Truth you can see, and truth you cannot
Understanding science’s relation to the unseen.
Does science seek truth? Can science find truth? How certain can we be of any apparent truths science finds?
Science has a long history of being considered to be truth-seeking. The full title of René Descartes’ Discourse on Method is Discourse on the Method of Rightly Conducting One’s Reason and of Seeking Truth in the Sciences. That seems pretty unambiguous. The idea persists to this day. John Polkinghorne, physicist and priest, is an advocate for such a position. He makes this clear in books with titles like Science and Religion in Quest of Truth . That being said, not everyone got the memo. When asked “What scientific concept would improve everybody’s cognitive toolkit?” Neil Gershenfeld, director of MIT’s Center for Bits and Atoms, said, “The most common misunderstanding about science is that scientists seek and find truth. They don’t.” This discrepancy of opinions between established physicists should suggest to us that, maybe, things are not as simple as Descartes would have us believe.
Let us therefore break the question down a little. And ask, irrespective of what scientists think they are doing, what can and does actually happen. Specifically —
Is science is able to find the truth?
Would scientists recognise the truth if they found it?
The history of phlogiston is instructive at this point.
Is it true that phlogiston exists?
There is a question which seems reasonable: why do some things (like matches) burn, while other things (like rocks) do not? Back in 1770, Joseph Priestly believed, following long scientific consideration, that the answer lay in phlogiston. If a thing had phlogiston in it, it would burn; and if it had no phlogiston in it, it would not burn. The more phlogiston it had, the more readily it would burn.
Does phlogiston exist? This seems like it should be easy enough to establish: either a thing exists, or it does not. Certainly, we might expect a positive result to be unambiguous: “here is phlogiston”; case closed. A general negative result (“there is no phlogiston anywhere” ) might be difficult, but we might imagine that a specific negative result (“there is no phlogiston involved in this specific reaction that has just been carried out”) should be within our grasp.
In 1775 Antoine-Laurent Lavoisier — a proponent of the atomic theory of gasses — devised an experiment in which he accounted for all of the atoms in a container before combustion and all of the atoms in a container after combustion. He showed that he could identify what all of them were, and none of them were phlogiston. Given that all matter is made of atoms, and there were no phlogiston atoms, phlogiston (if it existed) must be immaterial. Moreover, he weighed all the reactants before and after combustion and showed that immaterial phlogiston (if it existed) must be massless. Without mass and without material substance, there could be no phlogiston. Phlogiston theory was dead. Atomic theory reigned supreme.
While phlogiston theory was able to answer the question, “why can wood burn, but rock cannot,” atomic theory was mute on the issue. Still, if science cannot answer such things, maybe it is not such an important question. And even if it was important, maybe it never fell properly within the remit of science anyway: science tells us “how”, not “why”.
Against this line of reasoning, however, some people continued to insist that it was an important question, and it was rightly within the purview of science. A full century after Lavoisier, in 1885, Willard Gibbs was able to answer the question by invoking the concept of Gibbs energy. For what it’s worth, Gibbs energy is immaterial (because there are no “atoms of energy”) and, as near as you can measure, it is massless (because E=mc2 means the mass is tiny). Considering the Gibbs energy of the available oxygen per unit mass of the reactant will tell you exactly whether something will burn or not. Sure, “Gibbs energy of the available oxygen per unit mass of the reactant” is not as pithy as calling it “phlogiston”, but it ticks all the boxes. “Gibbs energy” is just a different way of naming what Priestly called “phlogiston”.
Did science find the truth? Kind of. If combustion is related to phlogiston/Gibbs energy then the scientific work of Priestly and Gibbs found the truth. And if combustion is unrelated to phlogiston/Gibbs energy then the scientific work of Lavoisier found the truth. Would scientists recognise the truth if they saw it? Apparently not. If Priestly was right, then then Lavoisier used science to reject the truth. And if Lavoisier was right, Gibbs used science to reject the truth.
But science works!
Richard Dawkins agrees with John Polkinghorne that science both seeks and finds truth. Asked to justify this belief, he responded —
“How do we justify our faith that science will gives us the truth?
It works: Planes fly. Cars drive. Computers compute.
If you base medicine on science, you cure people.
If you base the design of planes on science, they fly.
If you base the design of rockets on science, they reach the moon.
It works […]!”
