A simple matter made complex

Alice: I just bought a shelf from Ikea.

Bob: Strictly speaking, you bought the matter of a shelf from Ikea.

Alice: Well, that’s the thing that matters, isn’t it? 😛

Bob: Not really, since it’s the form that makes the matter a shelf.

Alice: That’s a different matter entirely, I was just —

Bob: Not so, it would be the same matter, just with a different form.

Alice: I was trying to say that there’s no disagreement of any substance here.

Bob: Agreed. For there to be a disagreement regarding substance, one of us would need to think the shelf had a substantial form.

Alice: No, I had something much simpler in mind.

Bob: Come now, you can’t seriously be considering whether the shelf is simple? It is evident that it must be a form-matter composite.

Alice: My point is that we’re talking in different categories.

Bob: Well, I wasn’t really thinking about the categories at all.

Alice: Yes, that was evident.

 

A web of links

I’ve been working on a number of larger projects over the past few months, and so haven’t had the opportunity to post anything in a while. I hope to be finishing up with some of these in the next few weeks. In the meantime, I’ve collected a number of interesting links (mostly videos) for your viewing pleasure.

Robert Kuhn over at Closer To Truth has recently interviewed Eleonore Stump on a number of interesting questions: What are persons? Do they have souls? Do heaven and hell really exist? And what is God’s eternity? Be sure to also check out earlier questions to her about God’s eternity and his relation to time.

Interested in music? Vox has some great videos discussing Rap and Kanye West, and Polyphonic asks what about John Bonham makes him such a good drummer.

If you thought American Sniper was obviously a pro-war movie, it might be worth reconsidering that assumption a bit more carefully. In their video essay, Storytellers argues that it is really a subtle and careful anti-war movie, and follows this up with a response video. On the topic of war movies, Storytellers also has an interesting discussion on the movie Jarhead.

Sticking with the theme of movies, Films&Stuff discusses the first Matrix movie and how it was structured around the theme of breaking rules. NerdWriter discusses how Lord of the Rings uses music as part of its story telling and what Logan means for superhero movies. The two Franco’s and Seth Rogen do a Q&A on the Disaster Artist. And Christopher Nolan does a Q&A on Dunkirk.

If like me, you quickly became tired of the Assassin’s Creed formula, then you might be pleasantly surprised by what the upcoming installment is shaping up to be.

If you enjoy (1) Let’s Play videos and (2) difficult platformers, then I can recommend BaerTaffy’s playthrough of The End is Nigh.

If you’re interested in Game Design, then I highly recommend Mark Brown’s discussion of Ori and the Blind Forest’s Ginso Tree level.

A while back Ian Bogost gave a talk on what makes things fun, and it turns out gameifying everything is not the way to do it.

Ever wanted to be able to speak backward? Well, Kurt Quinn can, and on Smarter Every Day they put this skill to the test.

You might have heard of the recent memo by Google employee James Damore, now commonly referred to as “the anti-diversity manifesto,” but more correctly called “the criticism-of-the-mechanisms-and-measures-used-for-increasing-diversity-without-consideration-for-alternative-solutions memo.” I guess the former is pithier. The reaction has been divided, to say the least. Some people seem to have not really read it all that charitably, while others have discussed the merits and possible corrections of the approach (see particularly the discussion between Grant and Alexander, and the responses of four scientists in relevant fields). Damore himself has recently been interviewed by Bloomberg.

Ever wondered why lowercase numbers don’t exist? Turns out they do!

A while back, over at the Augustine Collective, David Nolan discusses the role of emotions in Aquinas.

Feser on how to go to hell, how to think about angels, and the Benedict option.

Finally quantum mechanics. There’s William Wallace’s review of Smith’s book The Quantum Enigma, and Aaron Wall on intepreting the quantum world.

Fear of the Lord

Throughout the Scriptures — both Old and New testaments — God’s people are told to fear him, which at first glance seems to be an odd response to a God full of grace and love. Perhaps the most puzzling statement comes when the people of Israel first meet God at the mountain in Exodus 20. Notice what Moses says to the people in response to their fear:

Now when all the people saw the thunder and the flashes of lightning and the sound of the trumpet and the mountain smoking, the people were afraid and trembled, and they stood far off and said to Moses, “You speak to us, and we will listen; but do not let God speak to us, lest we die.” Moses said to the people, “Do not fear, for God has come to test you, that the fear of him may be before you, that you may not sin.” (Exodus 20:18-20)

On the face of it, Moses’ words seem so strange as to verge on contradiction. What could the fear of the Lord possibly be, that he can speak about it like this?

Perhaps the most common way of making sense of the phrase is by saying that it simply refers to the reverence of the Lord. While I don’t deny that it involves this, I struggle to see how this could be the whole story. Often the fear of the Lord is explained in genuinely scary terms, like our destruction or like the thunder and lightning in the above passage. These show us that God’s greatness can be a real danger to his people. It seems to me that we need a more satisfactory account that does justice to this, without collapsing into the opposite error of denying God’s graciousness.

We mentioned fear in an earlier post on faith and hope, where we said that fear is uncertainty with dissent. That is to say, we fear something because we are uncertain as to whether it will be good or bad for us. Naturally, this often results in us wanting to avoid the thing we fear, lest the bad thing happen. We saw an example of this in that earlier post when the disciples are confronted by Jesus’ power in calming the storm:

On that day, when evening had come, he said to them, “Let us go across to the other side.” And leaving the crowd, they took him with them in the boat, just as he was. And other boats were with him. And a great windstorm arose, and the waves were breaking into the boat, so that the boat was already filling. But he was in the stern, asleep on the cushion. And they woke him and said to him, “Teacher, do you not care that we are perishing?” And he awoke and rebuked the wind and said to the sea, “Peace! Be still!” And the wind ceased, and there was a great calm. He said to them, “Why are you so afraid? Have you still no faith?” And they were filled with great fear and said to one another, “Who then is this, that even the wind and the sea obey him?” (Mark 4:35-41)

The disciples can see that Jesus is powerful, but they are uncertain whether he is good powerful or bad powerful and so they fear him. Note, however, that the fear here is not the right way to respond to Jesus. This is why he asks in exasperation why they are still afraid as opposed to having faith.

Closely related to fear is dread, which is thinking with dissent. When we dread something we are not uncertain about whether it is bad but are convinced to some degree it is. For the sake of illustration, imagine we commit some crime. Initially, we fear being caught, since we’re uncertain about whether it will happen or not. Once we are caught, however, we dread the punishment because we’re pretty confident it will happen.

So we have these two notions, neither of which seem adequate accounts of the fear of the Lord. In both cases, we are repelled from the thing we fear or dread, but the Lord whom we are to fear wants us to draw closer to him. Nevertheless, this sense of fear does seem to be what Moses has in mind when he says, “Do not fear” to the people of Israel. Having been confronted with God in the thunder and lightning, their (quite understandable) response was to stand far off and avoid talking with him. They were repelled from the object of their fear. Moses then urges them not to respond to God in this manner.

As I see it, the fear of the Lord should be understood as follows. God is the source of all goodness, making him unequivocally good for us and something we should be drawn towards. Furthermore, because of his grace, he will accept us and bless us if we come to him. But if we turn away from him — if we turn away from the giver of life — we will die; if we make ourselves his enemies, we will be destroyed. And this would be something very bad for us indeed.

So the fear of the Lord stands somewhere between fear and dread as we’ve outlined them above. There is no uncertainty here, for God has made these terms abundantly clear. And our destruction is only anticipated if we choose to turn away from him. Perhaps we should say, then, that fear of the Lord is conditionality with dissent: the badness of punishment remains an open possibility so long as we are capable of turning away from God, but will not happen so long as we cling to him. We don’t have a word for this — and presumably neither did the author’s of Scripture — so we use the word “fear” as the best alternative.

The most significant difference between the fear of the Lord and fear in the typical sense is this: instead of being repelled by him, we are drawn to him and repelled by his absence. We are drawn to live with the giver of life and serve creator of everything, and we are repelled by what will happen if we choose death over life and something created over the creator.

This reading fits well with how the phrase is used throughout Scripture. We see this in Moses’ words above. There he explains that the fear of God must be before them so that they may not sin. And we see something similar in his sermons in Deuteronomy:

Now this is the commandment, the statutes and the rules that the Lord your God commanded me to teach you, that you may do them in the land to which you are going over, to possess it, that you may fear the Lord your God, you and your son and your son’s son, by keeping all his statutes and his commandments, which I command you, all the days of your life, and that your days may be long… It is the Lord your God you shall fear. Him you shall serve and by his name you shall swear. You shall not go after other gods, the gods of the peoples who are around you — for the Lord your God in your midst is a jealous God — lest the anger of the Lord your God be kindled against you, and he destroy you from off the face of the earth… And the Lord commanded us to do all these statutes, to fear the Lord our God, for our good always, that he might preserve us alive, as we are this day. And it will be righteousness for us, if we are careful to do all this commandment before the Lord our God, as he has commanded us. (6:1-2, 13-15, 24-25)

And again we see the same ideas coming up in the Psalms:

Blessed is everyone who fears the Lord, who walks in his ways!… Behold, thus shall the man be blessed who fears the Lord. (Psalm 128:1, 4)

And finally, in the New Testament we see it most clearly in Paul’s words to the Philippians:

Therefore, my beloved, as you have always obeyed, so now, not only as in my presence but much more in my absence, work out your own salvation with fear and trembling, for it is God who works in you, both to will and to work for his good pleasure. (Phillipians 2:12-13)

The verses that follow make it clear that Paul’s intention here is to urge them to continue living lives pleasing to God while they looked forward to “the day of Christ” (v16). This amounts to the same idea as we saw in Moses and the Psalms, but also taking into account the work of Christ.

