# Conjunction of Evidence and Multivalent Logic

Law and the New Logics 32-68 (H. Patrick Glenn & Lionel D. Smith eds., 2017) (Cambridge University Press)

Cornell Legal Studies Research Paper No. 14-32

37 Pages Posted: 27 Jul 2014 Last revised: 6 Jul 2017

See all articles by Kevin M. Clermont

## Kevin M. Clermont

Cornell Law School

Date Written: August 3, 2015

### Abstract

Classical logic and its attendant probability theory produce in law the troublesome conjunction paradox. They tell us that the conjoined likelihood of independent factual elements equals the product of each element’s likelihood. Meanwhile, the law requires only that each element of a cause of action meet the standard of proof. The seeming paradox is that if the cause entails more than one element, no assurance exists that the conjunction of the elements’ likelihoods will meet the standard of proof.

Multivalent logic, however, resolves this conjunction paradox. It maintains that the partial truth produced by factfinding fundamentally differs from the estimated probability of a fact becoming absolutely true as in a lottery. For elements found as partial truths, the elements’ conjoined likelihood logically equals the least likely element’s likelihood. So if each element meets the standard of proof, the conjunction of the cause of action’s elements does too.

The law very clearly tells its factfinders to apply the standard of proof element-by-element and not to apply the product rule. That is, the law follows multivalent logic and not classical logic. That much is unarguable reality. The further assertion herein is that law is wise to do so, as multivalent logic allows the law to perform its factfinding accurately.

Keywords: Evidence, Logic, Procedure, Proof, Conjunction

JEL Classification: K41

Suggested Citation

Clermont, Kevin M., Conjunction of Evidence and Multivalent Logic (August 3, 2015). Law and the New Logics 32-68 (H. Patrick Glenn & Lionel D. Smith eds., 2017) (Cambridge University Press), Cornell Legal Studies Research Paper No. 14-32, Available at SSRN: https://ssrn.com/abstract=2472383 or http://dx.doi.org/10.2139/ssrn.2472383