Note on infinity

A common caricature of the view of the mediaeval scholastics is that they wondered whether the number of angels who can dance on the head of a pin is infinite or not. In fact, this calumny was invented much later.

But another common view is that, after Aristotle told people that it was forbidden to think about completed infinities, nobody did so until Cantor broke the barrier.

I don’t think there was ever a time when people didn’t think about infinity. So I was interested to discover the metaphysical poet John Donne, in his poem Love’s Growth, perplexed by the question whether it is possible to make an infinite set bigger by adding something to it:

Methinks I lied all winter, when I swore
My love was infinite, if spring make it more.

About Peter Cameron

I count all the things that need to be counted.
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2 Responses to Note on infinity

  1. Wonderful! I always think of ‘boundary conditions’. With integer number the simple infinity describes the realm of ‘all integer number’ In this simple case the infinity boundary is the quality descriptor of the reality it contains: the quality of ‘integer numberness’. But without magnitude limit. Limited by quality of ‘integer numberness’, but unlimited in magnitude.

    Its this ambiguity of the nature of its reality which gives rise to the infinity paradoxes, perhaps. Although mathematicians appear to operate the logic of infinities inside the boundary, rather than across it or outside it?

  2. Jon Awbrey says:
    Nonne more fine than infinity
    Onneless it's love's divinity
    And when it commes to a ponne
    Yet nonne so romme I've Donne.

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