CAIN AND ABEL AS CHARACTER TRAITS:
A STUDY IN THE ALLEGORICAL TYPOLOGY
OF PHILO OF ALEXANDRIA[1]
Hindy Najman
The
writings of Philo of Alexandria contain three extensive treatments of the Cain
and Abel narrative: On the Sacrifices of Abel and Cain, The Worse Attacks
the Better, and On
the Posterity and
Exile of Cain. This
paper will argue that PhiloÕs interpretation of Cain and Abel is typological,
and that the types in question are both cosmological and psychological. The types of Cain and Abel are
presented as two aspects of the human soul, representing the human capacity for
good and the human capacity for evil. Consequently, reflection on these two
types can be a source of moral teaching.
My argument may sound controversial. For
Philo is sometimes said not to practice typological interpretation at all, but
rather allegorical
interpretation, and the two kinds of interpretation are sometimes thought to be mutually exclusive.
Before turning to the details of PhiloÕs interpretation of the Cain and Abel narratives,
then, I will first discuss the nature of typology and its relationship to
allegory. As I will argue, the idea that they are mutually exclusive arises
from particular theological presuppositions and has unfortunate consequences for the study of the history of
ancient biblical interpretation.
I will also question the claim that Philo does not engage in typological
interpretation by considering PhiloÕs interpretations and terminology. PhiloÕs
interpretation of the story of EveÕs children, I will argue, is at once both
typological and
allegorical, and it provides an important illustration of what is theologically
and historiographically
at stake.
I
Allegory
and typology have often been contrasted as two fundamentally different ways of interpreting
Scripture. While allegorical interpretation
has been said to focus on the cosmic and the spiritual, typological
interpretation has been characterized as more historical and literal.[2]
However, although it is true that allegorical interpretation tends to be cosmological and that
typological interpretations tend to be oriented towards history, the
distinction between the two is less clear‑cut than one might think. Since the reformation, scholars
have denigrated allegorical interpretation (e.g., in the writings of Philo of
Alexandria and of Origen) because it appeared far removed from the literal
sense of Scripture. Instead, typological interpretation (e.g., in the writings
of Paul) was celebrated.[3]
The focus on the literal sense of Scripture—and, since the enlightenment, on
historical study of the Bible—produced
anti‑allegorical
polemics that still find their way into current scholarship.
Philo himself uses the term ÒtuposÓ throughout his writings, so one would
think that there is good reason to call his interpretations typological.[4]
Still many scholars deny that Philo engages in typological exegesis at all. For
example, Goppelt writes:
PhiloÕs exposition of patriarchal history
contains no typological interpretation
at all. Whenever the historicity of the patriarchs has not been completely
destroyed by allegory, they are presented as ethical Òtypes,Ó or ideals, and do
not fit our definition according to which a type must point to something
greater in the future.[5]
In this passage, typological
interpretation is restricted to a particular kind of historical typology that can be found in the New
Testament. Central use of the term ÒtuposÓ in an interpretation is insufficient, according to
Goppelt, for classification of that interpretation as typological. It is also required that the
interpretation operate within the framework of salvation history. It is in this
sense of historicity[6] that
typology is said to be historical, whereas allegorical exegesis is said to be
symbolic, spiritual and interested only in the cosmic and the eternal, not in
the narrative of Scripture.
