The Quantum Thomist

Musings about quantum physics, classical philosophy, and the connection between the two.
The empiricist philosophy against Quantum Physics


The failure of nominalism
Last modified on Sun Jun 24 17:44:49 2018


I recently finished a series of posts outlining the basis of quantum field theory. These posts offer a basic and simplified (albeit not simple) outline of the scientific basis of my work. It is important to understand them, because everything else that I do builds on that. In the last of those posts, I suggested that Quantum physics was broadly consistent with Aristotelian metaphysics. Not completely consistent, of course: we have to make some modifications to Aristotle's world-view, most importantly his reluctance to view physics mathematically (although, to be fair to him, the mathematics needed to represent causality and space and time is well beyond what was available in his time, or even the medieval schoolmen who perfected his system). I don't claim that Aristotle's philosophy is the end of the discussion, only that it offers a better beginning for the search for a philosophy consistent with contemporary physics than the numerous alternatives that arose following the intellectual revolution that gave birth to Galilean and Newtonian physics.

Yes, but what about all those philosophies that sprung up since the Aristotelian world-view was originally overthrown? Surely there must be something of use there as well?

In some cases, yes, to an extent. For example, in my discussion of mechanism I highlighted that one triumph of the mechanical philosophy, indeed just about the only thing it got right, was the idea that physical objects and concepts such as space and time can and should be treated geometrically and mathematically. That was a big leap forward, and Aristotle was wrong to deny that it could or should be done. But there is no doubt that the majority of the axioms of the mechanical world-view, as it developed and dominated from the fourteenth through to the nineteenth centuries, is no longer feasible. An alternative needs to be found.

The empiricist philosophers, while wrong to say that their method was the only way we can gain understanding, nonetheless correctly highlighted the importance of empirical research; induction from carefully controlled experiments. They inspired a lot of good work in that regard. We understand a great deal more now than could have been possible through induction alone, and have undermined almost all of the empiricists grandiose claims about their epistemology, but Newtonian and modern science would not have got going without the head-start given by those early pioneers of the experimental method. Aristotle this time was not completely wrong: he valued observation, but did not appreciate the systematic and detailed experimentation that was necessary.

Aristotle was right to say that things could not be reduced to the sum of their parts (i.e. each phenomena ca be reduced to independent parts which can be studied individually, understood, then stitched back together again to give an understanding of the whole). Effective Hamiltonians are not linear sums of the fundamental Hamiltonian; one cannot just take what we understand about quarks and say that a proton is just three quarks bound together, and from that alone deduce that the properties of the proton are just the total properties of the quarks. It's harder than that. But nonetheless, the idea of the empiricists that one could understand complex ideas by thinking of them as a collection of various simple ideas is a useful first approximation in many systems. It can't get us all the way, but it can get us started.

But now I come to a view for which there is no merit whatsoever. No redeeming feature which we can learn from it while building up a philosophy of quantum physics. Nominalism. That is easily shown to be inconsistent with contemporary physics, and must be abandoned.

First of all, some definitions. Nominalism is the belief that there are no universals or abstract concepts, only physical particulars. The most important opposing school to nominalism is realism, which states that there are universals. The other school is conceptionalism, which states that universals exist, but only in our mental understanding and classifications, but not in the physical world.

A universal is basically something which is shared between numerous different objects. So, for example, two different oak trees share the universal oak. Perhaps the strongest form of realism, Plato's version, shows the relationship between the universal and the object in the clearest way. In Plato's philosophy, the real world is the world of abstract ideas, or forms. The physical world we see is only secondary, a dim reflection of that ideal world. Our bodies and senses are limited in that we can only see the physical world. But our intellect is capable of going beyond it, and grasping the forms themselves, and walking in the higher existence.

In the world of forms, there is one of each type of being, so there is a single oak tree. The analogy that Plato used was of a projector passing light through that real tree onto the physical world. The image appears numerous times, as it is reflected from different angles. But the quality of the wall where the projection is made is slightly different, so the image is slightly distorted in each case, and distorted in different ways. Thus we find differences between each physical oak tree. But all of them are nonetheless originated from that one universal oak, and thus they can all be said to share in the universal. Clearly, like all pictures, this has its limitations, and shouldn't be followed too literally. Its most obvious flaws are limitations of the illustration rather than the underlying physical idea behind it. The main idea is that everything in this world is a distorted reflection of that single individual universal.

Moderate Realism, or Aristotle's realism, takes this in a slightly different direction. It denies that there is a separate world of forms. Instead, it states that the form exists as a part of the various beings that institute it, or can be instituted in a mind. However it has no independent existence. I define the form in terms of a set of topologically connected under infinitesimal deformations effective Hamiltonians (a more useful definition for physicists than biologists, but since I'm a physicist I don't care too much about that). From this effective Hamiltonian, we can derive the structures, arrangements of matter, and properties of the beings. An ethanol molecule, for example, is the union between matter and form. When we have two ethanol molecules, they are distinguished from each other by having different matter, but they share the same form, in that they are each described by the same set of effective Hamiltonians.

