all learn about simple algebraic functions of the type:

f(x) = x + 1

This rule says: whatever the current value of x is, take that value and add 1 to it.

So if x = 1 and we apply the rule, then f(x) = 2. If x = 2.5, then f(x) = 3.5. And so on.

A function can involve any valid mathematical operation or combinations of them. And there is no theoretical limit on how complex a function can be. I've seen functions that take up whole pages of books.

We often meet this formalism in the context of a Cartesian graph. For example, if the height of a line on a graph is proportional to its length along the x-axis, then we can express this mathematically by saying that y is a function of x. In maths notation.

y = f(x); where f (x) = x + 1.

Or simply: y = x + 1.

This particular function describes a line at +45° that crosses the y-axis at y = 1. Note also that if the height (y) and length (x) are treated as the two orthogonal sides of a right-triangle, then we can begin to use trigonometry to describe how they change in relation to each other. Additionally, we can treat (x,y) as a matrix or as the description of a vector.

In physics, we would physically interpret an expression like y = x + 1 as showing how the value of y is proportional to the value of x. We also use calculus to show how one variable changes over time with respect to another, but I needn't to go into this.

Wavefunctions and Hilbert Spaces

The wavefunction 𝜓 is a mathematical rule (where 𝜓 is the Greek letter psi, pronounced like "sigh"). If we specify it in terms of location on the x-axis, 𝜓(x) gives us one complex number (ai + b; where i = √-1) for every possible value of x. And unless otherwise specified, x can be any real number, which we write as x ∈ ℝ (which we read as "x is a member of the set of real numbers"). In practice, we usually specify a limited range of values for x.

All the values of 𝜓(x), taken together, can be considered to define a vector in an abstract notional "space" we call a Hilbert space, after the mathematician David Hilbert. The quantum Hilbert space has as many dimensions as there are values of x, and since x ∈ ℝ, this means it has infinitely many dimensions. While this seems insane at first glance, since a "space" with infinitely many dimensions would be totally unwieldy, in fact, it allows physicists to treat 𝜓(x) as a single mathematical object and do maths with it. It is this property that allows us to talk about operations like adding two wavefunctions (which becomes important below).

We have to be careful here. In quantum mechanics, 𝜓 does not describe a objective, physical wave in space. Hilbert space is not an objective space. This is all just abstract mathematics. Moreover, there isn’t an a priori universal Hilbert space containing every possible 𝜓. Every system produces a distinct abstract space. 

That said, Sean Carroll and other proponents of the so-called "Many Worlds" interpretation first take the step of defining the system of interest as "the entire universe" and notionally assign this system a wavefunction 𝜓_universe. However, there is no way to write down an actual mathematical function for such an entity since it would have infinitely many variables. Even if we could write it down, there is no way to compute any results from such a function: it has no practical value. In gaining a realist ontology, we lose all ability to get information without introducing massive simplifications. Formally, you can define a universal 𝜓. But in practice, to get predictions, you always reduce to a local system, which is nothing other than ordinary quantum mechanics without the Many Worlds metaphysical overlay. So in practice, Many Worlds offers no advantage over "shut up and calculate". And since the Many Worlds ontology is extremely bizarre, I fail to see the attraction.

It is axiomatic for the standard textbook approach to quantum mechanics—deriving from the so-called "Copenhagen interpretation"—that there is no objective interpretation of 𝜓. Neutrally, we may say that the maths needn't correspond to anything in the world, it just happens to give the right answers. The maths itself is agnostic; it doesn't require any physical interpretation. Bohr and co positivistically insisted that it's not possible to have a physical interpretation because we cannot know the world on that scale.

As readers likely know, the physics community is deeply divided over (a) the possibility of realist interpretations, i.e. the issue of 𝜓-ontology and (b) which, if any, realist interpretation of 𝜓 is the right one. There is a vast amount of confusion and disagreement amongst physicists themselves over what the maths represents, which does not help the layperson at all. But again, we can skip over this and stay focussed on the goal.

The Schrödinger equation in Practice

To make use of the Schrödinger equation, a physicist must carefully consider what kind of system they are interested in and define 𝜓 so that it describes that system. Obviously, this selection is crucial for getting accurate results. And this is a point we have to come back to.

