Constructing a Periodic Table of Arguments

The existing classifications of arguments are unsatisfying in a number of ways. This paper proposes an alternative in the form of a Periodic Table of Arguments. The newly developed table can be used as a systematic and comprehensive point of reference for the analysis, evaluation and production of argumentative discourse as well as for various kinds of empirical and computational research in the field of argumentation theory. In present-day argumentation theory, several classifications of arguments have been developed. Among them are the new-rhetorical classification of Perelman and Olbrechts-Tyteca (1969), the classifications of Hastings (1962), Schellens (1985) and Kienpointner (1992), the pragma-dialectical classification of van Eemeren and Grootendorst (1992) and the new-dialectical classification of Walton, Reed and Macagno (2008). These classifications of arguments typically take the form of a list of "argument(ation) schemes." Scholars do not agree as to the exact number and nature of these schemes. The new-dialectical list, for example, mentions more than sixty different argument schemes, each of which consist of a varying number of premises and a conclusion.

The theoretical framework of the proposed Periodic Table of Arguments consists of three fundamental distinctions between the types of argument. The first distinction is between subject arguments and predicate arguments. This distinction is derived from a formal-linguistic analysis of the constituents of the three main types of argument schemes as they are distinguished in the pragma-dialectical theory of argumentation. The second distinction is between first-order and second-order arguments: in all sign argumentation, the propositional content of the standpoint is expressed by "Y is true of X," while in argumentation from authority the propositional content of the standpoint that is originally defended by the speaker is expressed only by "X"—making it a second-order predicate argument in which the acceptability of the whole standpoint is treated as a subject. The third distinction is made between the three types of propositions as developed within debate theory: propositions of policy (P), of value (V), and of fact (F). Every type of argument distinguished in the literature can be characterized by identifying the specific combination of the types of propositions of the standpoint and the argument that supports it (PP, PV, PF, VP, VV, VF, FP, FV, FF).

When taken together, the three distinctions can be used to construct a theoretical framework for argument characterization. Within this framework, types of argument are described as (1) subject arguments or predicate arguments; (2) first-order or second-order arguments; and (3) instantiating the combination of propositions PP, PV, PF, VP, VV, VF, FP, FV, or FF. By reconstructing some well-known descriptions of argument types as they are distinguished within the literature, it has been shown that it is in principle possible to construct a Periodic Table of Arguments on the basis of these three distinctions. The arguments, argument(ation) schemes or types of argument as described in the literature can be characterized by making use of the three distinctions that constitute the theoretical framework of the table. It may further be conjectured that the distinction between first-order and second-order arguments is reflected in the distinction made by classical scholars in dialectic and rhetoric between internal and external topics (topoi, loci) and is also reflected in the distinction made by present-day scholars in argumentation theory between reasonable and fallacious arguments.

The problems listed above can be avoided by developing a classification of arguments that is based on a set of formal ordering principles. The argument types distinguished in the Periodic Table—including argument from sign (Sig), argument from criterion (Cr), pragmatic argument (Pra), argument from authority (Au), argumentum ad baculum (B), argument from similarity (Sim), argument from equality (Eq), argument from tradition (T), and argument from commitment (Com)—can each be characterized along two orthogonal axes: predicate vs. subject argument, and first-order vs. second-order. This creates an extra dimension of argument characterization that indicates which of the possible propositional combinations (FF, VF, PF, VF, PF, FF, PF, VF, PF) is instantiated in the specific type of argument.

The word problem can be parsed into equations 𝑦 = 𝑥0 − 𝑥1, 𝑥1 = 1. The LLM cannot compute target variable 𝑦 without knowing the value of variable 𝑥0. Other examples can be found in Figures 1 to 3. In these cases, the desired behavior is for the LLM to ask the minimal set of questions that enables it to respond to the user query.