We are faced with various options:
- Dawkins is right. Planes fly, and this shows that science does find the truth. We then have to work out what went wrong with phlogiston.
- Science does not give us the truth, and planes do not fly. We then have to work out how we have been getting around all this time.
- Science does not give us the truth, but planes fly anyway. We then need to work out how a process that gives us the wrong answer makes working planes.
- There are different kinds of truth. Science is able to give us the kind of truth we need to build planes, but not the kind of truth we need to work out if phlogiston exists.
This essay will pursue Option 4. The possibility of different kinds of truth should not be alarming to us, as we have already looked at universal and relative truths (Re-Assembling Reality #8 and #10) and objective and subjective truths (Re-Assembling Reality #7 and #10). In understanding what is going on with planes and phlogiston, we turn to a new distinction: phenomenological and noumenological truth.
Phenomena and noumena
A phenomenon is the appearance of a thing, as it seems to our senses.
A noumenon is the thing in itself, as it exists.
Stepping onto an aeroplane in Hong Kong and stepping off that plane in Munich are phenomena. They constitute the appearances of things, as they seem to my senses. The invisible mechanism by which the plane gets off the ground is a noumenon.
When science calculates the lift on a plane’s wing it posits a noumenon; it proposes a model of a thing that is actually happening. That model may be calculating the effect of billions of hard spherical air molecules bouncing off the wing. We can call this a posited noumenon, rather than the noumenon itself because, of course, no one has ever actually seen an air molecule bouncing off an aeroplane wing. Ever. And even that observation would be one step removed from seeing billions of air molecules bouncing off a wing. And even that would be several steps removed from seeing bouncing air molecules causing the wing to rise. So science does not observe the noumenon. It posits a noumenon, and if calculations based on the posited noumenon give us the right answer, we are happy.
We are not, however, limited to a single model. We could posit one of a wide array of possible noumena. We might (as above) consider air as comprising billions of hard spheres. Or we might consider air as an infinitely divisible fluid. Or we might consider it as a weird entangled web of quantum particles. Or we might assume that air has nothing to do with lift, and it is all caused by pixie dust.
In real life, aeronautical engineers use models based on the first two ideas (spheres and fluids) and not on the second two (quantum particles and pixie dust). This choice of models has nothing to do with whether or not the engineers believe the models accurately represent reality, and everything to do with whether the models help us to get the right (phenomenological) answers: can we use the model to design planes that fly?
We may believe the quantum model to be true, but the engineers reject it in this setting because the maths is too hard and we cannot use it to design a plane wing. On the flip side, we may believe the hard spheres model to be untrue, but we adopt it in this setting because we can use it to design a plane wing.
We care deeply about the truth of phenomenological statements, but we are remarkably indifferent to the underlying noumena. Provided my plane does not crash (phenomenon), I do not care if it flies by pixie dust or not (noumenon). Provided an airline company can sell me a ticket and make money (phenomenon), it does not care if the lift is produced by atomic collisions or not (noumenon). Provided engineers can optimise the shape of the wing for maximum lift (phenomenon), they do not care if air is a continuous fluid or not (noumenon).
Immanuel Kant  held that science can only reliably speak about the truth of phenomenological statements, not noumenological ones. On a pragmatic level, this rarely causes a problem because, provided the noumena we posit in our models allow us to get a handle on the phenomena, many scientists are quite happy for the proposed noumena to be seen as nothing but helpful models, the truth of which is unimportant.
Attempts to rescue knowledge of noumena
Among those who are less happy to accept such a limitation of science, there are a number of ways in which this failure to seek or find noumenological truth might be soft-pedalled.
One may say that these posited noumena are our best guess at noumenological truth. By this reckoning, a geocentric universe was our best guess at what the universe was really like, until we had sufficient evidence to support a heliocentric model.
A second option is to say that these posited noumena are approximately true. By this reckoning, Newtonian mechanics approximates relativity in the low-velocity limit.
A third possibility is to claim that these posited noumena exhibit verisimilitude, or truth-likeness. By this account, a corpuscular description of light is not strictly true, but it has a certain truth-likeness compared to a wave-particle view.
We can take each option in turn and show that, in each case, there are instances where each one fails to capture how radically science does not care about noumenological truth. In each case, the disregard for noumenological truth does not hinder us from getting a sufficiently good grasp of the phenomena to permit fruitful technological developments from the application of science.
