bts@unc.UUCP (08/02/83)
I haven't been able to find either of Steven J. Brams'
books in the Math/Physics Library at UNC. This past Satur-
day night, however, I found a volume titled "Applied Game
Theory", edited by S.J.Brams, A.Schotter, and G.Schwodiauer,
published by Physica-Verlag in 1979. The last article in
the book is "Faith versus rationality in the Bible: game-
theoretic interpretations of sacrifice in the Old Testa-
ment", by Brams. In the interest of continuing this discus-
sion, I'll summarize parts of the article. (The book,
according to a card on the inside cover, cost $80.00. The
other articles are more mundane game theory. Given that it
was until re-bound a paperback, however, I'd say the book's
interesting.) All biblical quotes will be from the KJV,
other quotes from Brams.
Brams studies two stories in the Old Testament wherein
God tested the faith of fathers by seeing if they would
sacrifice their children. The first story is well known to
all of us: Abraham and Isaac (Genesis 22:1-18). There, God
called off the sacrifice at the last minute. The second
story is about Jephthah's sacrifice of his daughter (Judges
11:30-40). Since the latter story is not so familiar, I'll
start with a synopsis. During a battle, Jephthah
vowed a vow to the Lord and said, If You shall without
fail deliver the children of Ammon into my hands, then
whatever comes out of my house to meet me when I return
in peace from the children of Ammon, surely it shall
belong to the Lord, or I will offer it up for a burnt
offering. (Judges 11:30-31)
When Jephthah returned home, he was first greeted by his
daughter, his only child. Despite his grief and with his
daughter's consent, Jephthah went ahead with the sacrifice.
(He did give her a two month's delay (Judges 11:37) so that
she might "go up and down on the mountains and weep for
[her] virginity.") This time God did not intervene.
(At this point, by the way, there is an intriguing quo-
tation from the Encyclopedia Judaica, vol. 9, p. 1342, on
"Jephthah". It says that this story is "exceptional and
cannot be treated as indicative of the norm of human sacri-
fice in Israel". Would any scholars care to enlighten us as
to what that norm might have been?)
Brams models these stories as two-player games. In
each game, the father has two choices: to offer the sacri-
fice or to refuse. Since God moves second, He may make His
move based on the father's. Therefore, He has four choices:
He may
(1) reject the sacrifice if offered/forgive if the father
refuses,
(2) reject the sacrifice if offered/not forgive if the
father refuses,
(3) accept the sacrifice if offered/forgive if the father
refuses, or
(4) accept the sacrifice if offered/not forgive if the
father refuses.
Hence, there are eight outcomes to each game. Under the
assumptions that God would prefer not to have Isaac sacri-
ficed but would rather Jephthah kept his promise, Brams
ranks these outcomes from God's point of view. (This seems
weak to me. Brams rationalizes by saying that "since
Abraham's time, the Israelites had caused God much grief...
so He was not inclined to be sympathetic with people... who
were too quick to make solemn vows." (p. 440) The rankings
of outcomes according to the fathers can be disputed, too.)
Next, he ranks the outcomes for the fathers' under three
levels of faith: "faithful regardless", "wavers somewhat",
and "wavers seriously".
If the father is "faithful regardless", there is a
clear choice, in the sense of a dominant strategy. In the
other two cases, neither strategy is dominant. In those
cases, according to Brams, the father must try to anticipate
God's choice by assuming that God is a "rational" player.
Abraham will, in all cases, decide on just the strategy he
chose: to sacrifice Isaac. Jephthah, on the other hand,
will make the sacrifice in the "faithful regardless" and the
"wavers somewhat" cases, but he will refuse in the "wavers
seriously" case. By now, there are any number of holes in
Brams' arguments. Let's take his analysis for granted, how-
ever, and look at his conclusions.
