Re: Did prime numbers evolve?

On Apr 20, 6:13 am, d...@xxxxxxxxxxxxxxxxxxxxxxxxx (DK) wrote:
...
You can argue that, sure, but you can't prove it (and the proof
is likely impossible), and so I can, with the same strength, on
a gut level feeling, argue that no, calculators are merely
devices designed to deliver the same answers we do by means we
are capable of.

I agree that "proof" is not the right word to apply to this
problem.

... II + II = IV no matter how the mind functions or
what tricks it uses to perform the addition.

I am with you. I agree that this is entirely reasonable point
of view. All I am pointing to is that it is nothing but a
*belief*. There is nothing in what we know that affirmatively
shows that numbers exist any more than color "green". (Which we
know does not exist because we "know" it is just an
electromagnetic wave of ~ 500 nm).

<... additional arguments elided ...>

Philosophers have debated these questions for millenia and yet
today, 2,300 years after Plato and Aristotle, there is still no
agreed upon resolution.

One problem is that the very terms of the debate, "existence"
and "reality" are subject to alternate definitions.

Let's consider a number of candidates for existence:

myself
---
people
stones
trees
houses
---
stars
---
electrons
quarks
waves
photons
neutrinos
---
gravity
electromagnetism
nuclear forces
---
colors
tastes
sounds
---
minds
---
numbers
functions
lines
points
---
sentences
facts
propositions
theories
ideas
concepts

I've places dashed lines between groups that might possibly be
accepted or rejected together, but other people might put the
dashed lines elsewhere.

There have been philosophers taking different stances on all of
these things. Even the very first one, "myself", which seemed so
solidly established by Descartes' famous "I think therefore I
am", has been argued against by a few.

My personal view follows the "pragmatic" school. I think that
the concepts of "existence" and "reality" should be defined
"instrumentally". That means that if some entity is required for
some particular theory, and that theory accurately predicts our
experience in a very wide range of cases, with no known
countervailing cases, then the entity exists. I am hard
pressed to come up with a better definition of existence.

By that definition, things like electrons, photons, stars and
gravity clearly exist. Quarks probably do.

Numbers don't exist in the same sense. No one claims that they
are material objects or natural forces. But they are
instrumental in our explanation of the world. The explanations
we have in physics, chemistry, and every other science, depend on
the number system working the way it does.

So while I don't want to claim that numbers are "real" in the
material sense of having mass or energy or taking up space, I
would hold that they are objective, not subjective. We can't
explain things without them.

But, as I said above, there is still no consensus in the
philosophical community about these issues. The view that I have
just presented seems persuasive to me. Your mileage may vary.

Alan

.

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