Philosophy of Structure, Part 4: Matter and Form

This episode in the philosophy of structure series looks at the way structure inheres in material substances. Starting with Aristotle’s concept of hylomorphism (matter + form) we look at contemporary studies of this perspective in the thought of Kathrin Koslicki and Edward Feser. Most basic to this perspective is the idea of structures as the sorts of entities which make available positions or “slots” for other objects to occupy.

It’s been a while since I’ve done an episode for the philosophy of structure series. My interests and reading have taken some other directions over the last few months, dealing especially with theology. But they’ve circled back to the philosophy of structure, by way of theology interestingly enough, particularly in the scholastic theology of Thomas Aquinas. I’ve been wanting to get into some ideas in Aristotelian and Thomistic thought, but in order to do that I feel like there’s some groundwork I want to lay down first, that happens to pass through the philosophy of structure.

This discussion of structure will be a little more general; not as particular as the applications in music and chemistry discussed in previous episodes but more like the first episode on structure as such. But I’ll still refer to some examples in chemistry.

In addition to pre-modern philosophers like Aristotle and Aquinas, some living philosophers I’ve been reading recently are Edward Feser and Kathrin Koslicki. Feser in his books Scholastic Metaphysics: A Contemporary Introduction and Aristotle’s Revenge: The Metaphysical Foundations of Physical and Biological Science. And Koslicki in her book The Structure of Objects. Both Feser and Koslicki argue for a hylomorphic model of material substances. Hylomorphism, from the Greek words ὕλη, hyle, “matter”, and μορφή, morphē, “form”, is the view that physical objects are products of both matter and form. It’s also the view promoted by Aristotle and Aquinas. I take a note from Koslicki and also use the term “structure” to refer to the classical notion of form.

Koslicki gives the following definition of structure:

“Structures are precisely the sorts of entities which make available positions or places for other objects to occupy, provided that these occupants satisfy the type restrictions imposed by the structure on the positions in question; as a result of occupying these positions, the objects in question will exhibit a particular configuration or arrangement imposed on them by the structure.”

We can see the hylomorphic understanding at work here. The formal, structural component of an object is a set of open “slots” that stand in defined relations to each other. Or put another way, it’s the defined relations between these open slots that constitute the structure. But since this is hylomorphism and not just “morphism” these slots need to be filled to produce the substance. That’s the material component.

This is analogous, I think, to functions with variables. Like mathematical functions or functions in a computer program. In a linear function like y=mx+b, where m and b are constants you can see on a graph all the different values of the dependent variable y that correspond to all the different values of the independent variable x. You can substitute any number for x. That’s what makes it a variable. Or in a computer program you can define characters as variables, basically saying, “I don’t want to say exactly what this is now but I want to be able to insert values into it later.” Variables are, by nature, not fixed. They can have different values or be occupied by different objects. The function gives the general structure. But to get the output of a function you need to input specific values or objects for the variables. Similarly, for material substances structures can host various kinds of material components.

Chemical compounds are an instructive example of this kind of structural-material complex. For example, one kind of chemical structure is a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron. We could think of this as a structure with five open slots, which can be filled with different kinds of atoms. With a carbon in the center slot and hydrogens in each of the four corners the resulting compound is methane. With chlorine in the middle and oxygen in the corners it is perchlorate. With sulfur in the middle and oxygen in the corners it is sulfate. With phosphorus in the middle and oxygen in the corners it is phosphate. In all these cases the molecules have the same geometry and bond angles of 109.5°. It’s also possible to have a third kind of atom in the molecule as with thiazyl trifluoride, in which the center atom is sulfur and corners are occupied by three fluorines and one nitrogen. The takeaway from all this is that with this particular formal component, the structure of the tetrahedral molecular geometry, we have these open slots that can be filled by various kinds of atoms. But it’s the combination of this structure, plus the atoms, i.e. the material component, that makes the physical chemical compound. That’s the hylomorphic description.

Those are examples of a single formal/structural component with varying material elements. But it can also work the other way, with various chemical compounds having common material elements but varying structure.

