Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so (...) that ignorance of their nature is profound. (shrink)

In natural language understanding, a crucial goal is correctly interpreting open-textured phrases. In practice, disagreements over the meanings of open-textured phrases are often resolved through the generation and evaluation of interpretive arguments, arguments designed to support or attack a specific interpretation of an expression within a document. In this paper, we discuss some of our work towards the goal of automatically generating and evaluating interpretive arguments. We have curated a set of rules from the code of ethics of various professional (...) organizations and a set of associated scenarios that are ambiguous with respect to some open-textured phrase within the rule. We collected and evaluated arguments from both human annotators and state-of-the-art generative language models in order to determine the relative quality and persuasiveness of both sets of arguments. Finally, we performed a Turing test-inspired study in order to assess whether human annotators can tell the difference between human arguments and machine-generated arguments. The results show that machine-generated arguments, when prompted a certain way, can be consistently rated as more convincing than human-generated arguments, and to the untrained eye, the machine-generated arguments can convincingly sound human-like. (shrink)