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 a particular incline that is understood as either a downhill or an uphill. These are the same thing considered from different perspectives.

A virtual distinction arises when the two concepts pick out the same reality, but where this reality is understood with respect to two other really distinct things. In other words, we say that A is virtually distinct from B when (1) both A and B 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, and (3) C and D are really distinct from one another.

We saw some examples of virtual distinctions 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, 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 two aspects of faith, then, are virtually distinct from one another, because they are the same act understood 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 the configuration of one of the hydrogen atoms, and we can consider the configuration of the oxygen atom. These two concepts pick out the same underlying reality — the configuration making up the whole water molecule — but do so with respect to distinct elements of 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 develop this into a formalization of 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.

To give this a formal notation, we can write a series as S = (→sn) = (… → s3 → s2 → s1), where the index of each member represents the order of our tracing backward through the members, while the order of the members represents the order of reality. Thus, because s1 has the first index it is the first of in tracing, but because it is the last member it is the last in reality.

Technically we could drop the requirement that a series has a last member, 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.

Mathematical underpinnings of our notation

Note: if you’d rather not read a bunch of maths, and are happy with our above notation, then you’re welcome to skip this section.

We can give our series notation a mathematical underpinning by analyzing it in terms of a well-known mathematical structure: a sequence. The idea is simple: start with the sequence of indices (which represent our tracing backward up the series), match them up to members in the series, and then give those indexed members the reverse order to that of the indices. More formally, a series (or chain, or regress) is a structure S = (S, I, <, σ) where:

S1.
S is a non-empty set of members and I is a non-empty set of indices,
S2.
σ: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 (the members) and I (the indices) because, in general, the same member might appear multiple times within the series.

In (S2) the map σ connects the two sets 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 indices i and j, either i < j or i > j, and (S4) guarantees that 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 (in) = (1, 2, 3, 4, …).

Using the map σ, we can move from this sequence of indices to a series of indexed members, which are the true members of the series. For each i∈I, we have the indexed member si = (σ(i), i). They’re called indexed members because they’re members with an index attached. How do we order these indexed members? In order to get what we had earlier, we need the indexed members to be in the opposite order of their indices. So, if i and j are distinct indices with i < j, then their two corresponding indexed members will be si and sj respectively, with si > sj. Given that the starting order on I was a strict order, there is no problem with inverting it into a strict order on the indexed members, and so we can safely write our series with the above notation of S = (→sn) = (… → s3 → s2 → s1).

So, the members of the series S are the indexed members ordered inversely to their indices. So, s1 is the last member in the series. Notationally, we will refer to the series with either a bold-face S or the arrowed (→sn), depending on which is easier to read at the time. These two notations are interchangeable.

Some examples

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 backwards 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).

Some notes

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>i = (→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 α, which is true of a member if and only if that member is active. The necessary and sufficient conditions for α 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 each of its members is active, so that:

AS.
α(S) ⇒ (∀siS) α(si),

As an illustrative example, consider 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 would be active, but the second series would be inactive because it would have 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 α(sj) factors into the conditions of α(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 is called essentially ordered. In such a series, we distinguish between two types of members. A derivative member is not active of itself, but 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. An essentially ordered series is a dependent series because deriving activity from something is one way of depending upon it.

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 later members depend on earlier 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, the fact that in essentially ordered series the dependence in view is derivativeness, makes it relatively straightforward to give a necessary condition for the predicate α. Let η be a predicate which is true of a member if and only if that member is active of itself, so that η(s) if and only if s is a non-derivative member. Then we can explicitly give the following necessary condition of α:

ES.
α(si) ⇒ η(si) ∨ α(Sn>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:

α(S)
⇒ α(s1)
⇒ η(s1) ∨ α(s2)
⇒ η(s1) ∨ η(s2) ∨ α(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.
α(S) ⇒ (∃u∈S) η(u).

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.
α(S) ⇒ (∀s∈S) (∃u∈S) η(u) ∧ u ≤ 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(u) ⇒ (∀s∈S) u ≤ 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.
α(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 means for 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 the (PP) 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.

Updates

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.

On 15-16 Dec 2017 I reworked the introduction and order of formalizations, so that the maths section is now optional. I also changed the Greek letters used to be closer to their English counterparts (sigma for the map into the series, and alpha for the active predicate).

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/inactive 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 inactive series there will always be a first inactive 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.

The threefold whole

In his Metaphysics Δ Aristotle says there are two senses of the term “whole”:

Whole means that from which none of the things of which it is said to consist by nature are missing; and that which contains the things contained in such a way that they form one thing.

The first sense corresponds to our usage of the word when we say things like, “he managed to eat the whole sandwich” and “she read the whole book in one day.” The second sense corresponds to what we refer to when we speak of general part-whole relations, for instance when we say that my arms and legs are part of my body. This second sense is what we’re interested in here. Aristotle further divides this into two kinds:

But this occurs in two ways: either inasmuch as each is the one in question, or inasmuch as one thing is constituted of them.

These are two very different kinds of whole. The second kind is perhaps the one we’re most familiar with: bodies are constituted by organs, tables are constituted by legs and tops, computers are constituted by transistors and other electronics. This kind is referred to as integral, so that integral wholes are constituted by integral parts. We might not think to talk about the first kind as a whole, but it does fit one sense of the general definition. It’s a whole in the sense that a universal applies to (and thereby “contains”) all the particulars that instantiate it: humanness contains all individual humans, treeness contains all individual trees, and so on. This kind is referred to as universal, so that universal wholes apply to universal parts.

Aristotle construes the difference between these two kinds of whole in terms of how the parts are made “one” in different senses. Integral parts come together to form one individual which we call the whole. We refer to this as numerical unity. Universal parts are each themselves an individual which instantiate a common universal. We refer to this as specific unity.

Later the Scholastics discovered a third kind, which they called potential. How potential relates to integral and universal depends on how you analyse the differences between the kinds. Aquinas, for instance, analysed them in terms of the presence of a whole in its parts, which in turn correlates to how truly the whole can be predicated of its parts. This led him to placing the potential as midway between the integral and universal:

… the universal whole is in each part according to its entire essence and power; as animal in a man and in a horse; and therefore it is properly predicated of each part. But the integral whole is not in each part, neither according to its whole essence, nor according to its whole power. Therefore in no way can it be predicated of each part; yet in a way it is predicated, though improperly, of all the parts together; as if we were to say that the wall, roof, and foundations are a house. But the potential whole is in each part according to its whole essence, not, however, according to its whole power. Therefore in a way it can be predicated of each part, but not so properly as the universal whole. (ST I, Q77, A1, ad1)

Intrinsicality

My preferred analysis is in terms of the intrinsicality of the potency and act by which the parts of a whole are distinguished and unified respectively. For the remainder of this post we will unpack this, and reflect on how the different kinds relate to one another on this account.

Now, any material being is a mixture act and potency (or, equivalently, actualities and potentials). By this we mean that it has capacities for various states or behaviours, some of which are realised. We call these capacities potentials, and insofar as a potential is realised we call it an actuality or an actualised potential. For example a coffee cup has potentials for being various temperatures, a person has potentials for being various levels of educated in some subject, and a squirrel has potentials for jumping and running. That last example indicates that potentials aren’t always potentials for static states, but can also be potentials for dynamic activities. So also actualities can be static or dynamic, depending on the kind of potential they’re the actualisation of.

These two things, namely (1) the distinction between act and potency and (2) the realisation that individuals are mixtures of various acts and potencies, enable us account for very fundamental features of reality like change and multiplicity. We’ve spoken about change before, but it’s worth saying something about multiplicity here. Parmenides famously held that multiplicity is impossible since if A and B have being, then the only thing that can distinguish them is non-being, which is nothing. But if nothing distinguishes them then they are not distinguished, and therefore they are identical. Thus everything is one, a unity without multiplicity. His mistake was failing to realise (as we have) that being is divided into act and potency, and that beings are mixtures of these two principles. Two things can be unified by being actual in the same way, but diversified (or multiplied) by this common actuality resulting from the actualisation of distinct potencies. So you and I can be unified in our both being educated, but diversified by the fact that my being educated is the actualisation of my potency for being educated and your being educated is the actualisation of your distinct potency for being educated. So long as we properly divide being into act and potency, then, we can affirm both unity and multiplicity.[1]

So that’s act and potency, next we turn to intrinsicality. Intuitively, to be intrinsic to something is to be wholly contained within it. Slightly more formally, A’s being B is intrinsic to A relative to some C insofar as A’s being B doesn’t depend on C. Alice’s being educated is intrinsic to her relative to Bob’s being educated, for example, because it does not depend on Bob’s being educated. Intrinsicality is, naturally enough, contrasted with extrinsicality. In a water molecule, the hydrogen’s bonding to the oxygen is extrinsic insofar as it depends on the cooperation of the water molecule.

It’s clear enough that the primary sense in which we talk about the acts and potencies of something is as intrinsic acts and potencies, since these are what constitute the being of that thing. In order to outline all three kinds of whole, however, we will need to expand our focus to secondary senses. That being said, when considering something in terms of an act and potency at least one of these must be intrinsic to that thing, since if this weren’t the case, no sense could be made of our considering that thing rather than something else.

In general a whole, in the sense we’re interested, is “a unity of ordered parts.”[2] Parts, of themselves, are diverse and are brought together into a unity through an ordering of some kind, like an arrangement or structure or process. Now, since act unifies and potency diversifies, it follows that a whole arises through the actualisation of the potencies by which the parts are distinguished from one another. So for each part we can talk about the actualisation that unifies it with the other parts, and potency that distinguishes it from the other parts.

This allows us to state our taxonomy of the kinds of whole. For any part, either this unifying actualisation is intrinsic to the part or it is not. If it is extrinsic then, as we said above, the diversifying potency must be intrinsic to the part. If the actualisation is intrinsic, then either the potency is also intrinsic or it is not. An integral whole arises when we have an extrinsic act and intrinsic potency, a universal whole arises when we have an intrinsic act and intrinsic potency, and a potential whole arises when we have an intrinsic act and an extrinsic potency.

Breakdown of the three kinds of whole
Breakdown of the three kinds of whole

Integral wholes

All of this is rather abstract, and some examples might help for clarity. Starting with integral wholes we’ve already seen an example: a water molecule made up of hydrogen and oxygen molecules. Each of the parts has an intrinsic potential to be bonded with the others. There is one bond which actualises all of these distinct potencies resulting in one water molecule, and so this actualisation is extrinsic to the parts. Second, there’s a simple wooden table made up of a tabletop on four legs. Here each of the five pieces have potencies for being structured in various ways, and the binding of them together into the table is an actualisation of these potencies. And finally, there’s a living animal. What the parts are here is not totally obvious; they might be the various organs, the interconnected organic systems, or the cells, bones, and other organic materials. Whatever they end up being, the point of interest is that the extrinsic actualisation here is a dynamic process involving the parts, rather than the static structure of the table. This process is what constitutes the difference between a living animal on the one hand, and a corpse on the other.[3]

With these three examples in hand, we can introduce some technical vocabulary. In an integral whole call the extrinsic actualisation the configuration, and call a part with the configuration abstracted away an element. The element is that in which the intrinsic potency inheres. If we consider a hydrogen molecule while abstracting away whether it is free or bound in some other molecule, then we’re considering the hydrogen molecule element. When we consider a free-hydrogen-molecule or a water-bound-hydrogen-molecule, then we’re considering the element together with a configuration.

