Many philosophers who do not analyze laws of nature as the axioms and theorems of the best deductive systems nevertheless believe that membership in those systems is evidence for being a law. This raises the question, “If the best systems analysis fails, what explains the fact that being a member of the best systems is evidence for being a law?” In this essay I answer this question on behalf of Leibniz. I argue that although Leibniz’s philosophy of laws is inconsistent (...) with the best systems analysis, his philosophy of nature’s perfection enables him to explain why membership in the best systems is evidence for being a law of nature. (shrink)

Classical theories of harmony have been used to explain phenomena like beauty, happiness, health, virtue, pleasure, peace, and even ecological sustainability. With the intent of making these theories more accessible to designers, this article reviews the conception of harmony from about 500 BCE to the present. It begins with a brief overview of harmony in classical Chinese and Greek philosophy. Then it examines the role of harmony in the renaissance, the scientific revolution, and the early modern period across topics in (...) aesthetics, ethics, physics, politics, and economics. Finally, turning to the 20th century, this article highlights the conceptual function of harmony in psychology, neuroscience, computer science, and design. This synthesis concludes with a review of applications and implications for contemporary designers. An essential conclusion of this article is that harmony involves the integration of diversity into a greater whole; harmony is not pure agreement or “sameness.” Overall, we suggest that classical principles of harmony might serve as a theoretical framework to help designers develop a more sustainable and vibrant vision of the future. (shrink)

The purpose of this dissertation is to defend Pierre Fermat and Gottfried Wilhelm Leibniz against the charge of error made against them by Pierre Maupertuis that they errantly applied final causes to physics. This charge came in Maupertuis’ 1744 speech to the Paris Academy of Sciences, later published in different versions, entitled Accord Between Different Laws Which at First Seemed Incompatible. It is in this speech that Maupertuis lays claim to one of the most important discoveries in the history of (...) physics and science, The Principle of Least Action. From the date of this speech up until the end of the twentieth century, Maupertuis was credited with this discovery. Fermat discovered least time in optical physics, and Leibniz co-discovered infinitesimal calculus. When the credited discoverer of least action in physics accuses the discoverer of least time in optics and the co-discoverer of infinitesimal calculus of error before and audience of mathematicians, physicists and scientists, it is an event that calls out for investigation. The idea of final causes in physics is the idea that bodies move for an end purpose. During the early modern period, this challenged the intellectual establishment of the day with the idea of thinking in nature. The question which fueled the research for this dissertation is why such a man would accuse two other prominent intellects with such an unprovable metaphysical assumption. The research for this project started with a study of the positions of all three of these men regarding final causes in physics. The second phase was to research the historical context in which Accord Between Different Laws Which at First Seemed Incompatible was written and delivered. This context included the life of Maupertuis as member of the Paris Academy of Sciences and as later President of the Berlin Academy of Sciences. It also included the workings of three highly competitive, state funded, academies of science in Berlin, London and Paris. Research showed that no formal positions were held on the subject of final causes by either Maupertuis or Fermat. Only Leibniz demonstrated an established and well thought out position on the subject. Research did reveal the story of an ambitious man in Maupertuis, who made it the fulfillment of his ambition to rise in the ranks of math and science within the academies and establish himself as an intellectual great in European culture. Consequently, the life and career of Maupertuis illustrates the sociological dimension of scientific achievement. Accord Between Different Laws Which at First Seemed Incompatible turned out to be a politically calculated speech delivered for the purpose of career advancement. In 1744, Maupertuis was being considered by the King of Prussia, Frederick the Great, and the leadership of the Berlin Academy of Science for the presidency of that institution. Maupertuis knew this. Therefore, the work must be interpreted in this context. Consequently, the charge of error against Fermat and Leibniz by Maupertuis must be interpreted likewise. Discovery was made in contextual and Leibnizian research that Maupertuis was aware of Leibniz’s idea of action from 1738 on, and knowingly claimed to have discovered a generalized notion of action in physics which was not his. It is the story of ambition clouding human judgment. The Leibnizians attacked Maupertuis on this matter, led by a member of the Berlin Academy named Samuel Konig. In the “Konig Affair”, Konig accused Maupertuis of what is essentially plagiarism, and Maupertuis countered with charging Konig with forgery for claiming to have in his possession a letter from Leibniz to Jacob Hermann demonstrating Leibniz’s knowledge of least action. Maupertuis buries Konig in legal proceedings, but loses his reputation in the process. During the final stages of the Konig affair, Maupertuis admits to Patrick d’Arcy, a member of the Paris academy, that he had used Leibniz’s theory of action. Having lost his effective leadership as President of the Berlin Academy, Maupertuis spends the last years of his life in his native France without ever relinquishing his title and office. When at first examining the charge of error, the immediate notion is that this is a cause and effect argument. It appears to be an argument about the order of metaphysics before physics. This turns out not to be the case. Maupertuis agrees with Fermat and Leibniz at every turn. The charge is all about career success. (shrink)

