Todd Decker

Schopenhauer and Scruton on Music

Schopenhauer was one of the most influential modern philosophers to develop a philosophy of music. He thought of music as the most direct access to fundamental reality, which he called Will. Roger Scruton, in a reworked Schopenhauerian theory saw music as inducing a response of “overreaching intentionality” in which we acquire a first-person perspective on a state of mind that is not our own.

I’d like to talk about some stuff I’ve been reading on music from the philosophers Arthur Schopenhauer and Roger Scruton. Scruton I’ve been familiar with for a number of years. Schopenhauer I’ve known by name but never really studied much until more recently. This year I dove in and read his most important work, The World as Will and Representation, Volume 1. And that left me thinking, wow, why did I wait so long to study him? Such a fascinating thinker. For a long time the main things I knew about Schopenhauer were (1) that his big idea was that everything is ultimately Will, with a capital W, and (2) his pessimistic view that existence is suffering. His idea of Will especially I understood to have been influential in Nietzsche’s thought. And it’s true that those are important ideas in Schopenhauer’s thought. But they’re also much more interesting in the broader context of his whole system. That system is kind of weird. But that’s why I want to supplement him with Scruton, who kind of updates Schopenhauer for the 21st century while staying true to the upshot of his most important ideas.

One of the things I find fascinating about Schopenhauer is that he’s something of a triangulation of three influences, each that I find independently interesting. The first is his near contemporary, Immanuel Kant. And this was the most immediate influence. Everyone in Germany at the time was responding to Kant. And Schopenhauer considered himself a Kantian, though he modified his ideas in important ways. The second influence is Plato. And this really caught my attention because one of my major philosophical interests is the continuing but underappreciated relevance of Plato in modern times. So it’s interesting to me to see a nineteenth century thinker like Schopenhauer taking Plato seriously and expanding on his ideas. The third, kind of unusual but very intriguing influence, is the Upanishads, a major religious text in the Hindu tradition. Schopenhauer said of these: “I do not believe my doctrine could have come about before the Upanishads, Plato and Kant could cast their rays simultaneously into the mind of one man.” I won’t get much into the Upanishads here but it’s an interesting topic as well.

The first thing to highlight is Kant’s idea of noumenon and phenomenon, the noumenon being the “thing in itself” independent of our perception of it and the phenomenon being the representation we construct of it in our mind. It’s the difference between the world that’s “out there” versus the world as we know it and the unbridgeable gap between those two. Schopenhauer picks up on this idea and continues with it in his system of “will and representation”. And those two terms correspond to Kant’s noumenon and phenomenon. Representation is clear enough. It’s the picture of things that we have access to but is not the thing in itself. For Schopenhauer the thing in itself is Will, which requires some explanation.

Will is a striving toward that lies at the base of all things. His book was published decades before Darwin’s On the Origin of Species but I think there’s some affinity to the idea of struggle in Darwin’s thought. That striving is a fundamental driver behind all things and for Schopenhauer this applies even beyond just the organic domain. For Schopenhauer this is not the will of any particular subject, such as God, certainly not in his view since he was a staunch atheist. So this is will abstracted from any willing subject. I’m not going to say much more about this since it’s not a metaphysical model I buy into. On the subject of music I’ll go with Scruton’s adaptation. But I’ll mention briefly that if we were to suspend Schopenhauer’s atheistic condition for all this I do think there is some interesting potential here to see the world and being itself as grounded in theistic will, which I do actually.

But getting back to music, Schopenhauer sees music as one way to actually access Will directly, to access the deepest reality directly. In Schopenhauer’s aesthetic philosophy, i.e. his philosophy of art, arts such as literature, sculpture, painting, etc. approach Will, or the thing in itself by mirroring Platonic forms. Platonic forms being abstractions of a concept’s essential characteristics. And there are many ways to understand the ontology of that, which I won’t get into. But suffice it to say for the moment that both Plato and Schopenhauer understand there to be these entities, these forms, that transcend the physical universe, that subsist outside space and time. For Plato individual instances of physical entities are approximations of ideal, perfect forms. For Schopenhauer great art is a production of innate genius by which an artist accesses these pure, ideal forms and captures something of this transcendence in the work of art. And in Schopenhauer’s view all arts but music mediate the Will through the Platonic forms.

