Science, Marxism and the Big Bang: A Critical Review of 'Reason in Revolt'


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The infinite in mathematics

In the late nineteenth century the mathematician George Cantor dedicated his studies to the mathematical concepts of the infinite.

Woods says:

Thus, after Cantor, there can be no argument about the central place of the infinite in mathematics… Yet despite all the evidence, many modern mathematicians persist in denying the objectivity of infinity. (Reason in Revolt, p358)

How can this perversity of modern mathematics be resolved? Why, if there was to be no argument about the objective existence of infinity, did argument persist, "despite all the evidence"? The answer is to be found in discovering what Cantor actually showed. Cantor says that the infinite arises:

First when it is realised in the most complete form, in a fully independent other-worldly being, in Deo [in god] where I call it the Absolute… second when it occurs in the contingent, created world; third… as a mathematical magnitude…

I wish to make a sharp contrast between the Absolute and the transfinite, that is the actual infinities of the last two sorts, which are clearly limited, subject to further increase, and thus related to the finite. (Quoted by Barrow, The Infinite Book, p94)

In Cantor’s mathematics, only infinity in god coincides with Woods’ idea of the objectivity of infinity – an objectively existing infinite god. And indeed there was "no argument" about it.

 


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