Re: etc

imaginatorium@xxxxxxxxxxxxx wrote:
David Marcus wrote:
imaginatorium@xxxxxxxxxxxxx wrote:
David Marcus wrote:

Why not? If I generate one a second and keep doing it forever, then I
will have generated an infinite number of digits.

You will? But you just said above that you won't. You won't ever
finish, so there is no end, no point at which anything will have been
"generated".

Sorry. Wrong tense of the verb. I should have said, "I will generate".

Uh, don't think that works either. ("I will generate", in the absence
of any possible state in which "I will have generated", seems to be
false.)

Why? Anyway, since we are doing thought experiments, I don't see why I
can't imagine stepping out of time to consider the entire output of the
infinite process.

Consider the obvious algorithm for finding an even prime greater than
2:

Set x to 4
loop ( if x is prime, end with SUCCESS; else add 2 to x)

The only exit from this program is a successful one, so if I run it, I
assert "I will find an even prime greater than 2". Are you claiming
that your algorithm for "generating this infinite number of digits"
will end before mine? If not I suggest your "generation" is certainly
not going to be more successful than my search for an even prime
greater than 2.

I think you have to be _very_ careful here: careless talk fills the
crank heart with hope. Surely the reason for the axiom of infinity is
exactly something like the impossibility of "generating" the infinite
set by some sort of process.

(I've used 'algorithm' and 'process' interchangeably - perhaps it
should be 'process', because by normal definition an algorithm
necessarily terminates.)

I certainly didn't mean to imply the process ever ends. I'm just
defining a sequence. The range of the sequence is an infinite set. Of
course, you need the axiom of infinity to define a sequence.

Your algorithm runs forever. However, it doesn't produce any output
during this time. My process does.

--
David Marcus
.

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