Music however is highly privileged in Schopenhauer’s thought. Music is actually able to bypass even the Platonic forms and channel Will directly. This is necessarily non-propositional since Will is not something that we can access directly through representation, which any propositional description would amount to. Schopenhauer’s thought was very influential on the great composer Richard Wagner and on the philosopher Friedrich Nietzsche, who was also a talented musician. Wagner and Nietzsche were actually close friends for a time and were mutual admirers of Schopenhauer.

But from here I’d actually like to move on from Schopenhauer to Scruton, who I think gives a more intelligible account for some of these ideas, perhaps somewhat similar in effect to Schopenhauer’s, but less loaded with the particular nineteenth century German notions that are a little less relatable these days.

Scruton reinterprets Schopenhauer’s Will as what he calls “overreaching intentionality”. Intentionality is a concept he’s grabbing from phenomenology, particularly in the thought of Edmund Husserl. The basic idea of intentionality is that our thoughts are always about something or directed towards something. This direct-ness of thought or intention of thought toward something is intentionality. There are no be bald, free-standing thoughts.

In Scruton’s thought intentionality overreaches, not in any bad way, but in a way that we project intentionality onto things where it doesn’t truly apply in a literal way, but in ways that are still rewarding and valuable. Music is a consummate example of this. When you listen to a piece of music it feels like it’s about something. It feels like it’s intending and communicating certain emotions. In fact I’d say music does this more effectively than almost anything. It conveys emotion in its purest and most raw form. Yet, it’s hard, maybe impossible, to see any way to analyze how this kind of meaning could be conveyed. We don’t have in music the kind of linguistic analysis of signs and signifiers to the things signified like we have with language. And we can think of this in terms of Schopenhauer’s idea that music bypasses all these mediating channels, even analyzability, and gets to things themselves directly.

In Scruton’s thought music operates on its own kind of logic in its own kind of musical space, which has very different sorts of rules than physical space. We might think of this as a kind of abstract, mathematical space, but not so rigorously defined. The rules of musical space are particular to music itself. Here’s a passage from Scruton’s The Soul of the World:

“Music is a perceived resolution of the conflict between freedom and necessity, made available in a space of its own… You can see this very plainly if you ask yourself just what it is that moves, when music moves. The melody of the Beethoven began on C and moved up to E-flat. But what moved? Not C, which is stuck forever at C. Nor did anything release itself from that C and travel to E-flat—there is no musical ectoplasm that travels across the void between the semitones. If you go on pushing questions like those, you will soon come to the conclusion that there is something contradictory in the idea that a note can move along the pitch spectrum—no note can be identified independently of the place that it occupies, which makes it seem as though the idea of a place is in some way illegitimate. In all kinds of ways musical space defies our ordinary understanding of movement… nothing literally moves in musical space, but that in some way the idea of space cannot be eliminated from our experience of music.”

In Scruton’s estimation Schopenhauer was right to see music as a manifestation of an activity usually associated with a thinking and feeling subject, even if – in both Schopenhauer’s and Scruton’s view – it is not actually the activity of a thinking subject, but rather more of an as if condition. This intentionality is “overreaching”, in Scruton’s vocabulary. Here is Scruton talking about this in book Music as Art:

“Schopenhauer tells us that the non-conceptual awareness that we have of our own mental states is really an awareness of the will; he also tells us that the will is objectively presented to us without concepts in the work of music. In these two statements we can ‘divide through’ by the will, to use Wittgenstein’s metaphor: reference to the will is an unwarranted addition to another and more intelligible theory, which tells us that in self-knowledge we are acquainted with the very same thing that we hear in music.”