When we set out to model an electron in a hydrogen atom, for example, we have to choose an expression for 𝜓 whose outputs correspond to the abstract mathematical "state" of that electron. There's no point in choosing some other expression, because it won't give accurate results. Ideally, there is one and only one expression that perfectly describes the system, but in practice, there may be many others that approximate it.

For the sake of this essay, I will discuss the case in which 𝜓 is a function of location. In one dimension, we can state this as: 𝜓(x). When working in three spatial and one time dimensions, for technical reasons, we use spherical spatial coordinates, which are two angles and a length, as well as time: 𝜓(φ,θ,x,t). The three-dimensional maths is challenging, and physicists are not generally required to be able prove the theorem. They only need to know how to apply the end results.

Schrödinger himself began by describing an electron trapped in a one-dimensional box, as perhaps the simplest example of a quantum system (this is an example of a spherical cow approximation). This is very often the first actual calculation that students of quantum mechanics perform. How do we choose the correct expression for this system? In practice, this (somewhat ironically) can involve using approximations derived from classical physics, as well as some trial and error.

We know the the electron is a wave and so we expect it to oscillate with something like harmonic motion. In simple harmonic motion, the height of the wave on the y-axis changes as the sine of the position of the particle on the x-axis.

One of the simplest equations that satisfies our requirements, therefore, would be 𝜓(x) = sin x, though we must specify lower and upper limits for x reflecting the scale of the box.

However, it is not enough to specify the wavefunction and solve it as we might do in wave mechanics. Rather, we first need to do another procedure. We apply an operator to the wavefunction.

Just as a function is a rule applied to a number to produce another number, an operator is a rule applied to a function that produces another function. In this method, we identify operators by giving them a "hat".

So, if p is momentum (for historical reasons), then the operator that we apply to the wavefunction so that it gives us information about momentum is p̂. And we can express this application as p̂𝜓. For my purposes, further details on operators (including Dirac notation) don't matter. However, we may say that this is a powerful mathematical approach that allows us to extract information about any measurable property for which an operator can be defined, from just one underlying function. It's actually pretty cool.

There is one more step, which is applying the Born rule. Again, for the purposes of this essay, we don't need to say more about this, except that when we solve p̂ψ, the result is a vector (a quantity + a direction). The length of this vector is proportional to the probability that, when we make a measurement at x, we will find momentum p. And applying the Born rule gives us the actual probability.

So the procedure for using the Schrödinger equation has several steps. Using the example of 𝜓(x), and finding the momentum p at some location x, we get something like this:

• Identify an appropriate mathematical expression for the wavefunction 𝜓(x).
• Apply the momentum operator p̂𝜓(x).
• Solve the resulting function (which gives us a vector).
• Apply the Born Rule to obtain a probability.

So far so good (I hope).

To address the question—How can a particle be in two places at once?—we need to go back to step one.

Superposition is Neither Super nor Related to Position.

It is de rigueur to portray superposition as a description of a physical situation, but this is not what was intended. For example, Dirac's famous quantum mechanics textbook presents superposition as an a priori requirement of the theory, not a consequence of it. Any wavefunction 𝜓 must, by definition, be capable of being written as a combination of two or more other wavefunctions: 𝜓 = 𝜓₁ + 𝜓₂. Dirac simply stated this as an axiom. He offers no proof, no evidence, no argument, and no rationale.

We might do this with a problem where using one 𝜓 results in overly complicated maths. For example it's common to treat the double-slit experiment as two distinct systems involving slit 1 and slit 2. For example, we might say that 𝜓₁ describes a particle going only through slit 1, and 𝜓₂ describes a particle going through slit 2. The standard defence in this context looks like this:

• The interference pattern is real.
• The calculation that predicts it more or less requires 𝜓 = 𝜓₁ + 𝜓₂.
• Therefore, the physical state of the system before measurement must somehow correspond to 𝜓₁ + 𝜓₂.