All that this leads to is the following:
[It] is impossible to ascertain whether biblical char-
acters are blindly faithful or wavering. Thus a major
alternative explanation of their actions might be that
they did indeed waver, but anticipating God's rational
strategy, they were compelled by their own rationality
to demonstrate their faith by offering to sacrifice
their children. (p. 443)
Contrasting the two stories:
If God is sympathetic, as in Abraham's case, Abraham
can waver seriously and still rationalize the offering
of his son. Some wavering is possible if God is less
sympathetic, as in Jephthah's case, but if Jephthah
prizes his daughter above everything else, it is not
rational for him to offer to sacrifice her, given the
two sets of preferences I have postulated for God, and
Jephthah's awareness of these. (p. 443)
My feeling is that I don't need to bother pointing out the
holes in Brams' reasoning, if this is all it can offer
should I accept it. Perhaps the arguments presented in his
books are more compelling, and I suspect I'll look for them
in our main library next time I'm there.
Finally, for anyone who might be tempted to read Brams
for himself, some reassurance. I saw nothing at all in his
article which anyone might consider blasphemous-- except
possibly the idea that we can gain an understanding of how
God thinks by analyzing stories from the Bible.
Bruce Smith, UNC-CH
duke!unc!bts (USENET)
bts.unc@udel-relay (lesser NETworks)
Next: If my keyboard isn't incinerated by the flames
after this one, a review of Martin Gardner's 1961 religious
novel "The Flight of Peter Fromm".toddv@tekmdp.UUCP (Todd Vierheller) (08/03/83)
I am compelled to make mention of some things which are not inherently obvious.
1) Abraham wasn't counting on God to stop his sacrfice of Isaac. Rather,
he was counting on the faithfulness of God to keep His promises. Abraham
was confident that God would raise Isaac from the dead. After all, God
had promised that this son would be the father of many. Before you flame
all over me for my inductive leaps, etc., see Hebrews 11:17ff.
2) Jephthah's daughter was not sacrificed as a burnt offering to God. Although
an honest reading of the text might lead to this conclusion. (I don't have
a Bible with me so I'll have to rely on the accuracy of Bruce Smith's
quotes.) Notice the phrase "whatever comes out of my house . . . surely
it shall belong to the Lord, or I will offer it up for a burnt offering."
Did you catch the "or"? Jephthah didn't use his daughter for a burnt
offering, but he did give her to God (presumably for some service). She
didn't go to the mountains for two months to weep for her virginity because
she was going to die; she rather wept over her virginity because she was
destined to stay that way (not a pleasant thought for most of us).
You can feel free to flame about this one if you like.
Send flames to the net or direct to:
Todd Vierheller (Aloha Oregon)
UUCP: ...!{ucbvax or decvax}!teklabs!tekmdp!toddv (ignore return address)
CSNET: tekmdp!toddv @ tektronix
ARPA: tekmdp!toddv.tektronix @ rand-relaybts@unc.UUCP (08/04/83)
Todd Vierheller (tekmdp!toddv) has stated objections to
both of the Bible stories in my submission "Playing games
with God, II". First, he suggests that Jephthah's daughter
was not sacrificed as a burnt offering. Second, that Abra-
ham expected God to raise Isaac from the dead, anyway, after
he killed him. In short, that neither sacrifice was "real".
I have three reasons to believe that the story of
Jephthah's daughter really is a story of human sacrifice:
(1) Steven Brams (author of the article I was summarizing)
interpreted the story this way. While I'm not aware
that he's a biblical scholar as well as a game theor-
ist, I would hope that he had checked some authorities
about the story. (See point (2), below.)
(2) The reference in the Encyclopedia Judaica mentions
"human sacrifice" with regard to the story. I have not
looked this up, however; I'm trusting the accuracy of
Brams' quote.
(3) The conclusion of the story in Judges 11:39-40:
And at the end of two months she returned to her
father, who did to her according to his vow which
he had vowed. And she knew no man. And it was a
custom in Israel that the daughters of Israel went
yearly to tell again of the daughter of Jephthah
the Gileadite, four days in a year.