The nominalist, however, denies all this. He believes that there are only particular objects with similar properties. The only thing they have in common is the name we give them on account of those similarities. But that classification is only an illusion; ultimately there is nothing connecting the two different molecules.

The history of nominalism is a long one, and it is possibly an older doctrine than realism. It originally dated back to the ancient Greeks. However, modern nominalism began in the early middle ages. William of Ockham and Buridan are often credited as the first Western European nominalists (perhaps correctly, perhaps they were just pre-cursors who merely inspired the nominalists). However, it was not until the Renaissance and early modern period when the doctrine really began to flourish and dominate. Most later writers that I have seen just assumed that nominalism was correct, and discounted realism.

For example, Thomas Hobbes wrote,

This universality of one name to many things, hath been the cause that men think that the things themselves are universal. And do seriously contend, that besides Peter and John, and all the rest of the men that are, have been, or shall be in the world, there is yet somewhat else that we call man, (viz.) man in general, deceiving themselves by taking the universal, or general appellation, for the thing it signifies. For if one should desire the painter to make him the picture of a man, which is as much as to say, of a man in general; he meaneth no more, but that the painter shall choose what man he pleaseth to draw, which must needs be some of them that are, have been, or may be, none of which are universal. But when he would have him to draw the picture of the king, or any particular person, he limiteth the painter to that one person himself chooseth. It is plain therefore, that there is nothing universal but names; which are therefore also called indefinite; because we limit them not ourselves, but leave them to be applied by the hearer: whereas a singular name is limited or restrained to one of the many things it signifieth; as when we say, this man, pointing to him, or giving him his proper name, or by some such other way.

This argument against realism is easily answered. The realist will argue that the form doesn't map to a single state but a set of states. But a picture is a static image. We can only take pictures of single states. Therefore we cannot in principle paint a picture of the form in its entirety, but only one particular exemplification. Realists accept both individualisation and universals. Nominalists accept individualisation but deny universals. That a painter can paint an individual man demonstrates the principle of individualisation. But both realists and nominalists accept that. It says nothing about the existence of of universals. Both realists and nominalists deny that they can be painted (albeit for different reasons). Therefore Hobbes argument says nothing against realism and nothing in favour of nominalism, but merely reiterates what both sides accept.

Or Hume,

Thirdly, ’tis a principle generally receiv’d in philosophy, that every thing in nature is individual, and that ’tis utterly absurd to suppose a triangle really existent, which has no precise proportion of sides and angles. If this therefore be absurd in fact and reality, it must also be absurd in idea; since nothing of which we can form a clear and distinct idea is absurd and impossible. But to form the idea of an object, and to form an idea simply is the same thing; the reference of the idea to an object being an extraneous denomination, of which in itself it bears no mark or character. Now as ’tis impossible to form an idea of an object, that is possest of quantity and quality, and yet is possest of no precise degree of either; it follows, that there is an equal impossibility of forming an idea, that is not limited and confin’d in both these particulars. Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a particular object, tho’ the application of it in our reasoning be the same, as if it were universal.

So Hume was even worse than Hobbes in his attempt to justify nominalism. His argument, such as it is, is so dependent on Hume's wider empiricist philosophy, that is lacking in so many respects, that it is next to useless. No realist would say that the universal triangularity can be represented by a single triangle. No realist would accept Hume's presumption that the only way to understand something is to visualise it (to form an idea, in Hume's terminology). And even if we do so, the universal triangularity would correspond to a set of imaginable triangles rather than an individual one (but in reality, it is not the set of states, but the underlying principle that unites them). Hume's argument is basically to assume that we have to think of universals in the same way that we think of particulars, say that universals can't be thought of as particulars, and conclude that there are no universals. A realist would never accept that first assumption, nor the empiricist "reasoning" used to support it.

So are there any good arguments out there for nominalism? I think that there were, when physics was less advanced.

Nominalism arises naturally from the mechanical philosophy and mechanical physics combined with the atomic principle. For if everything can be reduced to the sum of its parts (as mechanism supposes) and those parts are a small number of corpuscles, with differences arising from different arrangements of those fundamental particles (as the atomic principle supposes), then objects may be similar in structure merely coincidentally. Newton's laws don't care whether it is one type of particle or another; they act on all matter in the same way. There is no mention of universals in Newtonian physics. All there is is matter, some of which superficially resembles others. If we were to take electrons and took them into classical physics, they would merely be two different particles with a similar mass and charge. Nothing in physics would depend on them both being the same type of particle. There is no reason why they should have the same mass; it is just a coincidence. Thus we can easily claim that the universal "electron" is redundant. If redundant, we may as well omit it, which leads us to nominalism, at least in this regard.