In this study I discuss G. W. Leibniz's (1646-1716) views on rational decision-making from the standpoint of both God and man. The Divine decision takes place within creation, as God freely chooses the best from an infinite number of possible worlds. While God's choice is based on absolutely certain knowledge, human decisions on practical matters are mostly based on uncertain knowledge. However, in many respects they could be regarded as analogous in more complicated situations. In addition to giving an overview (...) of the divine decision-making and discussing critically the criteria God favours in his choice, I provide an account of Leibniz's views on human deliberation, which includes some new ideas. One of these concerns is the importance of estimating probabilities – in making decisions one estimates both the goodness of the act itself and its consequences as far as the desired good is concerned. Another idea is related to the plurality of goods in complicated decisions and the competition this may provoke. Thirdly, heuristic models are used to sketch situations under deliberation in order to help in making the decision. Combining the views of Marcelo Dascal, Jaakko Hintikka and Simo Knuuttila, I argue that Leibniz applied two kinds of models of rational decision-making to practical controversies, often without explicating the details. The more simple, traditional pair of scales model is best suited to cases in which one has to decide for or against some option, or to distribute goods among parties and strive for a compromise. What may be of more help in more complicated deliberations is the novel vectorial model, which is an instance of the general mathematical doctrine of the calculus of variations. To illustrate this distinction, I discuss some cases in which he apparently applied these models in different kinds of situation. These examples support the view that the models had a systematic value in his theory of practical rationality. (shrink)

This work presents to dance and music scholarship the concept of competence, developed and deployed by Greimas, together with the semiotic concepts of counterpoint and harmony. I emphasize competence as a temporal process that requires sanction by an external entity and which corresponds to the level of surface narrative syntax within Greimas’s method of ‘generative trajectory’. To exemplify the application of the generative trajectory to dance, I present the case of the contrapunto de zapateo from Peru. In this step dance, (...) two or more dancers take turns and perform for an audience who claps and cheers for them and upon whom depends the appreciation of their competence. To better account for the complex relations between all actors of the contrapunto, I resort to the concept of semiotic counterpoint, which is first explained by means of input–output boxes, inspired by black box modeling in engineering. Counterpoint is also represented using equations, especially to address memory/retention and prediction/protention, with a subsequent discussion of its relevance and articulation to Greimas’s semiotics. Finally, I complement counterpoint with Leibniz’s definition of harmony and Spinoza’s principle of maximization of action, in order to account for different kinds of fluent interactions between dancers, arguing for its application not only to the contrapunto de zapateo, but also to dances such as Capoeira, breakdancing, and contact improvisation. (shrink)

According to the classical view, beauty is grounded on the universe’s objective harmony, defined by the formula of unity in variety. Concurrently, nature’s beauty is univocal and independent of subjective judgement. In this paper I will argue that, although Leibniz’s view coincides with this formula, his philosophy offers an explanation for subjective dissent in aesthetic judgements about nature. I will show that the acceptance of divergences on aesthetic value are the result of a conception of harmony that includes qualitative variety (...) and dissonance. (shrink)