> I was using a specific natural number (a 512 bit integer) as an
> example for
> creation and destruction of a specific integer (an instance of a class of
> integers). No more, no less.
That's plenty to bring out our difference of opinion. cf "creation and
destruction of a specific integer"
> Existence of a specific integer has nothing to do with existence of a
> production system for a class of integers. The recipe for a
> series is not the
> dish itself. That recipe is also just information, requiring encoding in a
> material carrier. It would have taken considerably more work to
> eradicate the
> entire production system, as it is a bit more widespread, and has
> a lot more
> vested interest than conservation of a specific, random integer, destilled
> from turbulent gas flow.
You say "a class of integers". Does this mean you don't believe the
integers are unique? I guess this is consistent with a non-platonist.
However, from the Peano axioms it can be shown that the integers are unique
up to isomorphism. Does the concept of "uniqueness up to isomorphism" seem
useful or important to you?
> The representation (hex, need to be told that above hex string
> represents an
> integer (ignoring underlying representations as two's complements,
> potentials, charge buckets and magnetic domains for the moment) indicates
> that even that "simple" information transfer was encrusted with lots of
> implicit context people take for granted. Roll back to
> Sumer, and hand out little clay tablets with that hex string. What does it
> mean? Nothing. Not even the alphabet to parse this exists.
> Animals evolve representations for quantities, because resource
> management is
> a critical survival skill. After a few iterations you get consensual
> encodings for interactive transfer, then noninteractive
> consensual encodings.
> I used patterns of luminous pixels (translated into Braille dots,
> for all what I know)
> instead of scratches on a bone fragent, because that encoding is more
> familiar, and easier to transmit.
> Wavefront reemitted from pebbles hitting retina, being processed
> on the fly,
> tranformed into a spatiotemporal electrochemical activity pattern is an
> instance of a measurement of a property. It takes a specific class of
> detectors to do. You cannot conduct that measurement in their absence.
The platonist interpretation of the above is simply that context is needed
to relate a given sentence (of symbols) back to the Platonic realm. Note
that the Platonic realm is *not* itself merely a bunch of sentences. It
comes with semantics!
> > You say the given integer exists because "it is it is physically
> > realizable *in principle*". That sounds like the platonic view to me -
> To me, this sounds like a confusion between a specific integer,
> and a recipe
> for such. It is quite difficult to feed a wedding throng with
> pages from a cookbook.
I can't work out what you are saying! You use terms like "specific integer"
and I've got no idea what you mean because you don't believe concepts exist
independently of "their production systems".
The integers are an example of a concept that is *decoupled* from specific
instances - by definition. A great deal of our thinking and language
involves generalisation. For example the word "chair" is associated with a
class of objects. You use generalisation in your sentences as much as
anyone else. Your lines of reasoning treat these abstractions as "things"
that can be manipulated - such as when I say "the boy kicked the ball" and
you form an image in your mind - even though the sentence involves
generalisations such as "boy" and "ball".
I presume your refutation (as a non-platonist) is that concepts only exist
while someone (or something) is there to think them. The problem with that
view is that many useful lines of reasoning involve the question "Does there
exist a concept x such that p(x)" without instantiating x. In other words,
it seems to be useful to conceptualise over the space of all possible
concepts. This is exactly what happens when we generalise specific integers
to the infinite set of all integers. I don't see how the non-platonist can
accept any lines of reasoning that involve the set of integers because it is
impossible to conceptualise every member of the set which (to them) would
imply that the set doesn't exist.
You agreed before with the hypothesis that a computer could exhibit
awareness. Suppose we have (say on optical disk) a program and we have a
computer on which we can run the program, but we haven't run the program
yet. We can a-priori ask the question "On the computer monitor, will we see
a simulated person laugh?". Do you believe this a-priori question has an
a-priori answer? After all, there is nothing mystical in a deterministic
computation. If so doesn't that mean that the simulated person exists
independently of running the actual simulation?
In fact, if we postulate that our universe is computable, then the question
"Does there exist a person who laughs" on the universal dove-tailer program
can be answered a-priori in the affirmative.
> > because the number is *not* actually physically realized and yet the
> > number is purported to have an independent existence. Are you saying
> > otherwise?
> > I think any form of symbolic manipulation of numbers is implicitly using
> > the platonic view. To say they spring into existence as they are
> > written down (which in any case only means they are realizable in
> Numbers don't write down themselves. Systems generate them, translate them
> into specific encodings, to be parsed by other instances of systems of the
> same class. Use a system of a different class, and you'll only
> parse garbage.
> ATGATAGTGGCCGTCCAACGGTAGACTCTAC might be a number, it might also be a
> shorthand for a linear biopolymer (5'-3'? there's some implicit
> context for
Naturally a sentence needs to be interpreted in context. I still believe my
> > principle) just seems silly to me.
> A cookbook is a promise of a meal, not the meal itself.
> > The Platonic view just says that every mathematical system free from
> > contradiction exists. Ie if it can exist then it does exist. There is
> Exists where? Two production systems of the same kind generate the same
> output. Surely, the output is contained within them? In there, somewhere?
> Mathematicians are production systems. Input is coffee, output is theorem.
> > no need to talk about different types of reality.
Concepts don't exist is some "place" in the Platonic viewpoint. They just