Leibniz
1) His Biography:
Known also as Gottfried Wilhelm Leibniz, this well-known German mathematician, philosopher, physicist, and statesman also went by the name of von Leibniz. Gottfried Leibniz is regarded as one of the finest and most important metaphysicians, philosophers, and logicians in history. He is well known for independently developing the differential and integral calculus. Additionally, he developed the Leibniz wheel and put forth significant theories regarding time, energy, and force.
On July 1, 1646, Gottfried Leibniz was born to prominent parents in Leipzig, Saxony, Germany. When Leibniz was only six years old, his father, a professor of moral philosophy at the city’s university, passed away. His mother was a wealthy local attorney’s daughter. Leibniz was an exceptional child. When he was only twelve years old, he acquired a command of Latin and began reading Greek intellectuals’ writings. When he was fourteen, he enrolled in the University of Leipzig, where he studied philosophy, mathematics, and law.
He applied for a law doctorate after graduating but was rejected because of his youth. Leibniz decided to present his thesis to the University of Altdorf, where the academics were so delighted that they handed him a professorship and a Doctor of Laws degree right away. Gottfried Leibniz was a brilliant polymath who was knowledgeable about practically every field of study and intellectual endeavour at the time. He made significant contributions to philology, theology, engineering, physics, law, and politics.
Calculus was a brand-new mathematical technique that he discovered, which was probably his biggest accomplishment. Dealing with constantly changing amounts is a common task for scientists. For his research on gravity, Newton had developed a similar methodology. As a result, the issue of who came first was hotly contested. Leibniz published his findings almost three years before Newton, in 1684, who started work on his version in 1665. The approach was, nevertheless, generally accepted to have been discovered simultaneously.
Leibniz also developed the first adder, subtractor, multiplier, and divider, as well as the binary number system. He developed the well-known monads hypothesis in terms of metaphysics, which clarified the connection between the soul and the body. Because he created the universal characteristic, a symbolic language that allows any piece of information to be represented in a natural and orderly fashion, Leibniz is frequently referred to be the father of symbolic logic. On November 14, 1716, in Hannover, Gottfried Leibniz passed away.
2) Main Works:
Monadology:
One of Gottfried Leibniz’s most well-known writings of his mature philosophy is The Monadology. It is a brief text that proposes a metaphysics of simple substances, or monads, in roughly 90 paragraphs.
New Essays on Human Understanding:
Theophilus (“lover of God” in Greek), who speaks for Leibniz, and Philalethes (“lover of truth,” in Greek), who speaks for Locke, are the two speakers in the book. At the start of Book II, the famous argument against the empiricist concept regarding the origin of thoughts is presented: “Except for the mind itself, nothing is in the mind without first being in the senses.” Leibniz, who supports an extreme view of innate cognition in which all thoughts and deeds of the soul are innate, extensively critiques all of Locke’s main objections to innate concepts. Along with his study of intrinsic concepts, Leibniz also critically examines Locke’s beliefs regarding personal identity, free will, mind-body dualism, language, necessary truth, and Locke’s alleged attempt to prove the presence of God.
Dissertation on the Art of Combinations:
Descartes is credited with the main idea of the work, which is that of an alphabet of human cognition. Just like words are made up of combinations of letters, all conceptions are nothing more than combinations of a relatively small number of simple notions. All truths can be stated as suitable combinations of concepts, which can then be broken down into simpler concepts, simplifying the analysis.
As a result, this alphabet would offer a logic of invention as opposed to the previously known logic of demonstration. Since every sentence consists of a subject and a predicate, it is possible to identify all the predicates that fit a given subject or all the subjects that fit a given predicate.
Discourse on Metaphysics:
In his brief work The Discourse on Metaphysics, Gottfried Wilhelm Leibniz constructs a philosophy that addresses the nature of matter, the motion and resistance of bodies, and the place of God in the cosmos. It is one of the few writings that consistently presents Leibniz’s earlier ideas.
Nova Methodus pro Maximis et Minimis:
Calculus was initially discussed in “Nova Methodus pro Maximis et Minimis,” which was the first book on the subject. In October 1684, Gottfried Leibniz published it in the Acta Eruditorum. It is thought to have given rise to infinitesimal calculus.