It seems an odd policy to apply the term
Òtypological interpretationÓ
only to interpretations with particular theological presuppositions. Indeed, others use such
presuppositions to distinguish different species of typology instead. Thus, for example,
Woolcombe writes:
There is no theological similarity whatever between the typology
of Philo and that of St Paul. The only point of contact between the two writers is their common use of the typological
vocabulary. But whereas in St Paul the vocabulary is harnessed to the
exposition of GodÕs redemptive
work in history, in Philo it is harnessed to allegorism. It is in fact hardly
possible to separate typology from allegorism in Philo, and if the word
typology must be used of certain aspects of Philonic exegesis, it should always be qualified by the
adjective symbolic, in contradistinction
to the historical typology
of the New Testament.[7]
However,
the extreme language in this passage—Òno theological similarity whateverÓ, nothing more than a lexical
Òpoint of contactÓ—suggests that it has the same underlying
motivation as the outright denial that Philo practices typological
interpretation: to enforce the sense of a radical distinction between Jewish
and Christian modes of exegesis. From a scholarly view‑point, such motivations should be
suspect. For they are all but bound to lead to the effacement of the profound
exegetical and theological continuities between ancient Judaism and early
Christianity.[8]
Nevertheless, Woolcombe is night to say
that, it is Òhardly possible
to separate typology from allegorism in PhiloÓ. PhiloÕs typological
interpretation should be seen as a species of allegorical interpretation. Indeed, as the term ÒallegorismÓ
suggests, Philo is interested in explaining the cosmic significance of biblical
texts. This interest should not, however, be misrepresented as incompatible
with respect for the literal meaning of the biblical text, whether narrative or
legal. As Goppelt writes:
He [Philo] retells and explains biblical
history and the very details of patriarchal and Mosaic history. Above all, he
insists that the literal sense of the Law must be fulfilled, quite apart from
its deeper‑meaning (Migr. Abr. 89‑93; Exsecr. 154).[9]
For
Philo, the narrative of Israel is the story of a community that strives for
perfection by observing Mosaic Law. But observance of Mosaic Law requires not
only attention to the laws in the Torah but also use of biblical narratives
within a moral pedagogy rooted within a deep account of the complexity of the
human soul. Indeed, as I will argue, PhiloÕs typological analysis of the Cain
and Abel narratives
should be understood as an exercise not only in cosmology but also in moral
psychology and paideia.[10]
II
It is not difficult to show that the term
tupos plays an
important role in PhiloÕs exegesis. For example, in De Opificio Mundi 18,
tupoi are implemented by
the ‑creator from the
archetype or paradigm of the overall plan for the cosmos:
Thus after having received in his own
soul, as it were in wax, the figures of these objects severally, he carries about the image of a
city which is the creation of his mind. Then by his innate power of memory, he recalls the images of the various
parts of this city, and imprints their types yet more distinctly in it: and
like a good craftsman
he begins to build the city of stones and timber, keeping his eye upon his pattern
and making the visible
and tangible objects correspond in each case to the incorporeal ideas.
In
another example from De Decalogo 10‑11, Philo describes transgressions upon the soul as tupoi and suggests that re‑educating the soul is a precondition for
receiving the law:
He who is about to receive the holy laws
must first cleanse his soul and purge away the deep‑set stains which it has contracted
through contact with the motley promiscuous horde of men in cities. And to this
he cannot attain except by dwelling apart, nor that at once but only long
afterwards, and not till the marks which
his old transgressions
have imprinted on him gradually grown faint, melted away and disappeared.
As in the above two examples, PhiloÕs
writings are replete with references
to tupos. In fact, ÒtuposÓ is a prominent member of a chain of words
that appear in PhiloÕs interpretations. Other members of the chain include ÒeikonÓ (image or copy), ÒcharacterÓ (stamp, standard,
or figure of letters, but also character type) and ÒPhantasiaÓ (impression or appearance). Perhaps it is helpful to think of tupos as character[11] or, more specifically, character trait.
The English or Greek word Òcharacte~Õ like ÒtypeÓ has
a meaning with two dimensions.
1) A tupos or character is a legible imprint. It is a mark left by
something else, which the mark now resembles as an image resembles an original. I will call this the
copying dimension of the meaning
of tupos. A tupos is a copy or eikon of
some original, which Philo calls an archetupos or paradigma. For example, according to Philo the
archetype of evil is Cain, so every self‑lover shares in CainÕs sin and in the murder of Abel:
Wherefore let every lover of self,
surnamed ÒCain,Ó be taught that he has slain that which shares AbelÕs name, the
specimen, the part, the impression stamped
to resemble him, not the original, not the class, not the pattern, though he
fancies that these, which are imperishable, have perished together with the
living beings. Let some one say, taunting and ridiculing him: What have you done, poor wretch?
Does not the God‑loving
creed, which you imagine you have annihilated, live with God? You have proved
to be your own murderer, having slain by guile that which alone had the power
to enable you to live a guiltless
life. (Det. 78)
Thus
according to Philo, types are less perfect than the originals, yet they imitate
the originals and resemble them as copies of those originals.
