In several posts, I have addressed Professor Haack’s attack on legal probabilism. See
Haack Attack on Legal Probabilism (May 6, 2012). The probabilistic mode of reasoning is not a modern innovation; nor is the notion that the universe is entirely determined, although revealed to humans as a stochastic phenomenon:
“I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.”
Ecclesiastes 9:11 King James Bible (Cambridge ed.)
The Old Testament describes the “casting of lots,” some sort of dice rolling or coin flipping, in a wide variety of human decision making. The practice is described repeatedly in the Old Testament, and half a dozen times in the New Testament.
Casting of lots figures more prominently in the Old Testament, in the making of important decisions, and in attempting to ascertain “God’s will.” The Bible describes matters of inheritance, Numbers 34:13; Joshua 14:2, and division of property, Joshua 14-21, Numbers 26:55, as decided by lots. Elections to important office, including offices and functions in the Temple, were determined by lot. 1 Chronicles 24:5, 31; 25:8-9; 26:13-14; Luke 1:9.
Casting lots was an early form of alternative dispute resolution – alternative to slaying and smiting. Proverbs describes the lot as used as a method to resolve quarrels. Proverbs 18:18. Lot casting determined fault in a variety of situations. Lots were cast to identify the culprit who had brought God’s wrath upon Jonah’s ship. Jonah 1:7 (“Come, let us cast lots, that we may know on whose account this evil has come upon us.”).
What we might take as a form of gambling appeared to have been understood by the Israelites as a method for receiving instruction from God. Proverbs 16:33 (“The lot is cast into the lap, but its every decision is from the Lord.”). This Old Testament fortune cookie suggests that the Lord knows the outcome of the lot casting, but mere mortals must wager. I like to think the passage means that events that appear to be stochastic to humans may have a divinely determined mechanism. In any event, the Bible describes various occasions on which lots were cast to access the inscrutable intentions and desires of the Lord. Numbers 26:55; 33:54; 34:13; 36:2; Joshua 18:6-10; 1 Chronicles 24:5,31; 1 Samuel 14:42; Leviticus 16:8-10 (distinguishing between sacrificial and scape goat).
In the New Testament, the Apostles cast lots to decide upon a replacement for Judas (Acts 1:26). Matthias was the winner. Matthew, Mark, and John describe Roman soldiers casting lots for Jesus’ garments (Matthew 27:35; Mark 15:24; John 19:24. See also Psalm 22:18. This use of lots by the Roman soldiers seems to have taken some of the magic out of lot casting, which fell into disrepute and gave way to consultations with the Holy Spirit for guidance on important decisions.
The Talmud deals with probabilistic inference in more mundane settings. The famous “Nine Shops” hypothetical poses 10 butcher shops in a town, nine of which sell kosher meat. The hypothetical addresses whether the dietary laws permit eating a piece of meat found in town, when its butchering cannot be attributed to either the nine kosher shops or the one non-kosher shop:
“A typical question involves objects whose identity is not known and reference is made to the likelihood that they derive from a specific type of source in order to determine their legal status, i.e. whether they be permitted or forbidden, ritually clean or unclean, etc. Thus, only meat which has been slaughtered in the prescribed manner is kasher, permitted for food. If it is known that most of the meat available in a town is kasher, there being, say, nine shops selling kasher meat and only one that sells non-kasher meat, then it can be assumed when an unidentified piece of meat is found in the street that it came from the majority and is therefore permitted.”
Nachum L. Rabinovitch, “Studies in the History of Probability and Statistics. XXII Probability in the Talmud,” 56 Biometrika 437, 437 (1969). Rabinovitch goes on to describe the Talmud’s resolution of this earthly dilemma: “follow the majority” or the most likely inference.
A small digression on this Talmudic hypothetical. First, why not try to find out whether someone has lost this package of meat? Or turn the package in to the local “lost and found.” Second, how can it be kosher to eat a piece of meat found lying around in the town? This is really not very appetizing, and it cannot be good hygiene. Third, why not open the package and determine whether it’s a nice pork tenderloin or a piece of cow? This alone could resolve the issue. Fourth, the hypothetical posed asks us to assume a 9:1 ratio of kosher to non-kosher shops, but what if the one non-kosher shop had a market share equal to the other nine? The majority rule could lead to an untoward result for those who wish to keep kosher.
The Talmud’s proposed resolution is, nevertheless, interesting in anticipating the controversy over the use of “naked statistical inferences” in deciding specific causation or discrimination cases. Of course, the 9:1 ratio is sufficiently high that it might allow an inference about the “likely” source of the meat. The more interesting case would have been a town with 11 butcher shops, six of which were kosher. Would the rabbis of old have had the intestinal fortitude to eat lost & found meat, on the basis of a ratio of 6:5?
In the 12th century, Maimonides rejected probabilistic conclusions for assigning criminal liability, at least where the death penalty was at issue:
“The 290th Commandment is a prohibition to carry out punishment on a high probability, even close to certainty . . .No punishment [should] be carried out except where . . . the matter is established in certainty beyond any doubt, and , moreover, it cannot be explained otherwise in any manner. If we do not punish on very strong probabilities, nothing can happen other than a sinner be freed; but if punishment be done on probability and opinion it is possible that one day we might kill an innocent man — and it is better and more desirable to free a thousand sinners, than ever kill one innocent.”
Stephen E. Fienberg, ed., The Evolving Role of Statistical Assessments as Evidence in the Courts 213 (N.Y. 1989), quoting from Nachum Rabinovitch, Probability and Statistical Inference in Ancient and Medieval Jewish Literature 111 (Toronto 1973).
Indiana Senate candidate and theocrat, Republican Richard E. Mourdock, recently opined that conception that results from rape was God’s will:
“I’ve struggled with it myself for a long time, but I came to realize that life is that gift from God. And even when life begins in that horrible situation of rape, that it is something that God intended to happen.”
Jonathan Weisman, “Rape Remark Jolts a Senate Race, and the Presidential One, Too,” N.Y. Times (Oct. 25, 2012 ).
Mourdock’s comments about pregnancies resulting from rape representing God’s will show that stochastic events continue to be interpreted as determined mechanistic events at some “higher plane.” Magical thinking is still with us.
