Trial by Mathematics – Reconsidered

10 Pages Posted: 31 Mar 2011 Last revised: 15 May 2011

See all articles by Peter Tillers

Peter Tillers

Yeshiva University - Benjamin N. Cardozo School of Law

Date Written: March 29, 2011


In 1970 Michael O. Finkelstein (with William B. Fairley) proposed that under some circumstances a jury in a criminal trial might be invited to use Bayes' Theorem to address the issue of the identity of the criminal perpetrator. In 1971 Laurence Tribe responded to this proposal with a rhetorically-powerful and wide-ranging attack on what he called "trial by mathematics." Finkelstein responded to Tribe's attack by further explaining, refining, and defending his proposal. Although Tribe soon fell silent – forever – on the use of mathematical and formal methods to dissect or regulate uncertain factual proof in legal proceedings, the Finkelstein-Tribe exchange precipitated a decades-long debate about "trial by mathematics." However, that debate, which continues to this day, became generally (but not uniformly) unproductive, sterile, and repetitive years ago. Although surely a variety of factors led to this desultory end, the debate about "trial by mathematics" was doomed to die with a whimper rather than a bang because two misunderstandings plagued much of the debate almost from the beginning. The first misunderstanding was a widespread failure to appreciate that mathematics (including the probability calculus and Bayes' Theorem) is part of a broader family, or class, of rigorous methods of reasoning, a family of methods that is often called "formal." The second misunderstanding was a widespread failure to appreciate that mathematical and formal analyses (including but not only those analyses that use numbers) can have a large variety of purposes. However, it is not too late to right this upended ship. Before any further major research project on "trial by mathematics" is begun, interested researchers in mathematics, probability, logic, and related fields, on the one hand, and interested legal professionals, on the other hand, should try to reach agreement about the possible distinct purposes that any given mathematical or formal analysis of inconclusive argument about uncertain factual hypotheses might serve. Putting aside the special (and comparatively trivial) case of mathematical and formal methods that make their appearance in legal settings because they are accoutrements of admissible forensic scientific evidence, I propose that discussants, researchers, and scholars of every stripe begin by carefully considering the possibility that mathematical and formal analysis of inconclusive argument about uncertain factual questions in legal proceedings could have any one (or more) of the following distinct purposes:

1. To predict how judges and jurors will resolve factual issues in litigation.

2. To devise methods that can replace existing methods of argument and deliberation in legal settings about factual issues.

3. To devise methods that mimic conventional methods of argument about factual issues in legal settings.

4. To devise methods that support or facilitate existing, or ordinary, argument and deliberation about factual issues in legal settings by legal actors (such as judges, lawyers, and jurors) who are generally illiterate in mathematical and formal analysis and argument.

5. To devise methods that would capture some but not all ingredients of argument in legal settings about factual questions questions.

6. To devise methods that perfect – that better express, that increase the transparency of – the logic or logics that are immanent, or present, in existing ordinary inconclusive reasoning about uncertain factual hypotheses that arise in legal settings.

7. To devise methods that have no practical purpose – and whose validity cannot be empirically tested – but that serve only to advance understanding – possibly contemplative understanding – of the nature of inconclusive argument about uncertain factual hypotheses in legal settings.

Keywords: factual inference, mathematical argument about inference, formal argument about inference, Bayesianism

Suggested Citation

Tillers, Peter, Trial by Mathematics – Reconsidered (March 29, 2011). Cardozo Legal Studies Research Paper No. 333, Available at SSRN: or

Peter Tillers (Contact Author)

Yeshiva University - Benjamin N. Cardozo School of Law ( email )

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