Re: The modern mathematical concept of infinity is indefensible
Albrecht
Klaus Cammin schrieb:
> Hi Mitch,
>
> Mitch Harris schrieb:
> > That sounds right (of course with Virgil's idea that we're really
> > seeing two-ness or the property of being two of a kind).
>
> No, I don't think so. If it's true, that one never will see the concept of
> the number 2, why should one see the property of being two of a kind? That
> property is a concept, too.
>
> Concepts are everywhere, but nowhere in nature.
> However they are in everbody's mind, aren't they?
>
>
How do you decide what is in mind and what is in nature? In fact,
there are only concepts and nothing more.
David Bernier
Are you a concept?
David Bernier
Nam Nguyen
Respectfully, would you know exactly all the quantum states in you?
>
> David Bernier
--
"To discover the proper approach to mathematical logic,
we must therefore examine the methods of the mathematician."
(Shoenfield, "Mathematical Logic")
Han de Bruijn
Uhm, sorry, _that_ escapes me ..
Han de Bruijn
Virgil
<c86a82e8-3b90-4ba2...@40g2000prx.googlegroups.com>,
Albrecht <albs...@gmx.de> wrote:
That would require numbers to be as physical as trees.
Virgil
What is the "concept" of having received a kick in the groin?
jesko
Concept are in Mind and they are constituted of matter but they are
not in the Body,
but surely they are in Nature as that in which men are.
reas...@gmail.com
Mathematics is a survival skill.
Any creature smarter than a flatworm knows math.
Repeated experiments have shown that animals
have highly developed math skills.
Every animal knows that more food is better
than less food. Just because humans can
quantize "more than" and "less than"
into things we call "numbers" doesn't
mean our math skills are any better
than a zebra's.
Math is an observational science.
Why are "two" apples more than
"one" apple, but less than "three"
apples? Because we can look
at piles of apples and observe
which pile is bigger.
There is no "mathematical" reason
why 2 comes between 1 and 3.
We can arbitrarily order natural
numbers any way we want and
we can still define any mathematical
operation like addition or multiplication.
Our mathematical systems are
designed to model what we observe
in nature. Sometimes math can
tell us what to look for.
Or it can just be wrong.
Russell
- 2 many 2 count
Albrecht
reaste...@gmail.com schrieb:
That's wrong. Since 2 is strong connected with OO, as 1 is with O and
3 is with OOO, there is a reason, and I think we can call it a
mathematical reason, that 2 comes between 1 and 3.
The naturals 1, 2, 3, 4, 5, ... or better and more fundamental O, OO,
OOO, OOOO, OOOOO, ... are the base of any mathematics and you are able
to invent other system to count, but each of them (with a potential
infinite power) uses the naturals as base.
> We can arbitrarily order natural
> numbers any way we want and
> we can still define any mathematical
> operation like addition or multiplication.
No, we can't. The naturals are the unchangeable root of any
mathematics, and they are given as they are. Nobody can change them by
wish. The naturals are part of our reality as e.g. causality, time,
space, gravitation, ...
Best regards
Albrecht S. Storz
David R Tribble
>> There is no "mathematical" reason
>> why 2 comes between 1 and 3.
>
Albrecht wrote:
> That's wrong. Since 2 is strong connected with OO, as 1 is with O and
> 3 is with OOO, there is a reason, and I think we can call it a
> mathematical reason, that 2 comes between 1 and 3.
>
> The naturals 1, 2, 3, 4, 5, ... or better and more fundamental O, OO,
> OOO, OOOO, OOOOO, ... are the base of any mathematics and you are able
> to invent other system to count, but each of them (with a potential
> infinite power) uses the naturals as base.
Russell's point was that 1,2,3,... is only one possible ordering
of the naturals. But yes, there is a "mathematical" reason that
2 is the successor of 1 and the predecessor of 3.
However, it has been pointed out to you before that there are
other mathematically sound systems that are not inherently based
on natural numbers, e.g., Boolean algebra and Group theory.