- Hello,

Good point Jud. The numeral 2 (a historical sociologically

defined term) is distinct from the number 2. This is to say that

the concept of 2 exists first and then I can assign a term (written

or spoken numeral) to describe it.

However, having established that `Numbers are `out there'.

It is time to reign in the imagination. Numbers are `out there' but

only in relation to the human intellect. It is good time to state

definitely that there is no intelligent life in the Universe apart

from the rational being known as man. Sorry trekkies. Prime numbers

appear to be a good `common knowledge' tool to explore this rational

conclusion.

But, gentlemen, we have found our first Realist! David

Underbakke!

I quote,

This is just like the properties of mathematics, and

prime numbers, that exist without regard to human comprehension.

This is realism. I.e. things exist whether I think about them or

not. Can you see how common sense says that prime numbers are

defined and therefore a product of the intellect. Therefore they

cannot have existed independently of the human intellect.

If I can bring any `new-agers' on board here. Moderate realism

(idealism) is like the intellect dipping into the stream of human

consciousness `out there', `realising' in the intellect what already

existed in this common stream, and in a wonderful way adding to this

stream by its own invention or co-operation in this stream.

Absolute realism is actually another form of Idealism or Platonism.

Realist say that things really exist independently of the intellect,

and idealists say that ideas exist independently of the intellect.

Thomism is an anthropocentric philosophy, humanity and people are the

apex of the natural world (and universe).

If anyone would like to pursue the foundations of this

thought, then contact me offlist. Otherwise I will confine my

thoughts to Page's new `philosophy of primes'.

Thanks to Page for initiating this new line of prime thought.

I have read your last `essay' and found it very interesting. What was

a nice surprise for myself was that your style of explanation is very

similar to my own. (Look at the sentence construction). This is

because you are an existential-realist-idealist, almost the perfect

combination. Do you have classical training in philosophy? Can I

make a suggestion. If you look through the post on this list you

will see that many concern prime number theorems. This is not an

accident. The theorem is a unit of knowledge. Your next step to

participate in the mathematical discussions in this list is to learn

some number theory, such as the properties of the prime numbers. I.e.

A prime p = 4*k + 1 or 4*k+3. Then you will see that many of the

primers on this list are very advanced thinkers although perhaps not

in the form that you are familiar with.

To conclude, live long and prosper earthmen.

Regards,

Paul Mills

Kenilworth,

England. > >

According to "The Mathematical Experience", by Davis and Hersh, page 334,

> > Russell and Whitehead proved that 1+1=2, using only logic.

>

>1+1=2 by definition. They proved 2+2=4 though

>(technically (1+1)+(1+1)=((1+1)+1)+1)

"Russell and Whitehead ... after 362 pages, the arithmetic proposition

1+1=2 is established." and they show part of that page which says "From

this proposition it will follow, when arithmetical addition has been

defined, that 1+1=2."

+--------------------------------------------------------+

| Jud McCranie |

| |

| ... algorithms are concepts that have existence apart |

| from any programming language. The word "algorithm" |

| denotes an abstract method of computing some output |

| from some input ... -- Donald Knuth, CACM, 1966 |

+--------------------------------------------------------+