But the last step is exactly the kind of logic that quantum mechanics itself has forbidden. We cannot say what the state of the system is prior to measuring it. Ergo, we cannot say where the particle is before we measure it and we definitely cannot say its in two places at once.

To be clear, 𝜓 = 𝜓₁ + 𝜓₂ is a purely mathematical exercise that has no physical objective counterpart. According to the formalism, 𝜓 is not an objective wave. So how can 𝜓₁ + 𝜓₂ have any objective meaning? It cannot. Anything said about a particle "being in multiple states at once", or "taking both/many paths", or "being in two places at once" is all just interpretive speculation. We don't know. And the historically dominant paradigm tells us that we cannot know and we should not even ask.

To be clear, the Schrödinger does not and cannot tell us what happens during the double slit experiment. It can only tell us the probable outcome. The fact that the objective effect appears to be caused by interference and the mathematical formalism involves 𝜓₁ + 𝜓₂ is entirely coincidental (according to the dominant paradigm).

Dirac has fully embraced the idea that quantum mechanics is purely about calculating probabilities and that it is not any kind of physical description. A physical description of matter on the sub-atomic scale is not possible in this view. And his goal does not involve providing any such thing. His goal is only to perfect and canonise the mathematics which Heisenberg and Born had presented as a fait accompli in 1927:

“We regard quantum mechanics as a complete theory for which the fundamental physical and mathematical hypotheses are no longer susceptible of modification.”—Report delivered at the 1927 Solvay Conference.

I noted above that we have to specify some expression for 𝜓 that makes sense for the system of interest. If the expression is for some kind of harmonic motion, then we must specify things like the amplitude, frequency, direction of travel, and phase. Our choices here are not, and cannot be, derived from first principles. Rather, they must be arbitrarily specified by the physicist.

Now, there are an almost infinite number of expressions of the type 𝜓(x) = sin (x). We can specify amplitude, etc., to any arbitrary level of detail.

• The function 𝜓(x) = 2 sin (x) will have twice the amplitude.
• The function 𝜓(x) = sin (2x) will have twice the frequency.
• The function 𝜓(x) = sin (-x) will travel in the opposite direction.

And so on.

A physicist may use general knowledge and a variety of rules of thumb to decide which exact function suits their purposes. As noted, this may involve using approximations derived from classical physics. We need to be clear that nothing in the quantum mechanical formalism can tell us where a particle is at a given time or when it will arrive at a given location. Whoever is doing the calculation has to supply this information.

Obviously, there are very many expressions that could be used. But in the final analysis, we need to decide which expression is ideal, or most nearly so. 

For a function like 𝜓(x) = sin (x), for example, we can add some variables: 𝜓(x) = A sin (kx). Where A can be understood as a scaling factor for amplitude, and k as a scaling factor for frequency. Both A and k can be any real number (A ∈ ℝ and k ∈ ℝ).

Even this very simple example clearly has an infinite number of possible variations since ℝ is an infinite set. There are infinitely many possible functions 𝜓₁, 𝜓₂, 𝜓₃, ... 𝜓_∞. Moreover, because of the nature of the mathematics involved, if 𝜓₁ and 𝜓₂ are both valid functions, then 𝜓₁ + 𝜓₂ is also a valid function. It was this property of linear differential equations that Dirac sought to canonise as superposition.

To my mind, there is an epistemic problem in that we have to identify the ideal expression from amongst the infinite possibilities. And having chosen one expression, we then perform a calculation, and it outputs probabilities for measurable quantities.

The 𝜓-ontologists try to turn this into a metaphysical problem. Sean Carroll likes to say "the wavefunction is real". 𝜓-ontologists then make the move that causes all the problems, i.e. they speculatively assert that the system is in all of these states until we specify (or measure) one. And thus "superposition" goes from being a mathematical abstraction to being an objective phenomena, and its only one more step to saying things like "a particle can be in two places at once". 

I hope I've shown that such statements are incoherent at face value. But I hope I've also made clear that such claims are incoherent in terms of quantum theory itself, since the Schrödinger equation can never under any circumstances tell us where a particle is, only the probability of finding it in some volume of space that we have to specify in advance. 

