Cardinal Value(s) in the Objectivist Ethics

[anonrobt]

This qualify as "near" 61 words away:

"Man

Man’s distinctive characteristic is his type of consciousness—a consciousness able to abstract, to form concepts, to apprehend reality by a process of reason . . . . [The] valid definition of man, within the context of his knowledge and of all of mankind’s knowledge to-date [is]: “A rational animal.”

(“Rational,” in this context, does not mean “acting invariably in accordance with reason”; it means “possessing the faculty of reason.” A full biological definition of man would include many subcategories of “animal,” but the general category and the ultimate definition remain the same.)"

Adam,

Do you mean Phylum: Chordata; Subphylum: Vertebrata; Class: Mammalia; Order: Primate; Family: Hominidae; Genus: Homo; Species: H. sapiens

If this were true it would mean that each human was part of the animal kingdom and not a special creation outside that kingdom of animals.

It is curious in retrospect to try to recapture that perspective that once prevailed.

I vaguely recall being made aware of that notion that humans were not part of the animal kingdom when I was a child.

Fortunately I was skeptical even then.

Some suspect I have become more gullible with age.

gulch

Actually, think it is H. sapiens sapiens [the same who thinks twice]

[Michael Stuart Kelly]

Kant's"categorical imperative" deals with "morality".

Xray,

And metaphysics and epistemology. The categorical imperative essentially comes from noumenal-land, which man cannot know but must obey.

Michael

[Alfonso Jones]

Kant's"categorical imperative" deals with "morality".

Xray,

And metaphysics and epistemology. The categorical imperative essentially comes from noumenal-land, which man cannot know but must obey.

Michael

Well and succinctly put, Michael.

Bill P

[Selene]

Folks:

Seems to include everything to me.

"Henceforth, the question before the house today then becomes, can an imaginary number (or the square root of negative one, for one example in mathematics) be compared with Kant's noumenal realm, a hypothetical realm where it is supposed that all of reality arises? The author believes this to be the case."

Adam

[UncleJim]

Folks:

Seems to include everything to me.

"Henceforth, the question before the house today then becomes, can an imaginary number (or the square root of negative one, for one example in mathematics) be compared with Kant's noumenal realm, a hypothetical realm where it is supposed that all of reality arises? The author believes this to be the case."

Adam

That depends on whether Kant knew what it was he was talking about. In other words: Did he have an actual sensual experience which translated into the conscious existence of a brain-image or was he hallucinating?

Note: An imaginary number is just that - imaginary!

[BaalChatzaf]

Folks:

Seems to include everything to me.

"Henceforth, the question before the house today then becomes, can an imaginary number (or the square root of negative one, for one example in mathematics) be compared with Kant's noumenal realm, a hypothetical realm where it is supposed that all of reality arises? The author believes this to be the case."

Adam

That depends on whether Kant knew what it was he was talking about. In other words: Did he have an actual sensual experience which translated into the conscious existence of a brain-image or was he hallucinating?

Note: An imaginary number is just that - imaginary!

So is an integer. Look the wide world over and never an integer shall you find.

Just an aside. It turns out the field (division ring) of complex numbers is isomorphic to the set of 2x2 matrices:

First row: a, -b

second row: b, a

all such matrices in which no both a and b are zero has a inverse matrix which corresponds to the reciprocal. The isomorphism is between the set of such matrices with matrix multiplication and matrix addition and the set complex numbers. The matrix:

First row : 0, - 1

Second row:-1, 0

corresponds to i, the imaginary unit. If you square this matrix by matrix multiplication you get

the matrix

first row : -1, 0

second row: 0, -1

which is the negation of the unit matrix that corresponds to good old 1.

So while imaginary numbers and all other numbers are abstractions which have no physical existence in the real world, as mathematical entities imaginary numbers are no harder to deal with than matrices of real numbers.