But now we come to quantum physics. Immediately we see a difference. For now each electron is merely a single excitation of a single universal electron field. The mass of an electron is determined by the coupling of that universal field to the scalar field in the standard model; the electric charge by the coupling to the photon field. All electrons arise from the same field, so they each have the same couplings, not by coincidence but by logical necessity.

That alone would seem to suggest the existence of a universal that describes electrons. The whole basis of quantum field theory is that it makes universals, namely the quantum fields themselves, its chief players. But there is more.

One of the most important results in quantum physics is the Pauli exclusion principle. This states that two fermions of the same type cannot be in the same state at the same time. It is why a lithium atom cannot have three electrons in its lowest energy level, but only one spin up and one spin down electron. The next electron must jump to the next highest level. That's why the different chemical elements have their different properties.

Ultimately, the exclusion principle arises from the commutation or anti-commutation relationships between the creation operators for the fields. Although you can pile as many Bosons into the same state as you like, that they are the same type of particle still affects the physics. In other words, the fundamental particles of nature come in distinct types, and this leads to clear experimental consequences.

My favourite example of this is the scattering experiment. We can fire two electrons towards each other, they "bounce" off each other, and we measure the angular distribution of the result. The final result of this experiment depends on whether the two particles are of the same type. For example, scatter two electrons, or two muons, and one would get a very different result than if one would scatter a muon against an electron, far more than we expect from the small difference in mass between the two particles. For example, we can perform the experiment at increasingly high energies, where the rest mass of the particles becomes less and less significant, but the dramatic difference will remain. This occurs because physics recognises that the two electrons are the same type of particle. For Bosons, the number of particles hitting the detector at right angles to the particle beams is twice what you would expect if the particles were from different fields. For Fermions, it is zero if they are the same type of particle, and non-zero otherwise.

Nature can recognise whether or not two particles are the same type, and the scattering distribution is adjusted accordingly. So types exist in nature, at least at the level of fundamental particles, and types are a kind of universal. Thus at the level of fundamental, physics nominalism is wrong. Realism and Nominalism have experimental consequences, and the experiments come out in favour of realism.

But if we accept realism at the most fundamental layer of physics, then we must also accept it at the next layer. We can construct the creation operator for the proton from the creation operators of the quarks and gluons. It is not simply a linear addition (as mechanism would suppose), but it nonetheless can be done in a systematic way that is the same for each proton. Thus the universal of quarks leads to the idea of the universal of protons. We can extend realism to the first layer of composite particles. From this, we can go to the next layer, and so on up the chain of physics and chemistry.

Nominalism states that there are no universals. Thanks to physics, we know that there are. Therefore nominalism is false. The question is whether there is anything that can be rescued for the philosophy. Any area of study separate from everything else where we can apply nominalist reasoning.

I admit that disproving nominalism in biology is a bit more of an issue in this construction. Here the universal is not one of identity but of resemblance. But by going back to the DNA sequence, and looking for infinitesimal changes between viable individuals we can circle off different species. Again, we have universals. Nominalism with regards to objects is false.

So far, I have just discussed nominalism in terms of universals of physical objects. Of course, there are also said to be universals of properties or observables. Realists say that there is a universal red. Nominalists deny this and say that the colours are only coincidentally similar. I personally dislike the fixation on such properties or predicates by philosophers. Firstly, one cannot generalise so easily. The physics of colour is very different from the physics of texture and so on, and to lump them all under the same category of predicate is misleading. Secondly, the form, or substance itself, is primary, and properties secondary. Many modern philosophers have made the mistake of thinking that that properties (what we directly sense) are more important to the nature of the being than the underlying abstract or mathematical form (what ultimately determines what something is). But it is the form we encounter first in a physical construction from first principles. Form is determined from the Hamiltonian, which is put together from the creation operators of the particles, which are fundamental. The properties are derived from the Hamiltonian, for example colour from the gaps in the energy bands of a substance. (We are, of course, in the nominalism against realism debate always speaking of colour as a property of an object rather than the interpretation of that as an image in our mind. They are two different definitions of the term, and should not be confused). And this gives us our answer regarding property realism. We have a universal regarding a particular paint pigment (the object). Everything that is derived from a universal must itself be a universal. From the universal form we derive the universal energy bands, and from those the universal of colour. The same for any other property. Thus we must be property realists as well as object realists.

A lot, not all but a lot, of modern philosophy takes Nominalism as one of its axioms. Some major philosophers made the mistake of establishing it as a basic principle, so much so that all their theories wholly depend on it. This means that a lot of what is taught in modern philosophy departments is directly contradicted by contemporary physics. And in any genuine disagreement, the philosophers must bow to the physicists, who have experiment to guide them. A great many of modern philosophers spend a great deal of time pondering over the details of theories that have been firmly disproved.

So the only remaining debate is not nominalism against realism, but which type of realism should we adopt.



Aquinas' first way and modern physics?


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