So here Scruton is saying that we can “divide through” or dispense with Schopenhauer’s notion of Will and the baggage of the elaborate philosophical system that come with it and just drive to the key insights, updating them to our present purposes and interests. Continuing again in that same passage:

“To put it in another way: music presents subjective awareness in objective form. In responding to expressive music, we are acquiring a ‘first-person’ perspective on a state of mind that is not our own – indeed which exists un-owned and objectified, in the imaginary realm of musical movement… According to this theory, sounds become music when they are organized in such a way as to invite acousmatic listening. Music is then heard to address the listener, I to you, and the listener responds with the overreaching attitudes that are the norm in interpersonal relations. These attitudes reach for the subjective horizon, the edge behind the musical object. The music invites the listener to adopt its own subjective point of view, through a kind of empathy that shows the world from a perspective that is no one’s and therefore everyone’s. All this is true of music in part because it is an abstract, non-representational art, in part because it avails itself of temporal organization in a non-physical space.”

Scruton’s reworked Schopenhauerian view is that music is able to uniquely access a kind of disembodied subjectivity in which we can participate. Maybe the closest thing to a “mind meld” or direct access to another person’s thoughts or subjective experience. Except with music it’s not any particular person’s thoughts we access, but rather thought and emotion as such, in as pure a form as can be imagined. Something to think about next time you find yourself deeply moved by a piece of music.

Leisure: The Basis of Culture

Jakob and Todd discuss leisure as a source of culture, drawing primarily on the thought of Josef Pieper and Bertrand Russell. How activities beyond work for the purposes of sustenance and material wealth can be good for their own sakes and even constitute higher goods; how a full life of genuine wealth implies an inbreaking of grace “overflowing into superfluities”.

Spacetime, Individuation, and Fiber Bundles

How can entities be picked out as individual and distinct entities? Sunny Auyang presents a Kantian model of spacetime as an absolute and indispensable structural scheme we project onto the world to organize it and to pick out individual elements, or events in it. Using fiber bundles she packs together a complex structure of individuating qualitative features that she links to individual points in spacetime.

I’d like to talk again about some stuff I’ve been reading in this book by Sunny Auyang, How is Quantum Field Theory Possible? Specifically in this latest chapter I read on the nature of space or spacetime and the possibility of individuation, individuation being the identification and distinction of entities as separate entities.

Both of these issues have a long history in the history of philosophy but Auyang focuses mostly on the work of the modern period of the last few centuries, most especially on Leibniz, Newton, and Kant. There’s a famous dichotomy or division between the models of space put forward by Leibniz and Newton. And the question there is whether space is an independently existing thing or just a way of conceptualizing the relations between actual entities, like their distances and orientations from each other. So Newton’s view was that space has an independent existence. Even if you took out all other entities in the universe space itself would still be there as its own thing. Also time. So both space and time are “absolute”. But for Leibniz these are relative or relational concepts. Lengths, areas, and volumes are relations between entities but if you take away the entities, the actual things there’s nothing left behind, no empty space. Now I’ve read that those are actually drastic simplifications of their views, which doesn’t surprise me. But regardless of that we can at least have those views in mind to start, with the understanding that they’re traditionally associated with Newton and Leibniz. Auyang actually divides both these views further, so that we have four; two Newton-type views and two Leibniz-type views. And I’ll just introduce those so we can use the descriptive names rather than these two proper names.

On the one side we have the substantival view and the absolute view. Spacetime is substantival if it exists independent of material entities. Spacetime is absolute if its concept is presupposed by the concept of individual entities and things. These are similar but slightly different ideas. Substantivalism is ontological, meaning it actually has to do with being, what is. Absoluteness is conceptual; it pertains to the way concepts fit together and what is necessary for certain concepts to work and be intelligible. These can coincide but they don’t have to. And Auyang is going to argue for a model of spacetime that is absolute but not substantival. So in her view spacetime is not a thing that exists independent of material entities but it is a concept that is required to conceptualize material entities.