Universal wholes

Moving on to universal wholes, let’s consider the example of the wooden table and how it differs depending on which kind of whole we’re considering. The integral whole in this case is the table itself, with the integral parts being the tabletop and legs. The universal whole, on the other hand, is tableness and the universal part of this whole is the individual table (that is, the particular instantiating tableness). Each table — each universal part — will have its own intrinsic actualisation that accounts for its being a table as opposed to something else. This actualisation is common to all tables (it is in virtue of this that we call them tables in the first place), but it is not some numerically one thing. Rather, each has their own instance of this actualisation, each being actualised in the same way.

Again we can introduce some technical vocabulary. Well actually, we can re-introduce some technical vocabulary first introduced by Aristotle. The common actualisation intrinsic to each universal part is called the form, and when we abstract away the form of a part we’re left with its matter. Of itself matter is indeterminate between a number of alternatives, and form is the determination to one of these. (Put in terms of act and potency, of itself matter has potencies for alternatives, and form actualises one of these potencies.) The difference with integral wholes may now be apparent: with integral wholes the elements are the individual pieces of wood, but with universal wholes the matter is the wood itself. After all, if we have a table of wood and we abstract away the table bit all we have left is the of wood bit.

Because much of modern science has focused on integral wholes, we as moderns will always be tempted to confuse form and matter for configuration and elements.[4] We’ve already seen the difference with the wooden table: the elements are the pieces while the matter is the wood. With the living animal the elements are often said to be the cells, and so the configuration would be the organising process of those cells.[5] For universal wholes, however, the matter of a living thing is called its body and the form of a living is called its soul.[6] Considered broadly, there are three classes of living things: plants, animals, and humans. The soul of a plant makes it vegetative, the soul of an animal makes it sentient, and the soul of a human makes it rational.[7] If we abstract away the particular soul of a living thing, then all we know is that it is living; and this matter we call a body. The lesson here is that form and matter carve up the world very differently from configuration and element.

One more example should do to get this point across: consider the case where my hand moves into your face. The motion of my hand alone is indeterminate between me attacking you, and me reaching to get something and hitting you by mistake. The form that determines which of these is the case is my intention. Together the motion (as matter) and the intention (as form) constitute my action. The configuration of my action, by contrast, would presumably pick out how I hit you with my hand, like the path my hand took through the air. This something very different from the intention of the action.

Potential wholes

Finally, potential wholes. Of the three kinds this is the most foreign to us, and it is also arguably the most fundamental. The key here is this: in both integral and universal wholes we have cases where a single act can actualise multiple potencies at once. This is clear enough in integral wholes, but it can also apply with universal wholes: an animal’s soul actualises potencies for walking, grasping, flexing, seeing, smelling, touching, and so on. Now, whenever a single act involves the actualisation of a number of potencies, we can distinguish between sub-acts of that act. If some act A is involves the actualisation of potencies P, Q, and R, then we can consider the sub-acts of A as the actualisation of P and the actualisation of Q and the actualisation of R. The potential whole is the act, and the potential parts are these sub-acts which are distinguish by extrinsic the potencies found in the elements.

Notice the difference here: the parts do not have potencies, but are just sub-acts we differentiate by reference to extrinsic potencies. Consider the water molecule again as an integral whole, so that we have a configuration of elements. Each part is the result of an element being actualised with the configuration, and so each part includes some potency inside it. The whole water molecule includes both potency (from the elements) and act (from the configuration). But now abstract away the elements so that all you’re left with is the configuration itself. This doesn’t include a potency; it is just an act. And when we sub-divide this configuration into sub-configurations (each the actualisation of a different element), these are also just acts: the configurings of the hydrogen molecules and the configuring of the oxygen molecule. Potency plays a role is distinguishing the sub-acts from one another, but the potencies are extrinsic to these sub-acts.

Something similar happens in the case of a form informing matter. For each distinct potency actualised by the form, we can discern a sub-act which is that form considered with respect to that extrinsic potency. The potential parts of a human soul are roughly the various powers it gives a human: vegetative powers like digestion, animal powers like walking and seeing, and rational powers like abstraction and judgement.[8]

So far we’ve illustrated potential wholes by reusing examples from integral and universal wholes. This is partly because we want to show the sense in which potential wholes are most fundamental, but also because it helps us gain some initial intuitions. There are other examples of potential wholes, two of which we’ll go through now. First, communities are potential wholes. This is true in general, but focus on one for now: an orchestra playing a piece of music. The playing is the result of a co-ordinated effort from all the members of the orchestra, and is a single activity of the orchestra. We can consider the sub-activities of this activity as the playing of the individual members, and these would be the potential parts of the playing of the orchestra as a whole.

Second, there are what we might call “composite actions” like faith. At its most general level, faith is thinking with assent. “Thinking” involves having intellectual confidence in something, less than certitude.[9] “Assent” picks out the mood of the thinking: that which I think I also desire. So thinking uses the intellect and assenting uses the will, but these are being used together in one and the same act, which we call faith. So then the act of faith is a potential whole with the potential parts of thinking and assenting, each distinguished by the rational faculty they are the use of.

With both integral and universal wholes we introduced technical vocabulary to capture the specific kind of act and potency at play in each case (configuration-element and form-matter). With potential wholes, however, the act in view seems to be as varied as actuality in general. As such, it seems the best we can do is distinguish between super-act and sub-act, where the super-act is the potential whole and the sub-act is the potential part. Depending on which kind of act we’re considering we’ll restrict the vocabulary, and we’ll usually drop the “super-” bit from the whole. We’ve been doing this all already: configurations and sub-configurations, activities and sub-activities, actions and sub-actions. We also sometimes spoke about the potential parts by using a proxy, as when we used powers as a proxy for sub-forms of an animal soul.

Conclusion

Aristotle discovered two kinds of whole: integral and universal. The Scholastics discovered a third, the potential whole, and extended Aristotle’s analysis of wholes in terms of predication. We saw an example of this in Aquinas, and in that case potential wholes fell between the other two kinds. With the present analysis in terms of intrinsicality there doesn’t seem to be a linear way of ordering the different kinds, although their relations are captured well in the diagram we saw earlier.

Notes

  1. One might wonder if we haven’t just pushed the question about what multiplicity is back a step, since multiplicity of things arises from multiplicity of potencies. But this misses the point since we’re not trying to give an analysis of multiplicity, but rather trying to account for the reality of multiplicity with our principles. Because Parmenides had just being and non-being he could not account for multiplicity. But because we have divided being into being-in-potency and being-in-act, we are thereby able to account for it.
  2. See Svoboda’s Thomas Aquinas on Whole and Part.
  3. Rob Koons discusses in some detail how this process interacts with the parts in his Stalwart vs. Faint-Hearted Hylomorphism. David Oderberg argues in his Synthetic Life and the Bruteness of Immanent Causation the process of life is one involving immanent causation.
  4. Even Eleonore Stump, who is a very careful expositor of Aquinas, falls into this trap. I made the same mistake in an earlier post.
  5. While it is common to refer to the elements of an organism as a cell, this is technically wrong. But the details are not particularly important to our present point.
  6. See Mike Flynn’s blogpost series In Search of Psyche (introduction, part 1, part 2, part 3, and part 4).
  7. This is a technical term: any animal we take to be rational is a human. See David Oderberg’s Can There Be a Superhuman Species? for a related discussion.
  8. We say they are “roughly” the powers, since strictly they are the vehicles of the powers. Every power is grounded in a particular intrinsic actualisation, which we call the vehicle of that power. But such technicality is not necessary here.
  9. As Aquinas said, “[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)

By grace through faith

Have you noticed that theological discussions about grace almost always tend to include questions about conversion? What I mean is that they often center around the process by which someone moves from hostility towards God to desiring him. In particular, the Christian understands this as coming to faith in God and his gospel.

In Protestant circles the debate about the “doctrines of grace” is about the extent and nature of man’s inability to turn to God by himself, God’s supernatural act to overcome this inability, and the relation all of this has to free will and predestination.[1] In Roman Catholic circles we see something similar, albeit with slightly different distinctions and approaches. St. Aquinas, for instance, speaks of grace as that by which God supernaturally moves man inwardly to the assent of faith.[2] Naturally, such language raises questions of man’s free will in the matter which led to much debate — most notably between the Banezians and the Molinists — and which continues to be discussed today.[3] We can take it back even further: St. Augustine also discusses grace and free will in these terms, and he was around all the way back in the 4th century.[4]

Why do I raise this? Well, because it seems to me that when St. Paul talks about grace he is rather indifferent to questions about conversion. Now technically, there’s nothing wrong with certain debates throughout the centuries using slightly different vocabulary to Paul in the first century; so long as we make the necessary distinctions it won’t get in the way of our understanding of Scripture. The problem, however, is that we don’t make these distinctions, and so it does get in the way of our understanding.

Before we proceed I should make the following disclaimer: I’m in no way discrediting the topics mentioned above as legitimate and important avenues of theological discussion. I myself have drawn much value from them. I’m just interested in the exegetical question.

Some context

It should not be forgotten that Paul was a Jew and so his theology was informed generally by Jewish thought, and particularly by the Old Testament. There is sometimes a tendency to separate New Testament from Old, but unless we have some principled reason for doing so I see no reason why we should. Jesus and the apostles did not understand Jesus’ ministry to have overthrown the old covenants, but rather as something that fulfilled them.

Now, in the Old Testament God’s sovereignty — his guidance of human actions and history — is taken for granted and considered as something obvious and foundational, without much need for exposition. God’s actions are primarily depicted in more “external” terms, such as judging Israel or the other nations, and attempting to convince Israel to return to him. Generally the Old Testament authors focus on human motivations and responsibility for their actions, and only every now and then do they add a throw-away comment about God’s sovereign activity in the background.[5] And only a handful of these could be construed as God’s sovereign role in Israel’s turning to him from their sinful rejection of him. These just aren’t considered pressing questions for these authors.

What is a pressing question — and one which comes up all the time — is whether God will accept them back if they choose to repent.[6] Whether, after rejecting him and returning, he will accept them again and forgive their earlier offense. There’s nothing saying he must forgive them, of course: just as someone who commits a crime is not absolved of it merely by choosing to act like a respectable citizen from that moment onwards, so neither is someone who turns to seek God thereby absolved of their previous sin.

With this we’ve stumbled across an important distinction, the blurring of which is at the heart of our tendency to include questions about conversion with questions about grace: on the one hand someone turns to seek God, and on the other God forgives and accepts them. It seems to me that when Paul discusses grace and related topics he follows the Old Testament in being primarily interested in the second of these issues. We, on the other hand, are often interested in the first. In this sense, then, it seems we’ve gotten things backwards.

A clarification

Before we continue, let’s try get more clear on what we’re talking about. Grace is the solution to a problem, and we’re trying to get at what the authors of Scripture thought this problem was. On the one hand there’s the problem of how someone converts, that is how they turn from rejecting God to desiring him. On the other hand there’s the problem, even once someone has turned to God, of how they become reconciled to him. Let’s call these the inability problem and the alienation problem respectively.

Now we restate everything I’ve been saying with the help of this clarification. For a long time now discussions about grace have had the problem of inability at a fairly central place, while the authors of Scripture seem to be more interested in the problem of alienation.

Romans

We can begin to see all of this from a number of interconnected perspectives. Grace is closely related to a number of important notions at the center of Christian theology, like justification and the work of the Holy Spirit, and so a complete discussion would need to include something on these other notions. Here we will confine ourselves to what Paul says more or less directly about grace, with the hopes of looking at the other notions in more depth some other time. We’ll focus our attention here closely on what Paul says in two of his letters: Romans and Ephesians.

