1. From 1672-1676, Leibniz made his discovery of calculus while he spent a few creative years in Paris. At this point he was a lawyer and had no mathematical training, yet within a few years he compiled the work of many great mathematicians and created calculus (Bardi, 2006). Leibniz had two scholarly papers of his calculus works published in 1684 and 1686. These two papers single handedly give him the credit for being the first creator of calculus. It took him the twenty years following to refine his work. This time included Leibniz examining Isaac Newton’s Opticks to further refine his work and studies. In 1704, Newton published “On the Quadrature of Curves” in the back of Opticks to establish, what he thought would be, his claim to owning the discovery of calculus (Bardi, 2006). Newton had been quietly smoldering with feelings of humiliation and jealousy towards Leibniz because he knew it was him who invented it first (Bardi, 2006). Newton discovered calculus from 1665-1666 and planned on publishing it around the same as his optics work publication but swore off publishing after the hate he received from his first work (Bardi, 2006). From then on even until after the death of Leibniz in 1716, Newton waged the war (Bardi, 2006). He has said, “Whether Mr. Leibniz invented it after me, or had it from me, is a question of no consequence, for second inventors have no rights (Bardi, 2006).” Leibniz took this threat seriously. He worked with other great minds in Europe and they wrote letters backing up his own cause. He would anonymously attack Newton and include these in his publishing (Bardi, 2006). These two great minds independently had brilliant ideas around the same time, so it was up to whoever published it first to get the credit. Leibniz happened to do so, and so is credited as the creator of calculus. A Gottfried of All Trades: Leibniz and His Trans-Field Exploits Benjamin Miller, Andrew Nauffts, Paige Pendleton Leibniz is widely held within the “pantheon of seven great philosophers (Ross, 1984),” and is considered a continental rationalist, alongside Descartes and Spinoza. Their beliefs boiled down to formal logic, to which Leibniz was a great contributor. Because he reserved any categorization of knowledge to what could be deduced from truths of reason, his ruminations on God, Man, Metaphysics, and even Arithmetic all rely on proofs. His Principle of Identity and Principle of Sufficient Reason are his keys to proving that anything and everything- from math to concerns with the soul and the Spiritual- can be broken down to their most basic, mechanical operations. This sort of analytic philosophy was based on definitions and symbolic thought rather than empirical evidence. Again, this approach was born of his refinements and contributions to the Binary System. This system instructed Leibniz to use a method of division (genus differentia) wherein things are branched by classes, and are composed of component concepts. Think: Sign, Signified, Signifier. The ruling class, or concept that is defined, must always be the most complex, whereas everything that informs it is simpler, until you have things in their simplest forms (sentence is the sign, the words or symbols are the signifiers, and the signified is the meaning ascribed to these symbols and concepts). In this subject-predicate approach, the relational stress is now between, and not within. Example: “Paris is the lover of Helen...asserts a relationship between two subjects...each is true only because the other is true…(and) Ultimately, God made Paris a lover because he was making Helen loved (Ross, 1984)” and vice-versa. So now the relationship between his arithmetic and his logic becomes obvious to one, and we can return to his second principle to view a similar relationship between his arithmetic, logic, and metaphysical beliefs, as the one above. He believed that God created the “best of all possible worlds (Ross, 1984),” because it is the way it is, and not any other way. Furthermore, things might seem bad (for instance, natural disasters, disease etc.-criticisms which were often used against this infamous statement of Leibniz, most famously in Candide by Voltaire) but only due to our perspective, whereas they might seem worst by another’s perspective. He wouldn’t create it another way, it’s a matter of perspective, rather. So, where in binary everything can be broken down to a 0 or a 1, the creation of the Earth reflects this symbology, too; pure being (God, or a 1), and nothingness (0). God’s creative act was therefore a “voluntary dilution of his own essence, and a mathematical computation (Ross, 1984)” reflecting perfect numbers. Key Terms Subject: “Identifies a substance (Ross, 1984).” Predicate: “Attributes a certain property to ‘Subject’ (Ross, 1984).” Principle of Identity: “This is the principle that a proposition is proved to be necessarily true if it either is itself an identical proposition, or can be reduced to one (Ross, 1984).” Identical Proposition: “[When] the predicate is explicitly identical with or included in the subject (Ross, 1984).” Principle of Sufficient Reason: States that nothing is without reason. Binary System: Numeral system which represents numeric values using two symbols: 0 (empty) and 1 (full). Logic and Philosophy Calculus Wars Boom Roasted. You Gott FRIED A Leibniz Wheel Works Cited Bardi, J. The calculus wars: Newton, Leibniz, and the greatest mathematical clash of all time. New York: Thunder's Mouth Press, 2006. 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New York: Oxford University Press, 1984. INTD 220: History of Physical Science Dr. McLean, Dr. Cope, Dr. Towsley Born July 1 st, 1646 1716 Death 1652 1654 1664 1666 1667 1672 1673 1675 1684 1700 1662 1661 1676 1715 1714 Father Dies Gains Access to Father’s Library Enters University of Leipzig Awarded Degree of Bachelor of Philosophy Awarded Degree of Master of Philosophy Rejected for a Degree of Doctor of Law; Leaves Leipzig Forever. Awarded Degree of Doctor of Law from University of Altdorf Arrives in Paris as a Diplomat Needs Financial Backing. Builds calculating machine (Leibniz Wheel). Presents it to Royal Society in London, Becomes an External Member. Discovered the Differential Calculus Visits London and is Shown Some of Newton’s Mathematical Papers Publishes His Discovery of the Differential Calculus Became a Foreign Member of the French Academy of Sciences Composes “Principles of Nature and Grace” and Monadology Began Correspondence with Samuel Clarke, Newton’s Disciple.