Koslicki says the following:

“In chemistry, the notion of structure is employed in the following two central ways: the chemical structure of a compound is given by stating (i) the types of constituents of which it consists, i.e. its formula; as well as (ii) the spatial (i.e., geometrical or topological) configuration exhibited by these constituents… the three-dimensional arrangement into which these constituents enter, is equally crucial in characterizing the chemically relevant behavior of a compound. This became apparent in the history of chemistry in connection with the phenomenon or isomers or chiral (“handed”) molecules, compounds which consist of the same constituents, i.e. have the same chemical formula, but whose constituents are differently arranged and which, as a result of this difference in arrangement, behave quite differently in specific circumstances.”

As an example, there are three different chemical compounds with the basic formula C3H4: three carbons and four hydrogens. There’s propadiene, which has a rigid, linear structure with two double bonds and the pairs of hydrogen atoms at each end on planes at right angles to each other. There’s propyne, which has a rigid triple bond and a freely rotating single bond. And there’s cyclopropene, which has a double bond and a ring structure. In this case all the material components are the same but the open slots that they occupy are arranged differently. So the overall structural-material complex is distinct in each case. Again, this is understood most comprehensively from a hylomorphic description.

One reason both material and structural components of a substance are important is that both contribute to its properties. For molecules that have a common structure it makes a difference what atoms fill the available slot. For one thing, different atoms have different masses so a compound with more massive atoms filling those positions is going to be a more massive compound overall.  Xenon tetroxide is much more massive than methane, having molecular weights of 195 g/mol and 16 g/mol, respectively, even though they have the same tetrahedral structure. For this same reason xenon tetroxide also has a higher boiling point than methane, 0 and -161.5 degrees Celsius, respectively. Then for isomers, molecules that have the same atoms but different structure, those structural differences can impart important differences in properties. For example, several compounds have the formula C3H6O: three carbons, six hydrogens, and one oxygen. But two are alcohols (allyl alcohol and cyclopropanol), one is an aldehyde (propionaldehyde), one is a ketone (acetone), one is an epoxide (propylene oxide), and one is an ether (methyl vinyl ether). These have boiling points ranging from 6 degrees Celsius for methyl vinyl ether to 101 degrees Celsius for cyclopropanol; quite a range. And all these isomers have slightly different heats of combustion, meaning they release different amounts of heat when they burn.

An important consideration with all of this is that the structural and material components of a substance also have explanatory power regarding the nature of that substance. Not only do we know from experiments that certain substances have different boiling points, heats of combustion, dipole moments, acidities, vapor pressures, and such, though we certainly do obtain such information from experiments. But knowledge about the structural and material components of substances also helps us understand why they have the properties that they do. That’s what we’re really after in science anyway. We’re not just trying to make a giant catalogue of properties. We want to understand the underlying reasons for things.

Beyond particular kinds of substances we’re also interested in the laws of nature that govern the behavior of many or all kinds of substances generally. In a way laws of nature are an even higher order of structure than that of the structural component of substance in the structural-material complex. In the structure of a substance there are open slots that can be filled with material elements that meet the structural requirements. Laws of nature are similarly structural but instead of slots being filled by material elements they are filled by events and conditions. These also behave like functions, associating elements between sets, like inputs to outputs.  The outputs are the things that actually occur. But the underlying reasons are represented in the function itself. In the case of physical sciences the natures and propensities of substances are expressed in the laws of nature. It is these laws that dictate what will result from a given set of inputs. We can’t observe these laws directly. We can only observe events. But given large sets of inputs and outputs we can try to figure out what the underlying laws, natures, and propensities must be.

At some point such repeated, higher-order abstraction moves beyond scientific practice itself to something more meta-scientific, reflection on the nature of the physical sciences as such. And this is intrinsically metaphysical. Metaphysics doesn’t replace physics but it can give deeper understanding of it. Many scientists are also metaphysicians, though they may not use that label. Aristotle distinguished between what he called experience and art. I think of these as corresponding to data and theory, physics and metaphysics. Here’s Aristotle in his Metaphysics:

“All men by nature desire to know… But yet we think that knowledge and understanding belong to art rather than to experience, and we suppose artists to be wiser than men of experience (which implies that Wisdom depends in all cases rather on knowledge); and this because the former know the cause, but the latter do not. For men of experience know that the thing is so, but do not know why, while the others know the ‘why’ and the cause. Again, we do not regard any of the senses as Wisdom; yet surely these give the most authoritative knowledge of particulars. But they do not tell us the ‘why’ of anything-e.g. why fire is hot; they only say that it is hot… Since we are seeking this knowledge, we must inquire of what kind are the causes and the principles, the knowledge of which is Wisdom.” 

