Leibniz on the Empty Term ‘Nothing’

This paper discusses Leibniz’s treatment of the term ‘nihil’ that appears in some logical papers about the notion of Real Addition. First, the paper argues that the term should be understood as an empty (singular) term and that sentences with empty terms can be true (§2). Second, it sketches a positive free logic to describe the logical behaviour of empty terms (§3). After explaining how this approach avoids a contradiction that threatens the introduction of the term ‘nihil’ in the Real Addition calculus (§4), and how this approach should be understood within Leibniz’s philosophy (§5), the paper assesses the prospects of such an approach with regard to two fundamental issues in Leibniz’s thought: the fictional nature of infinitesimals (§6), and the occurrence of the term ‘nothing’ in the proof of the existence of God that we find in the New Essays (§7).

Monotonicity, Convexity, Continuity, and Isomorphism: The Psychological Scaffolding of Arithmetic

With the natural numbers as our starting point, we obtain the arithmetic structure of real (as in R) addition and multiplication without relying on any algebraic tools; in particular, we leverage monotonicity, convexity, continuity, and isomorphism. Natural addition arises by minimizing against monotonicity. Rational addition arises from natural addition by minimizing against convexity. Real addition arises from rational addition via any one of three methods; unique convex extension, unique continuous extension, and unique monotonic extension. Real multiplication arises from real addition via isomorphism. Following these mathematical developments, we argue that each of the leveraged mathematical concepts ---monotonicity, convexity, continuity, and isomorphism --- enjoys, prior to its formal mathematical existence, an intuitive psychological existence. Taken together, these lines of argument suggest a way for psychological representation of algebraic structure to emerge from non-algebraic --- and psychologically plausible --- ingredients.

The Analytical Study of Medication during Fasting in the Perspective of Shariah Rulings

The beauty of religion Islam is not only to provide the complete life style and charter for one to lead his life smoothly but it flourishes the human life with its eternal directions and commands full of hidden pleasures coupled with physical and spiritual care of human body. In fact, the everlasting religion comprised of such rulings that help individuals in every walk of life until and unless these rulings are implemented and executed in a proper way according to the prescribed codes of Almighty Allah and his Messenger, Prophet Muhammad PBUH. The thorough study of Shariah rulings reveals the fact that to protect the man’s life or even to make it in comfort and ease, the gradual and steady relaxation has been observed like the one unable to perform prayer in standing position, legitimate for him to sit or even through gestures according to the status of his illness and disease. Similarly, the fasting is important part of Worship, obligation upon Muslim to observe fasting during Ramadan with intentions to get Allah’s pleasure and piousness. This research study emphasis on highlighting the shariah rulings about the medication during fasting in order to know the extent of use, specification in drugs like injections and drips along with some relevant discussion about the spirit of medicine permission. The study will be the real addition to the knowledge and will be fine guidance for the Practiced Muslims.

Ars Characteristica, Logical Calculus, and Natural Languages

This chapter discusses Gottfried Wilhelm Leibniz’s philosophical reflections on ars characteristica (“characteristic art,” the art of forming and arranging characters so that they agree with thoughts), logical calculus, and natural languages. It begins by providing an overview of Leibniz’s project for a universal language, his division of general science into analysis and synthesis, and his investigations on grammar. It then considers Leibniz’s notion of natural language in relation to words and particles, the logic of propositions, real addition and mereology, and the nature and origin of historical language based on the concepts of affect, onomatopoeia, and cases and circumstances. Finally, the article examines Leibniz’s views on artificial language and the nature of monads.