Starting with Romans, a brief summary is in order. In the opening chapters Paul seeks to establish that everyone is under sin and thereby alienated from God. By itself this wouldn’t have been surprising to his Jewish audience, who were familiar with the notion that the nations were alienated from God. They were the exception to this, however, because they were God’s chosen people: God had made a covenant with them (the sign of which was circumcision), and given them the law by which they could know and do his will. To their surprise, though, Paul goes on to include the Jews in his indictment. It is indeed to their advantage that they had all these things (3:1ff), but the law and circumcision themselves are not sufficient. Paul here echoes the prophets (cf. Micah 3, Isaiah 58) in criticizing the tendency to presume upon these Jewish sacraments without actually following through on them in their actions.[7] The fundamental thing needed is a change of heart — returning to God — which we trust will be graciously accepted by God (cf. Deuteronomy 30, Psalm 51, Hosea 14). The law and circumcision are not unrelated to this, of course: circumcision is the sign of the covenant, and the law gives the expression and end of this changed heart. But neither of these things in themselves are the grounds for their right-standing. Indeed, of itself, the law does not solve the problem of sin but only casts it in clearer light. (3:19-20)

It’s important for Paul in these opening chapters that everyone be found in the same boat. The Christians in Rome were divided over the place of the law and circumcision in the Christian life, since up until recently these had been defining features of God’s people. Paul’s point is that they of themselves do nothing to make one part of God’s people.

This sets the stage, then, for Paul’s proposal. While the law is not the solution to universal human alienation from God through sin, it does point to the solution: the person and work of Jesus the Christ. As he goes on to say, both Jew and Gentile “have sinned and fall short of the glory of God, and are justified by his grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a propitiation by his blood, to be received by faith.” (Rom 3:23-25)

The first thing to notice is that the grace Paul has in mind is received by faith, as opposed to being the cause of faith. Second, it would miss the overall thrust of Paul’s argument to think of this grace as that which causes some kind of desire for God. The Jew who mistakenly boasts in God on the basis of the law (2:17) desires God; his problem is his basis for boasting in God. Paul’s point is that because the law (and circumcision) does not form such a basis, it should also not be causing these divisions in the Roman church. Both Christian Jew and Gentile are right with God for the same reason: not because the Gentile has been circumcised and started following the distinctively Jewish laws (which would the just make him a Jew), but because both are justified through faith. Thus he continues, “For we hold that one is justified by faith apart from works of the law. Or is God the God of Jews only? Is he not the God of Gentiles also? Yes, of Gentiles also…” (3:28-29) To cast this in terms of conversion just misses the point. His point is that if a Gentile seeks God he needn’t become a Jew, for this would make God the God of only the Jews. By grace, God overcomes the alienation of both Jew and Gentile through faith. That the person seeks God is assumed; it’s not taken to be the result of anything (at least not here).[8]

The interpretation of these verses ripples through the remainder of the letter to the Romans. This is natural since Paul is starting in these early chapters the line of thought he will carry on through to the end. For our current purposes, perhaps one of the most interesting passages to look at in chapter 7:

Did that which is good [the law], then, bring death to me? By no means! It was sin, producing death in me through what is good, in order that sin might be shown to be sin, and through the commandment might become sinful beyond measure. For we know that the law is spiritual, but I am of the flesh, sold under sin. For I do not understand my own actions. For I do not do what I want, but I do the very thing I hate. Now if I do what I do not want, I agree with the law, that it is good. So now it is no longer I who do it, but sin that dwells within me. For I know that nothing good dwells in me, that is, in my flesh. For I have the desire to do what is right, but not the ability to carry it out. For I do not do the good I want, but the evil I do not want is what I keep on doing. Now if I do what I do not want, it is no longer I who do it, but sin that dwells within me.

So I find it to be a law that when I want to do right, evil lies close at hand. For I delight in the law of God, in my inner being, but I see in my members another law waging war against the law of my mind and making me captive to the law of sin that dwells in my members. Wretched man that I am! Who will deliver me from this body of death? Thanks be to God through Jesus Christ our Lord! So then, I myself serve the law of God with my mind, but with my flesh I serve the law of sin. (7:13-25)

There is much discussion about how best to interpret the perspective Paul is taking here. One option is that he’s talking about the Christian experience of the struggle with sin. It’s unclear, however, why sin would still produce death in a believer. Another option is that Paul is talking from the perspective of a Jew prior to the coming of Christ. It’s unclear, however, why Paul would speak in the present tense and why only now he takes this perspective (presumably he’s been speaking from the Christian perspective since at least 6:1).

I think both of these options are getting at something, but missing it slightly because each assumes the grace in question involves something like conversion. If we apply the correction we were talking about earlier, a nice third option becomes available: Paul is speaking from the perspective of the person who desires God — and who sees his law as good — but who is nonetheless alienated from God because of their sin. At this point he’s bracketing out the grace he’s mentioned before so that he can situate it as the solution he sees it as: the way a person who has turned to God but remains stained by sin, can be reconciled with God.

Put another way, we might say that Paul is considering two logically distinct stages in someone being made righteous through faith: the stage at which the person turns to God but is still under sin, and the stage at which God graciously accepts him and forgives his sin. The former stage takes up most of the space, and is summarized with the exasperated question, “Wretched man that I am! Who will deliver me from this body of death?” The latter stage let’s loose the solution Paul has been discussing for the past few chapters whereby he is able to exclaim, “Thanks be to God through Jesus Christ our Lord!”

This passage is pivotal in Paul’s argument in chapters 5-8. In it he comes to the end of a dialectic he’s been following since the beginning of chapter 5, getting ever and ever more detailed about the relationship between notions like the law, grace, sin, death, and life. In chapter 8 he’ll address all of these in reverse order, “redressing” them appropriately in his account of God’s work at the cross. Take, for example, 8:31-39. Sometimes v35 is read in terms of inability, and so taken to be talking about Christians persevering in their faith. But if we consider the surrounding context as well as the context of the quote in v36, it becomes clear that it should be read in terms of alienation. The love of Christ, here, is expressed in his interceding for us, and Paul’s point is that nothing will get in the way of his doing this. This section “redresses” 5:1-2, in which Paul explains that through Christ our faith is enough to be right with God.

One more example of Paul’s focus on alienation: most of the discussion in Romans involves correcting the error of some of the Jewish Christians who were saying that something in addition to faith was necessary to deal with the alienation from God. Paul’s point is that this grace from God directly connects faith to reconciliation with him, so that nothing additional is needed and so there is nothing aside from God’s mercy that we can point to as the means by which we dealt with it. In Chapter 11, however, Paul briefly addresses an erroneous thought that might enter the Gentile’s mind as a result of this. He says,

… do not be arrogant toward the branches. If you are, remember it is not you who support the root, but the root that supports you. Then you will say, “Branches were broken off so that I might be grafted in.” That is true. They were broken off because of their unbelief, but you stand fast through faith. So do not become proud, but fear. For if God did not spare the natural branches, neither will he spare you. Note then the kindness and the severity of God: severity toward those who have fallen, but God’s kindness to you, provided you continue in his kindness. Otherwise you too will be cut off. And even they, if they do not continue in their unbelief, will be grafted in, for God has the power to graft them in again. (11:18-23)

It is because we continue to trust in his dealing with the alienation, as opposed to us having fixed it somehow, that we continue to be grafted in. Notice towards the end that the grafting occurs logically after the belief, which doesn’t make sense if the problem in view is one of inability. The power (and grace) of God in focus is his ability to graft those who believe back in, ie. address their alienation from him and his people.

Ephesians

Let’s turn now to consider Ephesians more briefly. The passage I have in mind is Ephesians 2:1-10. Here Paul tells us that previously we were “dead in our trespasses” but that “by grace through faith” God has saved us. Here it is common to see people interpret the phrase “dead in our trespasses” as meaning that we are like corpses, incapable of turning to God. That is, they interpret the phrase to be a statement of the inability problem. In this case, God’s saving us “by grace through faith” refers to him giving us faith.

It seems to me, however, that this way of reading the passage divorces it from the broader Pauline context to which it belongs. When Paul talks about death in relation to sin or grace he has in mind a judgment or consequence, not an inability.[9] Indeed, our quote from Romans 7 above is a clear example of this. To be sure, there are cases where Paul does use death to refer to inability — he speaks of Abraham as considering his body “as good as dead” in Romans 4 — but these cases are not discussing death in the context of sin or grace. Biologically speaking Paul understands that death is the greatest of all inabilities, but theologically speaking he uses it to refer to judgment or consequence, which is part of the problem of alienation.

On an alienation reading, then, when Paul says that we were “dead in our trespasses” he means something like we were “under the reign of death” or we were “on the track to death.” And, importantly, this is true even if we’ve turned back to God since the stain of sin still alienates us from God. But he graciously saved us from this through Jesus, a grace we receive through faith. Paul is not here interested in our conversion per se, but in our movement from being worthy of judgment to being reconciled with God.

Besides making more sense in the broader Pauline context, there are three other reasons to prefer this alienation reading to the inability reading. First, Paul uses the phrase “dead in our trespasses” interchangeably with the phrase “children of wrath,” and the latter clearly refers to judgment. Second, Paul contrasts us being dead with us being “seated in the heavenly places” (v6), which is what we’d expect on the alienation reading, but not on the inability reading. Third, when Paul uses the phrase elsewhere it clearly refers to the alienation reading. In Colossians Paul says,

And you, who were dead in your trespasses and the uncircumcision of your flesh, God made alive together with him, having forgiven us all our trespasses, by cancelling the record of debt that stood against us with its legal demands. (2:13-14a)

Notice how God made us alive in this passage: by forgiving our sins. It is not by supernaturally enabling us to turn to him or by infusing us with faith, but by forgiving the thing keeping us alienated from him.

Coming back to the Ephesians passage, we have one more thing to comment on. Paul says towards the end that,

… by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast. (2:8-9)

On the inability reading, the gift is the faith. On the preferred alienation reading, the whole process is the gift: God’s grace in Jesus is received through faith. This has the advantage of cohering well with the parallel phrase in Romans 3 we discussed earlier, as well as connecting this gift in v8 with the discussion of the preceding verses about God’s grace. Paul is explaining to these people who desire God in their faith, that God has made a way for this to be enough to overcome the alienation of their sin. Nothing they did achieved this, it is was a gift from God.

Concluding thoughts

We’ve examined two passages where Paul is talking explicitly about grace and seen that in neither case is he particularly interested in the question of conversion or the inability of us to turn to him.[10] Paul is talking to people who now desire God and, reflecting on the Old Testament reassurances, is explaining how God has overcome the stain of sin in them and thereby reconciled them to himself. Just like the criminal’s repentance does not by itself undo their crimes, so neither does the sinners repentance by itself undo their sin. This is the problem Paul sees God’s grace solving. It is only because of God’s grace shown in the cross that this barrier can be overcome, and repentant sinners can be declared sons of God.

Had God not shown this grace, people might turn to him in faith but this would be in vain since they would still stand alienated from him. Indeed, there’s nothing they could do to change this since it’s a result of past sins and no-one can change the past. God’s grace bridges this gap and undoes the alienation for those who turn to him in faith. Now he waits for us to so turn. In this way, we receive this grace in faith.