2) A tupos or character trait is a disposition to
act in a particular way, a virtue or a vice. It is a disposition that a human
being may acquire through habit or education. I will call this the psychological
dimension of the
meaning of tupos. Here
it is important to note that, as with a piece of wax, i character trait imprinted upon a
human soul may be effaced, and the soul may be restamped with a different, even
opposite character trait. Hence the fragility of virtue. For there is no
guarantee that a soul will retain the good character with which it has been
imprinted. As Philo writes:
The mind, like wax, receives the impress and retains it
vividly, until forgetfulness, the opponent of memory levels out the imprint,
and makes it indistinct,
or entirely effaces it. (Deus 44)
But
the wax analogy also implies the possibility of repentance. For a bad character
trait, just like a good one, may be replaced. Here Philo is perhaps reworking
PlatoÕs discussion of the waxen imprints upon the soul in Theaetetus 191c ff. However, Plato is concerned with
the apprehension and retention of knowledge, while Philo focuses on the moral
formation of the soul through action.
Philo seems to believe, not only that all
human beings have the capacity for virtuous behavior, but also that everyone is
actually born in a state of goodness. It is then left to each individual to
reinforce this innate goodness through good action, or else it will be compromised through transgression. Notably,
not every place is conducive
to virtuous behavior. Most famously, Philo insists that the city is a place of
corruption. That is why Israel must leave Egypt and receive the law in the desert (Decal.
11).
It is helpful to compare IsraelÕs need to
leave the city with the philosopherÕs need to leave the cave in PlatoÕs Republic,
Book VII. The
philosopher returns to the cave to facilitate the enlightenment of his fellows,
and to put in order the city and its citizens as well as themselves (Republic
539e‑540b). Similarly, the Israelites must
sojourn in the wilderness so that they may eventually constitute a new more
perfect city in accordance with the law received in the wilderness.
In order to bring together the
cosmological and psychological dimensions of PhiloÕs typology, it is helpful to
note that the laws themselves are described as tupoi, images or impressions which the
Israelites are told to stamp upon their hearts. Cosmologically speaking, the
law of Moses is a copy of the law of nature.[12]
To live in accordance
with the law of Moses is to live in accordance with the cosmic order created by
God. Psychologically speaking, to observe Mosaic law is to efface the evil that
results from transgression and foolishness, and to restamp oneÕs soul with the character of
goodness and virtue. Consider PhiloÕs discussion of how ceasing from work on
the seventh day enables a soul to live in accordance with the great archetype:
Let us not then neglect this great
archetype of the two best lives, the practical and the contemplative, but with
that pattern ever before our eyes engrave in our hearts the clear image and
stamp of them both, so
making mortal nature, as far as may be, like the immortal by saying and doing
what we ought. (Decal. 101)
According to Philo, Cain exemplifies the ope
of wickedness, while
Abel exemplifies that of holiness. In a sense, these biblical characters are types. For every detail related about
them in the biblical narrative‑their
names, their chosen professions, their conceptions of God and their actions‑every single detail contains a moral lesson about the impression of vice or
virtue upon the human soul. I suggest that the reason for this is that Cain and
Abel exemplify character
traits, and their conflict exemplifies the conflict between these traits in
every human soul. The conflict between Cain and Abel becomes an allegory of
psychic conflict within the soul of every human being. Moreover they are to be
understood as two aspects of a single soul.
According to Philo, CainÕs deepest
problem is his flawed conception
of God, which is reflected in his very name. For Cain believes himself to
possess all things. In contrast, AbelÕs Òname means one who refers (all things)
to God.Ó (Sacr. 2).
The brothersÕ chosen professions reflect
and reinforce their fundamental
differences. Philo emphasizes that CainÕs chosen profession involves him with
earthly and inanimate objects. So he does not choose to prepare for a future
life and to pay attention to living things. Similarly, Philo points out that
Cain is called a tiller of the soil because he refers all things to himself and
to his own mind (Sacr. 51).
In fact, it is CainÕs lack of understanding that the land is really foreign and
belongs only to God that misleads him in the direction of a self‑loving character trait and ultimately
causes the destruction of his soul. In contrast, Abel chooses to tend living
beings. Thus:
AbelÕs choice of work as a shepherd is
understood as preparatory to rulership and kingship (QG 1.59)
The
praiseworthiness of shepherding and its connection to leadership is developed further in Life of
Moses and again in the
essay on the Sacrifices of Abel and Cain:
With good reason then is Abel who refers
all that is best to God called a shepherd. (Sacr. 51)
Unlike
Cain, Abel is prepared for a future life:
So then when God added the good
conviction Abel to the soul, he took away the foolish opinion, Cain. So too,
when Abraham left this mortal life, Òhe is added to the people of God,Ó (Gen
25:8), in that he inherited incorruption and became equal to the angels, for
angels‑‑those
unbodied and blessed souls‑are
the host and people of God. (Sacr.