Examples can be multiplied, but these passages show that understanding the fear of the Lord as conditionality with dissent does justice to its use in Scripture. Most importantly it explains why such fear is a good thing for the people of God to have, without undermining his greatness or his graciousness.

Dialogue on God’s interaction with the universe

Bob: How can an immaterial God interact with a material universe?

Alice: The question itself needs to be questioned before we can answer it.

Bob: How so? It seems like a fairly straightforward question.

Alice: Well, consider the word “interact.” God does not interact with anything. To interact requires action going in both directions, and since God is pure actuality this is impossible. Rather God acts on and through creatures without them acting on him.

Bob: Ok, so we’ll change the question to how an immaterial God can act on or through a material creature.

Alice: It’s better but still has problems. When you ask “how” God can act, what type of answer are you expecting?

Bob: I’m not sure I lay out exactly the type of answering I’m looking for, but I can give you illustrative examples. Fire heats by inducing mean molecular motion, I pick up things with my hands, and one stone acts on another by knocking into it. In each of these cases, I can point to the means or process by which some action is performed by one thing on another.

Alice: But on that account, the question is loaded! In each case, you could give some organ, part, or some material property by which one thing causes something in another thing. None of these kinds of answers apply to God since he has no organs, parts, or material properties. And to assume this in the question at hand is to preclude the possibility of giving an answer.

Bob: I grant your point but how, then, am I to proceed? Surely there’s a legitimate question to be asked here? And if we can’t use physical categories to have the conversation, then what can we use? After all, surely all our knowledge comes from our experiences of physical things?

Alice: It is true that all human cognition starts with sense data. But through abstraction and other intellective acts, we can move beyond these data, so that while our knowledge starts with our experiences it needn’t end with them. We do this, for example, when studying infinities in mathematics or when picking out idealized models in physics. Even in imagining things that don’t really exist, like fictional characters and stories, we are moving beyond what we have experienced. I agree that there is a legitimate question to be asked, but my point is that it should not be understood as a physical question but as a meta-physical one.

Bob: Ok, granted that the question — and therefore answer — is metaphysical, how would you answer?

Alice: One of the broadest distinctions we have in metaphysics is that between act and potency. Just as we’ve been saying, we come to understand this distinction through everyday phenomena like change and multiplicity. And once we understand act and potency, we can then move beyond these phenomena to talk about things beyond our everyday experience, like God. It is with categories such as these that we need to approach the question.

Bob: I understand the distinction between act and potency, and I understand that God is conceived of as a being of pure actuality. But how does this distinction answer the question?

Alice: It doesn’t by itself answer the question. But it is the first step in showing that the question is, in a way, misplaced.

Bob: I don’t see how it could be misplaced. After all, it seems quite natural to ask how a thing without arms or legs could act on material things.

Alice: Let me explain. Once we arrive at the distinction between act and potency we can draw out various corollaries, two of which interest us here. First, things act only insofar as they are in act. The basic idea behind this is that acting on something involves actualizing potentials in that thing, and since potency cannot actualize anything this can only happen insofar as the thing acting is in act. Second, potency limits act. When an act is understood as the actualization of this or that potency, it becomes qualified (or limited) by that potency. For example, the act of mean molecular motion is of itself not limited to a time or place or speed, but when it comes to actualize the potencies in something being heated then it will be limited in these ways.

Bob: I don’t see how all of this relates to the question. How do either of these help us find the metaphysical hand by which God acts on a material thing?

Alice: The point is that he doesn’t need such a hand in the first place! As material beings, we exist through the actualization of potencies in our matter. As such, our actions are limited in various ways, which is why we cause by means of organs, parts, tools, contact, etc. A particular fire can’t heat something across the world because it’s limited by its matter to a specific place and time. A particular stone can’t simply make another move whenever, but has to collide with it, because its causal influence is limited to where and when it is.

Bob: And what about God?

Alice: As we’ve said, God is pure actuality, which is to say that there is no potency in him that limits his action. He simply brings about his effects immediately, without any need for the various means we need as material beings. This is why I said the question is misplaced. If anything is surprising it’s that we limited beings can interact with each other, not that the unlimited God can act on us.

Bob: That may be evident upon later metaphysical reflection, but I think the question arises quite naturally from our everyday experience of how things interact with one another. After seeing that things typically interact by various means that depend on their materiality, we quite reasonably ask how it is that an immaterial God could do something similar.

Alice: That’s a fair point. The answer, then, is that an immaterial God does not do something similar. He does not interact, but rather he acts. And he does not act by means of something, but rather he acts immediately. His action is similar to ours in that it arises from him being in act, but it is different from ours in that his being in act is not limited by any potencies within himself.

Bob: I see. In a way, it is almost an inevitable consequence of his being the creator of everything. If he needed a means by which to act, then this means could not have been created by him.

Patience

A while ago my church was doing a series on the fruit of the Spirit, listed in Galatians 5:22-23. I did the sermon on patience, and below are the notes for this. The audio can be found at my church’s website. In addition to reading the list of the fruit in Galatians, we also read James 5:7-11, upon which the sermon is based. My broader approach to patience is based off Aquinas’s discussion in ST II-II Q136.

Be patient, therefore, brothers, until the coming of the Lord. See how the farmer waits for the precious fruit of the earth, being patient about it, until it receives the early and the late rains. You also, be patient. Establish your hearts, for the coming of the Lord is at hand. Do not grumble against one another, brothers, so that you may not be judged; behold, the Judge is standing at the door. As an example of suffering and patience, brothers, take the prophets who spoke in the name of the Lord. Behold, we consider those blessed who remained steadfast. You have heard of the steadfastness of Job, and you have seen the purpose of the Lord, how the Lord is compassionate and merciful. (James 5:7-11)

Introduction

One of the clearest messages in Scripture is that the people of God need to be patient. As we just saw in Galatians, Paul lists patience alongside things like love, goodness, and joy — which seem like pretty good things for Christians to have. Scripture often tells us that God’s people need to have endurance, steadfastness, or perseverance. It tells us to not dwell in anger, and it tells us to forgive one another. And a large chunk of God’s interactions with us is through him promising something and us having to wait for it.

But why should we be patient? How does patience follow from the gospel? And what is patience, actually? These are the questions we want to try and grapple with tonight.

There’s what we might call the “lazy” answer to these questions which is easy but ultimately unhelpful. It goes something like this: nice people are patient, Christians are supposed to be nice people, and so Christians are supposed to be patient. I say this is unhelpful because it tells us nearly nothing about patience, and doesn’t help us understand how patience flows from the gospel. So, let’s put that to one side and start over afresh.

Patience in general

Let’s start by trying to understand patience in general. In our passage James illustrates patience with the example of the farmer. The farmer sows the seed so that the ground will produce food. But he knows that this will not happen immediately. He knows that in order for the plant to produce this food, it needs to take in a number of rounds of rain, and this takes time. So he waits calmly without giving up. He keeps his composure. So patience is about keeping composure.

But it’s not just this, is it? We don’t call people patient when they’re calm and life is easy. James knows this, since he goes on to talk about patience in the face of suffering. And we can see this if we think through the farmer example a bit more. Let’s say he planted the seeds and then forgot about them. Then one day he’s like, “Oh! Crops!” In this case he wouldn’t be showing patience: he would just be forgetful. On the other hand let’s say he needed food and this was his only way of getting it. Or perhaps he finds it difficult to wait through both autumn and spring rains to get these crops. It’s in these cases that he would be waiting patiently. So patience involves keeping composure in the face of difficulty, whether it be suffering, or stress, or weakness, or something else.

So far so good, but we’re still missing something: when we’re patient, what motivates our patience? The farmer doesn’t wait just because he likes waiting, and we don’t endure suffering because we enjoy suffering. More generally, we aren’t patient because we like going through difficult times. The farmer has an end in mind, he has a goal: he waits patiently for the rain because this is how he gets his crops to produce food. If he gives up waiting he gives up on this food.

And this principle scales up and down: if he only waits one day, he wouldn’t get much more than what he planted. If he waits through only the autumn rains he would see the plant’s stalk and leaves — and he’d be able to eat those, which would be good to some extent. But if he waits through both autumn and spring rains, then he gets to enjoy the what James calls the “valuable crop,” which would be a great good. His waiting pays off in that it enables he to take hold of the great good.

And this is true in general when it comes to patience: we keep our composure in the face of difficulty because we look forward to a great good that we can only get if we don’t give up. This is the last aspect of patience.

Patience is keeping composure in the face of difficulty for the sake of some great good.

We can see this definition work out everywhere in life, most clearly when we’re being impatient. When you’re driving to work and you get fed up because of the traffic, you are not keeping your composure in the face of that difficulty — you’re being impatient with the other drivers. When you start ignoring someone at church because they’re irritating and you’ve given up, you are not keeping your composure in the face of that difficulty — you’re being impatient with them. When you continually struggle to overcome a particular sin but it’s difficult and so you give up on it, you are not keeping your composure in the face of that difficulty — you’re being impatient with yourself.

