Symbolic Logic is a relatively new subject, and the easiest methods of approach have not yet been determined. In point of arrangement, therefore, this Introduction has no predecessor. That is just why it was written: the need of some systematic guide, from the state of perfect innocence to a possible understanding of the classical literature, has become acute and commanding.
Logic and Implication: An Introduction to the General Algebraic Study of Non-classical Logics
This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions.
Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics.
What is Mathematical Logic?
Mathematical logic has grown from an exotic branch of mathematics into an indispensable tool in computer science as well as other parts of mathematics. This concise book presents the subject of mathematical logic in a lively and approachable fashion although logic can be a formidably abstruse topic, even for mathematicians.
This second edition of What is Mathematical Logic?, originally published 50 years ago, deals with important ideas in modern mathematical logic, without the detialed mathematical work required of those with a professional interest in logic. The ideas are set forth simply and clearly in a pleasant style and, despite the book’s relative brevity, all the basic material is covered in these pages. Three new chapters have been added, coevering automatic theorem proving, logic beyond traditional first order logic, and other logics including intuitionistic, free, and modal logics.
Students of computer science and mathematical logic will find it a stimulating introduction and valuable supplement for courses, including current further reading suggestions in this lively area at the intersection of mathematics, philosophy, and computer science.
Jaina Philosophy
The Jains are those who consider that the teaching of the omniscient Jinas is the expression of the eternal essential nature of the universe. The only extant teaching is that of Mahāvīra (traditional dates 599–527/510 BCE, in Magadha, South of modern Bihar), the last Jina of the current cosmic period.
In their practice, Jaina renunciants follow a rigorous method towards salvation, in which a non-violent way of life, the renunciation from a worldly ego, the dissociation of self and non-self, and a gradual purification of the self towards unobstructed knowledge, become as many different facets of the same effort to access to a superior order of being in which each self manifests its true nature.
This path came to involve structured monastic and lay communities; sets of practices—ritual and devotional acts, ascetic practices, rules of life; as well as conceptions of the world deposited in canonical and post-canonical corpuses, in systematic treatises, or in narrative literature. Jaina Philosophy is the set of philosophical investigations developed by thinkers as they appear in these different corpuses (Malvania & Soni 2007; Potter & Balcerowicz 2013, 2014). While several trends can be observed from the canonical period to modern thinkers via the mystics, the following principles are shared: Jaina metaphysics is an atomist and dualist conception of the world, it focuses on the nature of the self, on that of karmic matter, as well as on their principles of association. Jaina ethics consists of practices focused on non-violence, non-absolutism and non-attachment, which aim to disentangle the self and karmic matter and which help one to reach omniscience. Besides, Jaina philosophers are particular renown for developing a realist epistemology centered on “many-sidedness”.
Jaina philosophy is composed in Ardhamāgadhī, Jaina Māhārāṣṭrī, Śaurasenī, Sanskrit, Apabhraṃśa, Braj Bhāṣā, Kannada, Tamil, Gujarati, Hindi, to quote only the main languages. This entry provides Sanskrit terms only, because Sanskrit became the lingua franca of philosophical inter-doctrinal discussions in South Asia at the turn of the common era.
Dao Companion to Chinese Philosophy of Logic
This book is a companion to logical thought and logical thinking in China with a comparative and interdisciplinary perspective. It introduces the basic ideas and theories of Chinese thought in a comprehensive and analytical way. It covers thoughts in ancient, pre-modern and modern China from a historical point of view. It deals with topics in logical (including logico-philosophical) concepts and theories rooted in China, Indian and Western Logic transplanted to China, and the development of logical studies in contemporary China and other Chinese communities. The term “philosophy of logic” or “logico-philosophical thought” is used in this book to represent “logical thought” in a broad sense which includes thinking on logical concepts, modes of reasoning, and linguistic ideas related to logic and philosophical logic. Unique in its approach, the book uses Western logical theories and philosophy of language, Chinese philology, and history of ideas to deal with the basic ideas and major problems in logical thought and logical thinking in China. In doing so, it advances the understanding of the lost tradition in Chinese philosophical studies.
Logic in Practice
“It must be the desire of every reasonable person to know how to justify a contention which is of sufficient importance to be seriously questioned. The explicit formulation of the principles of sound reasoning is the concern of Logic”.
This book discusses the habit of sound reasoning which is acquired by consciously attending to the logical principles of sound reasoning, in order to apply them to test the soundness of arguments. It isn’t an introduction to logic but it encourages the practice of logic, of deciding whether reasons in argument are sound or unsound. Stress is laid upon the importance of considering language, which is a key instrument of our thinking and is imperfect.
Dialogical Logic
This entry presents the framework of « dialogical logic » in the initial Lorenzen and Lorenz tradition. The rules for the game and for building strategies are provided with step by step examples, helping the reader understand how the dialogue tables reflect a dynamic process of interaction between the players. Various logics are presented within this pluralistic framework: intuitionist logic, classical logic, and modal logics, with references to various other logics. In a second part of the entry, objections against the framework are considered, together with answers provided by the « Immanent Reasoning » variant, which stays within the Lorenzen and Lorenz tradition, and by the « Built-In Opponent » variant first developed by Catarina Dutilh Novaes, which develops a different dialogical tradition.
Indicative Conditionals
The chapter is an introduction to logical treatments of indicative conditionals, comparing truth-functional, non-truth-functional, and suppositional approaches. Some of the topics discussed are truth conditions, conditional belief, assertability, and issues with compounds of conditionals.
Feminist Perspectives on Science
Introduction: There are a variety of ways that feminists have reflected upon and engaged with science critically and constructively each of which might be thought of as perspectives on science. Feminists have detailed the historically gendered participation in the practice of science—the marginalization or exclusion of women from the profession and how their contributions have disappeared when they have participated. Feminists have also noted how the sciences have been slow to study women’s lives, bodies, and experiences. Thus from both the perspectives of the agents—the creators of scientific knowledge—and from the perspectives of the subjects of knowledge—the topics and interests focused on—the sciences often have not served women satisfactorily. We can think of these perspectives as generating two types of equity issues: limitations on the freedom to participate as reflected in the historical underrepresentation of women in the scientific professions and the relative lack of attention to research questions relevant to women’s lives.
Biocentrism
Abstract: The orthodox approach to the environment and its inhabitants is deemed to be anthropocentric in that it recognises the moral standing of human beings alone, and as such other beings are given at the most indirect moral consideration when their interests conflict with the interests of humans. However, many global environmental problems and worldwide practices directly affect not just human beings but many other creatures too. In the light of this, the anthropocentric approach has been accused by some philosophers of being too narrowly focused on human interests to creditably account for the true extent of our moral obligations. This article provides a conceptual outline of biocentrism as an alternative approach to ethics; one which widens the moral scope to include all living beings as candidates deserving of moral consideration. The article also discusses how this approach might be applied to contemporary ethical issues which are international in their dimension, including environmental issues, as well as issues concerning our use of animals in worldwide human practices.