Continuing my survey of alternatives to classical philosophy, and why they fall short in the light of contemporary physics, I take a look at nominalism, the belief that there are no universals (for example the species cat or the property red), but only particular objects (such as an individual cat or an individual perception of a colour). In this view, there is nothing linking different cats together beyond the name cat and an accidental similarity in arrangement of atoms.
The modern version of nominalism developed from the late middle ages, alongside what became classical mechanics. In the context of classical mechanics, it makes some sort of sense. Newton's laws make no mention of the type of particle we are dealing with, only the individual properties of that particle, and the classification of particles in terms of types or universals is thus seems to be redundant. If it is redundant, then it cannot be a feature of reality, but either an illusion, or something that exists only in the mental world but not the physical world.
However, quantum physics is very different. Here particles are individual excitations of continuous de-localised fields; all particles from the same field can be classified into one type, and their resemblance is not coincidental but logically necessary. The commutation relations linking the creation operators do make reference to the type of particle. Thus this idea has experimental consequences.
In this way, the realism against nominalism debate in philosophy is, perhaps surprisingly, something that can be settled by experiment. It is ultimately a matter of physics, leaving the philosophers just to pick up and sort out the pieces. Nominalism is disproved. This has significant implications for much of modern philosophy.
The empiricist world-view is (as I define the term) that our knowledge can only come from sensed data. In particular, since we only ever observe properties of beings, this philosophy, if true, would mean that we can never come to knowledge of the underlying structure of the being. It would, in short, make both metaphysics and theoretical physics impossible.
There is a difference between an empiricist philosophy and an empirical philosophy. An empirical philosophy states that observation is important. We need it to come to a true knowledge, we can't make progress without it. The empiricist states that only observation is important. Everything else is either derived from sensual data or is an illusion.
This actually makes a profound difference our underlying intellectual of reality. If one accepts the empiricist assumptions, then whatever models we create are distinct from whatever it is that goes on in the real world (if there is such a real world). We can only ever understand our models. Therefore we can never understand reality. This is rather problematic, both for the theologian and for the physicist.
But for an empirical philosophy, our intellectual models can be a genuine representation of what happens in nature. What happens in our model corresponds to something that happens in nature. Thus much of what we understand about our mental representations of reality also applies to reality. This is good news, both for physicists and theologians.
In fact, we can go further than that. By assuming that reality is capable of being understood, we can limit how that representation can be made. Many representations add something to what they represent, for example a coordinate system. Other representations take things away. What we should suppose is that nothing that it added into our representation should be present when we map back to reality, and nothing that is taken away should be added when we return to reality. This simple requirement places strong constraints on what the true representation of nature could be.
Every observation is interpreted though a metaphysical prism; every scientific observation even more so. Therefore it is important to get the metaphysics right before trying to understand what we see, hear, smell and touch. Of course, we can subsequently fine-tune our metaphysics through what we learn about reality.
And this means that the empiricists are wrong. We can tune our models from other means than sense data alone. We can map back from our models to physical reality, and make predictions, beyond what we have already seen. And sensual data alone is not enough to understand anything, because we need some means of interpreting that data -- a means that could not have originally come from our senses.
In this post, I focus in particular on the philosophy of one of the early inspirations behind empiricism, Locke, and discuss some of the things that he got wrong.
The issue of abortion, which I feel particularly strongly about, has just hit the headlines again. Since I don't have any other platform, I am going to rant about it here.
I want to wish Harry and Megan all the best in the future. And to make one comment about the sermon, concerning the preacher's failure to distinguish between different senses of the word "love".
Aristotle's philosophy was abandoned in the sixteenth and seventeenth centuries. Two philosophies vied to replace it: empiricism, and the mechanical philosophy. Since I am advocating a return to a modified Aristotelian approach, it is important to understand why it was first rejected, and if those reasons still apply today.