Conclusion

The idea that a particle can be in two places at once is clearly nonsense even by the criteria of the quantum mechanics formalism itself. The whole point of denying the relevance of realism was to avoid making definite statements about what is physically happening on a scale that we can neither see nor imagine (according to the logical positivists).

So coming up with a definite, objective interpretation—like particles that are in two places at once—flies in the face of the whole enterprise of quantum mechanics. The fact that the conclusion is bizarre is incidental since it is incoherent to begin with.

The problem is that while particles are objective; our theory is entirely abstract. Particles have mass. Mass is not an abstraction; mass has to be somewhere. So we need an objective theory to describe this. Quantum mechanics is simply not that theory. And nor is quantum field theory. 

I'm told that mathematically, Dirac's canonisation of superposition was a necessary move. And to be fair, the calculations do work as advertised. One can accurately and precisely calculate probabilities with this method. But no one has any idea what this means in physical terms, no one knows why it works or what causes the phenomena it is supposed to describe. When Richard Feynman said "No one understands quantum mechanics", this is what he mean. And nothing has changed since he said it.

It would help if scientists themselves could stop saying stupid things like "particles can be in two places at once". No, particles cannot be in two places at once, and nothing about quantum mechanics makes this true. There is simply no way for quantum mathematics, as we currently understand it, to tell us anything at all about where a particle is. The location of interest is something that the physicist doing the calculation has to supply for the Schrödinger equation, not something the equation can tell us (unlike in classical mechanics).

And if the equation cannot tell us the location of the particle, under any circumstances, then it certainly cannot tell us that it is in two places or many places. Simple logic alone tells us this much.

The Schrödinger equation can only provide us with probabilities. While there are a number of possible mathematical "states" the particle can be in, we do not know which one it is in until we measure it.

If we take Dirac and co at face value, then stating any pre-measurement physical fact is simply a contradiction in terms. Pretending that this is not problematic is itself a major problem. Had we been making steady progress towards some kind of resolution, it might be less ridiculous. But the fact is that a century has passed since quantum mechanics was proposed and physicists still have no idea how or why it works but still accept that "the fundamental physical and mathematical hypotheses are no longer susceptible of modification."

Feynman might have been right when he said that the universe is not obligated to make sense. But the fact is that, science is obligated to make sense. That used to be the whole point of science, and still is in every other branch of science other than quantum mechanics. No one says of evolutionary theory, for example, that it is all a mysterious blackbox that we cannot possibly understand. And no one would accept this as an answer. Indeed, a famous cartoon by Sydney Harris gently mocks this attitude...

The many metaphysical speculations that are termed "interpretations of quantum mechanics" all take the mathematical formalism that explicitly divorces quantum mechanics from realism as canonical and inviolable. And then they all fail miserably to say anything at all about reality. And this is where we are.

It is disappointing, to say the least.

~~Φ~~

Philosophical Detritus IV: Truth

"I swear by Almighty God to tell the truth,
the whole truth, and nothing but the truth."

—Traditional British courtroom oath

In this series of essays, fuelled by questions on the Quora website, I have been questioning the value of the legacy of certain abstract concepts in philosophy. I've argued for an epistemic-nominalist approach to abstraction, i.e. abstractions are ideas about things; they are not things in their own right. And I've tried to show that this means we have to reconsider the value of traditional metaphysics generally. No one has privileged access to reality; i.e. there is no epistemic privilege. And in view of this, I have explored how a pragmatic approach can at least net us a useful concept.

So far, I have applied this to the major concepts of "consciousness" and "reality". I have tried to show that commonly used definitions, including "common sense" definitions, are hopelessly confused and unhelpful. This is fueled by the long-standing, active, and growing dissensus on these abstract concepts, amongst professional philosophers. Philosophers not only lack agreement, but on these topics, they actively and vociferously disagree and are constantly coming up with new ways to disagree. Not only is the goal of a universal definition difficult, but the methods adopted virtually guarantee failure. Hence, we often fail to agree on important matters even after thousands of years of argument.

