
What a Number Is (1991) - signa11
http://www.csus.edu/indiv/o/oreyd/acp.htm_files/palaces.htm
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yesenadam
Minor comment:

>It is easy to despair as Wittgenstein did, that science and all philosophies
are ultimately closed systems of circular truths.

That doesn't seem at all right to me. Apart from the question of which
Wittgenstein you're talking about (early, later, possibly mid), I don't think
he despaired about either of these things. He seems to have felt that
philosophy consists of nothing but various confusions—hardly what our sentence
claims—of which it was his and philosophy's job to clear up once and for all
and leave behind. But he spent his life vigorously working away at many of
them. Often happily and very productively. What despair he felt I think had
other sources; he had a very strong ethical/mystical (for want of a better
word) sense; also frustration at his own and others' lack of ability to think
better.

Involving science in that sentence makes no sense at all to me. He was
involved with the Vienna Circle logical positivists, hardly despairers about
science. Later he often advised his philosophy students to give up philosophy
and do something useful to society, like medicine or labouring work, anything.
I don't remember any negativity towards science from him, except reminders
that some questions aren't scientific questions.

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hliyan
This is very interesting.

One could take this further and claim that even the most rudimentary
mathematical construct, the integer, is in the eye of the beholder. Counting
relies on certain perceive regularities: "boundaries" that allow us determine
where a the "identity" of an object, and "similarities" that allow us to group
together objects into counts.

The concept of an integer seems to presuppose the concepts of identity (or
distinctness) and regularity (for want of a better word). Whether all types of
neurologies will have the same ideas of identity and regularities (or objects
and classes?) and therefore the same concept of integers, is something that we
probably could not imagine because we can't step out of our own neurologies...

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jjaredsimpson
I don't understand this tendency to promote subjective experience from a
process occurring in a physical universe to some property which constrains the
universe and knowledge itself.

I prefer to believe the universe exists and whatever is possible is synonymous
with being physical law. Conscious subjective experience is one of those
phenomena not excluded by physical law.

But then this article claims and you also seems to claim something like:

> But what if somewhere else some consciousness has intuitive experiences
> about numbers which differ from our intuitive experiences.

I don't see why minds with intuitions creates any burden for numbers. From my
perspective Mathematics is at bottom a game of string manipulation.
Interpretations of those strings often can be applied to
understand/predict/manipulate the physical universe. But the only real thing
is the universe itself not the subjective interpretations in the minds.

The minds are real, obviously, they exist in the universe. Integers are an
interpretation of a particular string. Suppose some other mind is incapable of
an intuitive understanding an interpretation that we as humans have; I don't
see how the "integers" could possibly be affected.

None of us are concerned that dogs don't understand math. Why we be concerned
about the minds of aliens and what they find intuitive?

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gumby
Well, there are multiple ways to interpret quantum phenomena, and some of our
sensory organs (e.g. smell, taste, vision) seem to operate at the quantum
level, so why should we assume that our sensing is in some global sense
_authoritative_ rather than simply being evolutionarily optimised for macro
behaviour that's useful to us?

Although at the ground level the universe appears to be quantized (at least
below the Planck limit, at our macro scale it's mostly continuous. In fact in
most things, if not all real world things, integers live only in some platonic
universe. Perhaps we do a disservice to children by starting them with
discrete arithmetic.

> From my perspective Mathematics is at bottom a game of string manipulation.

I think this really can only be true of basic arithmetic. Even in arithmetic
we can reason about strings too long to be constructed in your our universe.

> None of us are concerned that dogs don't understand math. Why we be
> concerned about the minds of aliens and what they find intuitive?

They don't? Leaping to catch a frisbee is pretty advanced mathematics. I do
doubt that dogs understand integers. But these fundamental questions about
alien species whether dogs or some extraterrestrial intelligence are pretty
important epistemological inquiries.

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ggm
If your sense-impression of things as they are included the subatomic (ok, so
these are either very energetic aliens, or very tiny ones) would you consider
the concept of a 'thing' as rather odd? if you live embedded in fields, what
is this one-ness? There is no one: there are only varying amounts of
impressions of forces acting on you.

Maybe the Martin Gardiner book on the inherent polarity of the universe
provides the basis for a categorical One: lets all align with our
head|antenna|sense-unit|orifice-for-feeding pointing upward..

