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.

Smith’s epistemological argument for hylomorphism

The following quote comes from Wolfgang Smith’s The Quantum Enigma:

As Aristotle pointed out long ago, the act of knowing consists in a certain union of the intellect with its object. But how can the intellect be joined to the external thing? Such a union, clearly, can only be conceived in terms of a third entity or common element, which object and subject can both possess, each in its own appropriate mode; and it just be this tertium quid, precisely, that renders the object knowable.

But only in part! For it is not, after all, the external object — lock, stock and barrel — that “passes into the subject”, but only what I have termed the tertium quid. This “third factor”, moreover, answers to the question “What?”: it is what we know. And yet it does not simply coincide with the object as such, for as just noted, the latter is perforce “more” than the tertium quid.

Now the tertium quid, to be sure, is none other than the Aristotelian morphe, the form or quiddity of the existing thing. But inasmuch as the thing does not coincide with its morphe, one needs to postulate a second principle — an X, if you will — that distinguishes the two, or makes up for the difference, so to speak. And this X — which is perforce unknowable and had no quiddity — is evidently tantamount to materia. One arrives this, by way of epistemological considerations of a rather simple kind, at the basic conceptions of the hylomorphic paradigm.

How Aristotle starts the Nicomachean Ethics

In the opening passage of the Nicomachean Ethics Aristotle seeks to pick out the specific subject of his study for the remainder of the book. His discussion is often misunderstood, but a good understanding of it will serve us well in understanding the study of ethics. We will consider the passage bit by bit with comments and clarifications as we go along, doing our best to read it according to the principle of charity.

The good has the nature of an end

Every art and every inquiry, and similarly every action and choice, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim. (emphasis added)

Contrary to what some people think, Aristotle is not committing a quantifier shift fallacy here. Rather, he’s picking out some determinable, the good, which is common to all things done for some end. Let’s unpack this.

In general, something is less determinate (and therefore more indeterminate) if it is vaguer or less specific. So, for instance, red is less determinate that scarlet. Furthermore, determinateness comes in degrees: red is less determinate than scarlet, and coloured is less determinate than red. We use the term “determinable” to refer to some partially indeterminate feature which can be determined in some way. So, coloured is a determinable which red determines and red is a determinable which scarlet determines.

When two things resemble one another it is on account of them sharing some determinable feature which they each determine in some way: a scarlet thing resembles a crimson thing in that they are both red (that is, they share the determinable red), and both resemble a green thing in that they are all coloured things (that is, they share the determinable coloured). Just as determination comes in degrees, so too does resemblance: the scarlet and crimson things resemble each other at more levels of determination that the scarlet and green things. Speaking discretely, the scarlet and crimson things resemble each other as red and as coloured, whereas the scarlet and green thing only resemble each other as coloured.

In this opening passage Aristotle seeks to narrow the focus of his study by picking out the determinable that all desired things share, according to which they resemble each other as desired or as aimed at in some activity. He notes that whenever we desire or aim at something it is because of some good in it, and therefore the good is rightly declared to be this determinable he’s looking for. Now, just as what makes something one colour as opposed to another will depend on the particular way in which the determinable coloured has been determined, so too the reason why this or that thing is desirable or aimed at will depend on the particular thing in view. Good ice-cream and good vacations are desirable for different reasons, and so determinethe good in different ways, but they resemble each other in that they are pursued.

Later treatments would make explicit a question which, as far as I can tell, Aristotle leaves implicit or thinks obvious: is something good because I desire it, or do I desire it because it’s good? It cannot be the former, since I often desire things I later realise were in fact bad for me.

For haven’t we all had the experience of wanting something which we ourselves then admitted was not good? I wanted that last drink at the party, but afterwards I admit that it was not good for me. I wanted to drive 100 mph down the winding road, but later, on my hospital bed, I admit that it was not good. If wanting something made it good, then my wanting the last drink would have made it good for me. (Edmund Waldstein, The Good, the Highest Good, and the Common Good, thesis 2)

It must be, therefore, that I desire something because it seems good to me in some way. That is, the goodness I perceive causes the desire in me. Of course this perception may be incorrect, but the point remains that it because of the good I perceive in something (correctly or incorrectly) that attracts me to it as something worth pursuing.

Returning to our passage, Aristotle is noting here that in general the good “has the nature of an end” (cf. ST I-II Q9 A1 corp). An end is “that for the sake of which something is done” and a means is “that which is done for the sake of something”. These are complementary notions such that whenever we have one we also have the other. We see Aristotle make this same connection in the Physics where he lays out his four kinds of causes. In the passage he identifies ends as what later would be called final causes:

Then there are things which are causes in the sense that they are the ends of the other things, and are the good for which they are done. Without quibbling about whether it is an actual good or an apparent good, that at which other things are aimed — that is, their end — tends to be what is best. (Aristotle, Physics II.3 195a23-25)

Note that the Aristotelian “cause” is much broader than the modern’s “cause”. The modern usage most closely approximates the Aristotelian efficient cause. For those unfamiliar with the Aristotelian usage, perhaps “four kinds of explanations” is more helpful for conveying what he’s getting at.

Note also that the phrase “tends to be what is best” is just there to explain how ends and goods relate: something is good to the extent that it fulfills its end, and so to achieve its end in full is best (that is, most good). This is all he means.[1]

In summary, then, this first passage involves distilling this determinable the good, which is what accounts for the resemblance between things as desired in some activity. It picks out something as an end or that for the sake of which the activity is done.

Ends are better than means

But a certain difference is found among ends; some are activities, others are products apart from the activities that produce them. Where there are ends apart from the actions, it is the nature of the product to be better than the activities.

Now, as there are many actions, arts, and sciences, their ends also are many; the end of the medical art is health, that of shipbuilding a vessel, that of strategy victory, that of economics wealth. But where such arts fall under a single capacity — as bridle-making and the other arts concerned with the equipment of horses fall under the art of riding, and this and every military action under strategy, in the same way other arts fall under yet others — in all of these the ends of master arts are to be preferred to all the subordinate ends; for it is for the sake of the former that the latter are pursued. It makes no difference whether the activities themselves are then ends of the actions, or something else apart from the activities, as in the case of the sciences just mentioned.

Aristotle here makes distinctions regarding how activities and ends relate to one another. First, either the end and activity are the same or they are distinct. An orchestra playing a piece is an example of the former, since the performance is both the end and the activity. A carpenter making a chair is an example of the latter, since there’s a real distinction between the production of the chair (activity) and the chair (end). We must note that by “product” we don’t only mean physical objects that result from some activity, as the chair results from the carpentry. Rather, we mean any outcome which is distinct from the activity that brings it about. So, winning a sports game is the end and product pursued when playing the game.

Second, an activity can be made up of other activities. In this case, we might say that the subsuming activity is superordinate (or “master”), and the subsumed activities are subordinate. Subordinate activities are parts of superordinate activities.

Both distinctions show us different ways in which ends and means might arise and relate. Sometimes the end and the means are really the same thing, as when an activity is the end we desire. In this case, the distinction we impose is merely conceptual. Other times they are really distinct, as when an activity produces something external to it. Moreover, when one activity is subordinate to another the former is done for the sake of the latter, and so the former relates to the latter as a means to an end.

Twice in this passage he picks cases where there is a real distinction between ends and means (the product and activity, and the superordinate and subordinate activities), and notes that the end is always better than the means. This is true because “it is for the sake of the former that the latter are pursued”. That is, the end is more truly the thing desired, whereas the means is desired only in a derivative way. The end is desired through the means.