5)
The
birth of Abel only worsens CainÕs negative disposition. For AbelÕs disposition
is preferable to CainÕs, and so CainÕs soul abandons him when Abel is born.
It is a fact that there are two opposite
and contending views of life, one which ascribes all things to the mind as our
master, whether we are using our reason or our senses, in motion or at rest,
the other which follows God, whose handiwork it believes itself to be ... Now both these views or conceptions lie
in the womb of the single soul. But when they are brought to the birth they
must be separated, for enemies cannot live together forever. Thus, so long as
the soul had not brought forth the God‑loving principle in Abel, the self‑loving principle in Cain made her his dwelling. But
when she bore the principle which acknowledges the Cause, she abandoned that
which looks to the mind with its fancied wisdom. (Sacr. 2‑4)
As
Philo goes on to say,
the two opposite views of life represented by Cain and Abel cannot coexist in
peace. Like Jacob and Esau, Cain and Abel must be separated:
She had conceived the two contending
natures of good and evil and
considered earnestly, as wisdom bade her, received a vivid impression of each,
when she perceived them leaping and as in a skirmish preluding the war that should be between
them. And therefore she besought God to show her what had befallen her, and how
it might be remedied.
He answered her question thus: Òtwo nations are in the womb.Ó That was what had
befallen her‑to bear
both good and evil. But again Òtwo peoples shall be separated from thy womb.Ó
This is the remedy, that good and evil be separated and set apart from each
other and no longer have the same habitation. (Sacr. 4)
Note that, by the time of Jacob and Esau,
the philautos (the
self‑lover) has become
a type of a whole character and not just a character trait or type. However,
according to Philo, Cain and Abel may represent character traits, but not complete characters.
The
types of Cain and Abel do not live in sufficient separation, and they come into
conflict as a result of their different conceptions of worship. Reinforcing
through his daily actions his misconceived sense of his own importance, CainÕs
type is that of self‑lover:
Ôthe philautos (Sacr. 3). Consequently, he is in no hurry to
thank God for what he takes to be the fruits of his own labor. And, when he
gets around to it, he selfishly fails to offer the first of his crops to God.
Instead, he keeps the first and the best for himself. Again, Cain understands
the land to be his, while in fact it belongs to God. For Cain, humanity comes
first and his sustenance is more important than the acknowledgment of God:
There are two charges against the self‑lover (i.e., Cain): one that he made his
thank‑offering to God
Òafter some daysÓ[13] instead of
at once; the other that he offered of the fruits and not of the earliest
fruits, or in a single word the first fruits. (Sacr. 52)
Those who assert that everything that is
involved in thought or perception
or speech is a free gift of their own soul, seeing that they introduce an
impious and atheistic opinion, must be assigned to the race of Cain, who, while
incapable even of ruling himself, made bold to say that he had full possession
of all other things as well. (Post.
42)
These
charges are not directed only at Cain. They are directed at every self‑lover—that is at anyone who allows the type of
Cain to become the dominant character trait in oneÕs soul. AbelÕs sacrifice,
however, illustrates further his God‑loving nature:
But Abel brought other offerings and in
other manner. His offering was living, CainÕs was lifeless. His was first in
age and value, CainÕs but second. His had strength and superior fatness, CainÕs
had but weakness. For we are told that Abel offered of the firstlings of the
sheep and of their fat (Gen 4:4). (Sacr. 88)
Again,
of AbelÕs sacrifice Philo writes:
Abel offers the firstlings not only from the
first‑born, but from
the fat, showing that the gladness and richness of the soul, all that protects
and gives joy, should be set apart for God. (Sacr. 136)
Again,
Philo is not writing only about Abel, that is, the character in the Genesis
narrative. For Philo, the narrative is about the character trait in the soul. The character
trait of virtue is imprinted upon the soul in the form of grateful, joyous
acknowledgement of God. Of course, God prefers AbelÕs sacrifice. And it is in
jealous response to GodÕs preferential treatment that Cain kills Abel. But this
evil act does not solve CainÕs problem. It only exacerbates his problem by
removing the possibility that Cain will come under AbelÕs virtuous influence:
It would have been to the advantage of
Cain, the lover of self, to have guarded Abel; for had he carefully preserved
him, he would have been able to lay claim only to a mixed Òhalf and halfÓ life
indeed, but would not have drained the cup of sheer unmitigated wickedness. (Det. 68)
Thus
vice is self‑destructive.