Another way of getting to the complex numbers is to take the polynomial ring R[x] of polyomials with real co-efficients module the ideal generated by the polynomial x^2 + 1. This is the splitting field for the polynomial and it is what you get when you adjoin a root of x^2 + 1 = 0 to the real numbers. The two roots are i and -i. Again, it is no major brain exercise. There is nothing mystical, mysterious or magic about complex numbers and the imaginary unit. They are called "imaginary" for purely historical reasons, since when they were first encountered in the 16th century by Cardano and Tartaglia, neither of these worthy algebraists quite know what to make of them. So they called them imaginary or fantastic and such like sobriquets. After a while mathematicians grew accustomed and learned how to fit them in the context of other mathematics. Philosophers did not have the least idea of how to proceed, but that did not stop the mathematicians.

Ba'al Chatzaf

[UncleJim]

Folks:

Seems to include everything to me.

"Henceforth, the question before the house today then becomes, can an imaginary number (or the square root of negative one, for one example in mathematics) be compared with Kant's noumenal realm, a hypothetical realm where it is supposed that all of reality arises? The author believes this to be the case."

Adam

That depends on whether Kant knew what it was he was talking about. In other words: Did he have an actual sensual experience which translated into the conscious existence of a brain-image or was he hallucinating?

Note: An imaginary number is just that - imaginary!

So is an integer. Look the wide world over and never an integer shall you find.

Just an aside. It turns out the field (division ring) of complex numbers is isomorphic to the set of 2x2 matrices:

First row: a, -b

second row: b, a

all such matrices in which no both a and b are zero has a inverse matrix which corresponds to the reciprocal. The isomorphism is between the set of such matrices with matrix multiplication and matrix addition and the set complex numbers. The matrix:

First row : 0, - 1

Second row:-1, 0

corresponds to i, the imaginary unit. If you square this matrix by matrix multiplication you get

the matrix

first row : -1, 0

second row: 0, -1

which is the negation of the unit matrix that corresponds to good old 1.

So while imaginary numbers and all other numbers are abstractions which have no physical existence in the real world, as mathematical entities imaginary numbers are no harder to deal with than matrices of real numbers.

Another way of getting to the complex numbers is to take the polynomial ring R[x] of polyomials with real co-efficients module the ideal generated by the polynomial x^2 + 1. This is the splitting field for the polynomial and it is what you get when you adjoin a root of x^2 + 1 = 0 to the real numbers. The two roots are i and -i. Again, it is no major brain exercise. There is nothing mystical, mysterious or magic about complex numbers and the imaginary unit. They are called "imaginary" for purely historical reasons, since when they were first encountered in the 16th century by Cardano and Tartaglia, neither of these worthy algebraists quite know what to make of them. So they called them imaginary or fantastic and such like sobriquets. After a while mathematicians grew accustomed and learned how to fit them in the context of other mathematics. Philosophers did not have the least idea of how to proceed, but that did not stop the mathematicians.

Ba'al Chatzaf

The issue is not have imaginary numbers been made-up, the issue is what do they represent. When I talk about a horse (for example) it exists as an actual physical something the existence of which is mathematically designated with the symbol - 1. What does the symbole -1 designate the existence of?

Edited May 11, 2009 by UncleJim

[Selene]

Uncle Jim:

"What does the symbole -1 designate the existence of?"

The Intelligence Quotient of a marxist.

I know I got it right, so now ask the tough ones.

Adam

[BaalChatzaf]

The issue is not have imaginary numbers been made-up, the issue is what do they represent. When I talk about a horse (for example) it exists as an actual physical something the existence of which is mathematically designated with the symbol - 1. What does the symbole -1 designate the existence of?

See

http://en.wikipedia.org/wiki/Complex_number#Applications

Complex numbers which are a combination of real numbers and multiples of the imaginary unit are handy for representing phases of cyclic processes. They are very important in engineering, physics and signal processing.

Ba'al Chatzaf

[UncleJim]

Uncle Jim:

"What does the symbole -1 designate the existence of?"

The Intelligence Quotient of a marxist.

I know I got it right, so now ask the tough ones.

Adam

I was asked to participate in a debate about capitalism with a couple of Marxist socialists. Holly crap!

[UncleJim]

The issue is not have imaginary numbers been made-up, the issue is what do they represent. When I talk about a horse (for example) it exists as an actual physical something the existence of which is mathematically designated with the symbol - 1. What does the symbole -1 designate the existence of?