To make this more precise we need distinguish between the thing itself on the one hand and the thing desired on the other. Now, a thing is desired to the extent that it — and not something else — fulfills that desire, and so the desire for the thing itself is proportional to how closely it relates to the thing desired.[2] Thus, if just this or that feature of the thing is desired, then that feature is more desired that the thing itself. For instance, if I buy a torch because I want the lightbulb inside of it, then I desire the lightbulb more than I desire the torch. Conversely, if the thing itself is just one feature of what is desired, then the greater whole will be more desired than the thing itself. For instance, if I desire a violin performance because I desire an orchestra performance, then I desire the orchestra performance more than the violin performance.

Applying this to the cases Aristotle mentions, we can see why his claims are true. First, there’s the case when an activity is desired for the sake of some product really distinct from it. Here the activity is desired because of one of its features, namely the ability to bring about the desired product, and so the acquisition of the product is desired more than the activity itself. Second, there’s case of a subordinate activity being desired for the sake of some superordinate activity. Here the subordinate activity is desired because it is part of the superordinate activity, and so the superordinate activity desired more than the subordinate one.

We might also arrive at this conclusion from a slightly different angle. We’ve seen that goodness has the nature of an end. Thus to be better (that is, more good) is to be more of an end. Now, something is more of an end if it is closer to some final or ultimate end, as riding is closer to strategy than bridle-making.[3] But if A is a means to B, then B is closer to some final end, and is therefore more of an end, and therefore better.

At this point we must make two clarifications.

First, people sometimes mistakenly interpret Aristotle as assuming that bridle-making is only ever done for the sake of strategy. The passage does not require that we interpret him this way, and given his historical context he surely knew that bridle-making could also be done for the sake of other things, like recreation or sport. What he’s doing here is picking one of these instances as a concrete example of how activities might relate to one another such that some subsume others. If you prefer you could use an example where bridle-making is subsumed under some activity other than strategy, but the point would remain the same.

Second, to say that that ends are always better than means is not to say that things that are ends are always better than things that are means. Rather, we’re claiming that things considered as ends are always better than things considered as means. Part of the import of the first passage is that whenever we consider something better than another thing, it must be with respect to some end. But the complexity of human desires means that the same activity might be desirable for more than one reason, and therefore on account of more than one end. Imagine, as an example, that our friends have come together to study as a group. On the one hand, this might be desirable because studying produces knowledge. On the other, we might desire it because we enjoy spending time with our friends. The conclusion here, and Aristotle’s point, is that knowledge is better than studying considered as a means to knowledge. We’re saying nothing about the relationship between knowledge and studying considered as a part of spending time with friends.

In general, the claim that ends are always better than means is not the same as the claim that if B is ever a means to A, then A is always better than B. Rather, it is that claim that whenever and insofar as B is a means to A, A is better than it.

In summary, then, this passage notes certain helpful distinctions regarding activities and ends. Sometimes the activity and the end are the same, and sometimes they are distinct. In the latter case, the end is better than the activity. Activities themselves can often be divided into sub-activities (called subordinate activities), and in these cases the superordinate activities are better than the subordinate activities.

The chief good has the nature of a last end

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.

This passage has caused much confusion for readers, and it certainly would have been better if Aristotle had spent some more space clarifying his meaning here. Some have thought that by “chief good” Aristotle is picking out some particular final end of all human life. I’m inclined to think that he only introduces such a notion later in the first book, and even then with more nuance than some commentators would grant him. Alas, we will have to leave that for a future post.

But if he is not talking about a specific end, then what could he be talking about? Good question. In the first passage Aristotle arrived at this determinable the good which, having the nature of an end, is that for the sake of which everything is desired. Now, as with all determinables, we can determine this in various ways to various levels of specificity. So we can talk about the good, the good thing, the good artist, the good musician, the good violinist, the good first violinist, and so on. This parallels how we can talk about the coloured thing, the red thing, the scarlet thing, and so on. But notice how we could determine things differently, so that instead of determining coloured to red we could determine coloured to brightly coloured. This kind of “alternative determination” is what Aristotle is doing here in this third passage.[4] We’ll first discuss the structure, and then explain his defense.

The first part of the sentence reintroduces the notion already discussed in the first passage — this determinable the good — which he refers to as the “end of the things we do, which we desire for its own sake”. Now in the second passage you’ll recall he discussed ends and means and how they arise in various general ways, and he noted that the ends are always better than their means. Now consider some particular case where A is desired for the sake of B, B is desired for the sake of C, and so on, but where this chain comes to some final end Z. In this case Z is different from all the other members in the chain in that it is not desired for the sake of something else, or in other words it does not derive its desirability from another as a means derives its desirability from its end. This is the property Aristotle wishes to use in his alternative determination of the good, and it gives us this determinable the chief good. Now the chief good is still fairly indeterminate, and there is nothing in the notion itself that requires that it pick out one particular good in all cases. Depending on how we determine it we will get different goods: the chief medical good is health, the chief economic good is wealth, and the chief military good is victory. The important thing here is that the chief military good is not bridle-making, since the latter is an activity subordinated under the activity of strategy and as such derives its desirability from that superordinate activity.

So, if we were to repeat the passage, taking out the parentheses and highlighting corresponding determinables and their names, we would get the following:

If, then, there is some end of the things we do, which we desire for its own sake… and if we do not choose everything for the sake of something else… clearly this must be the good andthe chief good.

This, then, is the structure of the passage. But you’ll notice that Aristotle thinks that all chains of desire must end in some or other chief end. He summarises the reason for this in the second pair of parentheses when he says that if a specific chain didn’t come to an end then “the process would go on to infinity, so that our desire would be empty and vain”. Someone unfamiliar with the distinctions and arguments introduced by him in his other works like the Physics and Metaphysics can be forgiven for missing that he is just summarising and applying these here, as opposed to working them out from the start again. For the sake of clarity we will expand his summary slightly.

In those works Aristotle makes use of a general distinction between what would later become called per se causal chains and per accidens causal chains. These days they are also sometimes called essentially ordered causal chains and accidentally ordered causal chains respectively. The defining characteristic of a per se causal chain is that each member in the chain acts only insofar as it is acted upon, so that it derives its power to act from some other member in the chain. The standard example of such a chain is that of a stick which pushes a rock, which it does only insofar as it is pushed by me. On the other hand members in a per accidens causal chain do not depend on each other in this way. Here the standard example is that while my father depends on my grandfather for his coming to be, it is not the case that my father begets me only insofar as my grandfather begets him. (As a reminder note that while I’m using efficient causal chains as illustrative examples, the term “cause” here is used in the broader Aristotelian sense and not in the limited modern sense.)

Now, any particular per se causal chain requires an ultimate cause, by which we mean something with underived causal power in the relevant sense. This ultimate cause is also sometimes called a “first” cause, but when using this term we must remember that we aren’t concerned with something first in the sense of being earlier than all the other cause, but rather something being independent of the other causes and on which they depend. Indeed, when considering chains of final causes, this “first” cause is actually the last end.[5]

The reason why per se chains need ultimate causes is because each intermediate cause merely propagates the causal power it derives from another, so that unless there’s some originating cause there would be no causal power to propagate in the first place. Now because people are prone to misunderstand what’s being said we note that this point isn’t primarily concerned with the number of causes, but their kind — namely, that they are derivative causes. For example, it doesn’t matter how many water pipes you have, they will never by themselves be able to direct a flow of water unless something puts water into the system. Similarly, if everything in a collection can push only insofar as it is itself pushed, then that collection cannot by itself push anything.

Aristotle is here applying this to the notion of final causes: if everything in a collection produces desire in me only insofar as it derives that desirability from another, then that collection cannot by itself produce desire in me. What we need is something which is desired for its own sake and not for the sake of another, failing which the chain would have no power to produce desire in me (or, as Aristotle says, “our desire would be empty and vain”). This ultimate final cause, or ultimate end, would then be an example of a chief good.