3) Main Themes:
The Best Possible World:
Leibniz formulates arguably his most renowned, possibly most understandable, and undoubtedly most contentious topic in response to the philosophical question of why an all-powerful God would permit evil and suffering to exist. He responds to this question by stating that we exist in the finest conceivable universe, and if that is the case, then God is operating in the best manner to help all of humanity. Thus, what appears to be bad to the human mind actually becomes—if I may use the nicest possible term—something that is advantageous to the greater and flawless mind of God.
The Principle of Sufficient Reason:
Leibniz creates a school of thought that later became known as the concept of sufficient reason. In essence, this line of reasoning implies that one of humanity’s most fundamental unanswered problems is why, as opposed to merely how, the cosmos came into being. This philosophical thesis’ fundamental tenet is that nothing in the cosmos can or ever has happened for a purpose.
More importantly, unless there is a compelling reason for it to be true, neither a fact nor a truth can be genuine. Remember that this principle just states that a reason exists; it makes no inference as to whether or not this reason is now recognised. Only that is all that is known.
Connectivity:
The saying “the present is big with the future” is a favourite of Leibniz’s. This philosophical idea appears in several of his articles, and even when the phrase itself is not present, the basic idea is still applied. This topic essentially emphasises how everything is interconnected. The linkages between the present and the future will become apparent, even though they might not be immediately apparent. It is also true that ties to past states influence the present, just as the impacts of the present have an impact on the future.
This idea of connection applies to all aspects of the cosmos and is not just related to time. Even if they are not yet manifest, future facts already exist in the present. Based on what is occurring in the present, a person’s situation in the future is tied to that person in the present. This is a universal truth of all matter and material, down to the smallest atom.
A Godly Philosophy:
The assumption that God exists is fundamental to Leibniz’s entire body of work on philosophical reasoning. And not only does God exist, but Leibniz’s logical argument depends on God’s perfection. This theory holds that God designed the universe to have the highest possible degree of harmony between all things. In light of this, it is crucial to keep in mind that harmony cannot exist if everything is in a perfect state; as a result, God bestows perfection unequally and only to the degree that each soul is capable of receiving it in order for this harmony to continue to exist. Essentially, Leibniz’s philosophy cannot exist without faith in God, but those who do not believe are equally accepted by God and are a demonstration of that balance of harmony. This is the one undeniable and necessary fact that underlies everything.
5) Leibniz’s Calculus:
Leibniz and Sir Isaac Newton are credited with discovering calculus (differential and integral calculus). Leibniz’s journals state that on November 11, 1675, he used integral calculus for the first time to determine the region under the graph of a function called y = f. (x). He created a number of notations that are still in use today, such as the integral sign, which is a long stemmed S from the Latin word summa, and the d, which stands for differentials from the Latin term differentia. Before 1684, Leibniz had not written anything about his calculus.
In his 1693 article Supplementum geometriae dimensoriae, Leibniz illustrated the fundamental theorem of calculus—the inverse relation of integration and differentiation—which he had previously theorised. However, Isaac Barrow proved a more generalised geometric version of the theorem, and Newton created a supporting theory. James Gregory is credited with discovering the theorem in geometric form. As the concept evolved, Leibniz’s formalism and new notation made it more understandable. The differential calculus product rule is still referred to as “Leibniz’s law.” The Leibniz integral rule is another name for the theorem that specifies how and when to differentiate under the integral sign.
In order to build calculus, Leibniz took advantage of infinitesimals, manipulating them in a way that suggested they possessed paradoxical algebraic features. These were challenged by George Berkeley in his essay The Analyst and in De Motu. Leibnizian calculus, according to a recent analysis, was better supported and devoid of contradictions than Berkeley’s empiricist objections. Leibniz argued with John Keill, Newton, and others from 1711 until his death on whether he had independently developed calculus.
In spite of opposition from Karl Weierstrass’s disciples, the use of infinitesimals throughout mathematics has persisted in science, engineering, and even formal mathematics thanks to the differential, a crucial piece of computing equipment. In the framework of a field of hyperreal numbers, Abraham Robinson began developing a logical foundation for Leibniz’s infinitesimals in 1960. He did this by using model theory. Leibniz’s mathematical reasoning can be considered as having finally been validated by the non-standard analysis that follows. The standard part function applies the Leibnizian transcendental law of homogeneity, while Robinson’s transfer principle is a mathematical application of Leibniz’s heuristic law of continuity.