Indeed, Philo argues that it is preferable to die like Abel than to live like Cain, in a state of
eternal death:
But in my judgement and in that of my
friends, preferable to life with impious men would be death with pious men; for
awaiting those who die in this way there will be undying life, but awaiting those who
live in that way there will be
eternal death. (Post. 39)
Immediately
after CainÕs fratricide, God asks him, ÒWhere is your brother?Ó According to
Philo, the point of GodÕs question is to offer Cain an opportunity to confess
his sin and to repent:
Why does he who knows all ask the
fratricide, ÔWhere is Abel, your brother?Õ He wishes that man himself of his
own will shall
confess, in order that he may not pretend that all things seem to come about
through necessity. For he who killed through necessity would confess that he
acted unwillingly; for that which is not in our power is not to be blamed. But
he who sins of his own free will denies
it, for sinners are obliged to repent. Accordingly he [Moses] inserts in all
parts of his legislation that the Deity is not the cause of evil. (QG 1.68)
Cain rejects the offer to repent. Still,
GodÕs question, as interpreted by Philo, is of great significance. For it shows
that repentance is always possible, even for someone whose vicious character is
inscribed in his very name. Consequently, although God created everything,
including the archetype of evil, only man is responsible for the evil impressed
upon his soul and realized in the world.
The murder of Abel certainly does not
succeed in exterminating virtue from biblical history. For Seth, who is born
after AbelÕs death, continues to exemplify the type of goodness and holiness
exemplified by his dead brother.[14]
Later, all those who are deemed righteous are considered to be from the Òseed
of Seth,Ó while all those who are deemed evil are said to be from the Òseed of
Cain.Ó[15]
Those who assert that everything that is
involved in thought or perception
or speech is a free gift of their own soul, seeing that they introduce an
impious and atheistic opinion, must be assigned to the race of Cain, who, while
incapable even of ruling himself, made bold to say that he had full possession
of all other things as well. But those who do not claim as their own all that
is fair in creation, but acknowledge
all as due to the gift of God, being men of real nobility, sprung not from a
long line of rich ancestors but from lovers of virtue, must remain enrolled
under Seth as the head of their race. (Post. 42)
This
passage brings out two points to which I want to give special emphasis. First,
in PhiloÕs view, theology is the root of all good and of all evil. For it is
first and foremost oneÕs conception of God, and of oneÕs own relation to the
cosmos created by God, that impresses either the type of virtue or the type of
vice upon oneÕs soul. It is from oneÕs theology that choices and actions flow,
actions that tend to reinforce the initial impression of good or evil. And it
is oneÕs theology that determines whether one belongs to the race of Cain or to
the race of Seth‑although,
as I have said, Philo thinks that repentance is always possible. Second, the
story of Cain and Abel is important because they exemplify the ways in which
the archetypes of
virtue and vice‑the
tree of life and the tree of knowledge of good and evil‑may come to leave their copies upon the
human soul. In PhiloÕs view, our situation is fundamentally that of Cain and
Abel. We inhabit the same cosmos, and the formation of our souls is no less
dependent on our theological convictions, on the choices we make, on the
actions we perform, and on the influences to which we expose ourselves. So we
have much to learn from Cain and Abel. For they pioneered the kind of life that
each of us must live. And their tragic story exemplifies the pitfalls we must
all seek to avoid.
Since Cain and Abel exemplify types‑at once cosmological and psychological‑it is not surprising that they are echoed
by their successors in
the biblical narratives. Thus Philo compares Abraham, Jacob, Isaac and Moses
with Abel. And he compares Esau and Laban to Cain. In this way, PhiloÕs
typological interpretation of the Cain and Abel story enables him to use that
story as a lens through which to read other biblical narratives.