This was Aristotle’s justification for metaphysics. In contrast to this, Auguste Comte, a nineteenth century positivist, saw such metaphysics as something to overcome. He saw history progressing in three stages: theological, metaphysical, and positivistic. Each successive stage would shed the extraneous baggage of the former. In his view, even though educated people of his day had shed the superstitions of religion they still retained ideas of abstractions and invisible forces like gravity and magnetism that looked beyond the bare positive facts of the material world. Comte believed that metaphysics would eventually die out and we’d be left with only empirical data, just what happens, without making any kind of metaphysical inferences about it or even trying to give any kind of explanation for it.

I think Comte got the order of comprehension conceptually backwards, the reason being that structure is ineliminable from an intelligible account of the material world. A more sophisticated form of positivism, one that at least attempted explanation without recourse to metaphysics, reached an apex in the first half of the twentieth century. But it ran into insuperable difficulties, even though it still retains some popular support. But at the end of the day you really can’t have just data by itself. At least not if you’re after a satisfactory account of reality. Underlying, immaterial structures, like laws of nature, are indispensable to make it at all intelligible. Positivism has to give way to metaphysics.

I also happen to think, continuing in the opposite direction as Comte, that further investigation of metaphysics of this kind ultimately demonstrates that certain concepts found in the traditions of religious theology and philosophy are also indispensable to an adequate understanding of reality. My focus with this episode is on the philosophy of structure so I don’t mean to sneak in too much missionary work. But in full disclosure I do in fact think that’s where the logic of all this leads.

Reality is composed of multiple layers of structure. The hylomorphic model of substance is that material substances themselves are most intelligibly understood as structural-material complexes. That’s the best way to think about substances having the kind of properties that they have, with reasons for having the properties they do. Further, physical reality, with its various substances and objects, proceeds according to the natures and propensities inherent in its substances. Physical reality is most intelligibly understood as conforming to certain laws that govern the kinds of events that occur. These laws impose structure on everything around us.

Star Trek: Humanoid Origins

Rick and Todd get together to talk about humanoid origins in the Star Trek universe. We discuss two episodes. In “The Chase” the crew of the Enterprise discovers the traces of an ancient ancestor common, via panspermia, to humanoid species across the galaxy. In “Distant Origin” the crew of Voyager encounters a Voth scientist who has discovered that the Voth originated from Earth and are humanoid descendants of hadrosaurs.

A Life With the Holy Spirit

A life with the Holy Spirit is wonderful, exciting, challenging, and meaningful. One of my core beliefs is that there’s much more to reality and the possibilities of our existence than we can possibly imagine. Just a tremendous “more”. Greater in scope, finer in detail, richer in complexity and beauty. And this is something I can see most fully through the illumination of the Holy Spirit. It’s like something I never could have imagined possible before experiencing it. A taste of the overwhelming joy that comes from the power of the Holy Spirit goes a long way to shift a person’s perspective on what kind of life is possible. It changes everything.

We see a lot in the news about each generation becoming more secular over time. The rise of the “Nones” (N-O-N-E-S), those who belong to or believe in no religion. There are many ways to respond to that. Maybe this is a good thing and will ultimately lead to a more peaceful and tolerant world. Or maybe it’s a troubling sign that the foundations of our culture and civilization are eroding. Lots has been written in support of both of those and I’ve believed both of them at one time or another. And still haven’t fully rejected either of them. There’s lots of interesting stuff to talk about there. But what’s interested me most recently and motivated my missionary impulse is more the religious life itself and what it means not to have a rich religious life. In other words, what is it that people are missing out on?

I think what’s got me thinking about things in this way is just my own experience, especially recently, in living a life with the Holy Spirit, knowing what that’s like and how wonderful it is. Wonderful, exciting, challenging, and meaningful. One of my core beliefs is that there’s much more to reality and the possibilities of our existence than we can possibly imagine. Just a tremendous “more”. Greater in scope, finer in detail, richer in complexity and beauty. And this is something I can see most fully through the illumination of the Holy Spirit. It’s like something I never could have imagined possible before experiencing it. A taste of the overwhelming joy that comes from the power of the Holy Spirit goes a long way to shift a person’s perspective on what kind of life is possible. It changes everything.