Christian patience: the great good and source of difficulty

To understand Christian patience, then, we need to talk about the difficulties we face as Christians and the great good that helps us get through them. To start off we need to understand two things: (1) to be with God is the greatest anyone could ever hope for, but (2) our sin prevents us from being with him. So let’s unpack each of these.

God is the greatest good

I say God is good, but on the face of it referring God “a good” — or even “a great good” — can actually be slightly misleading, because he’s not just some good thing among the other good things we are familiar in everyday life. Good ice-cream, good paintings, good dogs, and good people are each is good and desirable, but only in a limited and qualified way. God, on the other hand, is good in an unlimited way. When I’m eating a good ice-cream, part of my desire is satisfied, but some part is left unsatisfied, since an ice-cream is not a painting, or a dog, or a good time with friends, or anything else I could want. This is because the ice-cream is limited — it’s just ice-cream. It would be different, though, if I could somehow experience God, since he is unlimited. There would be no part of me left unsatisfied. CS Lewis summarized this when he said,

He who has God and everything else has no more than he who has God only. (CS Lewis, The Weight of Glory)

Now, God is so good, so holy, and so beautiful that no-one can experience him all at once, at least not in this life. When we see goodness and beauty the various things throughout creation — when we see impressive animals, incredible plants, beautiful landscapes and valleys, when we amazed by the vastness of space, and when we’re occasionally pleased with ourselves — all we’re doing is looking through windows into this or that aspect of God’s infinite glory. And even then, these windows can be difficult to see through because of things like disease, and decay, and cruelty, and death. We never get to experience God’s glory all at once, but only bit-by-bit.

This idea that God’s beauty and goodness and holiness are expressed bit-by-bit throughout creation is spoken about in different ways in Scripture. So for example, David says, “The heavens declare the glory of God” (Ps 19:1), and the angels sang to Isaiah, “Holy, holy, holy is the Lord Almighty; the whole earth is full of his glory!” (Is 6:3).

Wouldn’t it be cool, though, if instead of having God’s beauty just a little bit at a time, we somehow were able to have all of it at once? It would be like all the good times in life now, minus all the bad, but scaled up infinitely. We know it would be awesome, but don’t know exactly what that would be like, since we’ve never experienced anything like it before. We don’t get it, we can’t at the moment. As finite creatures with finite experience of reality, we have no way of picturing the true awesomeness of an infinite God. And that’s actually where the problem starts.

Sin prevents us from accessing God

You see, we’re so familiar with the finite things here in our everyday life and so unfamiliar with the infiniteness of God, that we find it easy to replace the one for the other — to focus on limited goodness rather than unlimited goodness.

Sometimes you’ll hear sin being spoken about in terms of “giving into desire,” as if the one who has the strongest desire is the one most likely sin. But in some sense it’s because our desires aren’t strong enough that we give up wanting to be with God and settle the lesser things we’re familiar. Again, CS Lewis summarizes this well when he says,

It would seem that Our Lord finds our desires not too strong, but too weak. We are half-hearted creatures, fooling about with drink and sex and ambition when infinite joy is offered us, like an ignorant child who wants to go on making mud pies in a slum because he cannot imagine what is meant by the offer of a holiday at the sea. We are far too easily pleased. (CS Lewis, The Weight of Glory)

This giving up of God for some finite good is at the heart of we call sin. And sin always spirals into more sin. The more we choose finite goods over God, the more used it we become. It becomes easier to do again next time, and harder and harder to choose God. Sins we might’ve at one point thought unimaginable now become plausible, or even desirable. And so we spiral further and further away from God, alienating ourselves from him, and cutting ourselves off from ever seeing him face-to-face. This infinite goodness that is beyond our wildest dreams is now beyond our reach.

Again, the idea that our sin prevents us from accessing God is spoken about in different ways in Scripture. With Moses, for example, God said, “you cannot see my face, for no one may see me and live.” (Ex 33:20) And as Isaiah cried out when he saw God, “Woe is me! I am ruined! For I am a man of unclean lips… and my eyes have seen the King, the Lord Almighty.” (Is 6:5)

Christian patience: the gospel

It’s against this backdrop of us being cut off from infinite joy that the gospel shows us what Christian patience is all about. Because of Jesus the possibility of being with God in all his glory is once again brought within reach, so that anyone who wants it can have it. So, the greatest possible good we could hope for returns as something we can look forward to.

But we don’t get all of it right now, and this is where the difficulty comes in. When we turn to God our sin no longer alienates us from him, for sure, but we’re still people who find it easy to sin. As Paul says in his letter to the Romans,

So I find this law at work: Although I want to do good, evil is right there with me. For in my inner being I delight in God’s law; but I see another law at work in me, waging war against the law of my mind and making me a prisoner of the law of sin… What a wretched man I am! Who will rescue me from this body of death? (Rom 7:21-24)

As we are now, we’re caught in what we might call “the twilight of sin,” the time between when Christ first came — when he fixed our relationship with God — and when he will return again — when he will fix us and we will get to be with God. And it’s this second day — which James refers to as “the coming of the Lord” (Jas 5:7a, 8c) — that we are to look forward to.

It’s because we’re in this twilight that we need to show patience. Right now we are weak and still find it so easy to choose lesser goods over God. But, if we keep our composure, if we endure through these difficulties, then one day we will get to be with him.

Christian patience: our weakness

Now, maybe there’s a particular sin you’re struggling with at the moment, and which you keep lapsing back into. In this case, there are two ways to give up. Either (1) you’ll find a way to justify or ignore the sin, by convincing yourself it’s not really that bad or (2) you’ll distance yourself from God because you’ve failed him. In a way, these two responses are opposites of one another: the one says your failure is so big that God won’t want anything to do with you, and the other tries to underplay the failure so that it’s not really a failure in the end.

But please don’t give up! I know it’s difficult, but remember that this life and this difficulty are temporary, and that one day this burden will be lifted from you. Recognize sin as the failure it is, and remember that God’s love is big enough to overcome it! Hate your sin, and keep your eyes facing forward to the day it will be gone. As Paul reminds us, “He who calls you is faithful; he will surely do it.” (1 Thess 5:24) So be patient with yourself.

Christian patience: their weakness

But maybe it’s not your sin that you’re struggling with. As a community of people each weakened by sin in different ways, it’s inevitable that we’re going to fail each other sometimes. And as James says, we’ll be tempted to give up on one another, to grumble against each other. Either we’ll get angry at each other, or we’ll try avoid each other, or something in between, but it always results in more disunity than when we started.

When you’re tempted to give up on a fellow brother or sister the key thing to remember is this: the day that you look forward to — when your sin is removed and you are with God — is the same day that their sin is removed and they are with God. In other words, the day we long for is the day that we are all together in perfect unity. Now, if the day I look forward more than anything else involves me being with you in perfect unity, how could I not endure your failures now, and how could I not work for unity between us? Of course this doesn’t mean we shouldn’t correct each other, or rebuke each another, or things like that; what it means is that when we do these things that we should do them patiently.

Christian patience: the synthesis

Ultimately, if we are able to acknowledge our own sin without giving up on ourselves and if as a community we are able to bear with one another’s sins, then we will have created an environment in which we can help each other in our weakness. In the end this is part of the reason why God let’s us face these difficulties in the first place. As James says earlier in his letter,

Consider it pure joy, my brothers and sisters, whenever you face trials of many kinds, because you know that the testing of your faith produces perseverance. And let perseverance finish its work so that you may be mature and complete, not lacking anything. (Jas 1:2-4)

Christian patience: some perspective

As I close I want to ask a more general question. So far I’ve been speaking about how the gospel relates to patience in the Christian life: patience with ourselves in our struggle against sin, and patience with our fellow Christians in their struggles against sin. I focused on the Christian life because this is what the New Testament focuses on. But what about the everyday stuff, like when I get angry in traffic on my way to work, or when I get fed up with my parents or my children?

I think the gospel has something to say about these too, but with a difference. When it comes to our struggle with sin, we should never give up, because an infinite God is always worth enduring through a finite difficulty. But in everyday life many of the goods we look forward to are finite, and so giving up can sometimes be the right thing to do. For example, if at work we come up with a plan to meet a certain goal, but halfway through we realize it’s not worth it, then the right thing to do is to give up and try something else. So, however the gospel applies in these cases, it cannot be in the same way as it applies to the struggle with sin.

So, how does is apply? The thought that I keep coming back to is this: on a normal day small things like stubbing my toe easily irritate me. But if I was fighting in a war and I stubbed my toe, I doubt it would irritate me at all!

The point is that it’s all about perspective: we’re more prone to get impatient in cases we think are more important. But when we have an eye on the bigger picture, the struggles that once seemed so big tend to fall away.

This is where the gospel comes in: it says that the everyday things we see and do are not the whole story. That behind the scenes there’s a war going, between eternal life with God and eternal death without him. And that each of us are soldiers — of a kind — in this war. As Pauls says in his letter to the Ephesians,

Finally, be strong in the Lord and in the strength of his might. Put on the whole armor of God, that you may be able to stand against the schemes of the devil. For we do not wrestle against flesh and blood, but against the rulers, against the authorities, against the cosmic powers over this present darkness, against the spiritual forces of evil in the heavenly places. Therefore take up the whole armor of God, that you may be able to withstand in the evil day, and having done all, to stand firm. (Eph 6:10-13)

We would do well to remember all of this on our way to work tomorrow; when a driver in front of us forgets to indicate and we’re tempted to be impatient.