Notes

  1. Contemporary authors that jump to mind are people like Michael Horton, John Piper, Roger Olson, and Kenneth Keathley.
  2. “Therefore faith, as regards the assent which is the chief act of faith, is from God moving man inwardly by grace.” (ST II-II Q6 A1 corp.)
  3. See, for instance, Bernard Longeran’s incredible (and equally intense) book Grace and Freedom, Harm Goris’ Free Creatures of an Eternal God, and Alfred Fredosso’s God’s General Concurrence with Secondary Causes.
  4. See, for instance, his De libero arbitrio, his De natura et gratia, and his De gratia Christi et de peccato originali. See Eleonore Stump’s Augustine on Free Will for a nice contemporary discussion on all of this.
  5. See, for example, Genesis 50:20, 1 Samuel 2:25, and Isaiah 63:17.
  6. Many of us will be familiar with the promises of blessings for obedience and curses for disobedience in Deuteronomy 28-29, but we forget that after all this, in chapter 30, Moses reassures the Jews that after they’ve failed God and returned to him that he will mercifully restore their fortunes: “And when all these things come upon you, the blessing and the curse, which I have set before you, and you… return to the Lord your God… and obey his voice in all that I command you today, with all your heart and with all your soul, then the Lord your God will restore your fortunes and have mercy on you…” (30:1-3) Allusions to this promise from God appear throughout the Old Testament. See, for example, Psalm 32:1-2, 51:9, Isaiah 64:9, Ezekiel 18:21-23, and Zechariah 1:3.
  7. This the same problem Jesus had with the Pharisees. An example that jumps to mind is his criticism of the traditions of the Pharisees that were established under the pretense of serving God, but ended up merely undermining this purpose (cf. Mark 7:1-13). See also, this blog post.
  8. Perhaps people think in terms of conversion because in chapter 1 we have someone hostile to God. But this ignores chapter 2, where both Jew and Gentile seek to do Gods will.
  9. See, for example, Romans 1:32, 5:12, 6:21, 7:13-25, and Colossians 2:13-14. Note that in Ephesians 4:17-18, while he doesn’t use the word “dead,” he talks about “alienation from the life of God,” which fits well with my point here and plausibly refers back to what we was talking about here in Ephesians 2.
  10. This is not to say he is never interested in the question of conversion. It’s just not as prominent as some have come to think, and he doesn’t even use the word “grace” when discussing it. For example, in 1 Corinthians he talks about how the “natural person does not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned.” (2:14)

Because God said so

In a recent discussion with some friends, the question of why murder was wrong came up (actually, it was why Aquinas would say murder was wrong, but the discussion equally applies to the more general discussion to be had here). The answer “because God said so” quickly came up and, being a natural law theorist in the tradition of Aquinas, it left me unsatisfied. During later reflection on this, it occurred to me that there are at least three different questions at play here. Each of these questions might be answered in part with “because God said so,” but how each is fully cashed out is very different from the others. The three questions are as follows:

  1. Why is it bad to murder?
  2. How do I know whether it’s bad to murder?
  3. Why should I not murder?

The first question is a meta-ethical question about what makes things good, bad, virtuous, vicious, and so on. The second is a question of ethical epistemology about how we come to know the truth of the notions grounded by our meta-ethical answers. And the third is a question of normative ethics about what I should and shouldn’t do given the answers to the first two.

The three questions are related but very different from one another. Let’s take each of these questions in turn, discuss them in more depth, and outline what “because God said so” might look like as an answer. Now, of course, the details of the answers will depend on the meta-ethical framework we’re working from. For the majority of this post I’ll be working from a Thomistic natural law perspective, which I’ve discussed a number of times on this blog (eg. herehere, and here). Towards the end of this post, I’ll consider how another theistic meta-ethic (divine command theory) would differ from what was said.

Why is murder bad?

The fundamental thing that determines whether something is good or bad is whether it contributes to the fulfillment of your nature, the realization of your natural ends. Initially, it’s obvious why this would account for certain things being good or bad for me, such as not hurting or unnecessarily damaging myself. On the other hand, it is less clear how this would extend to the good of others, as when we say it is bad for me to murder another person. There are a number of ways to “extend” the notion of my good to include the good of others. I’ve sketched one before, and we can very briefly sketch another — in my opinion better — one by combining some previous discussions.

The fulfillment of our natural ends — and therefore the realization of our good — is achieved by us through the measured and unified expression of our natural powers. The active frustration of these powers would, therefore, be to that extent bad for us. Our natural ability, as rational animals, for co-operating toward a common end enables us to acquire what we might call “common powers” which are expressed through the participation in common endeavors. Consider the following example: by myself, I have the power to sing within a certain vocal range, but only with someone else am I able to harmonize within my vocal range. Here harmonization is a common power. Now, just as my frustrating a power is bad for me, so my frustrating a common power is a common bad for us. (Recall the kind of commonness we have in mind here.) Now, living amongst others gives us certain common powers, albeit ones less easily describable than “harmonization”. Murder would involve the frustration of some (or even all) of these powers and therefore be something bad.

Of course, much more needs to be said before this is a full account. The point to take away is that, however we flesh out the details, the way good and bad are grounded is ultimately based on the kind of beings we are (our natures). At this point is there any place for an answer like “because God says so”? Yes and no. Insofar as God creates and sustains us with the natures we have, he is the author of what is good or bad for us. But, he cannot do the impossible, and so he cannot arbitrarily decide what is good or bad for us any more than he can make a married bachelor or a square circle. So long as he creates a living being, he cannot make it good for that being to die. So long as he creates a rational being, he cannot make it good for that being to murder. So when it comes to natural law the “because God says so” answer needs to be understood in an indirect and qualified way.

But wait, there’s more. In section 2.5 here I mentioned that Aquinas distinguishes between four different fundamental kinds of law, one of which is the natural law we’ve been discussing so far. There’s also eternal law, which we’ll leave to one side. Then there’s positive law, which is law given by a legislator, and which is divided into human law (positive law given by a human legislator) and divine law (positive law given by a divine legislator). Now, natural law is often very vague and general and its application in particular cases requires careful consideration by wise people. So, as John Goyette says, “human law is essential for living the good life because it makes the general precepts of the natural law more specific.”[1] The same goes for divine law, with the obvious difference being that God is the legislator as opposed to humans.

In a sense both forms of positive law are authoritative because they’re based on natural law,[2] but they do establish new legal duties on us: so long as I am under a legislator who has imposed just duties on me, it is good for me to fulfill those duties and bad for me to fail in those duties. Because this goodness arises from positive law, we’ll refer to it as positive goodness. This positive goodness differs from the natural goodness mentioned above in an important way: natural goodness applies to us as humans whereas positive goodness applies to us as citizens under the legislator. So whereas natural goodness is applicable insofar as we have our particular nature, positive goodness only applies once the legislator has imposed the duties on us. So, then, with respect to positive goodness “because God says so” has direct relevance.

In the remainder of this post, if we do not specify the kind of goodness (or badness) in view then what we say applies equally to both outlined here.

How do I know whether it’s bad to murder?

This question differs from the first in that while the first concerned itself with ontology (what makes something bad) this question concerns itself with epistemology (how I know something is bad). Because of this, the number of potential answers (and so the potential for “because God says so” answers) increases.

The answers to the first question also apply to this question in the sense that one of the ways I can come to know whether murder is bad is by grasping what in reality makes it bad, or in other words, I can come to understand the ontological grounds for its badness. Indeed, this way of knowing the badness is in a sense primary in that it does not derive its correctness from other, deeper, reasons.

But I can come to know things in other ways, beyond the primary sense of grasping their underlying ontology, because I can come to know from others who know. I can come to learn the badness of murder from my parents, my school teachers, mentors, church leaders, the broader culture I find myself in, or some combination of authorities like these. If God has revealed himself (as some religions think he has), then he also stands as an authority that we can learn from. If God is concerned for our well-being and infallible in his judgments (again, as some religions think he is), then he is the uniquely perfect authority. And so, in this sense, “because God says so” takes on a special significance.

At this point, we must be careful not to forget the distinction between ontology and epistemology. Unlike in the previous section, here God’s revelation does not constitute the badness of murder but only perfectly informs us of it. All things being equal, we are justified in believing what we’re taught by the relevant authorities, and so a fortiori we are justified in believing what we’re taught by the perfect authority.

So we come to know what is bad by grasping the underlying ontological truths or by being taught by others. In the first case, all the “because God said so” answers in some sense carry over to the epistemological answers. In the second case, we have new “because God said so” answers insofar as he is a perfect authority on our nature (for natural goodness), and his will (for positive goodness).

Why should I not murder?

The first question was ontological, and the second was epistemological. This question is normative: it asks why I should act in a certain way. And just as the epistemological question was in a sense broader than the ontological one, so the normative question is broader still. Indeed, here the answers become manifold.

In general, a hypothetical imperative is a statement of the following form:

  1. If I want to achieve X, then I should do Y.

In cases where these apply, there’s something in the notion of X that entails that the way to achieve it is by means of Y. And this is largely mind-independent in that I should do Y even if I don’t understand enough about X to see that I should do Y. Consider a toy example:

  1. If I want to draw a straight line, then I should use a ruler.

This is true just by virtue of what drawing a straight line involves and the possible tools for achieving it. And it remains true even if I don’t know about rulers, or have temporarily forgotten about them, or hadn’t thought to use one, or any number of other reasons.

Now just as there are many motivations (X’s) for action, so too there are many of these imperatives and therefore many answers to the normative question. We’ve explained before that the imperative involving natural goodness is particularly interesting, because of the structure of the human will (section 2.4 here, cf. this and this). Taking the answer about natural goodness from the first question, an argument might be framed as follows:

  1. If I want what is good for me, then I should act so as to fulfill my natural ends.
  2. I do want what is good for me.
  3. Therefore, I should act so as to fulfill my natural ends.
  4. If I should act so as to fulfill my natural ends, then I should not murder.
  5. Therefore, I should not murder.

What’s interesting about this is that (2) is always true, since whenever we desire something it’s precisely because we see some good in it, and as noted above this remains true even in cases where our relevant judgments about what is good are incorrect. As Edward Feser says, “The mugger who admits that robbery is evil nevertheless takes his victim’s wallet because he thinks it would be good to have money to pay for his drugs.”[3]

Can something similar be said for the positive goodness discussed in the first section? It seems so: God is the legislator over all creation in charge of its common good, and since I should seek my good I should also, therefore, listen to his commands. (Again we note the dependence of positive goodness on the notion of natural goodness.)

So the previous “because God said so” answers carry over to answer the current question indirectly. However, these do not exhaust the possible motivations we might have. In addition to these, we might be motivated by a desire to follow God’s will, which itself perhaps follows from a love for him. We could also be motivated by the avoidance of punishment or the acquisition of reward. Each of these has analogs in human affairs too, of course, but we’re primarily interested in “because God said so” answers.

A different meta-ethical framework

How would things have been different if we’d approached these questions from a divine command theory perspective? On divine command theory, anything we’d get from natural law gets ignored, leaving positive divine law as the only form of goodness. Given the importance that natural goodness played in the discussion, it’s not surprising that this move also accompanies shifts in the logical ordering of things. So the normative force of God’s commands are taken as primitive and “morality” gets lifted to this somewhat mysterious and unique notion (cf. sections 1 and 2.1 here). The consequence of all of this is that “because God said so” takes on a more direct relevance more often, and plays a unique role in the ontological answer. The picture becomes flattened and therefore simpler, but wrong.[4]

Conclusion

If we take anything away from this it’s that the answer “because God said so” can be valid for very different reasons depending on what we mean by it. Let’s try and list the options that arose from the above discussion. Why should I not murder? “Because God said so.” In what sense? Well…

  1. Because it frustrates your natural ends established by God’s creative act, which is bad for you, as I know through philosophical investigation.
  2. Because it is bad for you, as revealed by God.
  3. Because it goes contrary to God’s law, which is bad for you, as revealed by God.
  4. Because it is contrary to God’s will.
  5. Because God will punish you if you do.

