[FOM] Re: Sharp mathematical distinction between potential and actual infinity?
Timothy Y. Chow
tchow at alum.mit.edu
Sun Sep 28 15:44:19 EDT 2003
On Sun, 28 Sep 2003, Dean Buckner wrote:
> The distinction between potential & actual is traditional and
> distinguishes that which could or can exist, from that which is, i.e.
> that which "actually" exists.
O.K., I like this. So perhaps there is a way of formulating mathematics
in terms of modal logic, rather than classical first-order logic? What
are some examples of what this might look like?
1. "For every prime, there actually/potentially exists a larger prime."
Which of these does Euclid's proof establish?
2. "There actually/potentially exists a set of all integers." Does it
make sense to use "potentially" here? Can a completed infinity
3. "A rule tells you what to do in all actually/potentially existing
scenarios." "Potentially" feels right here, which I think is a
I don't want to give more examples because I'm groping in the dark here.
Can someone else help out?
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