So that’s what interests me most. I think it’s great that the world is becoming wealthier and healthier, more peaceful and tolerant, and that people have more opportunities. I want that to continue. For sure. But there’s even more. Possibilities to life that go even more directly to the core of who we are and what we can be. It’s challenging. It’s all-demanding and all-transforming. But astoundingly, it’s worth it.

Jesus gave a dramatic illustration of this in a parable:

“Again, the kingdom of heaven is like a merchant seeking beautiful pearls, who, when he had found one pearl of great price, went and sold all that he had and bought it.” (Matthew 13:45-46)

This is how I feel about life with the Holy Spirit. It’s worth giving up anything that stands in the way of it and it’s worth doing anything to have it. Imagine what it must have been like for the disciples to hear this from Jesus. Peter spoke for all of them when he said: “See, we have left all and followed You.” (Matthew 19:27) Admirable and astounding devotion. But why would they have done that?

There’s probably some mystery to that. Dietrich Bonhoeffer proposed in his theology that the response of obedience evades justifying reasons and is attributable only to the “absolute, direct, and unaccountable authority of Jesus” (The Cost of Discipleship). That might be. Certainly there was a call and there always is. Paul said there has to be:

“How then shall they call on Him in whom they have not believed? And how shall they believe in Him of whom they have not heard? And how shall they hear without a preacher?” (Romans 10:14)

The disciples heard the call and they obeyed.

“As He passed by, He saw Levi the son of Alphaeus sitting at the tax office. And He said to him, ‘Follow Me.’ So he arose and followed Him.” (Mark 2:14)

“And Jesus, walking by the Sea of Galilee, saw two brothers, Simon called Peter, and Andrew his brother, casting a net into the sea; for they were fishermen. Then He said to them, ‘Follow Me, and I will make you fishers of men.’ They immediately left their nets and followed Him. Going on from there, He saw two other brothers, James the son of Zebedee, and John his brother, in the boat with Zebedee their father, mending their nets. He called them, and immediately they left the boat and their father, and followed Him.” (Matthew 4:18-22)

They just got up and left everything they had and immediately followed Christ.

Even if the Holy Spirit is not something you’ve personally experienced, these examples should at least give an idea of the absolute power of its driving force. Imagine the kind of purpose this grants to a person’s life. Sometimes we’re just looking for a reason to get up in the morning, go out the door, and go to work. The Spirit got these people to get up, leave everything, and not look back for a moment, to follow Christ. That’s a maximal sense of purpose right there. You think about one of Jesus’s wonderful paradoxes: “he who loses his life for My sake will find it.” (Matthew 10:39) Paul talked about walking “in newness of life” (Romans 6:4). The disciples had a completely new kind of life. They lost their old life but they found a new kind of life that was tremendously more alive.

Paul was someone who knew something about newness of life. His own life had taken a radical change in direction with his experience on the road to Damascus. From that moment on nothing was the same. Saul of Tarsus became Paul, servant of Christ Jesus. Like the other disciples he left everything and dedicated the rest of his life to Christ. Paul was a zealous missionary but we also see repeatedly in his letters his awareness that it is ultimately the Spirit that converts and transforms people. He told the Corinthians: “I planted, Apollos watered, but God gave the increase.” (1 Corinthians 3:6). Though he was very adept in rhetoric and knowledgeable of Torah everything ultimately came down to the work of the Spirit.

This is important. The Gospel of Christ is not just a system of ideas, though it is certainly intellectually rich and stimulating. But it’s much more than that. And it defies standard categories. Dietrich Bonhoeffer said:

“To try and force the Word on the world by hook or by crook is to make the living Word of God into a mere idea, and the world would be perfectly justified in refusing to listen to an idea for which it had no use.” (The Cost of Discipleship)

Paul plays up the unreasonableness of the Gospel, calling it “foolishness” to the “natural man” (1 Corinthians 2:14). I think that’s a bit of a deft rhetorical overstatement. The Gospel is coherent, consistent, and rational. But many systems of thought are coherent, consistent, and rational, at least on their own terms. What makes the Gospel different? Now I do think the rich Christian intellectual tradition can go a long way to make it appealing to the intellectually curious. It opens up a space. I say that out of my own experience. But there’s more. And it’s that more that separates it from the rest so that it’s not just one more system of thought among others. And that is something that is communicated by the Spirit.