I’ve tried to capture this diagrammatically in the following:

Solid arrows represent ontological priority. Broken arrows represent epistemological priority.
Solid arrows represent ontological priority. Broken arrows represent epistemological priority.

Notes

  1. John Goyette, On the Transcendence of the Common Good.
  2. Thomas Aquinas, ST I-II, Q. 90, Art. 4.
  3. Edward Feser, Classical Natural Law Theory, Property Rights, and Taxation.
  4. I take the fact that on divine command theory the term “good” is equivocal (as opposed to analogical), that authority and normative force need to be primitive or reduced to something consequentialist, and that “moral” picks out some special and mysterious class of facts. I consider all of these reasons to reject divine command theory as a viable alternative to Thomistic natural law theory.

The metaphysics of gender

I recently listened to this talk by John Finley titled The Metaphysics of Gender: A Thomistic Approach. Below are my notes of this. I skip the introductory remarks and follow the four-section division of the talk. Note that by “gender” here we do not mean the psychological or social construct introduced by modern feminists. Rather, by “gender” we mean the biological distinction between male and female. Some have come to refer to this as “sex” but in the introduction John notes that both terms have ambiguity and so he just picked one. By-and-large parentheses represent my own thoughts, but this is not always the case. And finally, the times for each of the sections are written next to each of their headings.

Aquinas’s position (8:56-20:30)

A man is a male human being and a woman is a female human being. Male and female are distinguished by their mode of generation: the male is that which can generate in another, while the female is that which can generate in itself. Whatever meanings man and woman could have, they need be connected to these meanings.

So, then, what is the connection between male or female on the one hand, and being human on the other? It does not affect that one has a human nature: one’s gender does not elevate or detract from one’s being a human being. Perhaps, it’s better to say that gender affects how one participates in human nature. “It might be better to say that men and women share human nature equally but differently, according to their respective generative abilities. In an analogous way, being blue-eyed and being brown-eyed pertain equally but differently to the human power of vision.” Nevertheless, gender must be a more significant personal attribute than eye-color, since it involves distinct organs, activities, and purposes. It is also more uniform than other less significant attributes, which appear more sporadically throughout the human population.

Thomas has two classifications of accidents: (1) a logical classification (in terms of genus, species, etc.) in The Disputed Questions on the Soul and (2) a metaphysical classification (as arising from form and matter) in On Being and Essence:

On the logical classification there are three sorts of accidents: proper accidents (eg. risibility in humans) result from the principles of the species and so characterise all members, inseparable accidents (eg. masculine and feminine) result from the principles of the individual through permanent causation and so characterise that member in a lasting fashion, and separable accidents (eg. sitting and walking) flow from the principles of the individual through temporary causation and so only characterise that member at particular times. The main focus here is the inseparable accidents, however it’s not clear what other examples of such accidents there are. Aquinas gives examples like eye color, bone structure, and natural temperament, but as noted above these seem less significant than gender. A question arises as to which principles of the individual (soul, or body, or both) bring these accidents about. This is addressed by his metaphysical classification in On Being and Essence.

Regarding the metaphysical classification, we note that the whole substance is the true subject of all accidents, but since humans are composed of two principles (form and matter) certain accidents flow more from form and others more from matter. Thomas describes four kinds of accident (two following from form primarily, and two following from matter primarily). First, of those following from form, rational activities — understanding and willing — occur entirely in the soul and have no share in matter (though there is a measure of dependence on the physical sense organs). “Other accidents following from form, like sensation, do have a share in matter since they properly reside in the composite substance. The soul, that is, originates powers of sensation but it can’t sense on its own.” “Moving downward, accidents following from matter will always have some relation to form since matter on its own is pure potency, uncharacterized by any feature.” So, in the third case, some accidents following from matter relate to a particular kind of form. For Aquinas, masculine and feminine are accidents that follow from matter but precisely in relation to an animal form. So when the animal dies, and the animal form is separated from the body, it is no longer gendered in a univocal way. Finally, “other accidents following from matter relate to a more general form, as one’s skin color occurs through matter’s relation to the form of some elemental mixture. The color thus remains even after the person has died.”

Combining the two accounts, Aquinas takes gender to be an inseparable accident following from one’s matter in direct relation to one’s substantial form as an animal. This helps us distinguish it from other inseparable accidents, as they would follow from one’s matter in direct relation to some form other than one’s animal substantial form. It seems that gender is the only example of this special class of inseparable accident we have, and so it is in this sense a metaphysically unique feature.

“Now, if being male or female relates necessarily to the form of an animal why does Thomas assigns gender’s origin to matter?” He gives two reasons:

First, for both Aristotle and Thomas, the male and female roles in generation are active and passive respectively. The male semen contains the formal principle of generation whereas the female seminal fluid contains the material principle, such that when the two come together a human is generated. Insofar as every act of generation is directed toward producing one’s likeness and since the male is more active is the generative act, the act naturally tends toward a male offspring, and a female results from an accidental alteration in the male semen. Since gender is determined by the manner in which the seminal matter has been affected, it is seen to follow from matter as opposed to form. Aquinas agrees that one’s reproductive power — as all powers — arise because of the soul, but the difference in gender is owed to a defect in the matter of the female (since the male, insofar as he is more active, has the more reproductive power more perfectly).

Second, for both Aristotle and Thomas since form is what makes matter to be a certain kind or species, a difference in form must result in a difference in species. Thus differences applying to individuals of the same species must be differences originating from matter.

Note that genders origination from matter does not mean that it has no bearing on the soul. “While the soul in its own right is not gendered, just as the soul on its own possesses no sensation, presumably the soul of a male can be derivatively considered a male soul and the same in the case of the female, since the soul’s identity is marked by it’s being the soul of a male or female body. One’s gender then, as following from the principles of the individual, characterizes the person as a whole.”

Brief evaluation of Thomas’s account (20:31-23:15)

Thomas’s logical classification of gender as an inseparable accident makes sense insofar as gender doesn’t apply to the species as a whole, but individual members. “Moreover, current biology’s understanding of genetic systems, chromosomal patterns, gonadal structures, and sexual organs affirms that the principles of the individual exercise permanent causation in their originating one gender or another.” In spite of this, the fact that gender seems to be in a class of its own — separate from other accidents — calls for further inquiry. And this inquiry would have to focus on Aquinas’s metaphysical account of gender arising from matter in relation to a specific form.

It’s not totally clear what it means for an accident to follow from the matter in relation to a specific form. If this is taken to mean simply that the accident flows from the principles of the individual as such, then it is well-taken since evidently, one gender is not a characteristic of the species. This would still leave open, however, which of the individual’s principles is at work here (soul, matter, or both). But Aquinas, in saying that the female gender arises from an accidental alteration of the semen, answers this second question. “That is, he holds not just that gender stems from the principles of the individual, but also that being male or female stems concretely from the side of one’s matter, rather than one’s substantial form or soul.”

Now, current biology, of course, has shown that the female reproductive abilities are not imperfect versions of the male ones. Man and woman, respectively, do not supply the active formal principle of generation and the passive material principle of generation. That a man’s production of semen and a woman’s ovulation each supply distinct elements of the offspring’s genetic material reveals that, in this capacity, the two are co-contributors to the offspring. Since man and woman do not relate generatively as perfect to imperfect it is not the case that any given act of generation seeks the male. As contemporary science shows, the male and female are equally intended at the biological level. So Thomas’s empirical reason for attributing gender to matter — the first reason I mentioned earlier — is no longer tenable.

This leaves us with the question of whether the second reason given still works. Is it true that gender must arise from the matter and not the form because the form cannot account for something that arises from the individual?

A revised account (23:16-36:42)

The aim here is to argue that the Thomistic principles suggest that gender flows more from substantial form than from matter, that is more from the soul than the body.

As both Aristotle and Aquinas saw, male and female are of a different category to black and white. The former are tied up with the essential teleos of the human being and contain the substance’s essence within their definitions, whereas the latter are not and do not. “The presence of an organ indicates a particular configuration of matter for the sake of one of the soul’s powers, which in turn flows from the essence of the soul. The soul itself arranges material structures as organs so that they might fittingly serve as means through which the soul’s various powers can operate effectively.” As Thomas says in The Disputed Questions on the Soul, “the soul constitutes diverse parts in the body even as it fits them for diverse operations.”

To unpack this we might say that like the vegetative powers the reproductive powers slowly manifest as the being matures, and as the soul actualizes and shapes the individual it constitutes these powers in particular organs within the body. Just like the sensory powers, if the soul were to leave the body so too would the generative powers. Unlike the sensory powers, however, not all humans share the same set of generative powers (instead we have something like a 50/50 split across the population).

The generative powers of man and woman should be considered, strictly speaking, co-generative, since they possess a two-fold formal object distinguished hierarchically. As “generative” they possess the same ultimate object, namely procreation of another human being. While as “co-” their proximate objects differ by way of offering distinct sexual organs and activities yet in relation with each other. The ultimate object of the co-generative powers points to the unity of nature shared by man and woman since another of the same species, whether male or female, is generated. The proximate object of the co-generative powers points to the distinction within human nature as found in either man or woman, albeit only at the level of the reproductive capacities.

Since the reproductive powers are two distinct co-generative — as opposed to one at varying levels of perfection — it seems clear that they must be accounted for by the substantial form of the individual. Of course, since the generative powers intrinsically depend on organs they would this should not be thought of as an attempt to separate the soul from the body, but rather to highlight the soul’s role in constituting the powers in the body. Thus we provisionally include gender in those accidents that stem from the soul and have a share in matter, as with the senses. In order to develop this account further, we address three objections.

The first objection is that modern biology seems to support Aquinas’s position that gender is better attributed to matter than soul. This is because modern biology teaches us that gender is intimately connected with various genetic networks, especially the chromosomal patterns XY or XX found in the zygote. But this does not so much entail that gender differentiation arises from matter primarily as show us more clearly how intimately related substantial form and matter relate to one another in the constitution of a human being. Any becoming of a substance requires appropriately disposed matter; after all, the being is generated by the actualization of potencies in the matter. But it is the resultant form (the actuality) that primarily characterizes the being the is generated.

The second objection comes from the second argument given by Aquinas above, that difference in form constitutes difference in species. Since men and women clearly share the same species, their difference must, therefore, arise from matter. Moreover, the notion of an individual brings forth — for Thomists at least — thoughts of matter insofar as it is the principle of individuation. But we must make a distinction between a universal form and a particular form. Aquinas grants that when a soul is commensurated to a particular body (that is, when they mutually limit one another so as to constitute an individual) in a sense it takes on additional characteristics, an obvious example being individuation even after separation from the body at death. It is inevitable that gender is of the form, since matter does not configure itself into particular organs (being indeterminate between any such configurations) it must be the soul that does so in and through matter “for the sake of the particular powers that work through those organs.”

The position I have argued affirms the notion that particular souls are essentially commensurated to particular bodies, but claims that within this commensuration gender begins at the level of the soul and is received into the corresponding matter accordingly designated by the genetic pattern.

