Infinity on the Web - A short, self-study course on the infinite
Introduction: What is the infinite?
What is the infinite? A common answer to this question is that infinity is what does not end or contain any boundary or limit. Can we talk about and understand infinity? How do we even begin to talk about it? Obviously we do talk about it. Human beings have been fascinated with the boundless and unending since the beginnings of conceptual thought. Although the infinite may or may not be an actuality, we can nonetheless acknowledge that we know something about ‘infinity’ as a concept. This immediately leads to the follow up question: what are concepts?
In order to hold off any complicated epistemological investigation, for the moment we can maintain that whenever we talk about concepts we are primarily referring to quasi-intangible things. Concepts have more in common with ideas, symbols, meanings, terms and representations (both about the world but also of other concepts) than they do with any concrete entities such as physical objects. Some concepts, it's true, are very closely connected to information conveyed to us by our senses. My idea of red, to take an example, is closely connected to my experiences of seeing red things. Other concepts however, and the infinite is a very good example of this second kind, are less closely related to direct experiences.
These web pages will attempt to give a reflective, analytical, account of the nature of infinity. Although the ultimate goal will be to arrive at a deeper understanding of the thing itself (infinity, in all its paradoxical splendor) the approach taken here will first seek to better understand infinity by examining it philosophically. Towards this end, I will not resist the temptation to either avoid conceptual analysis or give a synthetic overview of the ideas explored below dealing with the nature of the infinite.
Why study the Infinite?
Whether or not infinity is an actual presence and part of reality, or merely a concept we use to make sense of the enormity of the physical universe, it stands as an indispensable essential concept pertinent to both the humanities and the sciences. Thinking about infinity, therefore, is important because we cannot even begin to understand the nature of reality if we shun addressing important questions such as: what is the nature of the absolute?
The concept of infinity finds expression in art, relgion, philosophy and poetry. Many of these different representations of the infinite will be explored below. Since the infinite is also a central concept in modern science and mathematics, coming to grips with its meaning is important for making sense of our models of both the natural world and the underpinings of the modern scientific method.