McTaggart and meta-time

There is what I take to be an error common among my fellow Thomists regarding change and certain theories of time. Put tersely, this error says that the B-theory of time is committed to the Parmenidian denial of change. I had decided to write something about it, but after doing a bit of research, it occurred to me that a form of this error goes all the way back to the start of the contemporary debate about the nature of time. That is to say, a variant of this error is present in John McTaggart’s paper The Unreality of Time. Before I can write about the error of my fellow Thomists, then, it seems appropriate to first say something about McTaggart’s mistake. And that is the aim of this post.

As the name suggests, McTaggart’s paper puts forward an argument that time is unreal. In the course of doing this he introduces a distinction that is now commonplace in philosophy of time, namely the distinction between the A-series and B-series:

For the sake of brevity I shall speak of the series of positions running from the far past through the near past to the present, and then from the present to the near future and the far future, as the A series. The series of positions which runs from earlier to later I shall call the B series. The contents of a position in time are called events. The contents of a single position are admitted to be properly called a plurality of events. (I believe, however, that they can as truly, though not moretruly, be called a single event. This view is not universally accepted, and it is not necessary for my argument.) A position in time is called a moment.

The A-series is indexed by tensed terms like past, present, and future. The B-series, by contrast, is indexed by tenseless terms like earlier than, and later than. Both of these series index the same time into a time series (or timeline), but they do so differently: in an A-series there is a privileged moment we call “present,” and other moments are called past or present through reference to this moment. In a B-series, by contrast, there is no such privilege and all moments are, in a sense, on an equal footing.

McTaggart divides the time series into “moments” and calls the things at these moments “events.” Now, we need to clarify something here, because it’s key to understanding McTaggart’s mistake. We typically think of events as existing in reality and persisting across moments, as when I wave my hand for a few seconds. And at least initially McTaggart seems to talk in terms of change of reality, which aligns well with this typical way of thinking. However, he quickly switches to talking about change of the time series itself, which is what leads him into all manner of strange places. What do I mean by this? Let’s say I waved my hand from 12 to 12:05 and then stopped. Did the event of my waving go out of existence? Surely it did once 12:05 came along. But what if I asked whether the event happening at 12:02 went out of existence? On a typical reading — in which reality is the thing that changes — the answer would be the same, since I’ve just reworded the same question. But if we read it in terms of the time series rather than reality, then the question becomes whether me-waving-at-12:02 went out of existence. Do you see the difference? We are no longer asking about the event that spanned 12:02 (together with some other moments), but rather the particular slice of the event at 12:02 (rather than the slices at other moments).

As I said, in the course of his discussion McTaggart switches from talking about the event to talking about slices of the event. The confusing thing is that he refers to the latter as the event too. This is something important to keep in mind as we proceed.

With this in hand, we can formulate McTaggart’s argument as follows:

  1. Change is essential to time.
  2. Change is impossible if the moments of time are ordered only by the B-series.
  3. Therefore, the moments of time are at least ordered by the A-series.
  4. Being ordered by the A-series involves a contradiction.
  5. Therefore, the reality of time involves a contradiction.
  6. Therefore, there is no reality of time.

The relevant points here are (2) and (4). In defending both of these points, McTaggart makes unmotivated (and strange) assumptions about the nature of change and the interpretation of his distinction between the A- and B-series.

In discussing (2), he starts off well enough but quickly makes the switch that was discussed above:

If, then, a B series without an A series can constitute time, change must be possible without an A series. Let us suppose that the distinction of past, present and future does not apply to reality. Can change apply to reality? What is it that changes?

Could we say that, in a time which formed a B series but not an A series, the change consisted in the fact that an event ceased to be an event, while another event began to be an event? If this were the case, we should certainly have got a change.

But this is impossible. An event can never cease to be an event. It can never get out of any time series in which it once is. If N is ever earlier than O and later than M, it will always be, and has always been, earlier than O and later than M, since the relations of earlier and later are permanent.

The question in the first paragraph is about the application of change to reality. But by the time we get to the second paragraph he’s switched to talking about events as slices of real events. He correctly notes that if the slice of the event ceased to exist or came into existence, then “we should certainly have got a change.” But he incorrectly assumes that this change would be of the reality he was talking about in the previous paragraph. That he’s thinking in terms of slices becomes very clear in the third paragraph, when he evaluates the suggestion in the second. He says, for instance, that “An event can never cease to be an event. It can never get out of any time series in which it once is.” Now for a normal event to go out of existence, all that is required is for it not to exist at a later time. As soon as we start talking about getting out of the time series, then we’ve moved to talking about slices of events rather than real events. And once we start talking about that, then we’ve moved away from talking about change in reality toward talking about change of the time series.[1]

So we have that McTaggart intends to account for change in reality by reference to change in the time series. But now we have a problem, for this account seems to really only push the question of change up a level: from reality to the time series. What, then, accounts for the change in the time series? If we were to apply McTaggart’s account again, then we would have to posit a meta-time series which tracks the change of the time series. Changes in the time series would be accounted for by reference to changes in this meta-time series. But now we have the same problem again, for which we’d need to posit a meta-meta-time. And so on. Eventually we’d need be led to an infinitely nested collection of times and meta-times, and we wouldn’t have gotten any closer to accounting for the change we started with. In other words, McTaggart’s account of change leads to a vicious infinite regress.

This conclusion comes up in the paper a number of times in different forms, but it’s not clear to me whether McTaggart realizes that they’re all instances of the same problem. In the present section he rejects the possibility of the time series changing in this way (“the relations of earlier and later are permanent”), and thereby rejects the adequacy of the B-series given his account of change. Indeed, the same conviction continues through his entire rejection of the B-series being able to account for change. Consider, for instance, the paragraphs that follow:

Or shall we say that one event M merges itself into another event N, while preserving a certain identity by means of an unchanged element, so that we can say, not merely that M has ceased and N begun, but that it is M which has become N? Still, the same difficulty recurs. M and N may have a common element, but they are not the same event, or there would be no change. If therefore M changes into N at a certain moment, then, at that moment, M has ceased to be M, and N has begun to be N. But we have seen that no event can cease to be, or begin to be, itself, since it never ceases to have a place as itself in the B series. Thus, one event cannot change into another.

Neither can the change be looked for in the numerically different moments of absolute time, supposing such moments to exist. For the same arguments will apply here. Each such moment would have its own place in the B series, since each would be earlier or later than each of the others. And as the B series indicate permanent relations, no moment could ever cease to be, nor could it become another moment.

This entire discussion is predicated on the confusion between the change of reality and the change of the time series. Needless to say I think his criticism of the adequacy of the B-series to track change misses the mark, and this becomes fairly clear once we fix up this confusion. All one needs for change is that things can have different properties at different times, and nothing about this requires that we talk about these times in terms of past, present, and future (that is, the A-series). If time t1 is earlier than time t2, and I have different properties at these times, then I have changed. The B-series, then, is more than capable to track change.

McTaggart continues with his confusion when moving to discuss the A-series:

Since, therefore, what occurs in time [event-slices] never begins or ceases to be, or to be itself, and since, again, if there is to be change it must be change of what occurs in time (for the timeless never changes), I submit that only one alternative remains. Changes must happen to the events of such a nature that the occurrence of these changes does not hinder the events from being events, and the same events, both before and after the change.

Now what characteristics of an event are there which can change and yet leave the event the same event? (I use the word characteristic as a general term to include both the qualities which the event possesses, and the relations of which it is a term — or rather the fact that the event is a term of these relations.) It seems to me that there is only one class of such characteristics — namely, the determination of the event in question by the terms of the A series.

Here he envisages what we might call a “spotlight” theory of time. The ordered events permanently exist in the time series, and the present moment has a temporal spotlight shining on it. This enables us to track the progression of time by following the progression of this spotlight. Dropping the metaphor, this means that each of the event slices has one of three properties: it is past, it is present, or it is future. Only one such event slice is present, everything earlier than it is past, and everything later than it is future. McTaggart is forced into this because (1) he assumes change of reality involves change of the time series, and (2) he is convinced from preceding argumentation that this change cannot consist in the creation or destruction of event slices in the time series. Thus, his proposal: moments remain permanent without being created or destroyed, and the march of time consists in them merely changing their properties.

But this A-series proposal, just like the B-series proposal above, requires that there be some kind of meta-time. What, after all, would track the changes of the time series represented by the spotlight moving along it? Or, without metaphor, what would track the changes of the time series that occur when the event slices change their properties?

After much discussion about this McTaggart realizes that the way he’s construed things entails that there will be an infinite regress of times and meta-times. We might summarize the process as follows: we sought to give an account of change, and so we proposed the spotlight account. But this requires that we postulate a meta-time to track the change of the spotlight. If our original proposal was correct, then in order to account for this meta-time we need to propose a meta-spotlight. But this will in turn require a meta-meta-time. And so on. So we have a vicious infinite regress on our hands.

As far as it goes this is a valid conclusion, and one McTaggart could have raised when discussing the B-series earlier had he seen the implicit dependence upon meta-time there. As we’ve already said, however, instead of taking this as a reason to reject his account of change (in terms of the change of the time series), he takes it to mean that neither the A-series nor the B-series can be real. And since these are exhaustive options for time, he concludes that time cannot be real.

In fact, the problem isn’t with either the A-series or the B-series. As we did earlier, we can frame the infinite regress argument directly against McTaggart’s account of change without ever mentioning either series.