There’s something of the gospel that is incommunicable and even unimaginable by any other means. Paul wrote to the Corinthians, paraphrasing Isaiah:

“Eye has not seen, nor ear heard,

Nor have entered into the heart of man

The things which God has prepared for those who love Him.”

(1 Corinthians 2:9)

This reminds a little of Shakespeare’s Hamlet saying to Horatio: “There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.” Paul says that there is more out there than most of us have ever considered. How can you come to know and experience something you don’t even know is there? Paul says:

“But God has revealed them to us through His Spirit. For the Spirit searches all things, yes, the deep things of God. For what man knows the things of a man except the spirit of the man which is in him? Even so no one knows the things of God except the Spirit of God. Now we have received, not the spirit of the world, but the Spirit who is from God, that we might know the things that have been freely given to us by God.” (1 Corinthians 2:10-12)

“The deep things of God”. This is where the vault of the heavens, the upper ceiling capping off the limits of our imagination and what is possible can get blown open and expanded. Paul wanted the Church to be able “to comprehend with all the saints what is the width and length and depth and height—to know the love of Christ which passes knowledge; that you may be filled with all the fullness of God.” (Ephesians 3:18-19)

We see in Paul’s letters that he says many times that he’s praying for the Church so that the Spirit will be at work among them. He said to the Colossians:

“For this reason we also, since the day we heard it, do not cease to pray for you, and to ask that you may be filled with the knowledge of His will in all wisdom and spiritual understanding; that you may walk worthy of the Lord, fully pleasing Him, being fruitful in every good work and increasing in the knowledge of God; strengthened with all might, according to His glorious power, for all patience and longsuffering with joy; giving thanks to the Father who has qualified us to be partakers of the inheritance of the saints in the light.” (Colossians 1:9-12)

This stands out to me because it conforms very much to my own experience with the Spirit. In particular, the effect of being “strengthened with all might, according to His glorious power, for all patience and longsuffering with joy”. One of the things I’ve noticed that follows my experiences of being filled up with spiritual light is a change in my natural inclinations. To be more patient. My sphere of concern is redirected further outward, away from my own interests. This just happens. And it’s wonderful. These “fruits of the Spirit”. Paul listed various fruits of the Spirit in his letter to the Galatians:

“But the fruit of the Spirit is love, joy, peace, longsuffering, kindness, goodness, faithfulness, gentleness, self-control. Against such there is no law. And those who are Christ’s have crucified the flesh with its passions and desires. If we live in the Spirit, let us also walk in the Spirit.” (Galatians 5:22-25)

Doesn’t that sound wonderful? To have that kind of conversion of character? This is what it’s like to “walk in the Spirit”. And it’s not self-produced. It requires sacrifice and effort but the fruits come from the Holy Spirit.

Paul wrote to the Ephesians:

“Therefore I also, after I heard of your faith in the Lord Jesus and your love for all the saints, do not cease to give thanks for you, making mention of you in my prayers: that the God of our Lord Jesus Christ, the Father of glory, may give to you the spirit of wisdom and revelation in the knowledge of Him, the eyes of your understanding being enlightened; that you may know what is the hope of His calling, what are the riches of the glory of His inheritance in the saints.” (Ephesians 1:15-18)

Here’s another instance of the pattern in which a missionary prays for the church to be given the Spirit to illuminate and transform them. Paul says that, with the Spirit, the eyes of the understanding may be enlightened. This is the only way to be so enlightened because “no one knows the things of God except the Spirit of God” (1 Corinthians 2:11)

I imagine Paul’s desire for the Spirit to act on the church came from a place of deep love, which is itself a gift of the Spirit (1 Corinthians 13). This isn’t the kind of thing a person can just keep to oneself. It’s a sentiment I very much relate to and also feel deeply. The desire to see others experience the same power is persistent.

There are, of course, various sociological and political reasons that I can think of to want to see people in my community, local and global, have a strong religious base. Many benefits from that. Along with certain risks and potential harms that misdirected religiosity can have. But beyond all those important secondary effects is the primary work of the Spirit itself in a person’s soul. Like the pearl of great price, a life with the Holy Spirit is something I would do anything and give up anything to have. It strikes to the heart of the human soul and satisfies its deepest need for meaning and purpose.