So far we have left one thing in the passage unexplained: if the point about per se chains isn’t primarily about the number of causes, then why is Aristotle concerned that “the process would go on to infinity“? We can take Aristotle’s words in two ways, each of which complements the other. First, it might be that he’s using the term to pick out the notion of an infinite regress in the sense that there is no ultimate cause. This is sometimes how the term is used these days, and in this sense of the term it is consistent with there being infinitely many intermediate causes between the ultimate cause and the final effect (assuming such a thing is coherent). Second, while the point about per se chains isn’t primarily about quantity, it has a secondary consequence about quantity. It follows that the chain must be finite from the facts that (1) for each cause there is a next member of the chain (that which it causes), (2) there is a first member (the ultimate cause), and (3) there is a last member (the final effect).[6]

In summary, then, this last passage combines the insights from the first two and, by way of “alternative determination”, picks out the primary focus of the rest of the rest of his study, namely this determinable the chief good. This is just the beginning, however, and in a later post we will discuss the narrowing of his focus to the particularly human chief good that occurs later in the book.

Related resources

The biggest influence on the approach I followed here was David Oderberg, particularly his papers On an Alleged Fallacy in Aristotle and The Content and Structure of the Good. I quoted Edmund Waldstein’s The Good, the Highest Good, and the Common Good, and I highly recommend reading that too.

The notion of a determinable and it’s distinction from a cause is critically important for precision of thought. Ronald McArthur’s paper Universal in praedicando, universal in causando is an invaluable resource for understanding the distinction between predication (which corresponds to our determinables) and causation. I highly recommend it.

For more information on per se vs per accidens causal chains I recommend Edward Feser’s blogposts Cross on Scotus on causal series and Edwards on infinite causal seriesm Caleb Cohoe’s paper There Must Be a First, and Gaven Kerr’s paper Essentially Ordered Series Reconsidered. Cohoe’s paper is the one where I realised that additional reasons need to be given for thinking that per se causal chains are finite.

Notes

  1. In general something fails to fulfill its end only to the extent that it is prevented in some way, due to either internal defect or external interference. For instance, a carpenter might aim at making a chair which can hold people up and not fall down easily, and will only fail to achieve this if impeded by something internal (like lack of ability) or something external (like bad materials). Unless such interference occurs the carpenter will achieve their end in full, which is the best result. We’ve mentioned before that classical thinkers like Aristotle realised that there is a broad sense in which all things are orientated to certain ends given by their natures. And in the Physics he has this more general notion in mind. For instance, the development process of a dog is directed toward the growth of four legs with which the dog can walk, and only fails to achieve this when the dog has some kind of genetic defect or has some external blocker is present, like an accident or lack of food. Again, unless it is interfered with the process will achieve it’s end in full, which is the best result.
  2. In coming up with this phrasing I thought of a number of alternatives, which I include here for posterity: “the thing exhausts the desire without excess”, “the thing itself, and not some part or some greater whole, is what’s desired”, “the thing itself is desired, and not some part thereof or some whole of which it is part”, “the thing is desired neither merely in part or as a part”, “the whole of the thing is the whole of what’s desired”, “the thing is all and only what is desired”, “the thing in reality matches the thing desired”, “a thing is desired to the extent that it matches the object of that desire”, “the thing satisfies the desire without excess or deficit”, “of the thing itself and the thing desired, neither is a part of the other, but they agree completely”, “the thing itself, and not something more or less, fulfills the desire”.
  3. Shortly we will defend the claim that every chain of ends must have some final, ultimate, or “chief” end. However, this is not required for this point. If we have some infinite series of ends, then to say that B is more of an end than A it is sufficient that it be closer to some end C which is further along the chain.
  4. The rough idea is as follows: when we determine some determinable we contract or qualify it in some way. Now we come to know determinables through abstracting away these qualifications, and so the most “natural” way of determining them is by the same road we took to get there in the first place. But nothing in this constrains us to this, and we are free to qualify or contract in a different way to how we first arrived at the determinable. This different way is what I’m calling an “alternative determinations”.
  5. I’m reminded of the saying of Christ that “the last will be first, and the first last.” (Matt 20:16)
  6. While Aristotle wouldn’t have expressed it in these terms exactly, it seems from his other works that he understood the principles at play here. The three facts combined mean that the causal chain is one-to-one mappable onto a bounded contiguous range of natural numbers, which is only possible if the chain is finite.

How can a loving God send people to hell?

I was recently asked to contribute a piece for a local Christian magazine called Scope Magazine, on the topic of how a loving God could send people to hell. Below is the unedited version I sent them. The official (and slightly edited) version can be read online here.

Perhaps one of the most uncomfortable Christian doctrines is the doctrine of hell. How is it, the question goes, that a loving God can send people to hell? Surely a God who truly loved all of mankind would allow everyone, without exception, into heaven? It seems to me, however, that reality is not as clear-cut as it first appears. A complete discussion would take more space than we have available to us, so my goal here is to draw a broad outline of the reasons why.

Let’s start by defining our terms. What is hell? While it is often pictured as fire and brimstone, it seems that the essence of hell is to be the opposite of heaven. What, then, is heaven? Christians have traditionally understood heaven to be the everlasting and direct experience of God himself. But wait, isn’t heaven supposed to be fun? Well, it depends. God is the supremely good and most beautiful thing in all reality, and to the extent a person realizes this they will desire God above all else. To such a person nothing could be more pleasurable than such an experience. And to be cut off from such goodness and beauty would be, for anyone, an undesirable fate indeed.

What is love? At its core, love is willing the good of another, appreciating the good in them, and striving to be with them in some way. If the love is mutual, then we build an every-growing bond. If the love is not mutual, then what can we do but make ourselves available in the hopes that one day the love will perhaps become mutual? To force oneself upon the other does not seem to be in line with loving them; rather love calls for some measure of honoring their wishes.

Putting these two together we begin to see something like the doctrine of hell: God has revealed himself in such a way that anyone who sincerely and consistently seeks him out will come to know him, and those who willfully ignore him will not have him forced upon them, neither in this life nor in the next. As Frank Turek has said, “God loves you too much to force you into his presence against your will.” Furthermore, while there is a certain continuity between this life and the next, we must realize that resurrection brings with it some measure of transformation. And the same permanence of will that safeguards an everlasting desire for God in heaven also safeguards an everlasting obstinance toward God in hell.

Consider this from another angle: we note that respect for someone flows out of love for them. When it comes to their actions, this means recognizing their responsibility as proportional to their abilities. So, it is out of respect we treat adults like adults, children like children, and animals like animals. This respect governs how we praise and reward someone for the good they’ve done, and blame and punish them for the bad they’ve done. In short, our respect for someone leads to a desire for justice for them. So God’s love for us leads to a desire for justice for us, and so he holds each of us accountable in perfect proportion to the bad we’ve done.

Now, God is the ultimate king over all creation and a being of infinite worth. To reject him or ignore him, therefore, is to be responsible for a kind of “grand cosmic treason”. Since in this case, the victim is of infinite worth, this represents a crime of infinite gravity, for which justice demands an infinite punishment. More broadly, Christians have traditionally held that God will judge each person proportional to their response to what they have been given, which fits quite well with our intuitions on the matter even if we disagree on the particular outworkings.

In summary, God’s honor and respect for us, both of which flow from his love for us, seem to suggest something like the doctrine of hell when properly understood. Of course, it would be remiss of me not to mention one of the clearest expressions of God’s love, namely that he would make himself a man and die for us. While perhaps not immediately obvious how, this act secures two consequences relevant to our topic here: it enables us to respond to God so as to enter into that bond of mutual love, and it acquits us of our guilt before him and thereby redeems us from punishment.