As to the concern about this introducing a distinction between two species of human, we can say two things. Rather than being an additional power that future determines the essence of the individual, gender concerns the maintenance of the essence that the other powers constitute. “As oriented towards the species itself, [the generative powers] cannot in themselves constitute new species.” Second, as noted above gender is a co-generative power which differentiates it from the other powers given by the soul insofar as they are independent in some sense. They exclude each other in definition (“four-legged” excludes “winged”) or in fact (“scaled” excludes “feathered”). Gender’s nature, however, presupposes “one like itself” and so depends on and includes its contrary both in fact and in definition. Male is defined in terms of female and vice versa through the co-generative relation. The reproductive powers are not merely distinct as one sense is distinct from another, but as mutually dependent powers contributing to a single action (ie. generation). They are not to be understood as characterizing distinct species, then, but rather as integral parts of the same species considered at the reproductive level. (This is a consequence of us being social animals: humans are not wholly intelligible in terms of an individual, but require that that individual be understood in the context of some community. This reoccurs again at the higher level with powers that enable us to rationally cooperate, which are a consequence of us being political animals.)

The third objection takes issue with the description of co-generative powers. Why could we not accept that there is one generative power manifested in different ways, depending on the body to which the soul is united? This would entail that gender differentiation stems from matter as opposed to form. Note that this is much like Aquinas’s view insofar as he sees one power actualized to differing levels of perfection. Now in some sense, the objector is right, namely insofar as both generative powers have the same ultimate object. Because of this, they can be naturally grouped together, just as the various sensory powers can be naturally grouped together. But insofar as the generative powers have distinct proximate objects (their organs and activities), they can be distinguished. Interestingly, even in the woman, we see multiple generative powers in a single being: powers for generation, support, and nourishment of the offspring all of which are required for procreation (since the ultimate object of generative powers is a human and not merely a clump of flesh). Since there are really distinct generative powers, their distinction must arise from the substantial form and not the matter.

In order to affirm that a numerically single (that is, really identical) power to be differentiated only by matter, we would need to accept Aquinas’s account which, as we’ve seen, is falsified by modern biology. Otherwise, we’d need a “generic power” had by both male and female, which would need to be an abstract power or a power that includes both. But the first alternative is incoherent in Thomistic metaphysics (and even in much of modern metaphysics), and the second would involve an entire set of the person’s powers being denied and frustrated merely in virtue of them being an individual human. This “opposes Thomas’s thought and the majority of human experience.”

Being male or female, therefore, follows principally from one’s soul in relation to that soul’s correspondingly disposed matter.

Three ramifications (36:43-43:41)

The first concerns “gender’s status in relation to the person.” Gender is closely related to the person but is different from other such attributes. Other attributes (like free will, reason, soul, body, growth, and sensation) are understood when the human essence is abstracted from individuals and reproduction is like this. But it differs that when considered in itself the essence includes both male and female, but when it comes to exist there is a split into the co-generative powers. “The human essence in itself includes male and female; only a consideration of that essence as actually existent entails male or female.”

Turn, then, back to the metaphysical classification given above. We’ve seen that reproduction, like sensation, falls into the second category of those accidents which follow from form that have a share in matter. But given the differences between reproduction and sensation, there must be a real distinction within this category. The difference is between those accidents which flow from the nature itself, and those accidents which flow from the nature as it exists in this or that individual.

And in this sense, one’s gender is not as close to one’s fundamental humanity as are the other powers of the soul. Being man or woman — you might say — is more proper to the human individual than to the human individual. As Thomas would put it being gendered at all is proper to human nature, but being a man or a woman is proper to this instance of human nature, this soul and this matter.

All of the other accidents that flow primarily from the soul characterize the whole species, and so we call them the proper accidents (or properties), like sensation and risibility. But gender differs from the other individual accidents insofar as it characterizes one’s structure, abilities, and purpose. Insofar as the gender so characterises an individual we might say that it is “the primary attribute of the existing person”, not as something that constitutes the person (since this is given by the soul and matter), but as that which is most truly proper to individual person (so, in this sense, it’s like a property at the individual level).

The second concerns “gender’s status to the human essence or nature.” Man and woman are not distinct species of human nature, but nor are they merely individuals of human nature. It is good, therefore, to introduce some notions that can describe the genders with regards to their human nature. Man and woman are principles of the nature, they’re parts of it, they are ways of it existing or ways of a soul incarnating in a body, and they are relational as mutually fulfilling complements. “Thomas compares male and female to odd and even in the numerical realm.” But even this misses out the relational nature of humanity.

The third concerns “gender in its specifically human meaning as the intersection of eros and generation.” A slight modification of the Aristotelian definition of male and female is, “the male is what co-generates in another, the female is what co-generates in itself.” There’s nothing peculiar to humans here; we are gendered because we are animal. But human gender has richer meaning than non-human gender insofar as the procreative activity is integrally marked by rational choice.

By nature the generative act is a human act, and not just the act of a human. Thus, what is distinctively human in gender comes to light most manifestly in the “co-” dimension of the co-generative relationship to the extent that deliberation, choice, and love are integral moments within human sexual activity, which thus transcends merely instinctual limitations.

The distinctive human dimension of all this is one of the reasons that it is considered problematic if the human generative act occurs without proper mutual consent, since it “presents a co-generative act with the co- aspect as distinctively human. Since the entire act is co-generative, if one aspect lacks distinctively human structure, so does the whole.” That the co- aspect is human and therefore higher than mere biological generation, it elevates the generative aspect which is primarily animal. The biological tendency becomes subsumed into a conscious intention in love.

Further, as Thomas points out, generating another like oneself in the case of a human involves continued rational and affective dimensions beyond those of the sexual sphere, since the mature human only comes to be after an extensive period of support, nourishment, training, education, and love.

Beyond metaphysics (43:42-46:55)

Here we comment on some things beyond the metaphysical question but which depends on the metaphysical answer, namely issues in the psychological, social, and ethical realms. There are two putative objections that might be raised from modern concerns against the claim that gender stems from the soul. First is the issue of sex-reassignment surgery, second is the reality of intersex persons.

With regards to the first, if in fact sex-reassignment surgery actually changed one’s sex/gender then it would constitute a concern. However, even if such surgery can change the outward appearance of an organ it nonetheless leaves the patient sterile. So rather than say that one’s gender has changed it is more accurate to say that it has to some degree been lost (or blocked).

With regards to the second, just as with sensation defects and abnormalities are possible so too with gender. This arises from the fact that gender (like the senses) arises from the soul working in and through matter. “Aside from the assistance of medical technologies in such cases, it’s crucial to recall that one’s gender, though integral to the person, is neither the defining nor the most important aspect of the person.” To quote Thomas on the place of gender in human life:

Among animals there is a vital activity nobler than generation to which their life is principally directed. Therefore the masculine sex is not in continual union with the feminine in perfect animals, but only at the time of coition, so that we may consider that through coition male and female are made one. But [humans are] further ordered to a nobler vital activity, which is to understand. Therefore there had to be a greater reason for the distinction of these two forces in [them], so that the female should be produced separately from the male and yet they might be fleshly joined as one for the work of generation.

In commenting on this, John closes with:

The ultimate telos of a human being involving the flourishing of a life suffused with knowledge and love reminds us that relationality and fruitfulness occur in realms higher than the physical. If, with Aristophanes in the Symposium, one were tempted to picture the human being simply as a longing half, the passage just quoted offers a larger view. In his own way, Thomas calls to mind Socrates’ and Diotima’s assent to the beautiful.

Common goods

I had originally intended to tie up the thoughts begun in previous posts on natural and moral goodnesssubstantial activitiesbasic goods, and virtual existence, but it has since occurred to me that this would be too ambitious for a single blog post. So, I’ll attempt to approach the topic in installments as I find the time. Those previous discussions are important for the direction I want to go, since we will be using much of the terminology and conclusions there. As such I strongly recommend reading them if you haven’t done so, and perhaps even rereading them if you haven’t done so for a while. In this post we will be introducing the notion of common goods, which will be much of our focus hereon out.

In general something is good to the extent that it realises its end. This is what Aquinas meant when he said that the “good has the nature of an end” (ST Q94 A2 corp). We’re most familiar with ends as intended by rational beings, but these are just a small number of the ends we’re considering. Non-rational animals act for particular ends too, of course. Beyond this the development process of living things is directed toward the end of healthy adulthood. And we’ve seen every substance is in some sense directed toward its characteristic behaviours given by its nature. (Besides the posts linked above, I also discussed this in section 2.2 here.)

Since goods and ends are so linked, a common good is therefore the realisation of a common end. And since common ends belong to communities or societies, it follows that common goods are the goods of these communities. But what is a community? It turns out the answer isn’t a simple matter: there are alternatives and each putative answer gives a slightly different notion of what the commonness of common goods involves. For the remainder of this post we will be unpacking all of this, with the help of our foregoing discussions.

In our discussion on virtual existence we outlined the three ways parts relate to their wholes: (1) parts which are actually present in their aggregate, (2) parts considered in themselves which are virtually present in their substance, and (3) parts considered as parts which are actually present in their substance (in the sense that they derive their being from the substance itself, and this substance is actually present). In (1) the parts each maintain their individual ends, and the end of the aggregate is merely the sum of the ends of its parts. Substances, on the other hand, have ends intrinsic to themselves. In (2) the end of the substance “overrides” the ends the parts would otherwise have in isolation, and in (3) the parts have the same end as the substance because they share in its being and nature.

In our discussion on substantial and aggregate activities, we noted that there is an analogous sense in which activities can be understood as substances or aggregates. And everything we’ve said about wholes equally applies to activities. For instance, we can also speak of virtual existence in the context of substantial activities. We introduce the idea by applying our hylomorphic analysis of virtual existence to a concrete example. Imagine we’re considering an orchestra playing a piece of music, and imagine we zoom in on one of the violinist’s playing. Recall that an action can be analysed hylomorphically, with the matter being the movement and the form being the intention. And recall that the virtual existence of parts in themselves involves retaining the matter while “filling in” (through intellectual activity) a form the part would have in isolation from the whole. What do we get in the case of our imagined example? Well, the intention of the violinist considered as a part of the orchestra is to play with piece together with the rest of the orchestra members. An intention that we might fill in would be the violinist practicing the piece by themselves. In this way actions can exist virtually in the substantial activities they belong to.

Now, are communities to be understood as wholes, or activities, or some combination of the two? It doesn’t seem correct to identify the community with the activity because the parts of the activity are the individual actions whereas the parts of the community are the individuals themselves. At the same time it seems mistaken to completely divorce a community from its activity. The same group of humans could be an orchestra and a soccer team, for instance, but surely the orchestra is distinct from the soccer team? Put another when we consider the members of the orchestra we consider them as musicians, but when we consider the members of the soccer team we consider them as soccer players.

As such, it seems to me that we should consider communities in terms of both wholes and activities. Again, hylomorphism gives us a natural way of doing so: when considering a group of individuals it is their activity that determines what community they are. That is, the group is an otherwise indeterminate substratum and the activity is what determines them to being this or that community. That is, the group is the matter and the activity is the form of the community.

So communities represent a third category which is a hylomorphic combination of the first two. And just as there are three ways for parts to relate to their wholes, and three analogous ways for actions to relate to their activities, so there are three analogous ways for individuals to relate to their communities. How should we understand these in terms of the wholes and activities that make up the communities? With regards to matter (the whole), it seems intuitive that the underlying whole of a community will always be some kind of aggregate of individuals, each of which will be substances in their own right. With regards to form (the activity) we have three options: (1) an aggregate activity in which the individual actions actually exist, (2) a substantial activity in which the individual actions virtually exist, and (3) a substantial activity in which the individual actions actually exist. Each of these would translate to a different kind of community. In (1) the community is merely the aggregate of the individuals, and its end is the sum of the disparate ends of these individuals. In this case, the only things that can truly be called a substance are the individual substances. In (2) we see the reverse of this: the individuals are the parts of the community considered in themselves, and as such their individual ends will be “overridden” by the ends of the substantial community. (3) represents somewhat of a middle ground, and will be of much interest to us. Here the individuals are parts of the substantial community, but not in such a way that they have their ends overridden. This is because their actions are all directed toward the common end of the community.

