Recall that Odysseus was bound by an oath to join the Greeks in war against Troy. Odysseus tried to feign madness in order to escape his obligation. The wisest man of his time, Palamedes exposed Odysseus's madness as a fraud, forcing him to honor his oath. Odysseus contrived his revenge:
Palamedes was tried for treason, convicted and stoned to death.
Gorgias (483—375 B.C.E.) was the most celebrated rhetorician of antiquity. His speech, the Defense of Palamedes, is set during the trial of Palamedes for treason. This speech is credited with being the first example of an argument from probability. And it is still used to this day as a template for legal argumentation (whether lawyers today know it or not!).
Gorgias (and his teacher Tisias) realized that probabilities deserve higher esteem than truth. Rather than look to the facts, the jury is asked to weigh the odds that something happened as alleged by the prosecution.
The prosecution alleges that Palamedes contacted Priam and offered to convince the Greek army to return home in exchange for a bribe. The evidence is (1) a letter supposedly from Priam to Palamedes accepting this offer and (2) a small amount of Trojan-minted gold coins under Palamedes bed.
The defense argument is laid out as follows. Gorgias calls into question the motive and opportunity ascribed to Palamedes by the prosection.
Put simply, the risk doesn't justify the reward. The amount of money found buried in the tent was small. Palamedes doesn't need the money --- he's already very wealthy. Would such small amount of money be worth risking one's life, reputation and freedom? Especially to a rich, respected man like Palamedes? Furthermore, Palamedes doesn't want social status among the Trojan barbarians. So that couldn't be a motive either.
Here is a graphical representation of this defense argument using the causal idiom found in the paper:
In this setup, the motive is greed, the evidence is the Trojan gold found under Palamedes' mattress, the hypothesis we're interested in proving is Palamedes' guilt, and Palamedes' wealth limits the accuracy of the evidence.
Here is a formalization of this defense argument using the Palamedes probabilistic programming language:
/* Defense of Palamedes */ /* Part I: Causal idiom, motive */ Pr(Wealthy) gets 1 Pr(Motive) gets 0.50 Pr(Guilty| Motive) gets 0.95 Pr(Guilty|~Motive) gets 0.01 Pr(Gold| Motive, Wealthy) gets 0.5 Pr(Gold| Motive,~Wealthy) gets 1 Pr(Gold|~Motive, Wealthy) gets 0.5 Pr(Gold|~Motive,~Wealthy) gets 0.001 /* Queries */ Pr(Guilty|Gold,~Wealthy) Pr(Guilty|Gold, Wealthy)
Entering this code, the system returns immediately, telling us:
Pr(Guilty | Gold ∩ ~Wealthy) → 0.9490609390609391 Pr(Guilty | Gold ∩ Wealthy) → 0.48
So conditioning on Palamedes being wealthy cuts the odds he's guilty by about half from nearly 95% to under 50%.
Palamedes doesn't speak or write Trojan. Therefore, he would need an interpreter. An interpreter would need to be either slave or free. Slaves are untrustworthy and would snitch on him to get their freedom or to avoid torture. And a freeman would be free to refuse to conspire and testify against him. But no one has been identified as the interpreter, either slave or free.
Palamedes would need to communicate with Priam. They would need to send messages, like the alleged letter. But an intermediary would likely be spotted by guards. No intermediary was caught, and the guards spotted no one.
Since Priam couldn't trust Palamedes to keep his end of the bargain, he'd want to exchange pledges --- something very valuable. It was usual to exchange hostages. Palamedes' brother for Priam's son. But no such hostage exchange ocurred.
This portion of Gorgias's argument rests on the absence of evidence---If the prosecution is correct, we ought to find an interpreter, an intermediary and a hostage. But we found none of this.
Dan Piponi elaborated on how Bayes' theorem impies that "failing to find evidence for X should lower our estimate of the probability that X is true." More on this here, here, and here.