6) His Influence on Later Thinkers:
Leibniz’s reputation was deteriorating when he passed away. He is best known for one work, the Theodicee, whose purportedly key thesis was lampooned by Voltaire in his best-selling novel Candide. Candide’s final line in the book is “Non liquet,” which was the Roman Republic’s equivalent of the legal judgement “not proven.” Many people took Voltaire’s portrayal of Leibniz’s thoughts as an accurate account since it had such an impact. Therefore, a portion of the fault for the ongoing inability to appreciate and comprehend Leibniz’s views lies with Voltaire and his Candide. Christian Wolff was a devoted follower of Leibniz whose dogmatic and simplistic attitude did Leibniz’s reputation significant harm. Additionally, he had an impact on
David Hume, who studied his Theodicee and used parts ofhis ideas. In any case, Leibniz’s strong support of the rationalism and system building of the 17th century was falling out of favour with philosophers. His writings on history, law, and diplomacy were seen as being of passing interest. His correspondence’s breadth and depth went unnoticed. Leibniz’s entire body of work in mathematics and physics was disregarded as a result of widespread European scepticism that he had independently discovered calculus before Newton.
A supporter of Newton, Voltaire also penned Candide to refute Leibniz’s claims to have discovered calculus and Newton’s theory of universal gravity, at least in part. The Nouveaux Essais, which Kant closely examined, was published in 1765, marking the beginning of Leibniz’s arduous journey to his current position of fame. The first multi-volume edition of Leibniz’s writings was published by Louis Dutens in 1768. Several editions, including those produced by Erdmann, Foucher de Careil, Gerhardt, Gerland, Klopp, and Mollat, appeared in the 19th century. Leibniz’s letters to famous people like Antoine Arnauld, Samuel Clarke, Sophia of Hanover, and her daughter Sophia Charlotte of Hanover were published.
Leibniz’s metaphysics was the subject of a critique written by Bertrand Russell in 1900. Soon after, Louis Couturat edited a volume of Leibniz’s previously unpublished writings, mostly on logic, and produced an important study of the philosopher. They helped Leibniz gain some recognition among English-speaking analytical and linguistic philosophers of the 20th century (Leibniz had already been of great influence to many Germans such as Bernhard Riemann). For instance, Willard Quine frequently uses Leibniz’s word salva veritate, which means interchangeability without losing or compromising the truth.
However, it wasn’t until after World War II that the secondary literature on Leibniz began to really take off. Less than 30 of the English-language entries in Gregory Brown’s bibliography were published before 1946, which is particularly true in English-speaking nations. Leroy Loemker (1904–1985), through his translations and his interpretive articles in LeClerc, is largely responsible for American Leibniz studies (1973).
Leibniz’s standing as a philosopher, according to Nicholas Jolley, may be at its highest point since he was alive. His ideas of identity, individuation, and potential worlds are still used in analytical and modern philosophy. The “Intellectual Revolution” of the 17th century, which came before the more well-known Industrial and Commercial revolutions of the 18th and 19th centuries, has been more clearly shown by research on the history of 17th and 18th century concepts. The Leibniz Prize, which offers a yearly prize of 1.55 million euros for experimental results and 770,000 euros for theoretical ones, was established by the German government in 1985. Before the Fundamental Physics Prize, it was the largest award for scientific excellence in the world.
7) Some Quotes:
“This is the best of all possible worlds.”
― Gottfried Wilhelm Leibniz
“Music is the hidden arithmetical exercise of a mind unconscious that it is calculating.”
― Gottfried Wilhelm Leibniz
“There is nothing in the understanding which has not come from the senses, except the
understanding itself, or the one who understands.”
― Gottfried Wilhelm Leibniz, Philosophical Essays
“Nothing is in the intellect that was not first in the senses, except the intellect itself.”
― Gottfried Wilhelm Leibniz
“Nothing is necessitated whose opposite is possible.”
― Gottfried Wilhelm Leibniz, Discourse on Metaphysics and Other Essays
