- Dear All! Dear Stan!

Stan, you said that most mathematicians believe maths is invented.

But Roger Penrose (mathematician and superphysicist) says

that the opposite is the case.

[Quote from "my" message "Roger Penrose: Mathematics is discovered":]

"Certainly," he [Penrose]says, "mathematicians view mathematics

as something out there, which seems to have a reality independent of the

ordinary kind of reality of things like chairs, which we normally think of as real. It's sometimes referred to as a `Platonic world,' a Platonic reality.

[Unquote]

Do you know about gallup/poll results here?

Who is right, Stan or Roger?

By the way: Interestingly, Penrose views maths as a kind of reality, just like NKO and Plato, and also views maths as independent of "ordinary" reality, just as NKO and Plato.

Lastly, by the way, I consider this philosophical debate as relevant EP stuff. It's about human thinking and reasoning. I believe there are at least two distinct genotypes here, namely discoverists and inventists.

Best

NKO - I hate to say this but these words do not do justice to the process because the words were invented for different purposes e.g. everyday ordinary humdrum things. See below.
On Sun, Jan 20, 2013 at 11:00 AM, Nils K. <n-oeij@...> wrote:

Dear All! Dear Stan!

Stan, you said that most mathematicians believe maths is invented.

But Roger Penrose (mathematician and superphysicist) says

that the opposite is the case.

[Quote from "my" message "Roger Penrose: Mathematics is discovered":]

"Certainly," he [Penrose]says, "mathematicians view mathematics

as something out there, which seems to have a reality independent of the

ordinary kind of reality of things like chairs, which we normally think of as real. It's sometimes referred to as a `Platonic world,' a Platonic reality. …

They see things as something out there because of what Wigner wrote (e.g. Unreasonable Effectivenes...).

If something was arbitrarily created out of thin air why does it fit so perfectly into the real world phenomena?

By the way: Interestingly, Penrose views maths as a kind of reality, just like NKO and Plato, and also views maths as independent of "ordinary" reality, just as NKO and Plato.That word, "reality" is one of the buzzword, fogwords, or weasel words of philosophers, (still premedieval) and it onlyconfuses them.

"Reality" is like "existence"; it means too many things. Numbers do not exist in the same sense as bananas.

Lastly, by the way, I consider this philosophical debate as relevant EP stuff. It's about human thinking and reasoning. I believe there are at least two distinct genotypes here, namely discoverists and inventists.

Best

NKO

--

Regards,

Mark Hubey"Learning to think in mathematical terms is an essential part of becoming a liberally educated person. "-- Kenyon College Math Department Web Page - StanNKO,I don't have statistics about how many mathematicians come down on the invented vs the discovered side of the controversy. I based by earlier assertion on my perception that there has been no argument among mathematicians as to the validity of the work of Goedal and that of Cohen that, together, demonstrate the independence of the continuum hypothesis with respect to the axioms of set theory. Were mathematics to have some sort of separate reality, such an independence result couldn't exist. The continuum hypothesis would have to be either true or false.

On Sun, Jan 20, 2013 at 10:00 AM, Nils K. <n-oeij@...> wrote:Dear All! Dear Stan!

Stan, you said that most mathematicians believe maths is invented.

But Roger Penrose (mathematician and superphysicist) says

that the opposite is the case.

[Quote from "my" message "Roger Penrose: Mathematics is discovered":]

"Certainly," he [Penrose]says, "mathematicians view mathematics

as something out there, which seems to have a reality independent of the

ordinary kind of reality of things like chairs, which we normally think of as real. It's sometimes referred to as a `Platonic world,' a Platonic reality. …

[Unquote]

Do you know about gallup/poll results here?

Who is right, Stan or Roger?

By the way: Interestingly, Penrose views maths as a kind of reality, just like NKO and Plato, and also views maths as independent of "ordinary" reality, just as NKO and Plato.

Lastly, by the way, I consider this philosophical debate as relevant EP stuff. It's about human thinking and reasoning. I believe there are at least two distinct genotypes here, namely discoverists and inventists.

Best

NKO

--

Stan Franklin Professor Computer Science

W. Harry Feinstone Interdisciplinary Research Professor

Institute for Intelligent Systems

FedEx Institute of Technology

The University of Memphis

Memphis, TN 38152 USA

901-678-1341

<http://ccrg.cs.memphis.edu/~franklin/>

lab <http://ccrg.cs.memphis.edu/>

- Dear Stan, dear All!

