engleski

Separating the Two Infinities: Intelligence and the Projekt of Philosophy in the Third Millenium

In science and philosophy, the concept of the infinite is intimately tied to the quest for an understanding of the causes of the coming to be and passing away and the existence of all things. The concept of infinity employed in mathematics, physical science, and metaphysics, by describing the limits of explanation also provides a basis for explanation in an ultimate sense. A comparison of the metaphysical concept of the infinite with the concept of the infinite employed in mathematics and in physics reveals striking analogies and some important differences. This paper explores the characteristics of various concepts of infinity employed in mathematics and science: non-dumerability, non-quantifiability, 0-dimensionality, indeterminability (non-temporality, non-spatiality) and their relevance to philosophy's search for ultimate principles. Mathematical induction establishes a universal, quantifiable rule for an infinite sequence of cases or set, allowing us to make distinctions between different "types of infinity" (Cantor). Empirical induction proceeds from a series of observations of certain phenomena to the statement of a general law governing all occurences of such phenomena. A good scientific theory is a provisional hypothesis or model which accurately describes a large class of observations and makes definite predictions about the results of future observations.Hawking, seeking in his book A Brief History of Time a model of the Universe to account for the discovery of the red-shift, attempts to deal with theoretical problems raised by the apparent physical necessity for assuming the Universe had a beginning (singularity). Hawking's extrapolation from the unboundedness of space and time to the unnecessariness of postulating a creator God, however, involves a hidden paradigm change which undermines the validity of his argument. Explanation, namely, involves not only a search for causes, but also for reasons.Our knowledge of the essence of a thing is always only an approximation, which can approach, but never attain its goal. It is disproportionate with repect to our powers of cognition. Yet, without a momentary grasp of what a thing is we could recognize nothing at all. In this respect infinity is not "before" or "after" time, but represents an absolute limit universally present in the here and now. Every here and now is a singularity. Without infinity and contact with infinity not a breath can be taken, not an eyelid blink. Philosophy's job is to give an explanation or justification (logon didonai) of limit and limitation in this ultimate sense. Its task begins with the process of definition in the original sense of de-finire, a determination of the limits or boundaries of a thing in its concept, by identifying and distinguishing things and their behaviour according to their natural characteristics. The identification and definition of finite individuals is bounded by the infinite and borders on infinity, everywhere presupposing the fundamental intelligibility of the universe and the ultimate limitation of the individual and the process of definition and explanation by the infinite itself as the key to our ability to understand and to explain individual phenomena and the universe as a whole.

infinity; universe; individuals; thought; reality; definition; explanation; mathematics; physical science; metaphysics

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