Maybe true, maybe not. Nevertheless this is a more sophisticated critique than what has been posted so far.
BTW - extracting a finite amount of information from the plenitude is more akin to extracting a segment from an orange. Both the segment and the orange are infinite sets of points (of course this is the ideal orange, which is not made up of atoms!) In the case of the Plenitude, one extracts a set of infinite bitstrings, the set members having the common property of sharing the same meaning. At very least, the "something" extracted will be composed of a countable union of sets of bitstrings, each of which contains members with identical prefixes. The cardinality of both the Plenitude, and each of the somethings is c, so the carving of the orange is perhaps a fruitful thought. (Sorry couldn't resist the pun!). Cheers On Sat, Nov 12, 2005 at 10:28:46AM +0530, Aditya Varun Chadha wrote: > On 11/12/05, Russell Standish <[EMAIL PROTECTED]> wrote: > > But extracting something from the Plenitude is trivial, or so it seems > > to most people. If I have an infinite bin of dollar coins, and I owe > > you $10, I don't see any difficulty in paying you the $10. Do you? > > > > Please quote something from practical experience to the following effect: > > 1. you have an INFINITE amount of "something" (forAll x belongsTo > Ints, INFINITE > x) > 2. you can extract a known Finite amount of that "something" (in > finite time) from the given INFINITE set. > > The point is that we can only claim the ability to (physically) > "extract" elements from FINITE sets. In the physical sense we never > deal with "true infinity". Unless your Plenitude is finite, you cannot > talk of extracting some finite amount of it with confidence. > > I can extract $10 from $100, but I do not know whether I can extract > $10 from $INFINITE. Truely "continuous" entities do not exist (atleast > in the "matter" sense). > -- > Aditya Varun Chadha > adichad AT gmail.com > http://www.adichad.com -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------
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