--- In evolutionary-psychology@yahoogroups.com, Stan Franklin wrote:

I don't have statistics about how many mathematicians come down on the

invented vs the discovered side of the controversy. I based by earlier

assertion on my perception that there has been no argument among

mathematicians as to the validity of the work of Goedal and that of Cohen that, together, demonstrate the independence of the continuum hypothesis with respect to the axioms of set theory. Were mathematics to have some sort of separate reality, such an independence result couldn't exist. The continuum hypothesis would have to be either true or false.

NKO:

This (above) is outside my capacity in the philosophy and logic of

mathematics. I'm check mate here and now. But not totally silent.

I will try to come up with some comments, not necessarily going

against your conclusions above.

I will focus on "independence" and "independence result", core words

in your reasoning.

Independence (just as randomness) is main facts and mechanisms in

physics and biology. It's beyond human understanding that our

(enormous number of) genes are so extremely independent, and thereby

making evolutionary change possible. Both genetics, physiology, and

anatomy are modular, and each of the unlimited numbers of modules can

be changed a lot without changing other modules. Even human behavior

is modular, having no goverment, it's largely a "war" among behavior

modules (human instincts).

In physics waves are entangled. Entanglement is perhaps the most

crazy in quantum mechanics. Nevertheless waves are at the same time

independent, which is also crazy. As if this was not enough, we have

the double picture of the physical world: Waves and particles, which

Bohr and Einstein claimed is impossible for humans to understand.

But now I was talking about the physical world, but some of us are

claiming math be non-physical and absolutely independent of the

physical world. But, nevertheless, I find it strange that

INDEPENDENCE is ruled out in mathematics. I also find it strange that

mathematics is a branch of biology (i.e. only existing in human

brains), as the inventists are concluding. (Are they concluding so?)

I do think we cannot rule out that the specific INDEPENDENCE you,

Stan, talked about above, could be a integrated part of the non-

physical world of mathematics, in the same manner as the wave picture

is independent of the particle picture in physics. These pictures

depend on how we ask questions to nature. We can ask questions to

math as well. So?

Best,

NKO - StanHope this helps.NKO,Sorry, I should have said what independent meant in this technical context. It means that there are two sets of reasonable axioms for set theory (the underlying primitive basis for mathematics) under one of which the continuum hypothesis is true, and under the other it's false. You can have it either way depending on the axioms you start with.

On Thu, Jan 24, 2013 at 9:09 AM, Nils K. <n-oeij@...> wrote:

Dear Stan, dear All!NKO:

--- In evolutionary-psychology@yahoogroups.com, Stan Franklin wrote:

I don't have statistics about how many mathematicians come down on the

invented vs the discovered side of the controversy. I based by earlier

assertion on my perception that there has been no argument among

mathematicians as to the validity of the work of Goedal and that of Cohen that, together, demonstrate the independence of the continuum hypothesis with respect to the axioms of set theory. Were mathematics to have some sort of separate reality, such an independence result couldn't exist. The continuum hypothesis would have to be either true or false.

This (above) is outside my capacity in the philosophy and logic of

mathematics. I'm check mate here and now. But not totally silent.

I will try to come up with some comments, not necessarily going

against your conclusions above.

I will focus on "independence" and "independence result", core words

in your reasoning.

Independence (just as randomness) is main facts and mechanisms in

physics and biology. It's beyond human understanding that our

(enormous number of) genes are so extremely independent, and thereby

making evolutionary change possible. Both genetics, physiology, and

anatomy are modular, and each of the unlimited numbers of modules can

be changed a lot without changing other modules. Even human behavior

is modular, having no goverment, it's largely a "war" among behavior

modules (human instincts).

In physics waves are entangled. Entanglement is perhaps the most

crazy in quantum mechanics. Nevertheless waves are at the same time

independent, which is also crazy. As if this was not enough, we have

the double picture of the physical world: Waves and particles, which

Bohr and Einstein claimed is impossible for humans to understand.

But now I was talking about the physical world, but some of us are

claiming math be non-physical and absolutely independent of the

physical world. But, nevertheless, I find it strange that

INDEPENDENCE is ruled out in mathematics. I also find it strange that

mathematics is a branch of biology (i.e. only existing in human

brains), as the inventists are concluding. (Are they concluding so?)

I do think we cannot rule out that the specific INDEPENDENCE you,

Stan, talked about above, could be a integrated part of the non-

physical world of mathematics, in the same manner as the wave picture

is independent of the particle picture in physics. These pictures

depend on how we ask questions to nature. We can ask questions to

math as well. So?

Best,

NKO

--

Stan Franklin Professor Computer Science

W. Harry Feinstone Interdisciplinary Research Professor

Institute for Intelligent Systems

FedEx Institute of Technology

The University of Memphis

Memphis, TN 38152 USA

901-678-1341

<http://ccrg.cs.memphis.edu/~franklin/>

lab <http://ccrg.cs.memphis.edu/>