While the empiricists talked a good game, they didn't really achieve much of substance scientifically. However, mechanism is a very different story. The pioneers of the scientific revolution, Kepler, Descartes, Galileo, Boyle, Newton and so on were advocates of the mechanical philosophy in one form or another. The success of their physics (which had clear tensions with the older Aristotelian world-view) and mathematics led to the widespread acceptance of their philosophy. Aristotle's philosophy had led him to a flawed physics, while the mechanical philosophy combined with the experimental method seemingly got it right first time.
While perhaps not so dominant today, the mechanical philosophy was very influential in the development of other fields which aimed to emulate the success of the hard sciences, and it paved the way for modern atheism (although not all atheists today would agree with the philosophy, particularly as it was outlined by those early advocates).
However, physics has moved on since Newton's day. If Aristotle was rejected because mechanism was consistent with the new physics of the sixteenth and seventeenth century's and Aristotle's wasn't; what should we make of the situation where contemporary physics is consistent with Aristotle's world-view. But how does mechanism stack up against it?
I continue my introduction to Quantum Electrodynamics, and show how the mathematics described in the previous posts pays off. I discuss the possible interactions between photons and electrons. There are numerous routes from an initial state to a final state consistent with these interactions. For example, an electron can travel from A to B unmolested, or it can emit and absorb the same photon, or it can emit and absorb two photons, or it can emit a photon, which splits into an electron positron pair, which then annihilate each other into a photon, which is then absorbed back into the initial electron. All we observe is the electron at A and what seems to be the same electron at B. We don't know which of these sequence of events happened during the journey. Therefore, to calculate the likelihood that the electron travels from A to B, we have to calculate the likelihood for each individual route, and add these together.
However, quantum field theory is not a description where anything is possible. There are certain rules determining which interactions are possible and which are impossible. I compare these rules against the basic premises of Aristotelian philosophy. What I find is a great deal of consistency between the fundamental axioms of Aristotle's metaphysics and the physics of quantum fields. This suggests that however we interpret quantum physics, the philosophy behind that interpretation needs to be some variation of Aristotelian metaphysics.
I continue my introduction to Quantum Electrodynamics by putting in place one of the final and most important ingredients. So far, I have presented my basic axioms, described a notation that can represent states of matter and in particular change from one state to another, and shown how we can in principle use this state/operator notation to perform calculations which can then be compared against experiment. Now we need to discuss how the states evolve in time.
My tool to do this will be symmetry. I will demand that the representation used to describe reality satisfies a number of symmetries. Firstly, translation symmetry (the statement that there is no preferred origin of the universe); secondly Lorentz invariance (the symmetry behind special relativity); thirdly scale invariance (the idea that there is no preferred length scale in the universe); fourthly gauge invariance (that only relative and not absolute differences between the phases of likelihoods have physical significance). I combine the notation developed so far, basic observational data (for example the number of space and time dimensions), and the assumption that the likelihood of matter being in certain states has the same symmetry group as a circle. The result is a theory that has been tested to incredible precision and, baring that it is incomplete because it doesn't describe the other forces of nature, has never been refuted.
I continue with my introduction to quantum field theory. Building on my previous post, I look at how to symbolically manipulate operators representing the creation and annihilation of particles.
Once again, this post will be rather technical. I go through the details to illustrate the process of reasoning by which we go from the axioms to the conclusions, and convince the readers that we are not taking any short-cuts in the reasoning. I will summarise what all this means in a later post.
In previous posts, I have discussed some of the axioms of quantum field theory. Now, I begin to turn to how we can apply those axioms to answer real-world problems.
I continue my introduction to QFT by discussing some of the notation used to represent states (potentia) and creation, annihilation and change (actualisation of a potentia). I will then use this in subsequent posts to start showing how we can compute things.
This is all a bit dull, but it is dull in an exciting way. When building a new Castle, people want to see the turrets, gates and great halls. The foundations don't carry the same interest. But if you don't get the foundations right, you won't get any of the exciting bits either. So I just have to ask you to slog through this in anticipation of what is to come.
I comment on what I consider to be one of the worst sermons I have heard. The question is, what makes a successful Church? What makes a successful Bishop? What does it mean for something to be successful anyway? And by this measure, how many of our current Bishops are successful?