Example 1: Electron sea — not a best guess
Within a metal, atoms form a regular crystalline lattice. The position of each nucleus is fixed. Most of the electrons in the metal are bound to a specific nucleus, though one or two electrons per atom (with the exact number depending on the metal) are not bound to a specific nucleus. Paul Drude (1900) treated these free electrons as classical point particles which were free to move within the solid, not interacting with each other, but interacting with nuclei through collisions. For the present discussion, the Drude model has two notable features.
Firstly, it is spectacularly inaccurate with respect to what we believe is actually happening within a material (i.e. with respect to what we suppose the noumena to be like): it neglects interactions between electrons (which, being negatively charged, repel each other); it neglects long-range interactions between electrons and nuclei (which, being negatively and positively charged respectively, attract each other); it neglects any aspects of quantum behaviour, including the Pauli exclusion principle, Fermi-Dirac statistics, or the wave-like nature of electrons.
Secondly, it is surprisingly accurate in its predictions of certain macroscopic properties of metals (i.e. the phenomena) such as conductivity.
There have been subsequent models which improve on each of the above-listed shortcomings of the Drude model. Arnold Sommerfeld (1927), for example, included Fermi-Dirac statistics into the original Drude model which (unsurprisingly in hindsight) predicted the same (correct) conductivity as had been predicted by the basic Drude model.
On a naïve falsificationist view, if we know that the theory is wrong, or has been falsified, we should reject it. Pragmatically viewed, however, a scientist faced with the choice between using a model which is known to be wrong (but which is easy to picture and calculate), and a model which encapsulates our ‘best guess at truth’ (but which is harder to picture, and computationally challenging) will very reasonably opt for the model that is easier to use, if it provides good enough answers regarding the phenomena about which we care.
Example 2: Holes — not approximately true
Despite not being the best guess at truth, one might argue that the Dude model is at least an approximation of the truth. This leads to our next counter example.
Within a semiconductor there are particular states which electrons can occupy. It is possible to engineer a situation in which electrons occupy almost all of the states that it is possible for them to occupy. The empty states (i.e. those not occupied by electrons) have ‘holes’ where an electron could be, but is not. To calculate the electronic properties of such materials, you can either calculate the behaviour of every single electron within the material, or you can treat the hole as an object in its own right, and calculate how the hole behaves.
A macroscopic analogy to this is a bubble in a bottle of syrup. As the syrup above the bubble moves downwards to fill in the space where the bubble had been, the bubble moves upwards. It is possible to calculate properties of the bubble, such as its velocity and its effective mass, even though these do not correspond to any properties of the syrup itself. The syrup analogy imperfectly parallels the situation with holes, as the bubble contains a gas, so there really is something physically moving upwards. In the case of semiconductors, the hole genuinely contains nothing. Nonetheless, the hole can be assigned effective properties such as velocity, mass, charge, and spin.
The conception of a ‘hole’ as a particle with a particular mass, charge, and velocity is not a best guess at what is happening in the material: we know very well that a single hole moving to the left is really lots of electrons moving to the right.
But more than that: considering a ‘hole’ as a particle with a particular mass, charge, and velocity is not an approximation of what is happening in the material. The truth is that the material contains billions of negatively charged particles jostling each other and overall moving to the right, while the model assumes that the material contains a single positively charged particle freely moving left.
This simplifies the maths. It gives rise to the same predictions about the macroscopic properties of the material. But it is not an approximation. It willfully ignores the noumena, because by so doing we can more easily calculate the phenomena. And those phenomena are important because the transistors at the heart of the electronics revolution are designed by considering how their holes behave.
Example 3: Dirac sea vs. antimatter — not truth-like
With ‘holes’, of course, we know that the theory is incorrect. We also know (or believe we know) what is really happening. And we could — in principle, if we wanted to make life difficult — calculate things using the ‘correct’ model. But science is not always so clear regarding what is really happening. This is the situation we face with anti-matter.
Unless there is some reason to do otherwise, particles tend to occupy the lowest energy state available to them. A ball, for example, will roll off a table and land on the floor; it does not usually jump from the floor up onto a table.
When the ball lands on the floor the (potential) energy it had on the table is emitted as sound and heat. If the table is higher, the ball can fall further, and emit more sound and heat before coming to rest. This is relatively unspectacular, unless the table is positioned next to an infinitely deep hole. In such a case, the ball would, in the process of falling from one metre above the floor to an infinite distance below the floor, emit an infinite amount of energy.
