A more accurate understanding of infinity as a concept can help articulate more precise claims regarding the nature of god in philosophy of religion. A quantity is infinite if it is such that we can always take a part of it outside what has already been taken. Nov 21, 2004 infinity and the mind is a superb popular account of set theory as an approach to exploring the concept of infinity. If someone is to be judged of a crime and the evidence against him is overwhelming, then that person could argue that they must have. In the latter, levinas, according to a phenomenological method, describes how subjectivity arises from. The science and philosophy of the infinite princeton science library kindle edition by rucker, rudy.
In both theology and philosophy, infinity is explored in articles such as the ultimate, the absolute, god, and zenos paradoxes. One of his most important works is totality and infinity. The concept of infinity in the mind of the hindu ancients. Here is one of the points where the mathematical concept of infinity cannot help us clarify the concept of theological infinity. Very often this is taken as an argument in philosophy. If infinity is a concept, what is the biggest concept. The term infinity that is used in contemporary mathematics and science is based on a technical development of this earlier, informal concept of actual infinity. So, for instance, in the later 18th century continuity of a function was taken to mean that infinitesimal changes in the value of the argument induced infinitesimal changes in the value of the function.
He took the beginning or first principle to be an endless, unlimited primordial mass. Yet, ken points out that its easy to list what infinity is not, but a real definition can be far more elusive. Dispute over infinity divides mathematicians scientific. In philosophy, infinity can be attributed to infinite dimensions, as for instance in kants first antinomy. Nov 16, 2000 potential infinity enabled mathematicians to develop the concept of a limit, developed in the nineteenth century to establish the theory of calculus on a firm foundation. What makes us a philosophy forum is more about our approach to the discussions and debates than what subject is being debated.
Mathematicians say there are as many odd numbers as there are numbers altogether. Since davidson thinks that nonlinguistic creatures cant have the concept of belief, they cant have other concepts as well. Infinity in mathematics and logic the notion of infinity, and the problems, both philosophical and mathematical, that arise from it have been a central concern for over two millennia. Topics discussed extend far beyond philosophy and philosophers. The concept of infinity has fascinated philosophers and mathematicians for many centuries. The argument links having beliefs and concepts with having the concept of belief. This is one of the conundrums inherent in the concept of infinity, netz says. Why the concept of belief is needed to have other concepts is somewhat obscure in davidsons writings carruthers 1992. More recently, mathematicians have debated about the proper use of infinity. In greek philosophy, for example in anaximander, the boundless is.
In philosophy and theology, infinity is explored in articles under headings such as the ultimate, the absolute, god, and zenos paradoxes. Nevertheless, the critical philosophy judged that infinity only keeps its identity by virtue of its opposition to finitude, and consequently abandoned any hope for a synthesis. Infinity philosophy project gutenberg selfpublishing. Infinity is used to describe quantities which go on forever without end. The philosophy around ananta dates back to the veda. The concept of infinity from the ionic philosophers to aristotle thomas. To determine the nature of infinity, mathematicians face a choice between two new logical axioms.
Infinity is an abstract concept used to describe something that is endless or boundless. In mathematics, there is a clearly developed concept of the infinite. Actual infinite one of the most important contributions that aristotle had made to to study of infinity is identifying a dichotomy between what aristotle calls the potential infinite and the actual infinite. By contrast, the concept of actual infinity treats the infinite as timeless and complete. The philosophy forums at aim to be an oasis of intelligent indepth civil debate and discussion. This fact runs counter to the naive concept of infinity. Youre starting to understand the concept of infinity. Explore infinitis concept vehicle models, including the q80 sport sedan, and qx sport crossover.
This is a surprising definition because, before this definition was adopted, the idea that actually infinite wholes are equinumerous with some of their parts was taken as clear evidence that the concept of actual infinity is inherently paradoxical. Philosophy stack exchange is a question and answer site for those interested in the study of the fundamental nature of knowledge, reality, and existence. Welcome to the wikiversity learning project about the philosophy of infinity introduction. Hopefully, noone will offer a trite answer along the lines of god is the biggest concept. Rudy rucker, a computer scientist, mathematician, philosopher, and author joins john and ken to get to the roots of infinity. Before this turning point, the philosophical community generally believed aristotles concept of potential infinity should be the concept used in mathematics and science. For example, following the distinction made above between the absolute and merely infinite would lead us to believe that aquinas had in mind an infinity absolutely beyond human comprehension. Infinity, the concept of something that is unlimited, endless, without bound. Put another way, infinity is the concept that there is no largest number. Infinity is the concept of an object that is larger than any number.
Informally expressed, any infinite set can be matched up to a part of itself. I agree with mauro that cantor detected an infinite number of different kinds of infinity. Ill answer this question with some reference to history. Mathematics is the basis of all science for the simple fact that it allows us to measure, counting in its basic. The concept of infinity general philosophy science forums. The proof of his principle of infinity is presented in the ethics, book i. Cantor keeps this naive infinity, which he calls the absolute infinite, but he allows for many intermediate levels between the finite and the absolute infinite. These would all be misinterpretations of aquinass analogical concept of infinity. In infinity and the mind, rudy rucker leads an excursion to that stretch of the universe he calls the mindscape, where he explores infinity in all its forms. He expressed his intuitive beliefs in definitions and axioms to begin the structure of his philosophy.
It is a fascinating domain from mathematical set theory. They came up to the concept from a different angle. It is important in mathematics, cosmology, physics, computing, and the arts. In the philosophical approach, questions about the concept of infinity are linked to other parts of the philosophical discourse, such as ontology and epistemology and other important aspects of philosophy of mathematics. New york despite being in existence for more than 2,000 years, the concept of infinity has endured as an enigmatic, and oftentimes challenging, idea for mathematicians, physicists and philosophers. It is valid only when used to indicate a potentiality, never an actuality. If you reject all definitions of what we would use the word infinity to mean, then its tautological that infinity cannot be defined. Descartes, principles of philosophy, in the philosophical works of descartes, 1, trans.
