Date: Mar 22, 2013 7:26 PM
Subject: Re: Matheology § 224
On 3/22/2013 6:13 PM, fom wrote:
> On 3/22/2013 5:11 PM, William Hughes wrote:
>> On Mar 22, 10:49 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>>> All sets are finite, but not fixed.
>> I did not claim that all sets in
>> Potential infinity are fixed.
>> They are finite and thus not
>> different from finite sets.
>> WH: Infinite sets are different from finite sets
>> WH: but they do not contain anything
>> WH: "beyond any finite set".
>> WM: Of course.
>>> There is no upper threshold,
>>> contrary to every finite set.
>> More Wolkenmuekenheim logic
>> Every finite set has an upper threshold.
>> A potentially infinite set
>> does not have an upper threshold
>> A potentially infinite set is finite.
> And, when properly developed in a constructive
> framework, the objects to which that statement
> might apply are clearly understood as such.
Whoops. Misread WH's intent.
Nevertheless, although true for Markov's
system, the statements
When constructive objects are defined in terms
of potential realizability, then the potentially
realizable objects are finitely realized.
Potential realizability is understood ideally,
so that the generation of arbitrary constructive
objects is not limited.
And, the generation of any potentially realizable
constructive object involves finitely many
do not apply to WM's formulation.