While this thought experiment sounds improbable, the equations of relativity do allow for states of infinite negative energy. Paul Dirac (1930) noticed that, unless there were some reason for it to do otherwise, an electron with a finite positive energy could ‘fall’ to the lowest available energy state (which has infinite negative energy) and emit an infinite amount of energy on the way. The simple observation that matter does not spontaneously emit infinite amounts of energy led Dirac to seek some mechanism by which this is prevented.
His solution was that all possible negative-energy states (of which there is an infinite number) are already occupied by electrons, and so no more electrons can fall in. To return to our previous analogy, this is like saying there is an infinitely deep hole, but the ball cannot fall into it because the hole is already full of (an infinite number of) balls.
These negative-energy electrons, forming a so-called ‘Dirac sea’, would have an infinite (negative) charge density, which would have to be cancelled out by assuming that the bare vacuum has an infinite positive charge density. Improbable as this may sound, the model leads to a concrete prediction: a photon (particle of light) could excite an electron from the Dirac sea up to a positive energy level. This would mean that a photon in a vacuum could vanish and — in its place — would be an electron, and a hole in the Dirac sea. The hole would have the same (effective) mass as the electron, but opposite charge.
One disadvantage of this theory is that it posits as noumena an infinitely deep sea of infinitely many particles with infinite charge density, canceled out by the opposite infinite charge density of the vacuum. This, by many accounts, is inelegant.
On the other hand, one advantage of the theory is that it predicted a phenomenon that was experimentally observed two years later, in 1932: tracks of something that looks like a positively-charged electron. By the time of his Nobel Prize acceptance speech in 1933, Dirac had recast the noumena posited by his theory to be an empty vacuum from which a particle and an anti-particle had been created. Nonetheless, for those who were uncomfortable with these newly posited anti-particles, Dirac reverted to the Dirac sea picture to aid explanation.
The noumena posited by the two views are starkly at odds. Either the vacuum is electrically neutral, or it has an infinite charge density; either the process we now call ‘pair production’ involves the creation of two new particles, or it involves moving one particle from a negative energy state to a positive one.
This situation is radically different from the previous two examples. Previously, we knew what the right answer was, but we chose to ignore it on pragmatic grounds, because we were happy with accounting for the phenomena. In the current situation, however, we do not know what the right answer is. Maybe anti-matter is real or maybe it is no more real than the ‘holes’ in a semiconductor.
To use one theory when the other has every chance of being correct would seem to stretch claims of truth-likeness to breaking point. The greatest similarity the two models have is that they make identical predictions for when my detector should go “ping”. But this is a phenomenological truth.
Nonetheless, fully aware of the stark differences in reality invoked by the two models, Dirac viewed the choice of using one model rather than the other as nothing more consequential than a mathematical convenience:
“A hole [in the Dirac sea] is, in fact, just like an ordinary particle, and its identification with the positron [i.e. the anti-particle partner of the electron] seems the most reasonable way of getting over the difficulty of the appearance of negative energies in our equations.” 
Very few scientists are bothered by such a situation. Many have never even heard of the Dirac sea. Physics textbooks never point out that, for all we know, anti-matter is not real. They certainly never moot the possibility that matter is not real, and all particles of matter (including the matter that makes you and me) are merely holes in an anti-Dirac sea.
Pragmatically, considering the day-to-day practice of science, this neglect makes complete sense: given the theory can account for the phenomena, it changes little if the noumena which we assume to be correct are, potentially, almost entirely wrong in almost every possible respect.
Returning to disagreements
Dawkins was insistent and explicit that science gives us truth. He was not, however, explicit on what kind of truth science gives us. From his examples, though, we can infer it quite easily: “Planes fly. Cars drive. Computers compute.” He is talking about phenomenological truth. On that understanding, we can readily agree with Dawkins in this claim.
By contrast, claims like “wood burns because it has sufficient Gibbs Energy,” or “phlogiston does not exist” are noumenological claims. As our history of Priestley, Lavoisier, and Gibbs showed, science does not neatly converge to truth on these matters. In this light, we can understand Gershenfeld’s insistence that “Scientists [do not] seek and find truth.”