To summarize, then, McTaggart’s mistake was in confusing change to reality with change to time. Once this error is corrected, neither the A-series nor the B-series precludes the possibility of change, since both can track things having different properties at different times. And neither series necessarily leads one into an infinite regress.

Notes

  1. Initially McTaggart raises it as a hypothetical (“Could we say that…?”), and so long as it remains option that might admit of alternatives there is no problem in his argument. The only caveat would be that he cannot conclude to the unreality of time if he limits himself to only one option among others. The problem is that this is exactly what he does conclude.

We don’t do God

In a dialogue with the late Christopher Hitchens, John Haldane outlines why he thinks religion is crucial as a foundational political principle in societies made up of diverse cultures, religions, etc. Very roughly his position is (1) that the governing of such a society must be built around certain core notions like the respect for others’ rights or the pursuit of their well-being, and (2) that religion gives us the best (indeed, he thinks the only) grounds for motivating such respect or such a pursuit.

Backing up slightly it would be helpful to give some account of what we mean by “religion” and therefore, by contrast, “secularism.” The way I’ve come to understand it — and the way I think Haldane understands it too — is as follows: religion involves adding an extra layer to a worldview that admits of some form of transcendent reality, such that we can act justly or unjustly toward this reality. Religious living, then, is acting justly towards this reality. I deliberately phrase this in general terms because not all religions think this reality is one, or personal, or omniscient, or eternal, or any of the other attributes of the God of classical theism. Nevertheless they all have some notion of just activity toward this reality, even if perhaps they wouldn’t phrase it in exactly those terms. Secularism, by contrast, denies either (a) that there is a reality transcendent of us or (b) that we can act justly or unjustly toward it. For the purposes of living, then, the secularist has no interest in such a reality, even if they intellectually accept that it exists.

With this in hand, return to points (1) and (2) I mentioned above. I won’t say much regarding (1), but I appreciate that Haldane draws attention to the fact that “neutral” governance is an unachievable pipe dream. The point has been made in various ways before, but essentially it boils down to the fact that any governing system is committed (implicitly or explicitly) to a conception of the good that guides the decisions and trade-offs they make in governing.

With regards to (2) Haldane’s proposal for a religious grounding is that humans are created as image-bearers of God, and so our respect of other’s or our pursuit for their well-being would flow from our honouring God as part of our proper religious activity toward him. To phrase this in somewhat Thomistic terms, our respect for others is a participation in our respect for God. Of course, while this proposal doesn’t require the religion of a theistic sort, it does require a transcendent reality of which we can coherently be called image-bearers of as well as that justice toward this reality involve some form of honour. So while this proposal is certainly broader than the Abrahamic religions, it doesn’t extend to all religions.

At this point two clarifications can be made. First, contrary to what Hitchens assumes, Haldane’s proposal is not inconsistent with evolution, since the notion of creation he’s interested in is much broader than some seven-day account of creation. While it doesn’t even seem essential to Haldane’s proposal that we be created (since the key is that we’re image-bearers), even if we assume it is the creation could equally have occurred through evolution. This is an unfortunately common conflation found in the New Atheists, and is completely besides the point.

Second, and more importantly, Haldane is not proposing some form of divine command theory as his grounds. This point actually comes up explicitly in the discussion itself, but I thought it worth bringing attention to. His point is not that we respect each other our of duty imposed upon us by a God found in the revelation of a specific religion. Rather it is that grounding the motivation for following principles we can all agree to — such as the golden rule, or the respect of inviolable rights — requires a religious basis, and probably something like the particular basis he proposes.

Given these clarifications, what are we to make of Haldane’s position? The structure of the discussion unfortunately did not enable him to develop it to any great length or nuance, but we can comment on the gist of it that he managed to outline. As I’ve said already, I think point (1) is spot on. Regarding point (2), however, I’m inclined to think that it’s possible to develop an account of common goods that enables us to give the secular grounds of which Haldane is so skeptical. I’ve discussed this in one form or another on this blog for nearly two years, now that I look back. So to some extent I disagree with Haldane, but this disagreement is not as severe as might first appear, as can be seen in three points.

First, while I think such a secular grounds can be given, these ground are built on top of the nuanced Aristotelian teleological account of the good which Aquinas ably showed entails the existence of a supreme intelligence.[1] The grounds are secular in that they can be understood apart from religious considerations, even if they entail religious conclusions.[2]

Second, it must be admitted that the secular account doesn’t preclude the religious account given by Haldane. The two act together, enriching each other in ways sometimes inaccessible to the other. For instance, there is an existential impact of seeing all humans as images of a beloved Father that is out of reach for a purely secular account.

Third, while I think secular grounds can be given I have no illusions about how difficult such grounds would be to comprehend, let alone actually motivate someone to follow through on them. The difficulty of giving such an account has been a recurring theme since the time of Plato.[3] And once we have developed an account of goods and virtues, the particular kind commonness relevant to the project, powers and how they extend to common powers, the relation of common to private goods, rational duties, authority, justice, and so on, it’s difficult to be struck by anything other than the complexity and abstractness of it all, even if it appears to us satisfactory as a piece of systematic philosophy. And realistically, how many people will have the interest or capability to inform themselves of such an account? A further existential point is that such a dry account is far less motivating than the affection and honour found in the religious life. Overall then, I think a secular ground can be given, but that it is far too distant and disconnected from everyday life for it to be socially valuable. Haldane’s religious proposal is much better suited to this job.

In closing I want to clarify that neither the discussion between Hitchens and Haldane nor this post, are meant as an argument for religion. Rather, they’re discussions about the social value of religion in a diverse society.

Notes

  1. I am referring, of course, to Aquinas’s Fifth Way. Perhaps one of the clearest expositions of this is Edward Feser’s Between Aristotle and William Paley: Aquinas’s Fifth Way in Nova et Vetera Vol. 11, No. 3. See also Haldane’s own defense in his contribution to Atheism and Theism.
  2. This is not unlike what is true of many arguments for God’s existence, which run from things like change, existence, contingency, grades of perfection, and so on.
  3. As Rob Koons and Matthew O’Brien say in their article on poltical animals, “In attending to social nature, the ethically minded metaphysician must avoid both the Scylla of atomistic individualism and the Charybdis of organic collectivism. The attempt to navigate successfully the narrow strait between them has been a recurring theme in Western metaphysics, from the time of Plato to the present.”

The real distinction

Whenever we have two concepts, A and B, we can ask to what extent the things they pick out in reality are distinct. If they pick out distinct realities, then we say that there is a real distinction between them. If they pick out the same reality, however, then we say that there is a real identity between them. Even if two concepts are really identical with one another we can still meaningfully talk about a distinction between them, and Thomists say this can happen in two ways.

A conceptual (or merely logical) distinction is when the two concepts pick out the same reality in every way, and the only distinction to be had is in the way we’re considering that reality. For instance, Superman and Clark Kent are conceptually distinct from one another. There’s nothing true of Superman that is not also true of Clark Kent, and vice versa. Another example is the distinction between a downhill and an uphill. These are the same thing considered from different perspectives.

A virtual distinction arises when the two concepts pick out the same reality, where this reality is understood with respect to two other really distinct things. In other words, A is virtually distinct from B when (1) they both pick out some reality Z, (2) A is Z understood with respect to some C and B is Z understood with respect to some D, (3) and C and D are really distinct from one another. We saw examples of this when discussing potential wholes recently, and we’ll repeat two of them here. First, faith is thinking with assent. Of itself, faith is a single action by a human, but it has an intellective aspect (thinking) and a volitional aspect (assenting) each of which involves the use of a different power (the intellect and will respectively). These aspects of faith, then, are virtually distinct from one another, since they are the same act considered with respect to distinct powers. Second, a water molecule arises from a single bond configuring two hydrogen atoms with one oxygen atom. Now, we can consider one of the hydrogen atoms being configured, and we can consider the oxygen atom being configured. These two concepts pick out the same reality, namely the configuration making up the water molecule. But each is this configuration considered with respect to distinct elements in the water molecule. As such, they are virtually distinct from one another.

These, then, are the two non-real distinctions, and in each case we could say when such a distinction occurs. Can we do the same thing for real distinctions? One common proposal is that two concepts are really distinct when the realities they pick out are separable, that is when one can exist without the other. Now, certainly separability is a sufficient condition for a real distinction, but is it a necessary condition? For Thomists the answer is no, since we think that a real distinction can occur between inseparable things. In cases where two things are inseparable, then, what is the condition that accounts for their real distinction?

I want to suggest that what we said about virtual distinctions can help us answer this. Looking at the three sub-conditions I listed for virtual distinctions, the second is critical and what links the other two. It is because being understood with respect to C does not exclude being understood with respect to D that there can be one reality picked out by the two concepts. If one of these relations did exclude the other, then the two concepts must pick out distinct realities, and therefore be really distinct. We’ll call this the exclusion condition to distinguish it from the separability condition.

Now, if the exclusion condition is to be of value to us it cannot apply in all and only those cases the separability condition applies. There are clearly cases where the two conditions coincide. To give a simple example, let A pick out me thinking something, and let B pick out me thinking the opposite. Assuming I’m not beset with doublethink, these two realities exclude one another. And they are certainly separable from one another. To find a case of exclusion without separability we need to look a bit harder. Perhaps the most famous (or infamous) example is the distinction between essence and existence in created beings. Aquinas argues that this is a real distinction, despite the two being inseparable from one another. His argument is fairly involved, so here we’ll just sketch enough for illustrative purposes.