Im trying to remember the name of a concept i saw in one of my philosophy classes back in the days. A philosopher named zeno of elea, who lived from 490 b. C, is credited with introducing the idea of infinity. In greek philosophy, for example in anaximander, the boundless is the origin of all that is.
The concept of infinity has always demanded the attention of philosophical and mathematical thinkers. The ananta of the hindu ancients is the infinity of today. It can seem as though infinite and finite existence constitute two modes of the one transcendental perfection of existence. But you cant do that with infinity and the numbers, because you never run out of numbers. Infinityin philosophy the concept of infinity has always demanded the attention of philosophical and mathematical thinkers. That seems like saying there are as many men as there are people altogether which we know is untrue. Infinity is an elusive concept that can often be difficult to comprehend. Ludwig wittgenstein had reservations about the existence of actual infinities. New york despite being in existence for more than 2,000 years, the concept of infinity has endured as an enigmatic, and oftentimes challenging, idea for mathematicians, physicists and. Infinity is a useful concept for mathematicians and some philosophers have imagined that there are actual infinities such as infinite time, infinite space and an infinite god. You can say it is infinite in the sense that, no matter how many numbers you count, there is always another number. Emmanuel levinas is one of the greatest thinkers of the twentieth, but the complexity of his thought, as well as heideggers, prevents a real spread democratization of his work. Download it once and read it on your kindle device, pc, phones or tablets.
Summary there is no such a thing as a biggest concept. The mental infinity of the subject would be effectively bounded by its failure to encompass the objective world of finitude. As ananta occupies a significant place in philosophy, we may dare to guess that the philosophical basis of the concept of infinity finds its roots in ancient indian resource abundance. There is a use of the concept infinity which is valid, as aristotle observed, and that is the mathematical use.
This technical concept was not created until late in the 19 th century. In spite of yourself, joe, youre starting to get it. Ancient philosophy kalachakra, the wheel of time, is a representation of the cyclic view of time in some ancient philosophies since the earliest days of philosophy in ancient india and greece, the true nature of time has exercised some the greatest minds in history. You should do your research to understand what sorts of conceptual issues are resolved by the concept of infinity, such as zenos paradox. Potential infinity enabled mathematicians to develop the concept of a limit, developed in the nineteenth century to establish the theory of calculus on a firm foundation. Aug 29, 2015 the conference foundations of the formal sciences viii. It was an interesting exercise, but i was lousy in physics and have not, to this day, found a practical use for a mobius strip. The book tackles deep issues of mathematics, logic and philosophy. With the abandonment of infinitesimals in the 19th century this definition came to be replaced by one employing the more precise concept of limit. Infinity and the mind is a superb popular account of set theory as an approach to exploring the concept of infinity. In order to better define what infinity actually is, we brought in eugenia cheng, a mathematician and the author of.
Before that some were leery about the concept, but others, like leibniz, did. Continuity and infinitesimals stanford encyclopedia of. Rudy rucker explores topics such as godels theorems. So on this sort of prototype view which is sometimes termed the probabilistic or the statistical view of concepts, the relationship between a concept and the concepts used to analyze it is a statistical relation, rather than an entailment relation as in the classical theory. What is your philosophical understanding of the concept of. Rucker acquaints us with godels rotating universe, in which it is theoretically possible to travel into the past, and explains an. One of the most important contributions that aristotle had made to to study of infinity is identifying a dichotomy between what aristotle calls the potential infinite and the actual infinite. The concept of the mathematical infinity and economics. And if the construction is to make a new concept potential infinity starting from the concept infinity, thus meaning the kind of infinity that is potential, then it also does not help to explain how to come up with infinity in the first place. Since the time of the ancient greeks, the nature of infinity was the subject of many discussions among philosophers see infinity philosophy.
I have tried to summarise and explain quotations and to translate latin where possible, and to write around the subject, and in general to avoid it being simply a list of quotations. The concept of infinity as detected by cantor is much more subtle than a simple argumentation with symmetry captures. This question involves a likely paradoxical category mistake. It can seem like the infinity of esse commune is but the logical indeterminacy of a concept and the infinity of god the entitative analogue. Surely then, we can define infinity with some precision. We come across infinity when we talk about god, space, numbers themselves, and even in the division of matter. When leibniz injects the concept of infinity into the theory of life, he does so in the belief that this is a concept of which he has true mastery, and therefore one that can do real theoretical work for him. It is important to take special note that infinity is not a number. It is quite accessible to anyone who has studied high school mathematics. In philosophy and theology, infinity is explored in articles under headings such as the ultimate. Apr 02, 2002 it can seem like the infinity of esse commune is but the logical indeterminacy of a concept and the infinity of god the entitative analogue.
This concept is the starting point of his philosophy. Throughout the course of history, philosophers have differed on the infinity of space, god, and time. This page is a selection of philosophical writings about infinity with links to other resources on the net. Any serious thought about the nature of space, time, god or gods, mathematics, and motion quickly leads to more general concerns regarding the notion, or notions, of infinity intimately tied up with such issues. The science and philosophy of the infinite princeton science library.
Use features like bookmarks, note taking and highlighting while reading infinity and the mind. When i think of the concept of infinity, i am reminded of the mobius strip which we were shown in high school physics class. Infinity concept is a totally fictional concept that doesnt mean anything but was just introduced or fabricated to legalize so many illegal mathematics. However, you should not believe that there is no infinity blindly. For the last 100 years or more, mathematicians have been happy to use completed infinities in a variety of ways.