See

http://en.wikipedia.org/wiki/Complex_number#Applications

Complex numbers which are a combination of real numbers and multiples of the imaginary unit are handy for representing phases of cyclic processes. They are very important in engineering, physics and signal processing.

Ba'al Chatzaf

So you don't actually know? When I talk about 1-horse I can actually demonstrate what it is I am talking about.

[Dragonfly]

Complex numbers which are a combination of real numbers and multiples of the imaginary unit are handy for representing phases of cyclic processes. They are very important in engineering, physics and signal processing.

Not to mention their essential role in quantum mechanics, without which Uncle Jim wouldn't have had a computer to type on.

[Alfonso Jones]

The issue is not have imaginary numbers been made-up, the issue is what do they represent. When I talk about a horse (for example) it exists as an actual physical something the existence of which is mathematically designated with the symbol - 1. What does the symbole -1 designate the existence of?

See

http://en.wikipedia.org/wiki/Complex_number#Applications

Complex numbers which are a combination of real numbers and multiples of the imaginary unit are handy for representing phases of cyclic processes. They are very important in engineering, physics and signal processing.

Ba'al Chatzaf

So you don't actually know? When I talk about 1-horse I can actually demonstrate what it is I am talking about.

Jim -

Did you read the material at the link Bob provided at:

http://en.wikipedia.org/wiki/Complex_number#Applications

What was unclear to you about that?

Bill P

[UncleJim]

Complex numbers which are a combination of real numbers and multiples of the imaginary unit are handy for representing phases of cyclic processes. They are very important in engineering, physics and signal processing.

Not to mention their essential role in quantum mechanics, without which Uncle Jim wouldn't have had a computer to type on.

They are useful when trying to explain reality. They do not, are not intended to, represent a real something.

[Selene]

Folks:

But that is not what the argument is as far as I can see - and believe me addition is higher mathematics to me.

I am just looking from the outside and it seems like you are sliding past each other.

Adam

[Xray]

This qualify as "near" 61 words away:

"Man

Man’s distinctive characteristic is his type of consciousness—a consciousness able to abstract, to form concepts, to apprehend reality by a process of reason . . . . [The] valid definition of man, within the context of his knowledge and of all of mankind’s knowledge to-date [is]: “A rational animal.”

(“Rational,” in this context, does not mean “acting invariably in accordance with reason”; it means “possessing the faculty of reason.” A full biological definition of man would include many subcategories of “animal,” but the general category and the ultimate definition remain the same.)"

Adam,

Do you mean Phylum: Chordata; Subphylum: Vertebrata; Class: Mammalia; Order: Primate; Family: Hominidae; Genus: Homo; Species: H. sapiens

If this were true it would mean that each human was part of the animal kingdom and not a special creation outside that kingdom of animals.

It is curious in retrospect to try to recapture that perspective that once prevailed.

I vaguely recall being made aware of that notion that humans were not part of the animal kingdom when I was a child.

Fortunately I was skeptical even then.

Some suspect I have become more gullible with age.

gulch

Zoologists indeed do categorize human beings under e. g. "mammals", "primates",

the highest developed amimals, a category in which we find us together with other apes like chimpazees, orang-utans, gorillas. Homo sapies sapiens is no special "creation" - his brain just happened to develop to a very high degree during evolution.

Edited May 11, 2009 by Xray

[Xray]

Michael,

It appears there was considerable oversight of my # 223 post. Some commentary followed, but I saw no actual response to the issues raised. Maybe another try will work with a breakdown point by point.

"To my knowledge she never did make the statement that concept and category

have the same meaning. Often she used the two words near each other. Yet for

the life of me, I cannot find a fundamental difference between them." (Michael)

"Could you come up with at least one example where Rand used the two words

near each other?" I can't find the term, category, in the online lexicon. I

would be very interested in instances wherein Rand used the term, category." (Xray)

This goes to Rand's use of the word, concept, which in turn, goes to her epistemology. It appears to me that she used the word, concept, as a synonym

for category. Any example wherein she used the terms, concept and category,

"near each other" might help clarify the matter. Again, I ask, can you provide any examples of this?

"Concept - 1 : "something conceived in the mind : thought, notion" (Webster's)

Do you have any objections to this definition? If so, what and why?