Sherlock Holmes and I have a number of important things in common. We are both composites of form and matter, for instance, and we have similar sets of natural powers, even if he has some of these to a greater degree than I. The most salient point is that we share a common essence, on account of which we are both called human and by which we are distinguished from other kinds of substances. As far as I’m aware, however, I exist and he doesn’t. What this means is that our common essence itself cannot differentiate between an existing human and a non-existing human. Put another way, our essence of itself is indeterminate between existence and non-existence. I exist, then, because my essence has something else added to it which determines it to existence rather than non-existence. This something else is called esse in Latin, and is variously translated into English as “being” or “existence.”

All of this might sound like a convoluted way of saying what amounts to the tautology that I exist because I have existence. But such a complaint rides on an ambiguity. When I speak of a common essence shared by myself and Sherlock I do not have in mind some abstract universal that lies outside of each of us, but rather the particular feature found in each of us in virtue of which each of us fall under that universal in the first place. To illustrate the difference between these two consider the simple example of two groups of wood, each organised into a square shape. In this picture there is (1) the universal squareness which is instantiated twice, (2) the particular square organisation which is in the first group, and (3) the particular square organisation which is in the second group. It is in virtue of each of the groups having the organisation in itself that it can fall under the universal in the first place. So too with the common essence shared by Sherlock and myself.

Just as my essence is in me, so too its determination to existence is in me. It is because my essence is determined by esse and Sherlock’s is not that I exist and he doesn’t. So, then, our earlier conclusion really amounts to the non-tautologous claim that a certain fact about me (that I exist) is true in virtue of some feature in me (my esse).

Now, the argument I ran with myself and Sherlock can be applied to any being, so that all beings exist in virtue of esse within them. Esse, therefore, accounts for the similarity between all existing beings insofar as they exist, which is to say it unifies all existing beings qua existing. Essence, on the other hand, diversifies and differentiates these beings from one another, by qualifying their existence in different ways. For instance, two beings A and B are similar to each other in that they both have esse and thereby exist, but differ from one another in that A’s essence makes him an existing human whereas B’s essence makes him an existing angel. The essences of material beings additionally requires that their existence be qualified to a place and time, which allows multiple beings of the same species to exist.

Since esse unifies and essence diversifies, it follows that these two concepts exclude one another. And since a being can’t exist without its essence and esse these two are also inseparable from one another. So we have an example of a real distinction on the basis of exclusion without separability.

Before we close, we must introduce an important nuance. Strictly speaking, all that is needed for A to be a distinctly existing being from B is for A’s essence to qualify its existence in a way that B’s does not. Notice, however, that this leaves open two options regarding B’s essence: either it qualifies B’s existence in a way A’s essence does not, or it doesn’t qualify B’s existence at all. In the latter case, B’s essence would do nothing to exclude it from being really identical with B’s esse. Nevertheless, it is clear from the foregoing that at most one being can have unqualified existence, and so in all other beings there will be the real distinction between essence and esse we’ve been talking about.

Essentially ordered series

The notion of a series, or chain or regress, comes up a number of times in philosophical discussions. In this post, we’re going formalize the notion in general, and then turn our attention to essentially ordered series in particular.

Intuitively, a series is when we start with some member and from there we trace through the other members one at a time, possibly indefinitely. The order in which we trace or discover the members in the series can be (and often is) the inverse of their order in reality. This happens with causal chains, for instance, when we start with some effect A, which is caused by some B, which in turn is caused by some C, and so on. Here, tracing up the series — as we just did — involves tracing backward through the causes. In other words, later members in the tracing correspond to earlier causes in reality. The relevance of this point will become evident shortly.

Technically we could drop the requirement that a series has a starting point, allowing it to be infinitely extended in both directions. But for our purposes here this would just clutter the notation unnecessarily, so we’ll keep the requirement for the sake of clarity. Nevertheless, the central result of this post does not hinge on this requirement.

Formalism of series

More formally, a series (or chain, or regress) is a structure S = (S, I, <, α) where:

S1.
S is a set of members and I is a set of indices,
S2.
α:I→S is a map from indices to members,
S3.
< is a strict total order on I,
S4.
For each i∈I, if the subset of all indices greater than i is non-empty, then it has least element,
S5.
I has a least element, written 1.

In (S1) we separate S and I, the members and the indices, because in general the same member might appear multiple times within the series. In (S2) α connects the two and captures repetition in the series when two distinct indices map to the same member.

(S3) and (S4) tell us that the indices form a sequence. (S3) guarantees that for any distinct i and j, either si < sj or si > sj, and (S4) guarantees that for each index except the last has an index immediately after it, which we can label i+1. (S5), which is technically optional, allows us to write this sequence starting with a first member as (1, 2, 3, 4, …).

Using the connector between the members and the indices, we can move from the index sequence to the index member sequence, and from there to the indexed member series. Why we do this in two steps will become clear shortly. For any i∈I, the indexed member si is the member of S which is given by α(i). Both the sequence and series of indexed members have these members in them, but they differ in how they order these members. To avoid confusion, we will write the members of the sequence using asterisks (like si*) and leave the non-asterisks version for the members of the series (like si). The sequence of indexed members is ordered just as the indices are, so that si* < sj* if and only if i < j. We write this sequence with the usual mathematical notation as (sn) = (s1*, s2*, s3*, …). The series is indexed in the same way as the sequence, but with the order of the indexed members is inverted, so that si > sj if and only if i < j. We write the series using the notation (→sn) = (… → s3 → s2 → s1).

The upshot of all of this is that as we proceed forward through the sequence of indices, we proceed backward through the series of indexed members. This corresponds to our earlier comment about how the order we typically discover the members of a series is the inverse of the order these members have in reality. The sequence of indexed members is of technical interest to us as the mathematical foundation of our formalism, but for the purposes of further discussion, we will restrict ourselves to the series, as it more closely corresponds to common language about series in general. Thus, the above structure S we defined above primarily refers to the series of indexed members (→sn) with the order given by the inverse of the order of indices.

I admit that all of this is quite abstract, and so before continuing, we’ll consider some examples. As mentioned before, a familiar class of examples is causal chains. These start with some final effect (s1), and trace backward to its cause (s2,), and then to the cause of that cause (s3), and so on. For instance, consider the causal chain of me moving my arm, which in turn moves a stick, which in turn moves a stone. We would write this series as (me → arm → stick → stone). Similarly, we could we depict the series of the successive begetting of sons as (… → grandfather → father → me → son → grandson).

But causal chains are not the only kinds of series. Say we define word1 in terms of word2, word2 in terms of word3, and so on. This would give us a series of definitions (→wordn) = (… → word3 → word2 → word1). And, as we saw in a previous discussion, some good1 might be desirable as a means to some other good2, where this good2 is itself desirable as a means to some other good3, and so on. This would give us a series of desires ordered from means to ends, (→goodn) = (… → good3 → good2 → good1). Let’s say we took members from the moving chain above and ordered them as a desiring series: I desire to move my arm, as a means to moving the stick, as a means to moving the stone. This desiring series would then be written as (stone → stick → arm), which has the members in the opposite order from a causal chain.[1]

Each example so far is a series where earlier members depend on later members. Call such a series a “dependent series.” We’ll return to these below, but for now, we note that not every series is a dependent series. Imagine, for instance, we had three lights of different colors (red, blue, and green), such that only one light is on at a time, and where the light that’s on switches randomly and endlessly. The series of switched-on lights up until some time might then be something like (… → red → green → blue → blue → red).

Two final points on notation before we proceed. First, sometimes it will be helpful to talk about sub-series, which are taken from a series by excluding some of the later members. So, the sub-series as (→sn)n>i consists of all the indexed members of (→sn) that come before s(remember that the order of the indices is the inverse of the order of the indexed members in the series). Unsurprisingly, we write this as (→sn)n>i = (… → sn-3 → sn-2 → sn-1). Second, in the interest of not cluttering everything with brackets, we say that entailments have the lowest precedence of all logical operations, so that a statement like A ∧ B ⇒ C ∨ D is the same as a statement like (A ∧ B) ⇒ (C ∨ D).

Active series

For any series or member thereof, we can talk about its activity, in the sense of whether it is active or not. What it means to be active is determined by the series we’re considering: to be moving, to be begotten, to be defined, to be desired, or to be on are what it means to be active in each of our examples above respectively. The notion of activity enables us to distinguish genuine series from merely putative ones, and compare them within the same formalism. To see what I mean, consider the moving stone example again. Let’s say the stone is moving and there are two putative series that could be causing this: me moving it with a stick, and you kicking the stone with your foot. These would be depicted as (me → arm → stick → stone) and (you → foot → stone) respectively. Both series are putative because each would account for the movement of the stone if it were active. Nevertheless, only the one which is active actually accounts for the movement of the stone.

We encode the activity of a member with a predicate β, which is true of a member if and only if that member is active. The necessary and sufficient conditions for β will depend on the kind of series we’re considering, and sometimes we will be able to give an explicit formulation of it. Nevertheless, it is safe to say that a series is itself active only if it is non-empty and each of its members are active, so that:

AS.
β(S) ⇒ S ≠ ∅ ∧ (∀siS) β(si),

As an illustrative example, consider again the lights from earlier. Imagine we had three putative series for which lights went on in which order: (green → blue → red), (red → blue → red), and (blue → red). Now assume the lights went on in the order specified by the first of these. In this case, both the first and third series are active, but the second series is inactive because it has an inactive member.

