Online research in philosophy

Examples are presented of Aristotle’s use of non-idealized mathematics. Distinctions Husserl makes in Crisis help to delineate the features of this empiricalmathematics, which include the non-persistence of mathematical aspects of things and the selective application of mathematical traits and proper accidents. In antiquity, non-abstracted mathematics was involved with practical sciences that treat motion. The suggestion is made that these sciences were incorporated by Aristotle into natural philosophy without first being abstracted as pure mathematics—a state of affairs not envisioned by Husserl, for whom science recast natural ontology by means of the idealization of pure mathematics. The relation of empirical mathematics to life-world ontology is considered.

This paper addresses the question of 'What is technology?' in order to develop a framework for the assessment and regulation of technology. I suggest that technology is how we build our world, drawing on the distinctions between the world and the earth, and between the human activities of labour, work and action, made by Hannah Arendt. Arendt's thought has a number of implications for how we should think about and assess the world, and thus technology: the world should not be judged instrumentally, but in terms of whether it provides a place for human action. A model of a possible framework for technology assessment is provided by the UK planning system.

Natural philosophy encompassed all natural phenomena of the physical world. It sought to discover the physical causes of all natural effects and was little concerned with mathematics. By contrast, the exact mathematical sciences were narrowly confined to various computations that did not involve physical causes, functioning totally independently of natural philosophy. Although this began slowly to change in the late Middle Ages, a much more thoroughgoing union of natural philosophy and mathematics occurred in the seventeenth century and thereby made the Scientific Revolution possible. The title of Isaac Newton's great work, The Mathematical Principles of Natural Philosophy, perfectly reflects the new relationship. Natural philosophy became the 'Great Mother of the Sciences,' which by the nineteenth century had nourished the manifold chemical, physical, and biological sciences to maturity, thus enabling them to leave the 'Great Mother' and emerge as the multiplicity of independent sciences we know today.

Most contemporary philosophy of mathematics focuses on a small segment of mathematics, mainly the natural numbers and foundational disciplines like set theory. While there are good reasons for this approach, in this paper I will examine the philosophical problems associated with the area of mathematics known as applied mathematics. Here mathematicians pursue mathematical theories that are closely connected to the use of mathematics in the sciences and engineering. This area of mathematics seems to proceed using different methods and standards when compared to much of mathematics. I argue that applied mathematics can contribute to the philosophy of mathematics and our understanding of mathematics as a whole.

Starting from the thesis that the history of mathematics, for saving its duration and support as a scientific discipline, has to look for the needs and problems of contemporary mathematics, six main problems of contemporary mathematics are listed (concerning partly its social state) and subsequently, 16 questions about the history of mathematics. Moreover, some analogues between the work-sharing of the historians of mathematics and that of the scientists are stated.

In this essay, I use encounters with the white-tailed deer of Fire Island to explore the “call of the wild”—the attraction to value that exists in a natural world outside of human control. Value exists in nature to the extent that it avoids modification by human technology. Technology “fixes” the natural world by improving it for human use or by restoring degraded ecosystems. Technology creates a “new world,” an artifactual reality that is far removed from the “wildness” of nature. The technological “fix” of nature thus raises a moral issue: how is an artifact morally different from a natural and wild entity? Artifacts are human instruments; their value lies in their ability to meet human needs. Natural entities have no intrinsic functions; they were not created for any instrumental purpose. To attempt to manage natural entities is to deny their inherent autonomy: a form of domination. The moral claim of the wilderness is thus a claim against human technological domination. We have an obligation to struggle against this domination by preserving as much of the natural world as possible.

The book concludes that it is a mistake to think of Art as something subjective, or as an arbitrary social representation, and of Technology as an instrumental ...

The philosophy of mathematics provides a severe test for a materialist explanation of science. This is because mathematics is mostly abstract and mathematical theory is rarely tested directly in practice. All the main schools of the philosophy of mathematics — platonism, logicism, intuitionism, formalism — are varieties of idealism. Nevertheless all human ideas, including mathematical ideas, originate from our experience of the world and are rooted in reality. In the history of mathematics it can be seen that problems facing society have given a great impetus to the development of the subject. Thus the rise of trade and changes in technology have each led to great advances, though purely internal contradictions within mathematics have also been of considerable importance. Formal mathematical reasoning, like classical logic, has been highly successful in the evolution of science, but is inadequate for reasoning about indeterministic processes in a state of change. Thus formal logic and dialectics should be thought of as complementary and both are required for a fully scientific understanding of the world.

Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.