"It is the general term, all inclusive, so to speak. It takes in the whole

shooting match. Categorizing is but one of unlimited (ideas) concepts." (Xray)

Agree? disagree?

If disagree, why?

Example of a concept:

"A thing is—what it is; its characteristics constitute its identity." (Rand)

This is a conceived idea (concept) of entity identity. "A thing", not a group of things, nor the similarities of things.

Agree? Disagree?

If disagree, why?

TIA for your replies.

Edited May 11, 2009 by Xray

[tjohnson]

They are useful when trying to explain reality. They do not, are not intended to, represent a real something.

OK, so they are useful for explaining reality but not for representing real things? Do you not see a contradiction here?

[Dragonfly]

So you don't actually know? When I talk about 1-horse I can actually demonstrate what it is I am talking about.

And what do -3 horses look like?

[BaalChatzaf]

So you don't actually know? When I talk about 1-horse I can actually demonstrate what it is I am talking about.

And what do -3 horses look like?

Hee, hee.

Turn a horse through 90 degrees counter clockwise and you get i horse.

Or more exactly i*horse.

Ba'al Chatzaf

[Michael Stuart Kelly]

Xray,

I have been short on time recently. I will get to your questions.

Michael

[Brant Gaede]

This qualify as "near" 61 words away:

"Man

Man's distinctive characteristic is his type of consciousness—a consciousness able to abstract, to form concepts, to apprehend reality by a process of reason . . . . [The] valid definition of man, within the context of his knowledge and of all of mankind's knowledge to-date [is]: "A rational animal."

("Rational," in this context, does not mean "acting invariably in accordance with reason"; it means "possessing the faculty of reason." A full biological definition of man would include many subcategories of "animal," but the general category and the ultimate definition remain the same.)"

Adam,

Do you mean Phylum: Chordata; Subphylum: Vertebrata; Class: Mammalia; Order: Primate; Family: Hominidae; Genus: Homo; Species: H. sapiens

If this were true it would mean that each human was part of the animal kingdom and not a special creation outside that kingdom of animals.

It is curious in retrospect to try to recapture that perspective that once prevailed.

I vaguely recall being made aware of that notion that humans were not part of the animal kingdom when I was a child.

Fortunately I was skeptical even then.

Some suspect I have become more gullible with age.

gulch

Zoologists indeed do categorize human beings under e. g. "mammals", "primates",

the highest developed amimals, a category in which we find us together with other apes like chimpazees, orang-utans, gorillas. Homo sapies sapiens is no special "creation" - his brain just happened to develop to a very high degree during evolution.

Oh yes, h.s. is. Why? Because nature has never before found intelligence to be of high survival value in a species so h.s. is a fluke. There is no evidence of dinosaur civilizations.

--Brant

Edited May 14, 2009 by Brant Gaede

[BaalChatzaf]

Oh yes, h.s. is. Why? Because nature has never before found intelligence to be of high survival value in a species so h.s. is a fluke. There is no evidence of dinosaur civilizations.

--Brant

Natural Selection favors those characteristics which promote reproductive success. Intelligence has little to do with this. The ants, bees and cockroaches are much more effective reproducers than are humans. Long after humans are extinct, there will be ants, bees, wasps, termites and cockroaches.

Ba'al Chatzaf

[Selene]

Ba'al:

We all make these types of sweeping predictions and of course, they are, essentially, meaningless.

"Long after humans are extinct, there will be ants, bees, wasps, termites and cockroaches."

However, they all have that Sermon on the Mount type of power and sweep.

As an aspi, Ba'al there is no literal in that quote of yours.

Adam

[UncleJim]

Oh yes, h.s. is. Why? Because nature has never before found intelligence to be of high survival value in a species so h.s. is a fluke. There is no evidence of dinosaur civilizations.

--Brant

Natural Selection favors those characteristics which promote reproductive success. Intelligence has little to do with this. The ants, bees and cockroaches are much more effective reproducers than are humans. Long after humans are extinct, there will be ants, bees, wasps, termites and cockroaches.

Ba'al Chatzaf

What resource did you use to make this claim - ignorance?