Dependent series

Now, we want to focus specifically on dependent series. In such series, the activity of later members depends on the activity of earlier members. More formally, si depends on sj if and only if β(sj) factors into the conditions of β(si). We’ll call the inverse of dependence acting: an earlier member acts on a later member if and only if the latter being active depends on the former being active.

Before we continue we need to make a technical note about how the series and its members are being considered. A series is always considered in terms of an order given by a particular activity (and dependence) on the members themselves. Take the example of me moving the stone with the stick with my arm. When we write this as (me → arm → stick → stone) it must be understood that we are considering me, my arm, the stick, and the stone in terms of the movement only. This series is not meant as a universal description of dependence between the members, but just dependence with respect to a particular instance of movement. So, in the present series “me → arm” just means that on account of some activity within me I am imparting movement on to my arm; it says nothing about other ways my arm may or may not depend on me.

Essentially ordered series

The particular kind of dependent series we’re interested in here are essentially ordered series, in which the kind of dependence in view is derivation. A member in such a series is called derivative if it derives its activity from the previous member in the series: it is not active of itself, but rather it is active only insofar as the previous member is active. Or, put another way, a derivative member continues to be active only so long as the previous member continues to act on it. A non-derivative member, by contrast, does not need another to be active but is active of itself — it has underived activity.

The moving example from earlier is an essentially ordered series: the movement originates with me as the non-derivative member, and propagates through the derivative members (my arm, the stick, and the stone), each of which moves something only insofar as it is moved by something else. Something similar can be said for the defining series and the desiring series, each of which is also essentially ordered.

Traditionally essentially ordered series have been contrasted with accidentally ordered series, in which a member depends on later members for becoming active but not for continuing to be active. The begetting series from earlier is accidentally ordered: me begetting my son does not depend on my father simultaneously begetting me.

Now, because in essentially ordered series the dependence in view is derivation, defining β is — at least partially — a fairly straightforward matter. To start, let η be a predicate which is true of a member if and only if that member is active of itself. So η(s) if and only if s is a non-derivative member. Using this we can explicitly give some necessary conditions of β:

ES.
β(si) ⇒ η(si) ∨ β((→sn)n>i).

This formulation captures both the non-derivative and derivative cases. Non-derivative members are active of themselves and so can be active irrespective of the activity of the chain leading up to them. Derivative members, by contrast, are not active of themselves but by another, and so will only be active if the chain leading up to them is active.

From (ES), we see that the following holds for essentially ordered series:

β(S)
⇒ β(s1)
⇒ η(s1) ∨ β(s2)
⇒ η(s1) ∨ η(s2) ∨ β(s3)
⇒ …
⇒ η(s1) ∨ η(s2) ∨ η(s3) ∨ ….

Given that a disjunction is true only if one of its disjuncts is true, it follows that any active essentially ordered series must include a non-derivative member:

EN.
β(S) ⇒ (∃n∈S) η(n).

From (AS) and (EN) it follows fairly straightforwardly that in an active essentially ordered series, every derivative member is preceded by some non-derivative member:

ENP.
β(S) ⇒ (∀s∈S) (∃n∈S) η(n) ∧ n ≤ s.

Now, because non-derivative members are active regardless of the activity of the members before them, it follows that they do not depend on any members before them. And because essentially ordered series are a species of dependent series, we can say that if a member is non-derivative, then there are no members before it. We’ll call this the non-derivative independence of essentially ordered series, and formulate it as follows:

ENI.
η(n) ⇒ (∀s∈S) n ≤ s.

Together, (ENP) and (ENI) entail that any active essentially ordered series will have a first member which is non-derivative, which we call the primary member. We call this the primacy principle and formulate it as follows:

PP.
β(S) ⇒ (∃p∈S) (∀s∈S) η(p) ∧ p ≤ s.

This is the central result of this post.

Questions and objections

This property of essentially ordered series — that they must include a primary member — can and has been leveraged in a number of ways. It is perhaps most well-known for its controversial usage in first cause cosmological arguments arising from the Aristotelian tradition. We’ve seen previously how Aristotle uses it when arguing for the existence of chief goods. It is also the formal reason behind the intuition that circular definitions are vacuous. For the remainder of this post, we will address various questions and objections that might be raised, first two shorter ones and then two longer ones.

First, some will be quick to point out that what we’ve said here doesn’t prove that God exists. And this is true: the result given here is very general, and any successful argument for God’s existence would need additional premises to reach that conclusion.

Second, some might wonder if our use of infinite disjunctions is problematic. While infinitary logic can be tricky in some cases, our use of it here is fairly straightforward: all it requires is that a disjunction of falsehoods is itself false. As such, I see nothing objectionable in our use of it here.

Third, astute readers will notice that we have not shown, namely that every active essentially ordered series must be finite. This is noteworthy because it is at odds with traditional treatments of such series. For example, in his Nicomachean Ethics Aristotle argues for a chief good by denying an infinite regress of essentially ordered goods:

If, then, there is some end of the things we do, which we desire for its own sake (everything else being desired for the sake of this), and if we do not choose everything for the sake of something else (for at that rate the process would go on to infinity, so that our desire would be empty and vain), clearly this must be the good and the chief good. (NE, emphasis mine)

And in his Summa Contra Gentiles Aquinas argues for the prime mover by arguing against an infinite regress of essentially ordered movers:

In an ordinate series of movers and things moved, where namely throughout the series one is moved by the other, we must needs find that if the first mover be taken away or cease to move, none of the others will move or be moved: because the first is the cause of movement in all the others. Now if an ordinate series of movers and things moved proceed to infinity, there will be no first mover, but all will be intermediate movers as it were. Therefore it will be impossible for any of them to be moved: and thus nothing in the world will be moved. (SCG 13.14, emphasis mine)

Our result in (PP), however, is perfectly consistent with the series being infinite: all we need is for it to have a first member. This, for instance, is satisfied by the following series:

ω+n → … → ω+3 → ω+2 → ω+1 → ω → … → 3 → 2 → 1

where ω is the first ordinal infinity and n is some finite number. The question, then, is what the present result entails about the validity of the traditional treatments.

On the one hand, the key property leveraged by thinkers like Aristotle and Aquinas is not that there are finitely many members, but rather that there is a primary non-derivative member. Now it’s possible that they conflated the question of finitude with the question of primacy, but it’s also possible that they merely used the language of infinite regress to pick out the case where there is no such primary member — something we might more accurately call a vicious infinite regress. Either way in the worst case they were slightly mistaken about why a primary member is needed, but they were not mistaken that it is needed.

On the other hand, in the kinds of essentially ordered series Aristotle and Aquinas were considering, it is a corollary of (PP) that there are finitely many members in the series. In general, (S4) guarantees that every member in the series (except the first) has a previous member, but it does not guarantee that every member in the series (except the last) has a next member. It’s precisely because of this that there can be series with beginning and end, but with infinitely many members in between. However, if a series is such that every member (except the last) has a next member, then given (PP) that series will also be finite.[2] Now, each series discussed by Aristotle and Aquinas have this second property. And so they are somewhat justified in talking as they do.

Finally, we might wonder why it is not sufficient to have a chain of infinitely many active derivative members, where each is made active by the one before it.[3] After all, if the chain were finite we could pinpoint one derivative member not made active by a previous member. But in an infinite chain, it can be the case that each member is made active by the previous.

Now, behind this objection lies the unfortunately common confusion between a series considered as a part and a series considered as a whole. When we consider a series as a whole we’re considering it as if it is all there is, so far as the series is concerned. For a series considered as a whole to be active, then, it must contain within itself the necessary resources to account for its members being active. By contrast, for a series considered as a part to be active, it need only be part of a series which, considered as a whole, is active. To illustrate this, imagine we see a stone moving, then realize it’s being moved by a moving stick, and stop there. In this case, we’d be considering the two member series (stick → stone), where both members happen to be active. The series is active, but not when considered as a whole, since it needs additional members (like my arm, and me) to be able to account for the motion of its members.

Given this distinction the central question is what the conditions are for a series, considered as a whole, to be active.[4] Naturally, the answer will depend on the kind of series we’re considering, but merely pointing to a series in which all members are active is not enough to show that such a series considered as a whole can be active — as the previous example illustrates. What we need is an account of the distinctive characteristics of such a series, and a derivation from these what the conditions for activity are when such a series is considered as a whole.

Now, as we’ve seen the distinctive characteristic of essentially ordered series rests on the distinction between derivative and non-derivative members. Derivative members are only conditionally active, whereas non-derivative members are unconditionally active. Derivative members propagate the activity of earlier members, whereas non-derivative members originate the activity. The result encoded in (EPP) is that no members have their conditions actually met if all members are only conditionally active. Again, it’s that no member can propagate without some member originating. The point is not about the number of members, but about their kind. It doesn’t matter whether you have finitely or infinitely many pipes in a row, for instance, they will not propagate any water unless something originates the water. It doesn’t matter how many sticks you have, they will not move the stone unless something originates the movement.[5]

In short, then, the mistake of the objection is that it confuses the activity of an infinite series considered as a part, with the activity of an infinite series considered as a whole. The example does not contradict the present result because the objector has given us no reason for thinking the series in question is active when considered as a whole.

Update

This page was significantly rewritten on 26 Aug 2017. The notation for series was made easier to follow, by distinguishing the sequence from the series so that the latter could follow the order of the series in reality. I also reordered the conclusions and formulated more in symbolic terms.