This seems an excessive response if the daughter was
not sacrificed but only offered to God as a servant.
Todd is quite correct that the KJV never comes out and says
"Jephthah sacrificed his daughter as a burnt offering", at
least not in Chapter 11 of Judges. I agree that verse 31 is
ambiguous-- at least in the KJV. Here's another place where
scholars on the net can help us out.
Todd's other point is that Abraham might have offered
to sacrifice Isaac under the assumption that God would have
immediately raised his son from the dead. In support of
this he refers to the book of Hebrews, in New Testament.
Let's look at Hebrews 11:17-19, again from an office mate's
KJV:
By faith Abraham, when he was tested, offered up
Isaac. And he that had received the promises was
offering up his only-begotten, of whom it was
said, "in Isaac shall your seed be called." For
he was supposing that God was able to raise him
up, even from the dead-- from which he did get him
back, too, in a way of speaking.
This "Letter to the Hebrews" (Paul's?) is a later source
than Genesis, and, if this is one of Paul's letters, told
from a Christian rather than Jewish point of view. It looks
to me more like an attempt to find precedents for the sacri-
fice-of-an-only-son-with-subsequent-resurrection than an
explanation of the Old Testament story. But even accepting
this interpretation of Abraham and Isaac, we can only conclude
(with Brams) that Abraham might have acted by rationally ana-
lyzing God's intentions instead of acting on blind faith.
Bruce Smith, UNC-Chapel Hill
duke!unc!bts (USENET)
bts.unc@udel-relay (lesser NETworks)bch@unc.UUCP (08/04/83)
The story of Jephthah's daughter, in the New English Bible translation, goes as follows: "...Jephthah made this vow to the Lord: 'If thou wilt deliver the Ammonites into my hands, then the first creature that comes out of the door of my house to meet me when I return from them in peace shall be the Lord's; I will offer that as a whole-offering.' So Jephthah crossed over to attack the Ammonites, and the Lord delivered them into his hands. He routed them with great slaughter all the way from Aroer to Minnith, taking twenty towns, and as far as Abel-keramim. Thus Israel crushed Ammon. But when Jephthah came to his house in Mizpah, who should come out to meet him with tambour- ines and dances but his daughter, and she his only child; he had no other, neither son nor daughter. When he saw her, he rent his clothes and said, 'Alas, my daughter, you have broken my heart, such trouble you have brought upon me. I have made a vow to the Lord and I cannot go back.' She replied, 'Father, you have made a vow to the Lord; do to me what you have solemnly vowed, since the Lord has avenged you on the Ammonites, your enemies. But, father, grant me this one favour. For two months let me be, that I may roam [that I may go down country to] the hills with my companions and mourn that I must die a virgin.' 'Go', he said, and he let her depart for two months. She went with her companions and mourned her virginity on the hills. At the end of two months she came back to her father, and he fulfilled the vow he had made; she died a virgin. It became a tradition that the daugh- ters of Israel should go year by year and commemorate the fate of Jephthah's daughter, four days in every year." The term whole-offering is explained by context in Lev. 1:1-9 as follows: "If his offering is a whole-offering from the cattle, he shall present a male without blemish; he shall present it at the entrance to the Tent of the Presence before the Lord so as to secure acceptance for himself. He shall lay his hand on the head of the victim and will be accepted on his behalf to make expiation for him. He shall slaughter the bull before the Lord, and the Aaronite priests shall present the blood and fling it against the altar all round at the entrance of the Tent of the Presence. He shall then flay the victim and cut it up. The sons of Aaron the priest shall kindle a fire on the altar and arrange wood on the fire. The Aaronite priests shall arrange the pieces, including the head and the suet, on the wood on the altar-fire, the entrails and the shins shall be washed in water, and the priest shall burn it all on the altar as a whole-offering, a food-offering of soothing odour to the Lord." Except for the sex of the victim, it seems fairly clear that Jephthah's daughter was, in fact, a whole-offering human sacrifice. Byron Howes UNC - Chapel Hill