At least two of these views already have names: (1) is called atomic individualism and (2) is called organic collectivism. Matthew O’Brien and Robert Koons introduce them as follows:

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 organic collectivist holds that the most fundamentally real things (the “substances”) are complete and sovereign human societies; on this view, typified by Jean Jacques Rousseau, for example, individual human beings are merely cells of the social organism, with a nature, an identity, and an existence wholly dependent on that of the whole. In contrast, the atomistic individualist, such as Ayn Rand, holds that individual human beings are the substances, with societies as mere aggregations or “heaps” (to use Aristotle’s expression)….

For organic, collectivist pictures of human life, the good of individual human beings carries no weight, since, strictly speaking, there is no such thing as an individual: the good of the society as a whole is everything. For atomic individualists, the ‘common good’ consists of nothing but the sum of measures of the individual welfare of participants.

Their article doesn’t work from the exactly same distinctions we’ve made, but it’s clear from the quoted passage that for the organic collectivist the community’s being a substance in some way “overrides” the individuals that are part of it. That is, the community is a substance at the expense of the individuals, which corresponds with what we’ve said of (2). I don’t know of a name for (3), so for the sake our discussion here we will refer to it as unitivism.

So we have outlined the three views of (1) atomic individualism, (2) organic collectivism, and (3) untivism. Each gives us a different picture of what makes a community, as well as a different understanding of the commonness of common goods. It is this that we must unpack to adequately answer the question at hand.

Let’s start with atomic individualism. On this view the community is merely the sum of its individuals, and therefore so is its end, and thus the common good is also understood as an aggregate of individual goods. A good is common, in this sense, by virtue of being predicated of the many individuals of in the community. So, for instance, health or wealth would be common goods since it is good for each individual to be healthy and sufficiently wealthy. And the health of the community, for instance, would be the aggregate of the health of the individuals. Common goods, in this sense, are contrasted with singular goods in that to be common to be predicated of many whereas to be singular is to be predicated of one. So, we speak of the health of the community as opposed to the health of this or that individual.

Next consider organic collectivism. On this view the community is a substance at the expense of the individuals. Since it is a substance it has its own end, and this is what the common good would be. Since the individuals exist only virtually in the community, this common good overrides their individual goods. An example comes from some socialist economic theories, where individuals are to give up their individual right to private property in order to be part of the political community. So we find that common goods, in this sense, are contrasted with individual goods. The common good, in our example, being the common property which is contrary to the private property of individuals, or what we might call “individual property”.

Finally there’s unitivism. The unitivist agrees with organic collectivist that the community is a kind of substance, but disagrees that this comes in such a way as to override the individuals. We achieve this by noting that the realisation of the common end toward which all the members work together is a good for each member, and it is on account of their shared intention toward this end that they are considered a substantial community in the first place. Moreover the unitivist agrees with the atomic individualist that the goods of the community are the goods of the individuals, but disagrees that these goods are merely shared by virtue of predication and aggregation. We achieve this by noting that the common end is numerically the same for all the individuals, and its realisation is a single good shared by the individuals of the community without thereby being diminished. Consider, for instance, that the piece played by the orchestra is one and the same piece played by each of the musicians, a victory in war is one and the same victory for the entire nation, and so on. To use some Thomistic jargon the common good is a universal cause not a universal predicate. The common good, in this sense, is contrasted with private goods in that to be common is to be shareable with thereby being diminished and to be private is either to be unshareable or always diminished when shared.

Perhaps we should spend some more time unpacking this distinction between common and private goods. First some examples. We mentioned the playing of the piece for the orchestra and the victory in war for the winning nation are both common goods. Other examples are manifold, so long as we can identify the aggregate wholes engaging in substantial activities for common ends: victory in a sports game is a common good for the winning team, financial success is a common good for many companies, the picking up of a car by two friends is a common good for them. A previously mentioned example of a private good was food, for “if there is a loaf of bread between me and someone else, the more the I eat the less there is for the other person to eat.” Two other examples of private goods would be the two goods listed as common by the atomic individualist: health and wealth. While many individuals have health (on account of which it is a common predicate), they do not all share in one and the same health. Wealth is more or less a generalisation of food, in that the more money I give you the less I have for myself. Of course, private property would also be a private good.

Second, we note that in most (if not all) communities there will be certain private goods the members need in order to participate in and enjoy the common goods of that community. This often involves some form of equipment and training, but can also include other things. We will have cause to speak about this in more in later posts. We note this here because it reminds us that while common goods and private goods are contraries conceptually, they needn’t be (and often aren’t) contraries in practice.

Third, what we mean by activity should be construed quite broadly so as to apply to every kind of community we might consider. Indeed, once we do this we begin to see hierarchies of communities form. For instance, a soccer team participates in a soccer game, which itself is part of a larger tournament, which is run by the local soccer league, which is part of the national soccer league. The soccer team’s activity is also more than this or that game, but rather includes all their games as well as their practicing, recruiting, purchasing of equipment, and so on. The hierarchy of communities entails that when communities are parts of bigger ones, they can have private goods themselves. For example, playing a soccer game is a common good for both teams, but victory is private to one of the teams. That same victory, however, is common to the members of the winning team. So whether a good should be characterised as common or private depends on the community and individuals in focus.

Fourth, an important qualification: while common goods can be shared without thereby being diminished it doesn’t follow that sharing always leaves them undiminished. For instance, orchestras are limited in their size because once they get too big they become unmanageable. The same goes for political communities and friendships and presumably any community. Furthermore, including bad musicians in an orchestra might also diminish the end insofar as those musicians get in the way of the orchestra performing well. But in these cases it is not the sharing per se that is diminishing the good, but rather the sharing with too many people or sharing with bad musicians. With private goods, no matter how you share you will always diminish your ends.

Now, all three accounts of common goods can and do occur in reality. Of the three, however, it seems that the unitivist’s notion is most relevant to the study of the good of humans in social or political contexts. That we seek to study human goods means we are not primarily interested in goods that by their very nature occur at the expense of the human individuals. And that we seek to study human goods in social and political contexts means we are not primarily interested in goods that are mere aggregations of individual goods.

Contrastive probabilistic explanation

I want to propose something I’m not totally convinced is correct, but that I think is worth considering. In general we have the question about contrastive indeterministic explanation: an antecedent A can give rise to two different consequences B and C, it actually gives rise to B, and we want to know why it gave rise to B rather than C.

There are two cases that encode this, each prima facie in different ways (though they may be ultima facie reducible to the same case, more on this later): libertarian free choice and quantum indeterminism. Let’s take them in turn.

In a free choice we are impressed by reasons R for choosing between B and C. In the event we choose B, we want to know what explains why we chose B rather than C. The answer comes in being more precise about the content of R: it includes reasons R1 for choosing B over C and R2 for choosing C over B, and it’s in virtue of this that we are choosing between B and C in the first place (see section 4 in Divine Creative Freedom by Alexander Pruss). When we choose B then R1 explains why we chose it over C, and when we choose C then R2 explains why we chose it over B. Thus, the explanation is contrastive in virtue of the reasons themselves being contrastive. We’ll return to this shortly.

In an event of quantum indeterminism we have some quantum event — radioactive decay, say — that happens with a certain probability. Let A be the circumstance involving an atom at t1 which will decay with some probability, B be the circumstance involving it having decayed at t2, and C the circumstance involving it not having decayed at t2. In B, how would we explain why it had decayed rather than not?

The first Aristotelian step is to give an account of probabilistic causation, and the second is to elucidate the explanation this affords us. With regards to the first, something like what Feser has proposed here seems plausible, namely that the probabilistic behaviour the atom exhibits is grounded in its substantial form. This explains why the atom in the same antecedent state can result in two different consequent states, in a similar way to how the form of a material thing explains its inertia (see Nature and Inertia by Thomas McLaughlin for a fantastic discussion of this). It also plausibly explains why B is realised when it is realised. But it does not seem to explain why B was realised rather than C.

And here comes my proposal: there is no contrastive fact over and above the plain fact that B occurred and C did not. The difference between the two cases is a relation, and a relation is wholly grounded in the relata themselves (see Aquinas on the Ontological Status of Relations by Mark Henninger). Thus to explain why I am taller than you, it is sufficient to explain why I am my height, why you are your height, and note that the former is greater than the latter. There is no additional fact to explain. Similarly to explain B, and note that B excludes C, is sufficient to explain why B rather than C. If the situation were slightly different such that we had two identical atoms at t1 that at t2 realised B and C respectively, then to explain B for the first and to explain C for the second just is is to explain the outcome of the difference, since this consists precisely in the two outcomes being realised.

But wait! Why was there some irreducible contrastive fact to explain in the free choice case? Because in this case the content of the choice itself was contrastive. It was not that the relation between the choices had to be explained contrastively, but rather that in order to explain every aspect of the choice we also had to explain the contrastive aspects.

Uninstantiatables in Aristotelian Mathematics

Any successful Aristotelian foundations of mathematics needs to account for mathematical objects that are uninstantiated and even uninstantiatable. Examples include (1) positive whole (or “natural”) numbers larger than the number of objects in reality, (2) negative numbers, and (3) infinities.

Uninstantiated natural numbers

As the Aristotelian sees things, we abstract quantity and structure from reality, isolate certain aspects of these (which we call axioms), and extend these abstracted notions beyond our experience. Call these three stages abstraction, isolation, and extension respectively. Even though we can technically distinguish between isolation and extension, in practice these two steps occur together in the same cognitive action. We’ll use the term synthesis to refer to the activity involving isolation and extension. These activities of abstraction and synthesis are not unique to mathematics: we use them all the time. Once we have an concept of a horse and the concept of blackness, for instance, we can consider the combination of these two concepts without having ever seen a black horse. True, the Aristotelian says that “whatever is in the intellect was first in the senses”, but this mustn’t be taken to mean that a concept can exist in the intellect only if it was sensed. Rather it should be taken to mean that sensation provides the raw data from which concepts are abstracted. This is consist with some concepts being synthesized from others.

Once we understand this, then, the problem of uninstantiated whole numbers seems to disappear. Initially we come to see the concept of quantity by considering the relation from an aggregate to a unit. For instance, we consider the relation between a specific aggregate of apples and the unit apple. If we have six apples and six oranges, then the aggregate of apples is related to the unit apple in precisely the same way that the aggregate of oranges is related to the unit orange.[1] It is on account of this that we say that the two aggregates are of the same size. We can label all the various aggregate sizes: 1, 2, 3, 4, 5, … We can also see that all aggregates of size 3 contain aggregates of size 2, all aggregates of size 2 contain aggregates of size 1, and so on. Thus we come to see that there is an ordering amoung these numbers. We can also see that an aggregate of size 3 together with an aggregate of size 2 makes an aggregate of size 5, an 2 aggregates of size 3 together make an aggregate of size 6. Thus we come to understand addition and multiplication, and similarly with subtraction and division (restricting ourselves to just the natural numbers for the time being).

Depending on which mathematician you talk to, 0 will sometimes be considered a natural number and other times not. Typically we will use whatever is convenient at the time. We could get 0 by considering an empty aggregate’s relation to any unit, or by considering a non-empty aggregate’s relation to a unit not contained in that unit (the relation of 6 apples to the unit orange).