Notes

  1. Well, an efficient causal chain. The chain here is, in Scholastic nomenclature, a final causal chain.
  2. We leave the proof of this as an exercise to the reader.
  3. This objection is inspired by Paul Edwards’ famous objection to first cause arguments for God’s existence.
  4. From a formalization perspective, this means that our formalism of series considered as wholes can include the answer if done correctly. Indeed, this is why we introduced the active/non-active distinction so that we can “step outside” and analyze the differences.
  5. To be sure, there is a difference between finite and infinite cases, in that a finite non-active series there will always be a first non-active member. This will sometimes happen in the infinite cases, as we saw above with our ω+n example, but not always. This difference, however, does not entail that infinite series can be active without non-derivative members.

Faith and hope

Our goal here is to unpack the notion of faith so as to overcome confusions in modern thinking on the topic. Lacking a good understanding of the notion actively prevents many people, both Christian and non-Christian, from understanding Scripture. In this post, we will begin an account of faith and give examples from Scripture and everyday life where applicable.

Faith involves thinking

Sometimes, especially in Christian circles, you’ll here that faith is “trust.” This is a good start insofar as (1) our thinking about trust is less confused than our thinking about faith, and (2) it highlights the fact that faith can be both in a person as well as a fact. But it’s just a start, for to give a synonym is not to give an analysis.

Others, who are less charitable to religion, would have us believe that faith is “belief in spite of or contrary to the evidence.” Indeed, this is how Richard Dawkins defines it in his book The God Delusion and how Peter Boghossian defines it in his book A Manual for Creating Atheists. In the TV series Bones, the protagonist defines faith as “irrational belief in a logical impossibility.” Similarly, Bill O’Reilly once gave the advice to “base your opinions on faith when it comes to religious matters, and facts when it comes to secular matters.”

None of this, however, captures how Scripture uses the term or how we tend to use it when we don’t have some theological ax to grind. But it’s difficult to be completely wrong about something, and this “analysis” is no exception. While it’s wrong to say that faith need be contrary to evidence, it does seem that once we achieve “the certitude of sight” we cease to have faith.

This leads us to the realization that faith involves thinking, by which we mean a confidence in something that does not reach complete certitude. Thinking something to be true is to think it more likely true than its negation. Most or all of life involves thinking in this sense of the word. And this fits well with Hebrews 11:1 which says that “faith is the assurance of things hoped for, the conviction of things not seen.” Aquinas gives the following definition of thinking:

[Thinking] is more strictly taken for that consideration of the intellect, which is accompanied by some kind of inquiry, and which precedes the intellect’s arrival at the stage of perfection that comes with the certitude of sight. (ST II-II Q2 A1 corp)

Thinking well involves matching ones confidence in something in accordance with what the evidence allows. To be more confident than what the evidence allows is overconfidence, and to be less confident is to be unduly skeptical.

Faith is thinking with assent

But faith must be more than mere thinking. I don’t mean by this that faith involves overconfidence, but rather that faith has an extra dimension to it. I do not have faith in someone if I think they’re dangerous or evil. This is because faith is made up of both thinking and desiring. But it is not enough that the thing thought and the thing desired merely coincide with one another: if I think a chair is tall and desire the blueness of the chair, for instance, I do not thereby have faith in the chair. Rather, for faith to occur we need the thinking and the desiring to be essentially linked in a single act. In other words, faith occurs when our thinking and desiring are about the same thing, as when I want a sturdy chair and think this chair is sturdy. We say, then, that faith is thinking with assent.

Assent is a bit of a tricky word. It picks out the “mood” of the thinking, which in this context just means that the content of the thinking involves something desirable or wanted. And since we desire all and only what seems good to us, we might equally say that the thinking involves something that seems good to us.

Let’s consider some examples from everyday life. We have faith in a chair insofar as we think it will hold us up and we desire it to do so. We have faith in our spouse insofar as we think they will not cheat on us and desire that they do not do so. We have faith in someone’s word insofar as we think they will be true to it and desire them to be so. In the Chronicles of Narnia, the children had faith in Aslan insofar as they thought him powerful and saw this as a good thing.

It might be informative to compare faith to its contraries. Since faith has two elements, we have two axes to explore. On the axis of thought, we have thinking, uncertainty, and doubt. Thinking is as we defined above, uncertainty is being unsure either way, and doubt is thinking something is not the case. On the axis of desire, we have assent, quiescence, and dissent. Assent involves desiring, quiescence is indifference with respect to desire, and dissent is desiring something not be the case.

Dread, then, is thinking with dissent: we dread something we think will happen but don’t want to happen. Wishful thinking is a term used for doubting with assent or uncertainty with assent: when we want something we don’t think will happen, we have wishful thinking. Commonly hope is also used this way, but I don’t think this the primary sense of the word (more on that below). Fear is uncertainty with dissent: when something we take to be bad might or might not happen we fear it. Doubting with dissent is the other side of faith: you have faith in A then you doubt with dissent that not-A. Unfortunately, we do not have a word for this in English, so we’ll just a question mark in its place.

doubt uncertainty thinking
dissent ? fear dread
quiescence mere doubt mere uncertainty mere thinking
assent wishful thinking wishful thinking faith

When you know someone is powerful, but are unsure whether they are good, you fear them. When you don’t study for an exam but want to have done well, that’s wishful thinking. An example of two of these working out in Scripture comes in the calming of the storm:

On that day, when evening had come, he said to them, “Let us go across to the other side.” And leaving the crowd, they took him with them in the boat, just as he was. And other boats were with him. And a great windstorm arose, and the waves were breaking into the boat, so that the boat was already filling. But he was in the stern, asleep on the cushion. And they woke him and said to him, “Teacher, do you not care that we are perishing?” And he awoke and rebuked the wind and said to the sea, “Peace! Be still!” And the wind ceased, and there was a great calm. He said to them, “Why are you so afraid? Have you still no faith?” And they were filled with great fear and said to one another, “Who then is this, that even the wind and the sea obey him?” (Mark 4:35-41)

After seeing Jesus’ power, the disciples fail to have faith in him and instead fear him. They can see that he is powerful, but they are uncertain whether he is good powerful or bad powerful. This is ultimately rooted in their failure to understand what it means to be the Christ in its entirety. Compare this with the father’s response to Jesus later in the gospel:

Jesus asked the boy’s father, “How long has he been like this?”

“From childhood,” he answered. “It has often thrown him into fire or water to kill him. But if you can do anything, take pity on us and help us.”

“‘If you can’?” said Jesus. “Everything is possible for one who believes.”

Immediately the boy’s father exclaimed, “I do believe; help me overcome my unbelief!” (Mark 9:21-24)

Here the father thinks Jesus is good but doubts his power. His problem isn’t fear, but wishful thinking.

Faith and hope

So much for faith, what about hope? We can have faith in things, facts, and outcomes, but when Scripture talks about faith in a future outcome it calls it hope. “Expectation” is thinking that a future outcome will occur, and so hope is expectation with assent. In other words, hope is looking forward to an outcome we see as good or desirable.

Does faith come before hope, or does hope come before faith? It turns out the question is misplaced: neither comes first, but both can reinforce the other. Faith and hope are in the same thing (that is, they have the same object); the difference between them arises in us when we consider our relation to that thing in different ways. Take the example of the chair again. I have faith in the chair’s ability to hold me up, and I have hope that in a few seconds it will hold me up when I sit down on it. The object of my faith and my hope here are the same: the chair’s strength. The difference between faith and hope lies is in how I consider this object: either in itself (faith) or in its future outworking (hope).

The upshot of all of this is that in addition to the faith and hope there is some third thing — the object — and strictly speaking neither faith nor hope comes first, but both flow from this object. Nevertheless, it sometimes happens that we first place our faith or hope in something, and only later realize that the other follows from this. Because of this, there is a sense in which either can follow from the other, so that the two can mutually reinforce one another.

The close interplay between faith and hope is visible in Abraham’s story in Genesis. In chapters 12-17 God repeatedly promises Abraham that he will have many descendants who will be in right relationship with God, and who will be a blessing to the nations of the world. Then in chapter 21, Isaac is born and God promises that “through Isaac shall your offspring be named.” Then in chapter 22 God tells Abraham to sacrifice Isaac. Have you ever wondered why Abraham is praised for his actions here? It’s not because it’s good to kill children, or because God can somehow make murder good. Rather, as Eleonore Stump explains, it’s because Abraham has faith in God and hope in his promises to make Isaac a great nation even if he killed Isaac. Abraham obviously didn’t know how God would do that, but he’d been shown in the past that God was powerful and able to work beyond the limitations of humans. What he was doing here was holding on to God’s power and goodness:

No unbelief made him waver concerning the promise of God, but he grew strong in his faith as he gave glory to God, fully convinced that God was able to do what he had promised. That is why his faith was “counted to him as righteousness.” (Romans 4:20-22)

We see hope and faith reinforcing each other throughout Abraham’s interactions with God. Initially, the promise is given, which leads to hope which in turn leads to faith, and God repeats the promises a few times. But God also shows himself as someone capable of doing more than what Abraham could have physically imagined, which reinforces Abraham’s faith in him, resulting in more hope.

Conclusion

We’ve briefly discussed faith and hope quite generally, and used some passages from Scripture for illustrative examples. Later, in a follow up to our earlier post on grace, we will spell out the object of Christian faith in detail.