Is There A Logic Of Confirmation Transfer?

This article begins by exploring a lost topic in the philosophy of science:the properties of the relations evidence confirming h confirmsh' and, more generally, evidence confirming each ofh₁, h₂, ..., h_m confirms at least one of h₁, h₂,ldots;, h_n'.The Bayesian understanding of confirmation as positive evidential relevanceis employed throughout. The resulting formal system is, to say the least, oddlybehaved. Some aspects of this odd behaviour the system has in common withsome of the non-classical logics developed in the twentieth century. Oneaspect – its ``parasitism' on classical logic – it does not, and it is this featurethat makes the system an interesting focus for discussion of questions in thephilosophy of logic. We gain some purchase on an answer to a recently prominentquestion, namely, what is a logical system? More exactly, we ask whether satisfaction of formal constraints is sufficient for a relation to be considered a (logical) consequence relation. The question whether confirmation transfer yields a logical system is answered in the negative, despite confirmation transfer having the standard properties of a consequence relation, on the grounds that validity of sequents in the system is not determined by the meanings of the connectives that occur in formulas. Developing the system in a different direction, we find it bears on the project of ``proof-theoretic semantics': conferring meaning on connectives by means of introduction (and possibly elimination) rules is not an autonomous activity, rather it presupposes a prior, non-formal,notion of consequence. Some historical ramifications are alsoaddressed briefly.     

Is Default Logic a Reinvention of Inductive-Statistical Reasoning?

Currently there is hardly any connection between philosophy of science and Artificial Intelligence research. We argue that both fields can benefit from each other. As an example of this mutual benefit we discuss the relation between Inductive-Statistical Reasoning and Default Logic. One of the main topics in AI research is the study of common-sense reasoning with incomplete information. Default logic is especially developed to formalise this type of reasoning. We show that there is a striking resemblance between inductive-statistical reasoning and default logic. A central theme in the logical positivist study of inductive-statistical reasoning such as Hempels Criterion of Maximal Specificity turns out to be equally important in default logic. We also discuss to what extent the relevance of the results of Logical Positivism to AI research could contribute to a reevaluation of Logical Positivism in general.     

Is It Justifiable to Abandon All Search for a Logic of Discovery?

In his influential paper, ‘Why Was the Logic of Discovery Abandoned?’, Laudan contends that there has been no philosophical rationale for a logic of discovery since the emergence of consequentialism in the 19th century. It is the purpose of this paper to show that consequentialism does not involve the rejection of all types of logic of discovery. Laudan goes too far in his interpretation of the historical shift from generativism to consequentialism, and his claim that the context of pursuit belongs to neither discovery nor justification is based on narrow interpretations of the contexts of discovery and justification. As a result, Laudan draws unwarranted conclusions concerning both the early and contemporary defenders of a logic of discovery. A methodological logic of discovery—which involves self‐corrective methods of hypothesis generation that promote the long‐term goals of science and which require consequential support for justification—is a type of logic of discovery that survives the shift to consequentialism.     

Logic or rhetoric in law?

One of the most crucial questions in the philosophy of law deals with the very nature of legal reasoning. Does this reasoning belong to logic or to rhetoric? This debate, increasingly centered on rhetoric, is not merely a question of language use; it covers and indicates a more basic choice between formal legalism — focusing on rational deduction from the law — and pragmatic judiciarism — focusing on reasonable debate in the court. Today, it is necessary to circumscribe the respective fields of logic and rhetoric in the language of law, while showing how they are sometimes complementary in the resolution of legal problems. But, even when we have acknowledged the need for a rhetoric accompanied by logic, we have to define that rhetoric cautiously. I confront a narrow rhetoric, often called argumentation, with a wider one of interrogative nature. There are two conceptions of rationality at stake. Their comparison enables us to raise the question of the foundation of law, as a locus to use arguments, as well as to solve social problems.     

What is a Non-truth-functional Logic?