In this essay, I will tackle another legacy metaphysical concept from philosophy: "truth". Yet again, there is a profound and ongoing dissensus about what "truth" means and what value it holds. It seems obvious to us to ask, "What is true?" and "What is the truth?" But it is surprisingly difficult to answer such questions in a satisfying way. Beware, we are in deep, shark-infested waters here. There is a serious risk of drowning or being eaten alive. Let's dive in!

Truth

"True" is used in several senses, but the underlying sense of the word is "firm, reliable, certain, trustworthy." We are particularly concerned with the idea applied to statements and propositions; i.e. with telling the truth, or veracity.

When trying to define "true" and "truth", we immediately run into the problem of epistemic privilege. No one is in a position to state the truth with absolute certainty, because no one can possibly know what it is. And, if we don't know what truth is, then we don't know if any given statement is true or not. And yet we constantly make confident pronouncements on the truth of statements. I went most of my life not realising how utterly weird this situation is. Now I cannot unsee it. But I do think I can unfuck it, to some extent.

There are numerous competing definitions of "truth" that do not converge (this is always a bad sign). For example, we might invoke:

1. Correspondence Theory: Truth is a statement's accurate representation of objective reality.
2. Coherence Theory: Truth is the logical consistency of a statement within a larger system of beliefs.
3. Pragmatist Theory: Truth is what is useful, reliable, or works successfully in practice.
4. Consensus Theory: Truth is what is agreed upon by a specified group, often through ideal discourse.
5. Deflationary Theory: "Truth" is a redundant or logical concept that adds no substantial meaning beyond disquotation (e.g., " 'Snow is white' is true" just means snow is white).
6. Performative Theory: To call a statement true is to perform an act of endorsement or agreement.
7. Semantic Theory (Tarski): Truth is formally defined for a language by satisfying conditions like " 'Snow is white' is true if and only if snow is white."
8. Epistemic Theories: Truth is what is knowable or justifiable under ideal epistemic conditions.
9. Pluralist Theories: Different domains of discourse may require different truth properties (e.g., moral vs. factual truth).

All of these approaches have pros and cons. However, note that all the metaphysical definitions have the problem of epistemic privilege. For example, how can anything be said to represent "objective reality" when no one can possibly know what objective reality is? (If this is unclear, refer back to my essay on reality.) Defining "truth" in terms of "belief" fails because belief is a feeling about an idea, and belief can be false. And yet throwing out the concept of truth entirely seems too drastic.

I think we need to go back to basics. "Truth" is not just an abstract metaphysical concept; it's also a moral concept. Thus, we need to start by thinking about what morality is and why it has a claim on us. However, philosophy's problems also plague this topic. If anything, even after thousands of years of intellectual effort, there is an even greater dissensus around the concept of morality.

I believe we can do better than the present flailing around. To my mind, the place to start is (the late, great) Frans de Waal's work on morality in animals. Especially, his book:

• de Waal, Frans. (2013). The bonobo and the Atheist: In Search of Humanism Amongst the Primates. W.W. Norton & Co.

De Waal's 2011 TED talk Moral Behavior in Animals is an excellent introduction to the main themes in the book and useful for the short videos of the relevant experiments. No one watching this can come away thinking that capuchin monkeys do not understand fairness, for example.

I've written at length about morality, in the light of reading de Waal:

• The Evolution of Morality. Introduction and Deontology. (18 November 2016)
• The Evolution of Morality. Two Pillars of Morality - Reciprocity (25 November 2016)
• The Evolution of Morality. Two Pillars of Morality - Empathy. (02 December 2016)

We begin with a simple fact that I highlighted in my 20th anniversary essay: humans evolved an obligatory social lifestyle. We evolved to live in communities, and rare outliers notwithstanding, humans are obliged by our nature to live in communities. And we are not alone in this. Chimps, bonobos, gorillas, and many other mammals are obliged to live in social groups.

A social lifestyle offers numerous evolutionary advantages. We are stronger as a collective than we are as individuals. Indeed, large-scale cooperation is our evolutionary superpower. I'm aware that I assert this in a general climate of ideological individualism and a hegemonic political ideology that despises collectivism and asserts slogans such as "there is no such thing as society". Nonetheless, Humans are social creatures who live in communities and form societies that have cultures.

