[Bups-dis] Hegel and infinity

[Russo, Matteo]

There's an interesting idea which came to me during a lecture on 'bad infinity', it was so called because part of it referred to Hegel's conception of infinity in the science of logic. If I understood correctly our conventional notion of infinity such as that apparent in the number series is inaccurate principally because in this and other such cases the concept of infinity does not satisfy or complete itself. In the number series for example, although for any n, n + 1 is a number, that number is a finite quantity, therefore you never actually reach infinity you reach an infinite number of finite quantities. Infinity is the negation of finitude, therefore it is an immeasurable quantity, a quantity without limit. Hegel is thus arguing in some sense for the misuse of the concept 'infinity' perhaps in a similar way to that which Kant used to dismantle St Anselm's argument for the existence of God where he claimed existence is not a predicate. Here Hegel suggests that the concept of infinity is not being used properly, a more appropriate term for the number series would be continuous perhaps but not infinite. 

If you recall Agrippa's trilemma in which justification seems impossible without falling into circularity, dogmatism, or an infinite regress, the infinite regress is of interest here as it could possibly be attacked on this line of thought. According to Hegel it would be an example of 'bad infinity', the infinite regress is not infinite, every time you just reach yet another confined or limited proposition. 

It could be claimed that the relationship between numbers in the number series is slightly different as they are not justifying one another. Yet in some sense they proceed from one another, they form part of a chain which is intuitively interdependent so arguably they do 'justify' one another and the 'format' of their 'infinity' is the same. 

So if its not an infinite regress what kind of regress is it? It would intuitively seem to be a finite regress which suggests that there is no problem with justification in this way. Also Hegel has a positive conception of 'infinity', he claims that the process of discovery is ongoing, infinity does not reflect the fact that justification is impossible, but simply that we have not yet arrived at its fullest expression.

I enquired over this to one of my lecturers who says it's a topic at the cutting edge of modern philosophy, a book called 'all or nothing' by Paul Franks explores the possibility that the agrippan trilemma could be undermined by appeal to Hegel's conception of infinity.

I think it's a good topic I don't know enough about Hegel to comment extensively but I think it has potential, let me know what you think.

Matteo Russo