The Ethics of Logic: Gödel's Dichotomy and the Ethical Imperative

Abstract

The logic of ethical reasoning has been analysed in many different contexts in analytic philosophy. But is there such a thing as the ethics of logic? In other words, does logic, or the use of formal systems lead to certain commitments that can be considered ethical? In this paper I will explore these questions in the context of Kurt Gödel’s “Gibbs Lecture” delivered at Brown University in 1951. In this address to the American Mathematical Society Gödel assesses the philosophical consequences of his incompleteness theorems in terms of what Solomon Feferman has called “Gödel’s dichotomy,” according to which either “the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable Diophantine problems” [that is, basic arithmetical problems]. In my paper I will argue that both these options are thoroughly problematic in their epistemological implications. Gödel’s discussion, however, leaves a third option open, as well. For he concedes that the mind (human reasoning) can be represented by a finite machine (that is, by a well-defined formal logical system) which does not understand its own functioning and does not know its own consistency. Although Gödel does not consider this to be a genuine third option, I will argue that this conception is perhaps the most fruitful, or least problematic, model of how human reason can contain knowledge. As such, however, this approach requires certain commitments which can best be described as ethical. In particular, it calls for (1) a commitment to the consistency of human reasoning and (2) a commitment to truth, as the truth of the undecidable proposition pertaining to the consistent system of human reasoning. I will argue that these ethical commitments are inevitable once we deploy formal-logical systems to produce knowledge about reality. To this extent, therefore, these commitments constitute the ethics of logic.