In brief, de Waal identified two essential capacities shared by all social mammals (and some social birds, but I'll focus on mammals to keep it simple) that do a lot of work in explaining the evolutionary origins of morality: i.e. empathy and reciprocity. These capacities are minimally required for the social lifestyle of mammals. Note that social insects are a totally different story.

Empathy allows us to intuitively know how other individuals are feeling from interpreting (and internally modelling) cues such as posture, facial expressions, tone of voice, direction of gaze, and so on. This allows us to accurately judge the emotional impact of our actions on others. And their actions on each other. And this is the basis of moral rules about how we treat others. We don't need an external standard or judge to tell us that our actions resulted in happiness or hurt feelings. We simply know from observation. While the psychopath may not care, they still know.

Reciprocity involves responding in kind. If someone shares with us, we share with them. If someone is kind to us, we respond with kindness. Social animals keep track of what kind of relations they have with others, but also the relations of the rest of the group has with each other. It's vitally important—in evolutionary terms—to know how our community is functioning, what conflicts and alliances exist, and our place in all this.

Incidentally, this means that our sense of identity is not, and cannot be, only based on an autobiographical narrative (a story we tell ourselves about ourselves). Being obligatorily social, we also require a socio-biographical narrative (a story about our community and our place in it). While I arrived at this insight through reflecting on de Waal, ChatGPT tells me that it is similar to ideas found in Canadian philosopher Charles Taylor's Sources of the Self: The Making of the Modern Identity (1989).

Empathy and reciprocity lead humans to live in networks of responsive mutual obligations. And this leads to a deontological view of morality as being based on mutual obligation. This does not preclude anyone from talking in terms of virtue ethics or consequentialism or whatever. Indeed, taking these other perspectives can be advantageous. Rather, it means that we define "virtue" deontologically: A virtuous person is one who meets or exceeds their obligations to the community. Notably, the most virtuous people are seen to help others. Similarly, we judge the consequences of a person's actions in terms of whether or not they support or undermine their obligations.

Since none of us is perfect, it makes sense to have some way to deal with breakdowns in this system.* De Waal notes, for example, that the leading male chimp is constantly called on to mediate between other male chimps. If there is a fight, he always intervenes on the side of the weaker male. He goes out of his way to console the loser of a fight and makes sure that the two get back into harmony.

* There's a potential digression into rules and rule-following here that I will pass up for now, but see also the last of my series of essays on Searle's "social reality": Norms without Conscious Rule Following. (Here, again, there is an unexplored similarity to Taylor's philosophy).

From reciprocity, we get the idea of fairness. Fairness is everyone fulfilling their obligations. Unfairness is a failure of reciprocation. And justice involves restoring fairness.

Of course, how these basic elements are elaborated into systems of morality is wide open and dependent on many factors, including the local environment. Moral rules also get mixed with etiquette to make for complex mores, even without elaborate technology.

This brief outline is probably enough to be getting on with. But check the earlier, more extensive essays if things are unclear.

Truth is Both a Metaphysical Concept and a Moral Concept.

We now have two ideas to try to integrate:

1. My critique of metaphysical concepts applies: truth is a metaphysical concept, and no one has epistemic privilege. "The truth" as a metaphysical absolute is unknowable. And yet most people still see value in truth as a moral concept.
2. My view of morality as essentially deontological (deriving from mutual obligation).

The first idea means that, if I am ever called to give testimony in court, it will be interesting because I cannot make the traditional oaths (including the modern secular varieties). The lack of epistemic privilege means that I cannot promise to "tell the truth, the whole truth, and nothing but the truth." This would imply that I know "the truth" and that I'm capable of communicating it. While I might have a belief about the truth, no matter how sincere I might be in holding this belief, I can always be wrong. In which case, my belief is not the truth. And after all, belief is a feeling about an idea (and an involuntary feeling at that). Which raises the question: If belief is not a reliable guide to truth, why do we privilege it?

Rather ironically, given their role in justice and history, eyewitnesses are notoriously unreliable. It is common for several people to witness an event and for them all to tell different stories about what happened. What the court really wants is not that witnesses "tell the truth", since this is an unreasonable expectation of anyone who lacks epistemic privilege. The court wants to ensure that we do not set out to deceive the court. That is to say, the court wants us to be honest. And this lesser goal turns out to be a more straightforward proposition.