Here is a graphical representation of this defense argument using the consequence idiom found in the paper (ibid.):
Here is a formalization of this defense argument using the Palamedes probabilistic programming language:
/* Defense of Palamedes */ /* Part II: Absence of evidence is evidence of absence */ /* Not finding any of the evidence we expect reduces the chances of guilt */ likely gets 90%; unlikely gets 10% Pr(intermediary | guilty) gets likely Pr(intermediary |~guilty) gets unlikely Pr(intepreter | guilty) gets likely Pr(intepreter |~guilty) gets unlikely Pr(hostage | guilty) gets likely Pr(hostage |~guilty) gets unlikely Pr(guilty) gets 0.50 NB. presumption of innocence Pr(intermediary) gets unlikely Pr(intepreter) gets unlikely Pr(hostage) gets unlikely /* Query the system to get probability of guilt */ Pr(guilty |~intermediary, ~intepreter, ~hostage)//percent Pr(guilty |~intermediary, ~intepreter, ~hostage)//rat NB. Get the answer as a fraction
After inputting these commands, the system responds that the probability of guilt given there was no intermediary, no interpreter and no hostage is a mere 5.56% (or 1/18).
You can then find out the deductions the system used to infer these conclusions by calling the bayes() function:
bayes() →
key value
guilty| 0.50
guilty|~hostage Pr(guilty) * Pr(~hostage | guilty) / Pr(~hostage)
guilty|~hostage ∩ ~intepreter Pr(guilty | ~hostage) * Pr(~intepreter | guilty ∩ ~hostage) / Pr(~intepreter | ~hostage)
guilty|~hostage ∩ ~intepreter ∩ ~intermediary Pr(guilty | ~hostage ∩ ~intepreter) * Pr(~intermediary | guilty ∩ ~hostage ∩ ~intepreter) / Pr(~intermediary | ~hostage ∩ ~intepreter)
hostage| unlikely
hostage|guilty likely
intepreter| unlikely
intermediary| unlikely
~hostage| 1 - Pr(hostage)
~hostage|guilty 1 - Pr(hostage | guilty)
~intepreter|guilty ∩ ~hostage 1 - Pr(intepreter)
~intepreter|~hostage 1 - Pr(intepreter)
~intermediary|guilty ∩ ~hostage ∩ ~intepreter 1 - Pr(intermediary)
~intermediary|~hostage ∩ ~intepreter 1 - Pr(intermediary)
Aristotle finds fault in this argument (Rhet. 1402a12-13). His criticism may be summed up as: The improbable sometimes happens. Therefore, it is probable that improbable events will occur.
Plato is also critical of Gorgias' argument. In his dialogue Gorgias, he says rhetoric deals with doxa/belief rather than knowledge/epistemê. Gorgias wishes to persuade, not educate. Gorgias is a relativist who doesn't care about truth/falsehood or right/wrong, he only cares about being perceived as smart, and making money by instructing others in the art of rhetoric.
In modern day philosophy, the Argument from probability (or tōn eikotōn) is considered a fallacy. You commit this fallacy when you argue not from established facts, testimony, or the like, but from seemingly plausible claims. For instance, that "a person as tiny as I am couldn't have punched a guy that big so hard as to kill him," or that "an individual of my character and standing surely would never indulge in practices as infamous as those."
Aristotle seems to be invoking the law of truly large numbers: with a sample size large enough, any outrageous thing is likely to happen. To apply it here would be to ignore all the evidence in this particular case. We need to use the laws of probability to deduce a conditional probability of guilt given the available evidence.
Plato's criticism fails because as jurors we don't know and can't know what really happened. We need to rely on chains of evidence and how they connect to probabilities of guilt or innocence. The best we can do is to infer what really happened, based on what's likely(est) to have occurred.
Plato also resorts to an ad hominem attack on Gorgias, calling him greedy and a smart ass. How do we know Plato is telling the truth about Gorgias? And so what then, if Plato is right about his character? Gorgias may be the greediest man on earth, but that alone isn't enough to invalidate his argument. We must consider the argument on its own merits.
The argument from probability ought to be renamed the argument from possibility since it doesn't have anything to with probability whatsoever. There are many fallacies related to probability. Any argument that doesn't adhere to the strict rules of probability are guilty of committing fallacies. There are several common fallacies related specifically to reasoning with conditional probabilities. In my article on Palamedes' implementation of Bayesian networks, I outline the main rules which need to be adhered to and the common conditional probability fallacies. Gorgias's argument doesn't break any rules of probability.
Dialogue and Discovery: A Study in Socratic Method By Kenneth Seeskin
Gorgias and the New Sophistic Rhetoric By Bruce McComiskey
Selections from Gorgias's Defense of Palamedes
Textual allusion as rhetorical argumentation: Gorgias, Plato and Isocrates
Last update: Fri Sep 23 2016