Online research in philosophy

Rational Pavelka logic extends Lukasiewicz infinitely valued logic by adding truth constants r̄ for rationals in [0, 1]. We show that this is a conservative extension. We note that this shows that provability degree can be defined in Lukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963.

Classical logic -- Temporal logic -- Modal logic -- Conditional logic -- Relevantistic logic -- Intuitionistic logic.

In a recent article, the writer has broached the topic of indentifying distinctions in the modes of commentarial discourse within the exegetical works of the the Korean scholiast Wonhyo (617-686), taking note of (1) a rational/logical form of discourse that attempts to elucidate the point of a passage — and especially to resolve any doctrinal problems contained therein — using clear rational argumentation, and (2) an intuitive, poetic, form of discourse that tends to emphasize the fact that the ultimate Buddhist truth is inapprehensible through discriminatory thought. In that paper, attention was paid primarily to the second mode, which tends to be seen itself in the opening and closing portions of his commentaries — or in works, or portions of works — that deal primarily with issues of faith. In that paper, examples were drawn primarily from his commentaries on the Awakening of Mahāyāna Faith and the Sutra of Immeasurable Life . This paper advances that discussion by paying attention to the rational/logical strain of his work, which is clearly of equal, and possibly even greater importance. Here we look at passages from two of his works that both make use of logic, yet which also subject logic itself to a critique in terms of testing the limitations of its applicability in resolving the most fundamental of religious truths.

This paper outlines a realist approach to the social ontology of discourse. It seeks to synthesise some elements of the approach to discourse found in the early work of Michel Foucault with a critical realist understanding of the causal power of social structures. It will argue that discursive structures can be causally significant when they are normatively endorsed and enforced by specific groups of people; that it is not discourse as such but these groups—discursive circles—that are causally effective; and that such an account allows us to reconcile the role of discourse with that of the subject.

Is logic, feasibly, a product of natural selection? In this paper we treat this question as dependent upon the prior question of where logic is founded. After excluding other possibilities, we conclude that logic resides in our language, in the shape of inferential rules governing the logical vocabulary of the language. This means that knowledge of (the laws of) logic is inseparable from the possession of the logical constants they govern. In this sense, logic may be seen as a product of natural selection: the emergence of logic requires the development of creatures who can wield structured languages of a specific complexity, and who are capable of putting the languages to use within specific discursive practices.

CHAPTER I The Spirit and Method of Logic Natural Logic There is a natural logic as well as a rational one, just as there is both a mother tongue and a ...

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance.

The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three-valued logic, its decision procedure is almost as efficient as that of the classical logic. It therefore provides a rational and convenient system in which to formalize English arguments.

This paper is concerned with the competing and complimentary relationships between intersubjectivity and discursive logic. It contends that the ultimate failure of Husserlian phenomenology is a testament to the dilemma of subjectivist philosophy. Indeed, political philosophy requires a paradigm-shift from subjectivity to intersubjectivity. With this in mind, this paper examines the classical encounter between morality and ethical life in connection with discursive ethics. While it argues that Habermas still retains a strong residue of subjectivist philosophy, it attempts to clarify the discursive analysis of Foucault and probes into its applicability to practical philosophy.

In this paper, I discuss the analysis of logic in the pragmatic approach recently proposed by Brandom. I consider different consequence relations, formalized by classical, intuitionistic and linear logic, and I will argue that the formal theory developed by Brandom, even if provides powerful foundational insights on the relationship between logic and discursive practices, cannot account for important reasoning patterns represented by non-monotonic or resource-sensitive inferences. Then, I will present an incompatibility semantics in the framework of linear logic which allow to refine Brandom’s concept of defeasible inference and to account for those non-monotonic and relevant inferences that are expressible in linear logic. Moreover, I will suggest an interpretation of discursive practices based on an abstract notion of agreement on what counts as a reason which is deeply connected with linear logic semantics.