At this point we will have experienced a number of aggregates, but there will inevitably be aggregates of sizes that are impossible for us to experience (either because of cognitive limitations or limitations on the number of things in reality). As we saw earlier, however, this does not stop us from having concepts of such aggregates. Through a (usually complicated and messy) combination of abstraction and synthesis we can come to consider any and all natural numbers.

Negative numbers

What about negative numbers? At this point we move from talking about natural numbers to talking about integers, which are whole numbers that are either positive or negative or zero. We might be tempted to try and extend our work above to negative numbers in straightforward way. After all, surely all natural numbers are also integers? Well, kind of.

We said above that natural numbers are relations between aggregates and units. Integers, on the other hand, are relations of difference between two aggregates. Let’s return to our apples and oranges. Say we have 10 apples and 6 oranges. One of the relations between these two aggregates is that if I take away 4 apples from the former, then I will have two aggregates of the same size. More precisely, there will be in a one-to-one correspondence between apples and oranges such that every fruit is matched to some other fruit. This same relation holds between an aggregate of 11 apples and 7 oranges, 9 apples and 5 oranges, and so on. This relation (or any relation co-extensive with it) is the negative integer 4. Now imagine I had it the other way around: 6 apples and 10 oranges, 8 apples and 12 oranges, and so on. These are related in a way inverse to negative 4, since now in order to make the former equal size to the latter we’d need to add 4 apples. This relation is the positive integer 4.

This parallels what we do when constructing the integers out of the natural numbers in first year mathematics courses. Starting with the Peano axioms we get the natural numbers. Then we build the integers up from pairs of natural numbers, where the pair (a,b) intuitively represents the difference between a and b.[2]

Just as we came to understand ordering, addition, subtraction, multiplication, and division with the natural numbers, so we can with the integers. Assume you have two integers x and y. As we have seen, each integer is a relation between two natural numbers, so let x be the relation from a to b andy be the relation from c to d (where a, b, c, and d are all natural numbers), written as x = (a, b) and y = (c, d) respectively. Again, as we have seen, an integer can be a relation between more than one pair of natural numbers, as when the integer -4 holds between 5 and 1, 6 and 2, 7 and 3, and so on. Using this fact we can align a and c, by which I mean the following: because of how the natural numbers are ordered either a > c, a < c, or a = c. If a > c then a – c is a natural number and y = (c + a – c, d + a – c) = (a, d + a -c). If a < c then we do this the other way and get x = (a + c – a, b + c – a) = (c, b + c – a). And finally, if a = c then we needn’t change anything. At the end of this alignment we will have three variables e, f, and g such that x = (e, f) and y = (e, g). Given this alignment, we say that the ordering between x and yis the same as the ordering between f and g. The intuition behind this is as follows: if both x and yrepresent adding or removing a certain amount from an aggregate of size e, then the ordering of the two integers is the same as the ordering between these two results.

Next consider addition. Once again assume we have two integers x = (a, b) and y = (c, d). This time, however, align b and c to give us x = (f, e) and y = (e, g). Then x + y = (f, g). The intuition here is that the addition of two integers is the same as applying the one to the result of the other.

I will leave subtraction, multiplication, and division as an exercise to the reader. Each time you will extend the respective operation from the natural numbers. There is, however, a new operation that arises with integers which we might call “additive inversion”: a is the additive inverse of b if and only ifa = -b. This is fairly simple to get using the notion of relations: for any integer x, x = (a, b) if and only if -x = (b, a).

In summary then, integers are understood as relation of differences between aggregates, and so negative numbers do not pose much of a problem for the Aristotelian. As before, through a combination of abstraction and synthesis we can come to consider any and all integers, even those we haven’t (or couldn’t have) experienced.

Infinities

As you might expect, when we start talking about infinites we need to get more abstract and precise in our approach. One of the hallmarks of modern mathematics is that we seek a universal foundation for the things we study. Often this is some form of set theory, but in the past century we’ve also seen that categories, topoi, types, and others can serve as a foundation equally as well. For any of these foundations, the Aristotelian can do something similar to what we were doing above for numbers. For the sake of simplicity here we’ll just use sets as our foundation, and not worry too much about their details. I will also treat 0 as a natural number here, which is an inconsequential philosophically but helps with presentation. (If you’d prefer to not think of 0 as a natural number, then you can assume we’re talking about non-negative integers.)

We’ve previously explained that when the mathematician speaks of “defining” things in terms of sets, what he really does is establish what we called a “correspondence of aspect using analogy”. This involves “encoding” those things in terms of sets such that the relevant aspects of the things are captured from the perspective of the set. So, for instance, say we wanted to study ordering amoung the natural numbers. We can do this from the perspective of sets by considering the following “definition”:

  1. Let 0 be defined as ∅, the empty set.
  2. Let any natural number n be defined as {0, 1, 2, 3, … n-1}, the set of all previously defined natural numbers.

When writing this definition out verbosely, we’ll get the following:

  • 0 = ∅
  • 1 = {0} = {∅}
  • 2 = {0, 1} = {∅, {∅}}
  • 3 = {0, 1, 2} = {∅, {∅}, {∅, {∅}}}

From this perspective, one number is less than another number when the former is contained in the latter. That is, “1 < 20” is the same as saying that “1 ∈ 20”. This way, we can study the ordering amoung the natural numbers quite easily from the perspective of sets.

Notice that this definition only captures those aspects we want to study about numbers. If we wanted to study a different aspect, we might need a different set-theoretic definition of numbers. On the other hand, two different definitions might be equivalent for the purposes of studying a given aspect. Consider another putative set-theoretic definition of natural numbers:

  1. Let 0 be defined as ∅, the empty set.
  2. Let any natural number n be defined as {*n-1*}.

So, verbosely, this looks as follows:

  • 0 = ∅
  • 1 = {∅}
  • 2 = {{∅}}
  • 3 = {{{∅}}}

Using this definition it would be a lot more difficult to define what “1 < 20” means in terms of sets, but it would be equally as easy to define what “19 is immediately before 20” means as the first definition (namely, “19 ∈ 20”).

The point of all of this, for our purposes, is that not all definitions are equal, and it is this very fact that we exploit when studying infinities. We will focus on two “types” of infinity: cardinal infinities and ordinal infinites. In case you didn’t know there are an infinite number of each of these infinites. (Just let that sink in.)

Now natural numbers have a bunch of aspects, and we study different infinites by focusing on one of these to the exclusion of the others. This restriction effectively enables us to go beyond the finiteness of numbers. Depending on which restriction we make, we get a different type of infinity.

The aspects of numbers include quantity, matching, and ordering. Now both matching and ordering are more fundamental than quantity. This video gives a good explanation of why matching is more fundamental, but basically the idea is that I can know facts about matching or ordering without knowing the quantities involved. For instance, I can know that there are as many people as there are chairs in the room without knowing how many there are of either, and I can know that you finished the race before me without knowing our respective places.

Cardinal infinities

When we choose to focus on the matching aspect of numbers we study cardinal infinities. These are the infinites marked by the Hebrew letter ℵ (aleph). If we have two sets X and Y, there are three possibilities for matching:

  1. We can pair elements of X and Y such that every element in X is paired with exactly one element in Y, and there are no elements in Y left over. For finite sets this occurs when the two sets are the same size.
  2. No matter how we pair the elements one-to-one, there will always be some elements in Y left over. For finite sets this occurs when Y is bigger than X.
  3. No matter how we pair the elements one-to-one, we will never be able to pair every element in X. For finite sets this occurs when X is bigger than Y.

If we just focus on matching we can talk of the “size” of infinite sets, in terms similar to those just listed, but we must avoid thinking that we’ll get exactly the same kinds of results as in the finite cases. In finite cases sizes link to quantities, and it is exactly this link that we remove in order to study infinities. For instance, we can match each natural number to an even number such than none are left over, and so there are “as many” natural numbers as there are even numbers. The cardinal infinites represent the various “infinite sizes” that we could have. ℵ0 is the “size” of the natural numbers and any set for which we can give pair with the natural numbers with no left overs on either side. Thus, ℵ0 is also the size of the even numbers. When speaking precisely, we might say that infinite sets don’t have “size”, but rather cardinality. Cardinality is a notion that captures “matchability” or “pairability”. In finite cases, size and cardinality are the same. Of course, we rarely speak so precisely, and happily use the words interchangeably for infinite cases too.

An early result in set theory from Georg Cantor is that for any set (finite or infinite), the set of all subsets of that set will always be a bigger cardinality than that original set. This means that there are bigger infinities than ℵ0. One case he proved in particular was that no matter how you match up the natural numbers with the real numbers (points on the continuum, or numbers that can be represented with decimal expansions), there will always be some real numbers left over. So if we have a set of cardinality ℵ0, we say that the cardinality of the set of all subsets of that set is ℵ1, and the cardinality of the set of all subsets of that set is ℵ2, and so on.

Notice how the Aristotelian has no problems with any of this, for all we’ve done is the same thing we’ve been doing all along: abstraction and synthesis. In this case we’ve abstracted the notion of matching and synthesised the general notion of cardinality.

Ordinal infinities

We do something similar with ordinal infinites, which focus on the aspect of order. Imagine we went with the first set-theoretic definition of natural numbers given above. What number would set of all natural numbers represent? Presumably none of them, since no natural number is such that all natural numbers is less than it. But from the perspective of order, it would represent what we’d informally take to be the infinite-th position in a list. Just as before we have a general notion of ordinalwhich, when finite, agrees with the usual meaning of position or index, but which can also be used of infinite positions. And just as before we have a specific letter for ordinal infinities: the Greek symbol ω (omega). The first ordinal infinity is ω0, and using our first set-theoretic definition we have that ω0 = {0, 1, 2, 3, …}.

At this point we can see an interesting difference between the two different set-theoretic definitions we gave above: only the former is capable of capturing ω0. We can understand this from two perspectives. Formally, from a set-theoretic perspective the axiom of foundation prohibits infinitely nested sets, and this is exactly what we’d need if we were to give the definition of ω0 on the second account. Informally, from an intuitive perspective because ω0 is the infinite-th position there cannot be a natural number that is immediately before it. But this second definition effectively encodes the natural numbers in terms of the natural number immediately before them (n is defined solely in terms of n-1).

For the Aristotelian, this serves to show that what we can synthesise depends on how we abstract.

Now, just like the cardinals, there is more than one ordinal infinity. Unlike the cardinals, the next ordinal after ω0 is ω0+1 = {0, 1, 2, 3, …, ω0}.[3] Then it’s ω0+2, ω0+3, …, ω1 (=ω0+ω0), ω1+1, and so on.

Again the Aristotelian has no problems with any of this. In this case we’ve abstracted the notion of order and synthesised the general notion of ordinality.

Notes

  1. Readers will note that this establishes an analogy of proper proportionality of the form “apple aggregate : apple :: orange aggregate : orange”.
  2. We later take equivalence classes of these pairs, which corresponds to the idea that the same difference relation that holds between 6 and 10 also holds between 7 and 11, 8 and 12, and so on.
  3. With the cardinals, ℵ0+1=ℵ0. For instance, if we have some set {a, 0, 1, 2, 3, 4, …} which is cardinality ℵ0+1, then we can create a paring from {0, 1, 2, 3, 4, …} to it as follows: 0 → a, 1 → 0, 2 → 1, 3 → 2, … Thus, given how cardinals are defined, {a, 0, 1, 2, 3, 4, …} also has cardinality ℵ0.