The proposition that “promises ought to be kept is one of the most important normative ideas or value judgements in our daily lives. But what about “illegal promises”? That is to say, what about promises that are, legally or morally speaking, malum in se or inherently wrongful, such as voluntary exchanges that are inherently immoral or wrongful, like bribes, blackmail, murder, etc.? In short, what moral obligations, if any, do such promises impose? Although many of the greatest thinkers in Western (...) civilization have offered a wide variety of theories to explain the source of promissory obligations, it turns out there is a blind spot in this centuries-old conversation, for few theorists have given the problem of illegal or immoral promises any sustained thought. Nevertheless, illegal or immoral promises should be of theoretical interest to us because such promises may help us delimit the outer boundaries of promissory obligations. (shrink)

Two of the most important ideas in the philosophy of law are the “Coase Theorem” and the “Prisoner’s Dilemma.” In this paper, the authors explore the relation between these two influential models through a creative thought-experiment. Specifically, the paper presents a pure Coasean version of the Prisoner’s Dilemma, one in which property rights are well-defined and transactions costs are zero (i.e. the prisoners are allowed to openly communicate and bargain with each other), in order to test the truth value of (...) the Coase Theorem. In addition, the paper explores what effect (a) uncertainty, (b) exponential discounting, (c) and elasticity have on the behavior of the prisoners in the Coasean version of the dilemma. Lastly, the paper considers the role of the prosecutor (and third-parties generally) in the Prisoner’s Dilemma and closes with some parting thoughts about the complexity of the dilemma. The authors then conclude by identifying the conditions under which the Prisoner’s Dilemma refutes the Coase Theorem. (shrink)

The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents simple Bayesian solutions to different versions of the blue bus problem. In addition, the author expresses his solutions in standard and visual formats, i.e. in terms of probabilities and natural frequencies.

A comparaison between classical cavalier persepective and what really we see, called "natural perspective. A simple mathematical analysis is added.

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

What lessons can legal scholars learn from the life and work of W. D. "Bill" Hamilton, a lifelong student of nature? From my small corner of the legal Academia, three aspects of Bill Hamilton’s work in evolutionary biology stand out in particular: (i) Hamilton’s simple and beautiful model of social behavior in terms of costs and benefits; (ii) his fruitful collaboration with the political theorist Robert Axelrod and their unexpected yet elegant solution of the Prisoner’s Dilemma, an important game or (...) puzzle that had defied solution until Hamilton and Axelrod came along; and (iii) Hamilton’s conception of science generally -- and in particular his view of the process of scientific justification -- as a form of trial advocacy. In this review of Ullica Segerstråle’s recently-published biography of Bill Hamilton, the author briefly recounts and reviews each one of these important contributions. (shrink)