From morality to nature and back again

Below is a talk I recently gave at a local apologetics meet-up. The goal was to introduce and partially defend natural law theory to a group of fellow-Protestants who, as far as I was aware, had not engaged extensively with natural law theory before. The talk was recorded in various parts, with video coming in the second part. At the end there is a collection of resources for those interested in some further reading.

In our previous meeting I got the impression that my views on morality as an Aristotelian and Thomist are particularly different from the views of many of you here, as well as Protestants more generally these days. I have two goals here tonight. The first is to introduce and partially defend the views I’ve come to hold on these issues, and the second is to explain how these relate particularly to Protestant approaches to Scripture and modern uses of the moral argument for God’s existence.

We’ll be concerning ourselves primarily with issues of meta-ethics, which is that subfield of ethics that concerns itself with (1) what we mean by certain terms like “good”, “moral”, “virtue”, “justice”, “ought”, as well as (2) how such things are grounded, by which we mean giving an account of what makes things good, moral, virtuous, etc. There are roughly two meta-ethical theories I want to talk about:

  1. Divine command theory, which I imagine is the view many of us here hold.
  2. Natural law theory, which is the view I want to recommend as best.

Now, before we start I should note that these two theories have very different approaches in terms of how they are developed. Like most modern meta-ethical theories, the divine command theory we’ll be talking about takes the term “moral” as picking out some special or mysterious class of facts that need to be defined and grounded by the theory. On the other hand, for the classical natural law theory we’ll be talking about, the term “moral” doesn’t pick out any particularly special, and is defined before we even start the theory. The focus of natural law theory is instead the notion of “goodness”.

This is noteworthy because we’re going to use the word “moral” in both senses tonight, and it can get confusing unless you keep this difference in mind.

1. Essentialist Divine Command Theory

I imagine the divine command theory that is most commonly held here is the so-called essentialist divine command theory defended by people like William Lane Craig and Robert Adams.[1] We can sketch the rough outlines of the theory in about 7 points:

  1. “Moral” picks out those fact which are most fundamental and important. If our government commands us to do something immoral, for example, we still have a duty to refrain from listening to them, since our moral duties are more important than our duties to our government.
  2. We divide moral facts into moral values and moral duties. Moral value refers to the worth or goodness of something. Moral duties refer to the moral obligations or prohibitions that apply to us, what we ought and ought not do, rights and wrongs.
  3. Moral value is ultimately grounded in God’s nature or essence, in the sense that he is the paradigm of moral goodness. Because God is a person, persons are morally valuable. Because God is loving, love is morally good. And so on.
  4. Moral duties are grounded in God’s commands to us, which are given explicitly through revelation or implicitly through conscience. The idea here is that in general duties arise from commands from qualified authorities. For example, when a policeman commands me to do something I have a legal duty to do that, since policemen are qualified legal authorities. God, being the paradigm of moral goodness, is uniquely qualified to be a perfect moral authority, and so his commands constitute moral duties.
  5. God’s commands, and therefore our duties, are not arbitrary because they are based on God’s unchanging nature, which we said in (3) is the paradigm of moral goodness. Nor are they based on something external or “bigger” than him because his nature is something internal to him.
  6. Moral virtues are those habits that dispose us to doing good and right things as they are grounded in God’s nature and commands.
  7. Because moral duties arise from God in this way, it seems that so must our personal motivations for obeying them. In a Christian context this would mean that the reason we follow God’s commands is out (1) love for God and desire to be with him, and (2) fear of just punishment.

2. Thomistic Natural Law Theory

We move now to natural law theory. The particular brand of natural law that I’m interested in here is the one from by Thomas Aquinas, who himself was developing the natural law theory of Aristotle.

2.1. Morality is about practical reason

Now, as I said, as a classical theory we have the term “moral” defined upfront: “moral” picks out things relating to the will, and therefore also our actions. For example, classically we can by divide reason into speculative reason and practical reason. Speculative reason relates to our intellect and has to do with applying reason to further expand our understanding of reality. The habits that lead to good speculative reasoning are called the intellectual virtues. Practical reason relates to our will and has to do with applying reason to govern how we will and act. So habits that lead to good practical reasoning are called moral virtues.

So, while we might have inherited the word “moral” from Aristotle, it no longer has the same meaning. Classically, it did not denote some special or fundamental class of value of duty, it wasnot connected with the will of God in such a way that he could be said to be a lawgiver, and it does not carry the psychological weight of being bound by some law. In his Ethics Aristotle discusses both moral and intellectual virtues, with neither being more important than the other.[2] The reason for this is that both moral and intellectual virtues part of being a good human.

As we said, the best starting point would be how classical natural law understands the notion of “goodness”.

2.2. Good has the nature of an end

Aquinas said that in general the good “has the nature of an end”[3] and we’ll use this as our starting point. In a way, though, our modern ears aren’t prepared for this definition, because we’ve been taught to think of conscious deliberation whenever we think of something working for an end. But for Aristotle and Aquinas our consciousness is just a special case of the goal-directedness that exists throughout nature. For them, everything that exists has tendencies toward certain ends determined by its nature.

The thought is roughly as follows: at every level things exhibit certain natural regularities or tendencies toward certain effects. We see this in living things, like how hearts regularly pump blood, or how dogs regularly grow up to have four legs so they can walk, or how seeds regularly grow into trees. We also see this in non-living things, like how matches tend to combust when struck, the moon tends to orbit the earth, salt regularly dissolves in water, rocks regularly fall to the ground, and so on. In each case we have something consistently producing its specific effect unless its prevented from doing so in some way.

And notice that each regularity involves the production a specific effect rather than something else or nothing at all. Matches produce fire as opposed to producing ice or nothing at all. Seeds grow into trees and not into rocks. Salt dissolves as opposed to combusting. Rocks fall as opposed to exploding. And the same goes for all the numerous regularities that exist throughout the universe. But, that things consistently work to produce their specific effects seems to make sense only if “there is something in them that is directed at or points to specifically those outcomes rather than any others”.[4]

So, in some broad sense hearts are directed at pumping blood, the development process of dogs works to produce an organism that walks on four legs, matches are directed at combusting when struck, salt is directed to dissolving in water, and so on. At the end of the day we find that everything that exhibits some form of natural regularity must be directed by its nature towards that behaviour as kind of end or goal. This is the kind of “teleology” that Aristotle and Aquinas have in mind when they talk about goal-directedness in nature, which by-and-large isn’t due to the conscious deliberation of the things themselves. Of course, working this out completely requires a fairly lengthy side-track into metaphysics and philosophy of nature, but hopefully the examples I gave will give you enough of an intuition.

Now, let’s go back to what Aquinas was saying about good having the nature of an end. What he’s getting at is that whenever we talk about an end we can also talk about goodness: something is good to the extent it fulfills its end and bad or defective to the extent that it fails to fulfill its end. If I’m playing a sports match, for instance, then my actions are good for me to the extent that they help me win the game. On the other hand, losing the game would be bad for me, and could happen because I played badly or because my opponent played better than me. A chair is good to the extent that it realizes the carpenter’s end of making something that holds people up and doesn’t fall over. And a music performance is good the extent that it achieves the orchestra’s end of playing the piece.

2.3. Natural goodness

So we have that (1) everything is in some sense directed toward certain ends by their nature and (2) whenever somethings works for an end we have a measure of goodness for that thing. This gives us a very general sense of goodness that applies to almost everything. Because this notion of goodness is so closely linked with the natures of things we can call it “natural goodness”.

It might sound odd, but this natural goodness is in some sense both relative and objective. It is relative because what is good for you is dependent on the kind of thing that you are. If you had had a different nature, then different things would be good for you. It’s bad for cats to have two legs, but it is good for humans to have two legs. A good match causes fire when used, and a good fire extinguisher stops fire when used. However it’s still objective because at the more fundamental levels you don’t decide your own nature, and cannot change it.