Gershenfeld’s goes on to clarify what scientists actually do: “They make and test models.” Theories about phlogiston, or atoms, or Gibbs energy provide models. They may help us to understand phenomena (like whether my wood will burn) but they do not and cannot shed light on the noumena (like whether or not phlogiston exists). On that understanding, we can readily agree with Gershenfeld in his claim.
Having now found that we agree with everyone, is all controversy over? Not quite. These conclusions, even when people agree with them, have implications which are quite uncomfortable.
Even though Dawkins says that planes flying justifies the truth-giving nature of science, he does not first and foremost get excited about aeronautics. He is an evolutionary biologist. And he gets excited about evolution. So let us work through the reasoning outlined in this essay and apply it to subjects of more interest to Dawkins than aeronautics.
To summarise the logic of the Essay so far, let us consider three statements, and how they are (or are not) connected:
— “My aeroplane flies.”
— “We have a model which would account for this. In our model, air is made of hard spheres.”
— “Air is made of hard spheres.”
The first statement is about phenomena. Science can testify to its truth. There is unlikely to be any discovery in future which concludes that, actually, my plane did not really fly. We can have full confidence in this statement.
The second statement is about models. That’s fine. Model all you want.
The third statement is about noumena. It does not logically follow from the previous two statements. It may be true, or it may not be true. Scientists may believe it to be true. They may believe it to not be true and use models based on it anyway. In any event, any scientific testimony in this area is unreliable. The confidence we have in the phenomenological statement does not carry through to the noumenological statement.
That may seem uncontentious. Let us consider some other similar sets of statements:
— “This patient’s arm twitches when I apply an electrical current.”
— “We have a model which would account for this. In our model, biological systems are nothing but matter in motion.”
— “Biological systems are nothing but matter in motion.”
— “Radio-telescopes measure a nearly uniform background signal from all directions in the sky.”
— “We have a model which would account for this. In our model, the universe is 13.7 billion years old.”
— “The universe is 13.7 billion years old.”
— “Human spines and dolphin spines bend in similar ways.”
— “We have a model which would account for this. In our model, humans and dolphins evolved from a common ancestor.”
— “Humans and dolphins evolved from a common ancestor.”
We like the idea that science gives us truth. But we must recognise that scientific testimony regarding the truth of the noumenological statements is unreliable. And no number of planes flying will change that. That does not exclude these statements from scientific discussion. But it does require that we refrain from conferring on them the kind of certainty that science accords to phenomenological statements.
This Essay is adapted from a previously published book chapter by Mike Brownnutt .
 Descartes, René (1998). Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences. (Donald A. Cress, Trans.). Discourse on method. Indianapolis, IN: Hackett Classics. (Original work published 1637.)
 Polkinghorne, John (2012). Science and religion in quest of truth. New Haven, CT: Yale University Press.
 Gershenfeld, Neil (2011). “Annual Question 2011: What Scientific Concept Would Improve Everybody’s Cognitive Toolkit?” The Edge.
 Leslie V. Woodcock (2005). “Phlogiston Theory and Chemical Revolutions”, Bull. Hist. Chem., 30:63.
 Richard Dawkins (2013). “In Conversation with Richard Dawkins” Think Week, Oxford.
 Immanuel Kant (1998). Critique of pure reason. (Paul Guyer, Trans.). Allen W. Wood (Ed.). Cambridge: Cambridge University Press. Especially Chapter 3. (Original work published 1781.)
 Paul Dirac (1965). “Nobel lecture: Theory of electrons and positrons.” In Nobel lectures, physics 1922–1941 (pp. 320–325). Amsterdam: Elsevier Publishing Company. (Original work published 1933.)
 M. Brownnutt (2018). “Science and Religion: What kinds of truth do they seek?” in Christian Mind in the Emerging World: Academic faith integration in Asian contexts from a global perspective, Leung Wing Tai, Peter Ng, Vaughan Mak (Eds.). (pp. 240‑267). Newcastle upon Tyne: Cambridge Scholars Publishing.
This essay and the Re-Assembling Reality Medium series are brought to you by the University of Hong Kong’s Common Core Curriculum Course CCHU9061 Science and Religion: Questioning Truth, Knowledge and Life, with the support of the Faith and Science Collaborative Research Forum and the Asian Religious Connections research cluster of the Hong Kong Institute for the Humanities and Social Sciences.