At the same time, however, Philo also
reads the Cain and Abel narrative through a lens provided by other biblical
passages. In particular,
Philo repeatedly connects Cain and Abel with laws that are given only later in the
biblical story. This is because, I suggest, Cain and Abel represent the problem
for which the law of Moses is the solution. As the story of Cain and Abel shows, we are all highly impressionable
and therefore capable of great good or great evil, and each of us is
responsible for the effects upon our soul of every choice or action. However,
as I said earlier, the laws of Moses are images or impressions, which the
Israelites are told to stamp upon their hearts. The laws provide, as it were,
solutions to the problems exemplified by Cain. They are designed to implant healthy
theological
convictions, to efface evil impressions and to reinforce good ones. Thus, for
example, the tiller of soil is commanded to bring the first fruits as an
offering to God, and to profess GodÕs dominion over a land to which the farmer is ultimately foreign.
PhiloÕs analysis of Cain brings out the wisdom of this law, which manifests a
deep understanding of the human soul.
I have argued, then, that PhiloÕs
interpretation of the Cain and Abel narrative in Genesis 4 may justly be called
typological, and that his typology has both cosmological and psychological
dimensions. Indeed, the
children of Eve have a special importance within PhiloÕs biblical exegesis as a
whole. For their story illustrates—in
an exemplary fashion—some
of the central presuppositions of PhiloÕs exegetical endeavor: the
impressionability of the human soul, which can be horrifying or sublime; the
responsibility of each individual for himself or herself, which is endless; and
the intimate relationship between cosmic structures and Mosaic laws, which both
stem from a single creator and from a perfect paradigm.
[1] I have benefited from the incisive comments of John Cavadini, Mary Rose D'Angelo, Paul Franks, Eric Gruen, Graham Hammill, Blake Leyerle, John P. Meier, Judith Newman, David O'Connor, Michael Signer and Gregory E. Sterling.
[2] J. Danielou, From Shadows to Reality: Studies in the Biblical Typology of the Fathers, London 1960 and Jon Whitman, Interpretation and Allegory: Antiquity to the Modern Period, Leiden 2000, esp. 33‑45‑1 K.J. Woolcombe, ÒThe Biblical Origins and Patrisitic Development of TypologyÓ, in Essays on Typology, Naperville, 1957, 39‑75.
[3] See Thomas H. Luxon, Literal Figures: Puritan Allegory and the Reformation Crisis in Representation, Chicago, 1995, 34‑76.
[4] E.g., De Opif. Mundi 19, 34, 71; Leg. 1.61, 1,100, 3.83; Sacr. 135, 137; Det. 76 78, 83; Post. 94, 99; Deus 43‑44; Mos. 2.76; Decal. 101.
[5] L. Goppelt, TYPOS: The Typological Interpretation of the Old Testament in the New, Grand Rapids 1982, TYPOS, 46.
[6] See Luxon, 53: ÒThe real reality signified in typology turns out to be every bit as ahistorical, spiritual, eternal, timeless, ever present (and so, historically speaking, ever absent) as God and his majesty, the very things typology was first defined as prohibited from figuring.Ó
[7] Woolcombe, ÒThe Biblical Origins and Patristic Development of TypologyÓ, 65.
[8] On the deep connections between Jewish and Christian interpretive traditions, see James L. Kugel, Traditions of the Bible: A Guide to the Bible as it was at the start of the Common Era, Cambridge, 1998, and Daniel Boyarin, Border Lines‑ Hybrids, Heretics, and the Partition of Judaeo‑Christianity, Philadelphia 2004.
[9] Goppelt, Typos, 48.
[10] Cf. John Chrysostom, On Vainglory, 39 where the Cain and Abel narrative is taken to be an important text for moral pedagogy. See also L. Kovacs, ÒDivine Pedagogy and the Gnostic Teacher according to Clement of AlexandriaÓ, JECS 9 (2001), 3‑25.
[11] See, e.g., Leg. 1.61 where character is a synonym for tuposis.
[12] See my article ÒA Written Copy of the Law of Nature: an Unthinkable Paradox?Ó StPhA 15 (2003) forthcoming.
[13] Philo is referring to Gen. 4:3.
[14] Although the biblical text implies that Seth is a replacement for Abel, Philo explicitly rejects the idea that one person can replace another.
[15] For further discussion about the descendents of Cain and Seth see the contributions of J. Tubach and G.P. Luttikhuizen to this volume, below, pp. 187‑201 and 203‑17.