Now, this natural goodness serves as the springboard for all ethical reasoning in natural law theory. The basic idea is that because we can study our human nature through various empirical methods and philosophical reasoning, we can also come to a better understanding on how to live well as humans.

2.4. Accountability, duty, and authority

While we can’t go through all the details here, what I would like to do is give you a rough idea of how on natural law theory we can move from this natural goodness to thinks like moral accountability, duties, and authority.

Accountability, it seems to me, is ambiguous between two things, which we’ll take in turn: responsibility and punishment. We noted earlier that moral virtues are a special case of virtues in general, and I think something similar happens when you consider moral responsibility and responsibility in general. In general, being responsible for an action means that that action was up to you. And people typically that one’s responsibility is in some way proportional to one’s knowledge, or at least one’s capacity for knowledge. The idea here is that an action is up to you only to the extent that you understand what you’re doing. So we generally hold adults more responsible for their actions than children, who we hold more responsible for their actions than our pets, who we hold more responsible for their actions than this or that rock.

Now, humans have been traditionally been called rational animals. We don’t mean by this that humans are always perfectly rational: they’re not. Roughly, what makes animals rational is their ability to grasp and be conscious of universal concepts that particular things fall under. So there’s the particular human called Socrates, and there’s the universal concept of humanness which Socrates, Plato, and all other humans fall under. All animals are conscious in some way of particular things, but rational are those animals which are also conscious universal concepts. Now, this ability to understand universal concepts means we have the ability to understand the natural goodness and evil, that we were talking about earlier, both for ourselves and for others, as well as the ability to choose to pursue or avoid this goodness. This additional understanding about our actions results in us being held more responsible for them, and this additional layer or responsibility is what we mean by “moral” responsibility. At the end of the day, we say that an action is morally good or evil to the extent that the end or means willed in that action are naturally good or evil.

For example, if due to genetic defect or accident I have only one leg this is bad for me but I am not responsible it. In this case we have a natural evil without a moral evil. On the other hand, if I cut my own leg off then this is an evil for which I am responsible. In this case we have a natural evil with a moral dimension, since the natural evil is the product of my will.

As for punishment, one way it arises is as follows: humans are not merely rational animals but also political animals, by which we mean that it is natural and good for us to be part of various communities like families, sports teams, companies, friendships, and states. When a part is a detriment to the good of the whole, it is good for that part to be removed from that whole or to otherwise incur some debt so as to restore the good of the whole.[5, 6] For example, if my hand has gangrene it is good for me to cut it off. This removal or debt will be punishment, and if properly administered it will have to be done according to the principle of retributive justice.[7]

What about duties? On divine command theory we have divine legal duties which arise from God’s commands to us. And although it’s not as big a focus in natural law, we can also say something about duties. We’ve seen that our nature sets certain ends for us, and to the extent that an action contributes to our fulfillment of these ends it is good. This gives us the fact that, if I will the good, then I ought act so as to fulfill my natural ends. But if we think about it, in general we act for something because we will it, and we will it because it seems good to us in some way. “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.”[8] What this means, however, is that we always will what seems good to us, even if sometimes we incorrectly prioritize some goods over others. Combining this with our earlier fact we get to the following conclusion:

  1. If I will the good, then I ought act so as to fulfill my natural ends.
  2. I do will the good.
  3. Therefore, I ought act so as to fulfill my natural ends.[9]

After some reflection on our natures this will result in various duties such as “I ought not steal”, “I ought not murder”, “I ought honor my parents”, and so on. But what kind of duty is this? It’s certainly not a legal duty that we get from divine command theory, since it doesn’t arise from any command. We might call it a rational or a natural duty since it arises out of our natural capacity for practical reason. It serves to show us that we should be interested in what is naturally good for us.

And finally, what of authority? Here we combine some of the points we’ve already made. The idea here is that someone has authority over me if they are in charge of my good, since I ought seek my good, and therefore I ought listen to their commands. Different people will have authority over different areas of my life and to different degrees depending on their position and qualification, and in each case something like this idea applies.

2.5. The four laws

Now, is there any place for a divine legislator on natural law theory? This is one of the main areas where Aristotle and Aquinas differ. For Aristotle, God is not a divine legislator and the only place he takes in the ethics is as the object of our highest end which is philosophical contemplation about him. Aquinas, however, thinks Aristotle made a mistake here. In unpacking what he thinks is the correct view, Aquinas explains that there are ultimately four kinds of law:

  1. There’s the eternal law, which embodies God’s knowledge of all the various natures of things he could have created, and so what would have been good for them.
  2. There’s the natural law, which is what we’ve been speaking about here. For humans this forms the foundation for all our practical reasoning. It tells us what it means to act well as the kinds of things that we are. It’s called “natural” law because all of this derives from our natures.
  3. There’s human law, which are laws promulgated by a human legislator in charge of a community. Natural law is often very vague and general and it’s application in particular cases requires careful consideration by wise people. “[H]uman law is essential for living the good life because it makes the general precepts of the natural law more specific.”[10] Human law is authoritative because it’s based on natural law.
  4. Finally there’s the divine law, which are laws promulgated by God, the divine legislator. This law most closely represents that law that we think of in divine command theory, and they are the laws that are proclaimed through some form of revelation.

So there is a place for divine law, but it’s embedded in this bigger theory of ethics. Ultimately I think every intuition we have explained in divine command theory can be relocated somewhere in natural law theory, with a richer foundation, since natural law gives us accounts of things like authority, responsibility, and so on.

3. Modern Protestant objections

So with that overview of natural law theory, let’s talk briefly about it means for Protestantism. I think a lot of Protestants these days are quite resistant to the idea that moral prescriptions or substantial moral knowledge might come from somewhere outside of scripture. I say “these days”, because neither the church historically nor the reformers themselves had a problem with natural law theory. John Calvin, for example, said the following in his Institutes:

It is a fact that the law of God which we call the moral law is nothing else than a testimony of the natural law and of that conscience which God has engraved upon the minds of men.[11]

I think our modern hesitance arises from a combination of two things. On the one hand there’s been an increasing loss of acquaintance with natural law thinking in the past few hundred years, because of what I take to be certain philosophical errors of the early moderns like Descartes and Locke. Recently we’ve started correcting these errors, but our culture as a whole has lost its grip on this kind of thinking. And when we consider certain doctrines like original sin and sola scriptura against this backdrop they might seem to be at odds with what I’ve been saying.

So consider original sin, which says that our natures have been disordered, which in turn undermines our ability for unaided reason and therefore the moral conclusions we draw from it. But there’s nothing in this that contradicts what I’ve been saying. The claim that we can come to know ethical truths through philosophical reflection does not require that we be infallible in our conclusions. All that follows from our fallibility is that our understanding of ourselves, like our understanding of any part of nature, needs to be a community effort that spans many generations and societies. And the same thing can be said of our understanding of scripture itself. To quote John Goyette:

The collective effort required for the development of the arts and sciences is, for Aquinas, one of the reasons why man is a political animal. But the same is true of human law: it a collective effort requiring experience and time, and the wisdom of the wise. Just as men perfect the arts and sciences as part of a community, so do men perfect their knowledge of the natural moral law by participating in the [political community].[10]

What about the doctrine of sola scriptura, or “scripture alone”? There seem to be a number of slightly different of ways of formulating the doctrine, [12] but if it’s to be consistent with scripture it can’t claim that scripture is the only source of moral knowledge, for two reasons. First, because scripture itself references other sources like conscience. One of the clearest places where we see this is in Paul’s letter to the Romans where he talks about the Gentiles and he says that even though they haven’t been given the law through revelation, “they show that the requirements of the law are written on their hearts, their consciences also bearing witness.”[13]