On the other side Auyang also distinguishes between the relational view and the structural view. I think this is an even more subtle distinction. The difference between these two is a matter of logical priority, looking at what comes first. So recall that with the relational view the concept of space arises from the relations between entities. Dimensions like length, area, and volume are these relations that we perceive between the entities around us. They’re already there and we perceive them. The structural view is the Kantian view, from Immanuel Kant, that space, and we can say also spacetime, are concepts that we project onto the world to organize it bring structure to it. So we as subjects come first. I’m describing that a little differently than she does in the book but that’s the way it makes most sense for me to think about it. And I think it’s consistent with her view. And between these options Auyang is going to argue for a model of spacetime that is structural rather than relational. So it’s more the Kantian model. So bringing these two together her view of spacetime is absolute and structural. In other words, spacetime is a concept that is required for us to conceptualize material entities, and it is a structure that we project onto the world to organize it and make sense of it.

With that in place let’s get to individuation of entities. How do we say that a thing is the same thing across time, something that we can index or label? And how do we say of a thing that it is this thing and not some other thing? “An entity is an individual that can be singly picked out, referred to, and made into the subject of propositions.” Aristotle said that it incorporates two elements. It’s both a this and a what-it-is. These are the notions of individuality and kind. A specific entity is not only a thing but it is this thing. It’s indexed and labeled. It’s also a certain kind of thing. That doesn’t individuate the single entity from other members of that same kind but it distinguishes that class of entities as a kind. Then within that set of that kind of entity they must be further differentiated and identified as individuals. That gets very complex. Other philosophers instead have also argued for the importance of a cluster-of-qualities notion. An entity is no more than the sum of its qualities. If you get specific enough about your qualities maybe that’s all you need. Every entity has a unique spatio-temporal history at least, even if indistinguishable in all other qualities. At least we may so argue. So some important concepts here are individuality, kind, and qualities. These are ways of individuating.

So we’re going to look at a model of these entities. And the first thing to address is that we’re going to look at this through the lens of quantum field theory rather than classical mechanics. So the primary form of matter, the material entities I’ve been talking about before, shift from discrete mass points in space to continuous fields comprising discrete events. Auyang doesn’t mention this but it reminds me a little bit of Alfred North Whitehead’s process philosophy in which he substituted a substance ontology of things to a process ontology of events. Auyang’s quantum field theory is rather different from that, nevertheless, it was something that came to mind. So anyway, the basic entities we’re going to consider now are events.

A field is a continuous system. “The world of fields is full, in contrast to the mechanistic world, in which particles are separated by empty space.” Every point in a field is assigned a value. So say we have a field, that we’ll call the greek letter ψ, for every point x in that field there will be a value ψ(x). And that field variable ψ(x) doesn’t have to be scalar, i.e. just a number. It can be a vector, tensor, or spinor as well. Actually I’m most accustomed to thinking of field variables as vectors like with a gravitational field or an electric field. So with a gravitational field for instance every point in the field around mass M has a vector oriented toward mass M. And then the magnitude of those vectors varies with the distance from mass M. And that’s just an example, the field variable could be any number of things. And that’s important for individuation because we’re going to want to account for the qualities of an individual event with which we can distinguish it. But also one key idea to keep in mind is that the field variable ψ is indexed to some point x in the field. That’s another method of individuation.

So let’s look at how both qualities and numerical identity get taken up in Auyang’s model. To give a bit of a road map before diving into the details her model will include. She’s going to use 6 major pieces: D, G, π, M, x, and ψ.

D is what’s called the total space.
G is a local symmetry group.
π is a map.
M is a base space.
x is a position in the base space M.
And ψ(x) is an event.

All of this will be put together in a fiber bundle structure. And we’ll get into what all that means in a minute.

First let’s talk about symmetry groups, which will be this G in her model. The concept of the this-something, the individuality of events, is incorporated in field theories through two symmetry groups. Symmetry is a key idea in physics. A related term is invariance, also a very important concept. And it’s basically what it sounds like. It’s some property that doesn’t change. More specifically, we’re interested in the very particular circumstances under which it doesn’t change, called transformations. So you have some object, you transform it in some way – say you rotate it for example – the features that don’t change in that transformation are invariants. And this can tell us important things. The big conservation laws in physics come from invariants as we know from what is called Noether’s Theorem. For example, conservation of energy comes from time invariance. Conservation of momentum comes from translational invariance. Conservation of angular momentum comes from rotational invariance. Very significant. Okay, so backing up again to symmetry groups – that was the whole reason for getting into this. A symmetry group is the group of all transformations under which the object is invariant. Some objects have lots of symmetry – they’ll be invariant under many transformation – others have very little. But the key is that the group of all those transformations where it is invariant – that’s a symmetry group.