What is the fundamental insight behind truth-functionality? When is a logic interpretable by way of a truth-functional semantics? To address such questions in a satisfactory way, a formal definition of truth-functionality from the point of view of abstract logics is clearly called for. As a matter of fact, such a definition has been available at least since the 70s, though to this day it still remains not very widely well-known.A clear distinction can be drawn between logics characterizable through: (1) genuinely finite-valued truth-tabular semantics; (2) no finite-valued but only an infinite-valued truthtabular semantics; (3) no truth-tabular semantics at all. Any of those logics, however, can in principle be characterized through non-truth-functional valuation semantics, at least as soon as their associated consequence relations respect the usual tarskian postulates. So, paradoxical as that might seem at first, it turns out that truth-functional logics may be adequately characterized by non-truth-functional semantics. Now, what feature of a given logic would guarantee it to dwell in class (1) or in class (2), irrespective of its circumstantial semantic characterization?The present contribution will recall and examine the basic definitions, presuppositions and results concerning truth-functionality of logics, and exhibit examples of logics indigenous to each of the aforementioned classes. Some problems pertaining to those definitions and to some of their conceivable generalizations will also be touched upon.     

The Logic of the Development of Feminism; or,Is MacKinnon to Feminism as Parmenides Is to Greek Philosophy?

Catharine MacKinnon's investigation of the role of sexuality in the subordination of women is a logical culmination of radical feminist thought. If this is correct, the position of her work relative to radical feminism is analogous to the place Parmenides's work occupied in ancient Greek philosophy. Critics of MacKinnon's work have missed their target completely and must engage her work in a different way if feminist theory is to progress past its current stalemated malaise.     

Consequence and Interpolation in ?ukasiewicz Logic

Building on Wójcicki??s work on infinite-valued ?ukasiewicz logic ?_??, we give a self-contained proof of the deductive interpolation theorem for ?_??. This paper aims at introducing the reader to the geometry of ?ukasiewicz logic.     

Can First-Order Logical Truth be Defined in Purely Extensional Terms?

W. V. Quine thinks logical truth can be defined in purely extensional terms, as follows: a logical truth is a true sentence that exemplifies a logical form all of whose instances are true. P. F. Strawson objects that one cannot say what it is for a particular use of a sentence to exemplify a logical form without appealing to intensional notions, and hence that Quine's efforts to define logical truth in purely extensional terms cannot succeed. Quine's reply to this criticism is confused in ways that have not yet been noticed in the literature. This may seem to favour Strawson's side of the debate. In fact, however, a proper analysis of the difficulties that Quine's reply faces suggests a new way to clarify and defend the view that logical truth can be defined in purely extensional terms.     

Logic and eloquence: A Ramusian revolution?

Logic and eloquence: A Ramusian revolution?     

Logic and Reasoning: do the facts matter?

Modern logic is undergoing a cognitive turn, side-stepping Frege’s ‘antipsychologism’. Collaborations between logicians and colleagues in more empirical fields are growing, especially in research on reasoning and information update by intelligent agents. We place this border-crossing research in the context of long-standing contacts between logic and empirical facts, since pure normativity has never been a plausible stance. We also discuss what the fall of Frege’s Wall means for a new agenda of logic as a theory of rational agency, and what might then be a viable understanding of ‘psychologism’ as a friend rather than an enemy of logical theory. Edited by Hannes Leitgeb     

What Is Music? Is There a Definitive Answer?

Philosophers frequently defend definitions by appealing to intuitions and contemporary folk classificatory norms. I raise methodological concerns that undermine some of these defenses. Focusing on Andrew Kania's recent definition of music, I argue that the way in which it has been developed leads to problems, and I show that a number of other definitions of interest to philosophers of art (and others) run into similar problems.     

What Is Dissent?

Res Publica - Dissent is a word we come across frequently these days. We read it in the newspapers, use it in discussions with friends and colleagues—perhaps even engage in the...