The second reason is because scripture must presuppose some knowledge of the world, and this knowledge includes some things pertaining to morality. J. Budziszewski gives the following example:

Consider for example the prologue to the Ten Commandments, where God reminds the Hebrew people of their indebtedness to Him: “And God spoke all these words, saying, ‘I am the LORD your God, who brought you out of the land of Egypt, out of the house of bondage. You shall have no other gods before me ….'” How is it that the people of Israel, before the proclamation of the law, already know the law of gratitude? The answer is that the basics of natural law are already impressed upon the innermost design of the created moral intellect. We know a part of God’s will for us even before receiving it in words.[14]

3.1. The role scripture

I suppose we might wonder what does scripture adds if we can to know moral conclusions apart from it. There are a number of things we can say here.[15]

  1. In general there are things about God and ourselves that we can’t know through unaided reason and scripture is needed for these. Things like God’s triune nature or his dealings in human history, particularly what we call redemptive history, what will happen after we die, that marriage is a symbol for Christ and the church, and so on.
  2. Because of God’s revelation to us through scripture and through Jesus we are able know God personally, which wouldn’t be possible otherwise, since friendship requires communication between friends. As Jesus says in John’s gospel, “No longer do I call you servants, for the servant does not know what his master is doing; but I have called you friends, for all that I have heard from my Father I have made known to you.”[16]
  3. Revelation of God’s commands serves to introduce divine law and duties, which we wouldn’t have otherwise.
  4. Revelation about morality serves as a guide and summary of natural law. We’ve already seen that it can be difficult to work out the details of natural law, and besides that not everyone has the gifts or time to work them out. So through revelation God enables more people to know and will the good.

4. Apologetics

As we close I want to say a few things about what natural law means for apologetics today.

4.1. The moral argument

Like most arguments for God’s existence the “moral argument” is really a family of arguments. The one most heard today is formulated as follows:

  1. If God does not exist, then objective moral values and duties do not exist.
  2. Objective moral values and duties do exist.
  3. Therefore, God exists.

The question I want to address is how natural law effects the prospects for a moral argument like this.

Now, Aquinas gave arguments for God’s existence in various places throughout his writings, although most famous are the so-called “five ways” he lays out in the Summa Theologica. As far as I can tell Aquinas never gave a moral argument. I think the reason for this is that from a natural law perspective morality is not some special part of reality that calls out for an explanation, but is rather the result of the combination of otherwise non-moral features of reality: (1) the goal-directedness we see throughout nature and (2) the wills of rational beings.

The closest thing Aquinas gives to a moral argument is his fifth way, which is a teleological argument.[17] I should note, though, that the teleology Aquinas has in mind is different from the kinds of teleology we see in modern arguments for God’s existence.[18] He’s not concerned with the complexity of living things or the fine-tuning of the universe, for instance, but rather the goal-directedness we spoke about earlier, which is required by the various regularities that exist at all levels of nature both complex and simple.

Now, the question arises of how something can be directed toward and end. It’s clear how this happens with intelligent beings, since there the end in some sense existing in the intellect of that being, and so it can guide the actions of that being. But with non-intelligent things, since they lack an intellect, their ends can’t influence them in the same way. So it seems that non-intelligent things must be directed toward their ends by something with intelligence. And in fact, we could see why this is the case if we spent some time analyzing the notion of intelligence, but we don’t have time for that now. This is how Aquinas summarizes what we’ve been saying in his fifth way:

Now whatever lacks intelligence cannot tend towards an end, unless it be directed by some being endowed with knowledge and intelligence; as the arrow is shot to its mark by the archer. Therefore some intelligent being exits by whom all natural things are directed to their end; and this being we call God.[19]

Of course there is still lots to be unpacked. After he gives his five ways, Aquinas spends some time explaining why this is the being we call God. He argues for God’s oneness, goodness, omnipotence, omniscience, simplicity, eternity, and a host of other divine attributes, but we just don’t have time to give and defend those arguments now.

Coming back to the moral argument. I think technically we can still use it as I formulated it, but we must recognise that it is partly dependent upon something like the fifth way for its soundness. At the end of the day I think much moral debate can be had without reference to God, since it is based on what is knowable about our nature. But ultimately I think any viable ethics depends on God, including natural law.

4.2. Cultural apologetics

Finally, from the perspective of cultural apologetics natural law serves as a common ground for Christians and non-Christians to discuss ethical issues, since particular moral conclusions do not depend on whether one thinks God exists or not. For example, atheist philosopher Phillipa Foot has said that,

… the Summa Theologica is one of the best sources we have for moral philosophy, and moreover that St. Thomas’s ethical writings are as useful to the atheist as to the Catholic or other Christian believer.[20]

In the Western world it’s becoming increasingly important that we be able to defend the value of human life, and of family life, and particularly the rights of children. Our culture truly is a “culture of death”, in which people think it’s OK to kill innocent human beings so long as they’re young enough or helpless enough, and more generally in which we ignore the rights of children so that adults can do what they want. All too often these days I see people object to things like these on so-called “religious grounds” and then get ignored because the secular world doesn’t share their religious convictions. But there are good arguments wholly apart from any religious confession, and these need to be the primary go-to point for us.

A secondary point is that as we show the reasonableness of so-called “traditional” moral conclusions, we also show in part the reasonableness of the Christian worldview. In this way natural law can help show our culture that Christianity is an intellectually viable worldview, which is something they’ve forgotten amongst all the hype with the New Atheists.

Other resources

For more on natural law, Feser’s blogpost Whose nature? Which law? which goes into more detail about this technical word “natural”. There’s also his article Natural Law, Natural Rights, and Private Property, which has a short introduction to natural law as well as an example application of it to property rights. If you’re interested in structure of the approach many natural law theorists take when unpacking the specifics of natural law, see my blogpost Goods, basic goods, and facultiesand David Oderberg’s paper The Structure and Content of the Good.

On the topic of original sin, there’s J. Budziszewski’s three-part blogpost series Natural Law and Original Sin (part 1, part 2, part 3).

On the relationship between God and natural law see Edward Feser’s blogposts Natural law or supernatural law? and Does morality depend on God? While the fifth way is a sound argument for God’s existence, I tend to prefer the second way. See Edward Feser’s An Aristotelian Proof for the Existence of God for a good talk on this, as well as a taste of how we might go about arguing why we call this being God. If you’re interested in the fifth way, I recommend his paper Between Aristotle and William Paley: Aquinas’s Fifth Way.

Finally, one of the things that cam up in the question time was the notion of divine simplicity. William Lane Craig on divine simplicity is a blogpost by Edward Feser where he discusses some contemporary objections, and On Three Problems of Divine Simplicity is a paper by Alexander Pruss doing likewise.

For more, see the notes below, as well as the long list of categorised resources over at my blog.