The two symmetry groups pertinent to the field theories here are the local symmetry group and the spatio-temporal symmetry group. And these embody different aspects of the individuation of entities. “The idea of kinds is embodied in the local symmetry group, which pertains not to spatio-temporal but to qualitative features. The symmetry group circumscribes a set of possible states and defines a natural kind.” So recall one of the important ideas for identification or individuation was quality. Well the state of an entity covers its qualities. But for localization and identification, its numerical identity, we need a global whole, rather than a local whole, and that is represented by a spatio-temporal symmetry group. “The identities of the events are the invariants in the spatio-temporal symmetry structure.” These two symmetries give us the quality and numerical identity of the entities.

To fit this all together Auyang presents a model for the structure of local symmetries. And she does this using fiber bundles. Fiber bundles are great mathematical tools. The most straightforward way I like to think about fiber bundles is that they are a way to relate single points in some base space to more complex structures in another space. And when I say “space” here these can be abstract spaces, though at least one of these in what follows, the base space, will in fact be a spatio-temporal space. The great thing about this is that it lets us sneak a lot of structure into a spatio-temporal position. And that’s good because we need a lot of structure for these individuating elements. A spatio-temporal position is just one of these individuating elements. We want to bring qualities in there too.

So let’s look at Auyang’s model. This is the featured image for this episode by the way if want to look at it. The objects D, G, and M are differential manifolds, which is basically just a kind of space or surface. These manifolds can be actually spatial or spatio-temporal, which will be the case with our base space M. But they can also be, and often are abstract, which will be the case for our total space D and our local symmetry group G in this model. The first manifold, our total space D, is a set of abstract qualities. So this is where we’re going to get the qualities for our entities from. Then she also has a local symmetry group, G, which is also a manifold. We can label the abstract qualities in D as θ, θ’, and so forth. “At this starting point, both D and G are abstract and meaningless. Our aim is to find the minimal conceptual structure in which we can recognize events as individuals”.

The symmetry group G acts on the total space D and collects subsets of elements in D that are equivalent to each other. Each of these subsets we’ll call a G orbit. The elements in a single G orbit are equivalent to each other. We can start with quality θ and θ’ – those will go into one G orbit. Then we can pick out ξ and ξ’. This divides D up into these G orbit subsets until all elements in D are accounted for. None of resultant G-orbits share common elements. D still has all the same elements as before but they are divided into these subsets. This is quite useful for our purposes of individuation. We have some organization here of all this information.

Next we can take a G orbit and introduce a map π that sends all elements in a G orbit, θ, θ’, for example, sends all those elements onto a single point x. This point x is on another manifold M, a base space. There’s also an inverse map, π^-1, that canonically assigns a unique element x in M to each G orbit in D. M is what’s called a quotient of D by the equivalence relation G. It’s not given in advance but falls out from D. Every spacetime point, x, in the spatio-temporal structure, M, is associated with an event, ψ(x), in the total space D. Speaking of this in terms of set theory, D becomes a set with an indexing set M.

So now we have all the pieces put together: D, G, π, M, x, and ψ. And to review, D is the total space, G is a local symmetry group, π is a map, M is a base space, x is a position in the base space M, and ψ(x) is an event. And what’s the significance of all this in the “real world”, so to speak? M is usually called spacetime and x is a point in spacetime, the spatio-temporal position of an event ψ(x). But the identity of an ψ(x) includes more than just it’s spatio-temporal position, even though it’s indexed to that position. All that extra information is in the total space D. It’s divided up by the local symmetry group G. And then it’s mapped onto the spacetime base space M by the map π. The cool thing about the fiber bundle is that it allows us to cram a lot of information into a single point in spacetime, or at least link it to a lot of extra information.

