The (Uncomputable!) Meaning of Ethically Charged Natural Language, for Robots, and Us, from Hypergraphical Inferential Semantics

Abstract

The year is 2030. A two-young-child, two-parent household, the Rubensteins, owns and employs a state-of-the-art household robot, Rodney. With the parents out, the children ask Rodney to perform some action �� that violates a Rubensteinian ethical principle ���� . Rodney replies: (��1 ) “Doing that would be (morally) wrong, kids.” The argument the children give Rodney in protest is that another household, the Müllers, also has a robot, Ralph; and the kids argue that he routinely performs �� . As a matter of fact, Ralph’s doing �� violates no Müllerian ethical principle ���� . Ralph’s response to the very same request from the children he tends is: (��2 ) “Okay, doing that is (morally) fine, kids.” What is the meaning of the utterances made by Rodney and Ralph? We answer this question by presenting and employing a novel, formal, inferential theory of meaning in natural language: hypergraphical inferential semantics (ℋℐ�� ), which is in the general spirit of proof-theoretic semantics, which is in turn antithetical to Montagovian model-theoretic semantics. ℋℐ�� , applied even to sentences logically simpler than ��1 and ��2 , implies that human-level natural language understanding (NLU) is Turing-uncomputable.