Notes

  1. See, for instance, Robert Adams’s Finite and Infinite Goods. In contrast to essentialist versions of divine command theory there are the voluntarist versions like the one put forward by Ockham, which place both values and duties at God’s commands. I’ve also discussed what I call derivative divine command theory, in which duties are prior to values.
  2. I mean more important in the sense of needing to be studied. He thinks that the intellectual virtues are better than the moral virtues, since the highest end of man (or, to use modern terminology, man’s superordinate basic good) is philosophical contemplation of God.
  3. ST I-II Q9 A1 corp.
  4. Edward Feser, Scholastic Metaphysics.
  5. “Now every part is directed to the whole, as imperfect to perfect, wherefore every part is naturally for the sake of the whole. For this reason we observe that if the health of the whole body demands the excision of a member, through its being decayed or infectious to the other members, it will be both praiseworthy and advantageous to have it cut away. Now every individual person is compared to the whole community, as part to whole. Therefore if a man be dangerous and infectious to the community, on account of some sin, it is praiseworthy and advantageous that he be killed in order to safeguard the common good…” (ST II-II Q64 A2 corp)
  6. “… whatever rises up against an order, is put down by that order or by the principle thereof. And because sin is an inordinate act, it is evident that whoever sins, commits an offense against an order: wherefore he is put down, in consequence, by that same order, which repression is punishment.” (ST I-II Q87 A1 corp) This is a more general version of what was said in [5]. I’ve briefly discussed this comment elsewhere.
  7. The argument, very briefly, is as follows: in order for the good of the whole to be best upheld, punishment ought only be of guilty people, ought be proportional to the crime, and ought be equal (ie. like punishment for like crimes). There are at most four putative theories of justice: deterrence, correction, preventative, and retributive. Only the last safeguards all three of these conditions. This is not to say that punishment couldn’t also include deterrence, correction, and prevention, but it must minimally be based on the principal of retribution. A supporting argument is that only retributive justice sees the agent as a human, and is therefore the only theory that affords them proper respect. Deterrence sees only a behaviour, correction only a patient, and prevention only a future threat.
  8. Edward Feser, Classical Natural Law Theory, Property Rights, and Taxation.
  9. Compare this argument to the following: (1) If I will to draw a straight line, then I ought use a ruler, (2) I will to draw a straight line, (3) Therefore, I ought use a ruler. (3) is consistent with me not realising that rulers are the best way of drawing straight lines. Similarly, that I will the good is consistent with me not having a perfect grasp of what that involves. And even once I realise it involves acting so as to fulfill my natural ends, I still won’t have a perfect grasp of what such fulfillment involves.
  10. John Goyette, On the Transcendence of the Common Good
  11. John Calvin, Institutes of the Christian Religion, IV. XX. 15
  12. This arises because we need to find a formulation that is not the Roman Catholic doctrine ofprima scriptura but at the same time doesn’t lead to self-defeat.
  13. Romans 2:15, New International Version.
  14. J. Budziszewski, Does Sola Scriptura Mean “No Natural Law”?
  15. I’m particularly fond of what John O’Callaghan says about the general relationship between theology and philosophy here. A noteworthy quote is: “Theology doesn’t take place in a vacuum just because it something heard from the mouth of God… and so we need to understand what’s presupposed to being able to hear what is being preached to us or what is being revealed to us, and then a systematic reflection upon it. Theology shouldn’t take place in a vacuum.”
  16. John 15:15, English Standard Version.
  17. For a lengthy and substantive defense of Aquinas’s fifth way see Edward Feser’s Between Aristotle and William Paley: Aquinas’ Fifth Way.
  18. See Edward Feser’s Teleology: A Shopper’s Guide.
  19. ST I Q2 A3 corp.
  20. Phillipa Foot, Virtues and Vices.

That orders regulate

In Summa Theologica II-I Q87 A1 corp. Aquinas says the following:

Now it is evident that all things contained in an order, are, in a manner, one, in relation to the principle of that order. Consequently, whatever rises up against an order, is put down by that order or by the principle thereof. And because sin is an inordinate act, it is evident that whoever sins, commits an offense against an order: wherefore he is put down, in consequence, by that same order, which repression is punishment.

The idea is that when one is directed (or “ordered”) toward an end, one is also directed away from contrary ends. Thus insofar as a part moves contrary to the ends of the whole (or “rises up against the order”, an “inordinate act”), it will be counteracted (“put down”) because of the directedness of the whole towards its ends (“by that order or principle thereof”). This will apply to substantial activities which, as we’ll see in a later post, gives us the correct analysis of common goods and human communities in general.

What’s particularly interesting is that from this simple fact we can derive the three, otherwise intuitive, criteria for just punishment:

  1. Guilt: we should only punish those who go contrary to the good of a community, since the order of the whole will only counteract those parts which move contrary to it.
  2. Proportion: punishment should be proportioned to crimes, since the order of the whole need only to counteract enough to restore itself from the part’s deviation.
  3. Equity: punishments are alike to the extent that their crimes are alike, since the reason for the counteraction is the deviation itself and not some irrelevant factor.

Lonergan on Aquinas on Causation

Below is an excerpt from Bernard Lonergan’s incredible book Grace and Freedom, discussing Thomas Aquinas’s views on causation and how they relate to Aristotle’s views on the topic. Except for the term “actio” I’ve replaced Latin phrases with their English translations in square brackets.

Causation is the common feature of both operation and cooperation; its nature is of fundamental importance in this inquiry. But if St Thomas certainly disagreed with Hume, who held causation to be purely subjective, it is less clear what object he considered to constitute the objective reference of the proposition “A causes B.” Was causation for him something in between A and B? Or was it simply the relation of dependence of B on A? Or was it some entity added to A as actually causing? Let us take each of these three views in turn.

As to the first view, that causation is in between cause and effect, St Thomas constantly and explicitly denied it in the case of divine activity. Avicennist biology had distinguished between a [a moving power commanding (something)] and a [a motive power effecting (something)], and St Albert had drawn a parallel distinction between the [divine created power] and a [divine uncreated power]. But St Thomas, while he used the biological opinion at least in his commentary on the Sentences, always asserted that God was his own virtue, operated without any mediating virtue, indeed operated [by the immediacy of power]. The matter is less clear with regard to causation by creatures. Even in later works there is a variety of expressions which appear to imply something in between agent and recipient. Still, it should seem that these are but modes of expression or of conception; for what is in between, if it is something, must be either substance or accident; but causation as such can hardly be another substance; and if it were an accident, it would have to be either the miracle of an accident without a subject, or else, what St Thomas denied, an accident in transit from one subject to another.

On the second view, causation is simply the relation of dependence in the effect with respect to the cause. This is the Aristotelian position presented in the Physics and explained by St Thomas as follows. First of all, this analysis prescinded from the case of the mover being moved accidentally; for instance, a terrestrial body acts through contact and cannot touch without being touched; but this does not prove that the cause as cause undergoes change but only that the terrestrial body as cause does so. In the second place, it was argued that the emergence of a motion or change involved the actuation of both the active potency of the cause and the passive potency of the effect. In the third, place the thesis was stated: one and the same act actuates both potencies, and this act is the motion produced in the object moved. Fourthly, there came the ground of this position: if causation, actio, were an entity inherent in the cause, then, since it is a motion, it would follow either that “[every moving thing is moved],” or else that motion inheres in a subject without the subject being moved; but the latter is contradictory, and the former would preclude the idea of an immovable mover; therefore, causation is not inherent in the cause but in the effect. Finally, the objective difference between action and passion was explained: both are really identical with the motion of the recipient; they differ notionally, for action is this motion as from the cause, [movement of this as from this], while passion is the same motion as inhering in the effect, [movement of this as in this].

It would seem that St Thomas accepted this Aristotelian analysis as true and did not merely study it as a detached and indifferent commentator. Not only did he repeat the same exposition in commenting the parallel passage in the Metaphysics, while in the De anima he argued that sound and hearing, instances of action and passion, must be one and the same reality, else every mover would be moved; but in works that are entirely his own the same view at least occasionally turns up. In the Summa theologiae the definition of actual grace appeals to the third book of the Physics for the doctrine that “[an act of a mover is a movement in the thing moved]”; the analysis of the idea of creation was based upon the Aristotelian identification of action and passion with motion; and the fact that this identification involved no confusion of action with passion was adduced to solve the object against the Blessed Trinity, namely, that since the divine Persons were identical with the divine substance they must be identical with one another. Still, this is not the whole story. In his commentary on the Sentences St Thomas brushed aside the notion that action and passion were on and the same reality, while in the parallel passage in the Summa theologiae a solution is found that does not compromise the authority of Aristotle. This difference involves a change attitude, prior to the Pars prima and perhaps posterior to the De potentia, raising the question of the initial Thomist view.