The main goal that Auyang is working toward with this model is individuation. And to do that she needs enough complexity to carry the kind and quality features of individual entities, as well as spatio-temporal position. What happens in this model is that a spacetime position, x, signifies the identity of an event ψ(x). x uniquely designates ψ(x) and marks it out from others. The symmetry group, G, whose features are typical of all ψ(x), signifies a kind; since it collects those features as group. Then the spatio-temporal structure, M, is a system for identifying individuals in that group. So this “sortal concept that individuates entities in a world involves two operations” that will mark out (1) kinds and (2) numerical identity. First the local symmetry group, G, forms identical equivalence classes of qualities for this notion of kinds. Second the projection map, π, introduces numerical identity for each of these equivalence classes. These together secure the individuality of an event, ψ(x).

One thing we can certainly say about this kind of model is that it is analyzable. Events and spacetime positions are not just given in this view. There’s complex interplay between spacetime positions of events and all the qualities of those events. This is what we get with field theories. Even if we look at the world in the most primitive level, as Auyung says, with field theories, “to articulate even this primitive world requires minimal conceptual structure more complicated than that in many philosophies, which regard sets of entities as given.” So is this necessary, are we just making things more complicated than they need to be? Quoting Auyang again: “Field theories have not added complications, they have made explicit the implicit assumptions taken for granted.” I’m not prepared to defend that point but I’m fine with going along with it for the time being.

To wrap things up let’s look at some ways for thinking about this spatio-temporal structure, M. The complexity of the full conceptual structure of this model (D, M, G, π) is what makes it analyzable and it enables us to examine M’s possible meaning. Auyang characteristically promotes a Kantian take on all this. This is to see M as a “scheme of individuation and identification that we project into the world via the inverse map π^-1 and by which we present the world to ourselves as comprising distinct entities.” Recall that in Kant’s thought the world is intelligible to us only because we apply categories of understanding to the raw sense data we bring in, and we use these categories to organize it all and make sense of it. Auyung is saying that this is what M does; this is what the spatio-temporal structure, or our concept of spacetime does.

And this idea of space being what individuates things has a long history. For example, speaking of Kant, in Kant’s philosophy space is what makes identity and difference possible. Hermann Weyl called space the “principium individuationis”, which is really fun to say with the classical Latin pronunciation of the ‘v’. But that’s just this idea we’ve been talking about, individuation, the manner in which a thing is identified as distinguished from other things. Weyl also said space “makes the existence of numerically different things possible which are equal in every respect”. So it’s not just the qualities (non-spatial) that are important. You need space to distinguish entities that are otherwise identical. This doesn’t mean that space is substantival, some independently existing substance. But it is conceptually indispensable. So, say it is something that we bring to the scene, something we impose as an organizing tool. It’s still indispensable for the possibility of individuation. So it’s absolute in that sense.

So to review, I’ll put these in Kantian terms. We start off with what is “out there”, just this pre-conceptualized mass of stuff, our total space D. How is that intelligible? We come at it via a conceptual structure, the mental categories of space and time, or spacetime, M. Then we project these spatial and temporal conceptual categories onto the world using the inverse map π^-1. This inverse map is able to pick out individual entities in the total space D that are distinguishable by an organizing operation of the local symmetry group G. The local symmetry group G has divided up the total space D into G-orbits with common elements. Our spatial and temporal categories pick these subsets out as events ψ(x) that are mapped onto spacetime M. And that brings the whole structure together in a way that we can see everything together and pick out individual events as individual elements.

Star Wars Episode II: Jeff and Todd Strike Back

We talk about George Lucas, his background and influences. Flash Gordon, Akira Kurosawa, Horse Opera and Spaghetti Westerns. The sequel trilogy: overall coherence, the Star Wars tradition of seeing contradictions “from a certain point of view”. The sequel trilogy characters: Rey, Rose, and Vice Admiral Holdo.