Classical logic, argument and dialectic

A well studied instantiation of Dung's abstract theory of argumentation yields argumentation-based characterisations of non-monotonic inference over possibly inconsistent sets of classical formulae. This provides for single-agent reasoning in terms of argument and counter-argument, and distributed non-monotonic reasoning in the form of dialogues between computational and/or human agents. However, features of existing formalisations of classical logic argumentation (Cl-Arg) that ensure satisfaction of rationality postulates, preclude applications of Cl-Arg that account for real-world dialectical uses of arguments by resource-bounded agents. This paper formalises dialectical classical logic argumentation that both satisfies these practical desiderata and is provably rational. In contrast to standard approaches to Cl-Arg we: 1) draw an epistemic distinction between an argument's premises accepted as true, and those assumed true for the sake of argument, so formalising the dialectical move whereby arguments\u2019 premises are shown to be inconsistent, and avoiding the foreign commitment problem that arises in dialogical applications; 2) provide an account of Cl-Arg suitable for real-world use by eschewing the need to check that an argument's premises are subset minimal and consistent, and identifying a minimal set of assumptions as to the arguments that must be constructed from a set of formulae in order to ensure that the outcome of evaluation is rational. We then illustrate our approach with a natural deduction proof theory for propositional classical logic that allows measurement of the \u2018depth\u2019 of an argument, such that the construction of depth-bounded arguments is a tractable problem, and each increase in depth naturally equates with an increase in the inferential capabilities of real-world agents. We also provide a resource-bounded argumentative characterisation of non-monotonic inference as defined by Brewka's Preferred Subtheories

Greek and Roman Logic

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry

The Philosophical Basis of the method of antilogic

The paper is devoted to the sophistic method of "two-fold arguments" (antilogic). The traditional understanding of antilogic understood as an expression of agonistic and eristic tendencies of the sophists has been in recent decades, under the influence of G.B. Kerferd, replaced by the understanding of antilogic as an independent argumentative technique, having its own sources, essence, and goals. Following the interpretation of G.B. Kerferd, according to which the foundation of the antilogic is the opposition of two logoi resulting from contradictions or opposites, necessarily associated with the contradictory character of the sensual world, in the paper it is argued that the philosophical basis of antilogic should be sought in the presentation of the views attributed to Protagoras and "adherents of flux" in Plato's dialogue Theaetetus

Recent Hegel Literature: General Surveys and the Young Hegel

This is an offprint version of the article published in Telos (1980). The version made available in Digital Common was supplied by the author and is made available with permission of the publisher, Telos Press.Publisher's Versiontru

Hegel's Nonfoundationalism: A Phenomenological Account of the Structure of Philosophy of Right

In the Phenomenology Hegel insists there are no presupposed standards of truth: standards are internal. "Consciousness provides its own criterion from within itself, so that the investigation becomes a comparison of consciousness with itself"(PhdG 84). We need only contemplate "the matter in hand as it is in and for itself"(PhdG 84). The Phenomenology is a characterisation of consciousness taking on increasingly adequate forms, testing its own internal standards against experience. The Philosophy of Right is a search for right, not, as in the Phenomenology, for the reality of cognition; but one of the methods Hegel adopts and which helps make sense of the structure of Philosophy of Right is the method he uses in the Phenomenology. This paper offers an alternative, though not necessarily conflicting, interpretation to that given in recent accounts of Philosophy of Right that emphasize its "logical spirit." While the phenomenological account is not necessarily incompatible with these others, it will point to a nonfoundational interpretation of Hegel's phenomenological method that is