In earlier works, then, the theory of causation seems to have been worked out on the analogy of the familiar distinction between the [being towards] and the [being in] of the relation. In action one has to distinguish between a formal content described as [from an agent] or [as proceeding from an agent to another], and on the other hand, a reality, substantial or accidental, termed the [principle of action] or the [cause of action] or even loosely actio. This terminology is to be found no less in the commentary on the Sentences than in the De potentia, but at least in the latter work it also is quite clear that the formal content is no more than a notional entity. In the two passages quoted below, the reader will be able to verify the following six propositions: (A) change from rest to activity is change in an improper and metaphorical sense; (B) the reverse change from activity to rest takes place without any real change in the agent; (C) when the agent is acting there is no composition of agent and action; (D) what remains unchanged is the [principle] or [cause of action]; (E) what comes and goes without changing the agent is the formal content, [from an agent]; (F) the analysis holds even in the case of a created agent such as fire.

And so a relation is something inhering (in a subject), though that does not result from the mere fact that it is a relation; as action, too, from the fact that it is action, is considered as from an agent, but as an accident it is considered as in the acting subject. And therefore, there is nothing to prevent an accident of this kind (B) from ceasing to be without (involving) a change of that (subject) in which it is, because its being is not realized insofar as it is in that subject, but insofar as it passes on to another; with the removal of that (passing on), the being of this accident is removed (E) in what regards the act but remains (D) in what regards the cause; as is the case also when, with the removal of the material (to be heated), the heating (F) is removed, though the cause of heating remains (De potentia, q. 7, a. 9, ad 7m)

But that which is attributed to something as proceeding from it to something else does not enter into composition with it, as (C) neither does action (enter into composition) with the agent… without any change in that which is related to another, a relation can cease to be through the change alone of the other; as also is clear about action (B), that there is no movement as regards action except metaphorically and improperly; as we say that (A) one passing from leisure to act is changed; which would not be the case if relation or action signified something remaining in the subject (Ibid. a. 8 c.)

If our interpretation of these passages is correct, then at least in the De potentia St Thomas had arrived at a theory of action that was in essential agreement with Aristotle’s. Evidently the two terminologies differ completely: on the Aristotelian view action is a relation of dependence in the effect; on the Thomist view action is a formal content attributed to the cause as causing. But these differences only serve to emphasize the fundamental identity of the two positions: both philosophers keenly realized that causation must not be thought to involve any real change in the cause as cause; Aristotle, because he conceived action as a motion, placed it in the effect; St Thomas, who conceived it simply as a formal content, was able to place it in the cause; but though they proceed by different routes, both arrive at the same goal, namely, that the objective difference between [to be able to act] and [to actually act] is attained without any change emerging in the cause as such.

This real agreement in terminological difference solves the problem of St Thomas’s thought on causation. John of St Thomas listed the passages in which action is placed, now in the agent and now in the recipient; from this he drew the conclusion that action, according to St Thomas, was inchoatively in the agent and perfectively in the recipient. But in point of fact St Thomas simply had two ways of saying that action involved no new entity in the agent; and so far was he from differing really from Aristotle that he seems to have been quite unaware of even his terminological departure from the Aristotelian position. This latter fact not only solves Cajetan’s perplexity over the apparent divergence between the commentary on the Physics and regular Thomist usage but also provides the most conclusive evidence against such as position of Billuart’s that a real distinction in the agent between [power to act] and [the act itself] is one of the pillars of Thomist thought.

On the transitivity of strict preference

The notion of comparing alternatives often comes up in philosophy, particularly when discussing practical reason. There are various names for this (we can talk about the reasons for choosing A over B, or how A is better than B, or how A is more desirable to B, or how A is preferred to B) but they all amount to the same thing.

The other day I was reading the SEP article on preference and was struck by this counterexample to transitivity of strict preference (I recall my friends mentioning it to me in the past, but I only thought about it critically this time around). In this quote, X≻Y represents that X is strictly preferred to Y, and X∼Y represents indifference between X and Y:

In an important type of counterexample to transitivity of strict preference, different properties of the alternatives dominate in different pairwise comparisons. Consider an agent choosing between three boxes of Christmas ornaments… Each box contains three balls, coloured red, blue and green, respectively; they are represented by the vectors ⟨R1,G1,B1⟩, ⟨R2,G2,B2⟩, and ⟨R3,G3,B3⟩. The agent strictly prefers box 1 to box 2, since they contain (to her) equally attractive blue and green balls, but the red ball of box 1 is more attractive than that of box 2. She prefers box 2 to box 3, since they are equal but for the green ball of box 2, which is more attractive than that of box 3. And finally, she prefers box 3 to box 1, since they are equal but for the blue ball of box 3, which is more attractive than that of box 1. Thus,

a. R1≻R2∼R3∼R1,
b. G1∼G2≻G3∼G1,
c. B1∼B2∼B3≻B1; and
d. ⟨R1,G1,B1⟩≻⟨R2,G2,B2⟩≻⟨R3,G3,B3⟩≻⟨R1,G1,B1⟩.

The described situation yields a preference cycle, which contradicts transitivity of strict preference.

(Note that I’ve added the labels to the listed conditions for the sake of this discussion.)

Now, I haven’t read much of the modern discussion on transitivity of preference (indeed, I didn’t even finish reading the article), so perhaps what I’m about to say is really obvious.

It seems clear to me that the above counterexample motivates the otherwise very natural distinction between (1) being better in some respect and (2) being better simply. Ultimately it has to do with why we prefer something over another. For instance, assume I prefer red balls over blue balls. Then I prefer this red ball over that blue ball simply, and I prefer this box of green and red balls over that box of green and blue balls in some respect.

I say this distinction is “very natural” because it seems necessary if we are to make sense of trade-offs, which are manifold in everyday experience. As a trivial example (which I find myself in often), imagine you need to pick one of two routes to your destination. Route A is longer but has prettier scenery and conversely route B is shorter but has uglier scenery. You have to pick one, but whatever choice you make will involve a trade-off. On account of what is this a trade-off? Well, surely it’s because shorter routes are preferable to longer ones and prettier routes are preferable to uglier ones. That is, A is better in some respect (prettiness) and B is better in some other respect (length).

This distinction resolves the above counterexample by showing us that (a)-(d) equivocate on “≻”. In (a)-(c) X≻Y means X is strictly preferred to Y simply, but in (d) it means X is strictly preferred to Y in some respect.

The SEP article immediately goes on to say the following:

These and similar examples can be used to show that actual human beings may have cyclic preferences. It does not necessarily follow, however, that the same applies to the idealizedrational agents of preference logic. Perhaps such patterns are due to irrationality or to factors, such as lack of knowledge or discrimination, that prevent actual humans from being rational.

Perhaps, but I’m inclined to think life’s more complicated than that. It seems pretty intuitive that there are various types of goods that are incommensurable. One way we might make this intuition precise is as follows: in general there seem to be two ways in which A is better than B:

  1. A and B are both means to C and A is a better means.
  2. B is a means to A.

(1) is where this whole business of comparing of alternatives comes in. Given our above discussion we realise that A can be a better means either in some respect or simply. Aristotle mentions something like (2) at the beginning of the Nicomachean Ethics. The guiding intuition here is that ends are preferred to means because “it is for the sake of the former that the latter are pursued” (I.1 1094a15-16).

Now, combining this with our previous discussion on basic human goods, the fact that there are multiple basic goods suggests that at least sometimes two goods will be incommensurable.