One day, it might be interesting to look at how we managed to put so much emphasis on knowing the unknowable, but I want to stay on the track of extracting something workable from the existing mess.

A functioning community requires that we trust the other members of the community to fulfil their obligations. If we are standing shoulder to shoulder, driving off a leopard, for example, it only works if enough of us stand our ground. A leopard will easily kill a lone human or chimp. But a group of us is much more intimidating. Five chimps, or humans with sticks, can easily drive a leopard off if they work together. Trust requires that we not deliberately try to deceive others.

No matter how honest I am, my view could be incorrect, inaccurate, or imprecise, and I might not know it. All I can promise is that I'm not deliberately trying to deceive you. And, morally, that is all you can ask of me. So if I appear in court, the only oath I could take would be to promise to be honest. It's up to the jury to decide if what I say is salient to assigning blame for a transgression.

I think this generalises. My moral obligation is not to "tell the truth", but to refrain from deliberate deception. Or, more positively, my obligation is for honesty rather the truthfulness. This makes allowance for my "knowledge" to be imperfect or even incorrect, it allows for the vagaries of memory, it allows for unexamined bias, and so on. Being honest does not guarantee accuracy or precision.

Something we need to be wary of is the relativisation of truth, which I see as a function of ideological individualism. We see this in the idea of a "personal truth". This is something that one person believes and asserts to be true. But when contradicted, they simply assert, "that's your truth", and "my truth" is unaffected by your truth.

While the standard metaphysical definitions fail to be meaningful or useful, the idea of a "personal truth" is catastrophic. Equating opinion with truth only creates confusion and uncertainty. At least those people who try to define truth by some external standard have the goal of reducing uncertainty.

Note that, in the ideal, science is not concerned with "truth" as many lay-people imagine. Rather, scientists examine phenomena and compare notes to produce heuristics that make predictions to some arbitrary level of accuracy and precision. It's not that Newton's laws of motion are untrue and that Einstein's are. Rather the situation is that, under such conditions as we encounter here on Earth, Newton's laws are sufficiently accurate and precise for our purposes. We can predict the future with confidence. But when we start to look on larger scales of mass, length, and energy the accuracy and precision of Newton's laws declines. And we find that Einstein's laws of motion provide better accuracy and precision.

Scientists make and test inferences about phenomena by close observation and comparing notes. While such inferences are incredibly, almost miraculously reliable, we still cannot claim that they are true in any deeper sense.

Conclusion

Thousands of years of documented arguments about "truth"—from a variety of cultures—have left a legacy of dissensus and confusion. Something that seems so straightforward as "telling the truth" turns out to be impossibly complicated. Not only do we not know the truth about anything, but we cannot even agree on how we would know it if we came across it.

Questions such as "What is true?" or "What is the truth?" can never be answered in a way that will satisfy everyone.

"Truth" is another legacy of philosophy that does more harm than good. Since metaphysical knowledge requires epistemic privilege that no one can possibly have, telling "the truth, the whole truth, and nothing but the truth" is an unattainable goal.

Morality does not arise out of metaphysics or commandments from some supernatural being. It emerges pragmatically from evolving to live in social groups that require cohesion to function. Evolution equipped us to live in societies bound by mutual obligations. And the moral obligation that emerges from this is not to "tell the truth", but to be honest. That is to say, we do not deliberately set out to deceive.

The problem of the zeitgeist is less that we live in a "post-truth era" and more that we live in an era characterised by dishonesty.

Pragmatically, honesty is attainable because it only requires that we not set out to deceive. This allows that our beliefs about what is true can be sincere but mistaken.

Honesty is a virtue because it promotes the trust and cooperation necessary for a group to fulfil its evolutionary function. The consequence of dishonesty is a breakdown of trust and cohesion.

However, all of the above notwithstanding, the idea of truth and the many discourses centred on it are deeply ingrained and unlikely to change. So expect confusion to reign.

~~Φ~~