The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...) development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

For Jizang (549−623), a prominent philosophical exponent of Chinese Madhyamaka, all things are empty of determinate form or nature. Given anything X, no linguistic item can truly and conclusively be applied to X in the sense of positing a determinate form or nature therein. This philosophy of ontic indeterminacy is connected closely with his notion of the Way (dao), which seems to indicate a kind of ineffable principle of reality. However, Jizang also equates the Way with nonacquisition as a conscious (...) state of freedom from any attachment and definite understanding whatsoever. The issue then becomes pressing as to how we are to understand Jizang's notion of the Way. Does it indicate some metaphysical principle or reality? Is it actually a skilful expedient to lead one to the consummate state of complete spiritual freedom? How is this issue related to Jizang's conception of ontic indeterminacy? In this book chapter, I examine Jizang's key writings in an attempt to clarify his ontological position. (shrink)

What is the rational response when confronted with a set of propositions each of which we have some reason to accept, and yet which taken together form an inconsistent class? This was, in a nutshell, the problem addressed by the Jaina logicians of classical India, and the solution they gave is, I think, of great interest, both for what it tells us about the relationship between rationality and consistency, and for what we can learn about the logical basis of philosophical (...) pluralism. The Jainas claim that we can continue to reason in spite of the presence of inconsistencies, and indeed construct a many-valued logical system tailored to the purpose. My aim in this paper is to offer a new interpretation of that system and to try to draw out some of its philosophical implications. (shrink)

When the original Dutch version of this book was presented in 1971 to the University of Leiden as a thesis for the Doctorate in philosophy, I was prevented by the academic mores of that university from expressing my sincere thanks to three members of the Philosophical Faculty for their support of and interest in my pursuits. I take the liberty of doing so now, two and a half years later. First and foremost I want to thank Professor G. Nuchelmans warmly (...) for his expert guidance of my research. A number of my most im portant sources were brought to my attention by him. During the whole process of composing this book his criticism and encouragement were carried out in a truly academic spirit. He thereby provided working conditions that are a sine qua non for every author who is attempting to approach controversial matters in a scientific manner, conditions which, however, were not easily available at that time. In a later phase I also came into contact with Professors L. M. de Rijk and J. B. Ubbink, with both of whom I had highly stimulating discussions and exchanges of ideas. The present edition contains some entirely new sections, viz. 1-9, IV-29, V-9, V-20, VII-14 (iii), (iv), VII-17 (i), VIII-22, IX-17, IX-19, X-9 and XI-8. Section X-9 was inspired by a remark made by Professor A. (shrink)

The advantages and disadvantages of formalization in philosophy are summarized. It is concluded that formalized philosophy is an endangered speciality that needs to be revitalized and to increase its interactions with non-formalized philosophy. The enigmatic style that is common in philosophical logic must give way to explicit discussions of the problematic relationship between formal models and the philosophical concepts and issues that motivated their development.

The article concerns two axiom systems of Słupecki for the functionally complete three-valued propositional logic: W1–W6 and A1–A9. The article proves that both of them are inadequate—W1–W6 is semantically incomplete, on the other hand, A1–A9 governs a functionally incomplete calculus, and thus, it cannot be a semantically complete axiom system for the functionally complete three-valued logic.

The work of Hugh MacColl (1837–1909) suffered the same fate after his death as before it:despite being vaguely alluded to and in part even commended, on the whole it has remained an unknown quantity. Even worse, those of his ideas which have played a decisive role in the history of logic have been credited to his successors; this is especially the case with the definition of strict implication and the first formal development of formal modal logic. This paper takes an (...) initial step towards a rectification of this unfortunate misrepresentation, presenting a bibliography of MacColl’s most significant publications with particular regard to their reception. (shrink)

On the basis of a ten-place comparative value relation, artificially reduced to a binary relation, some human value structures are studied and a concept of value kinematics is proposed. A miniature value logic is outlined, making it possible with precision to handle several explicated value notions and to analyze interrelations between them. Finally, the question is discussed whether health can be said to be an absolute and an intrinsic value.

A method of constructing Hilbert-type axiom systems for standard many-valued propositional logics was offered by Rosser and Turquette. Although this method is considered to be a solution of the problem of axiomatisability of a wide class of many-valued logics, the article demonstrates that it fails to produce adequate axiom systems. The article concerns finitely many-valued propositional logics of Łukasiewicz. It proves that if standard propositional connectives of the Rosser–Turquette axiom systems are definable in terms of the propositional connectives of Łukasiewicz’s (...) logics, and thus, they are normal ones, then every Rosser–Turquette axiom system for a finite-valued Łukasiewicz’s logic is semantically incomplete. (shrink)

Traditionally legal theorists, whenever engaged in controversy, have agreed on one point: legal norms are par excellence rules which impose obligations. The author examines this assumption, which from another perspective (that of constitutional law, for instance) appears less obvious. In fact, constitutional rules are commoniy empowering norms, norms which do not create duties but powers. To this objection many theorists would reply that empowering rules are incomplete and that they are to be understood as parts of duty‐creating rules. A different (...) position from this traditional stance is that defended in Kelsen's later writings, according to which the fundamental type of norm is the empowering norm. The author discusses Kelsen's three theories on the “ideal form” or structure of the legal norm, with special attention to the third of these, the empowerment theory. (shrink)