Question for old-timer's: Peikoff's view on certainty

[tjohnson]

What does that got to do with it?

Your so-called space is merely a logical extension of the concretes. Without the concretes, it would not be imagined at all.

Michael

You seem to be saying that mathematical objects have their origins in our own perceptions and, if so, I don't have a problem with that, but in advanced mathematics there is little or no resemblance to anything we perceive. This is perhaps the most fascinating thing about mathematics, that is appears so disconnected from perceptions and yet can uncover relations that can be seen empirically.

[Michael Stuart Kelly]

You seem to be saying that mathematical objects have their origins in our own perceptions and, if so, I don't have a problem with that, but in advanced mathematics there is little or no resemblance to anything we perceive. This is perhaps the most fascinating thing about mathematics, that is appears so disconnected from perceptions and yet can uncover relations that can be seen empirically.

GS,

The origins is all I am saying. And maybe that the reason advanced math can uncover empirical relations is because of this origin. I am certainly not saying that the methodology of math is the same thing as a perceptual concrete.

The only reason for a need to say it at all is that people who wish to bash Rand (and Peikoff) from the academic side overly emphasize the advanced math as some kind of proof against them and pretend that Objectivists demand that all math correspond to a physical thing "out there" that it is measuring, sort of like a numerical concept for perceptual concretes. In some ranting and railing against this, I have even read passionate discourses about how math is completely cut off from our perceptions, without even a basic origin. This is usually called "a priori knowledge" or "analytical" or "abstract" (with a somewhat different meaning than Objectivists give it) or something like that during these rants.

I keep saying this, but there is plenty of legitimate stuff to criticize in Rand (and Peikoff). There is no need to pretend that they are against advanced math and abstract theorizing. But that is the impression that is constantly sold.

(I do admit that Peikoff's cosmology, comments on quantum physics and several other pronouncements are strange and do lend themselves to bashing. Idem for several melodramatic statements by Rand.)

Michael

[tjohnson]

GS,

The origins is all I am saying. And maybe that the reason advanced math can uncover empirical relations is because of this origin. I am certainly not saying that the methodology of math is the same thing as a perceptual concrete.

Korzybski theorized that not only was mathematics similar in structure to nature but it was also similar in structure to our nervous system. It's a rather radical idea but one can imagine an example by thinking about how our eyes integrate static pictures into a continuously changing image similar to what is done in integral calculus. This may explain why mathematics does have such success in discovering relations because, after all, our consciousness is a joint phenomenon of what is around us and how we interact with it.

[BaalChatzaf]

GS,

The origins is all I am saying. And maybe that the reason advanced math can uncover empirical relations is because of this origin. I am certainly not saying that the methodology of math is the same thing as a perceptual concrete.

Korzybski theorized that not only was mathematics similar in structure to nature but it was also similar in structure to our nervous system. It's a rather radical idea but one can imagine an example by thinking about how our eyes integrate static pictures into a continuously changing image similar to what is done in integral calculus. This may explain why mathematics does have such success in discovering relations because, after all, our consciousness is a joint phenomenon of what is around us and how we interact with it.

How is an uncountably infinite, linearly ordered, locally compact set similar to our nervous system?

Ba'al Chatzaf

[tjohnson]

How is an uncountably infinite, linearly ordered, locally compact set similar to our nervous system?

Ba'al Chatzaf

Good question. I like fiber bundles myself.

http://en.wikipedia.org/wiki/Bundle_(mathematics)

Edited September 12, 2007 by general semanticist

[Michael Stuart Kelly]

How is an uncountably infinite, linearly ordered, locally compact set similar to our nervous system?

Bob,

From common sense:

Uncountably infinite. The infinite does not exist in the sense of establishing a limit on it. For human use, it only exists as a possibility on which to locate limited things. With sight, to use one example, there is no limit to how many new things it is capable of seeing (from the thing end and restricted to things that fall within the size, etc., that can be seen). So long as the conditions for seeing are met, the range of objects and backgrounds that can be seen are uncountably infinite.

Linearly ordered. In a more general way, there are the nerves. We are basically processing tubes and tubes are linear. You progress from the beginning, go through the middle and get to the end. That's the linear way tubes work.

Locally compact. There are pretty clear laws of nature operating on the nervous system that do not apply to other things. There are not many and they are local to nervous systems.

Big-picture-wise, there are similarities.

Michael

[BaalChatzaf]

How is an uncountably infinite, linearly ordered, locally compact set similar to our nervous system?

Bob,

From common sense:

Uncountably infinite. The infinite does not exist in the sense of establishing a limit on it. For human use, it only exists as a possibility on which to locate limited things. With sight, to use one example, there is no limit to how many new things it is capable of seeing (from the thing end and restricted to things that fall within the size, etc., that can be seen). So long as the conditions for seeing are met, the range of objects and backgrounds that can be seen are uncountably infinite.

Linearly ordered. In a more general way, there are the nerves. We are basically processing tubes and tubes are linear. You progress from the beginning, go through the middle and get to the end. That's the linear way tubes work.

Locally compact. There are pretty clear laws of nature operating on the nervous system that do not apply to other things. There are not many and they are local to nervous systems.

Big-picture-wise, there are similarities.

Michael

Big Picture wise how are Klein Bottles (a kind of four dimensional manifold with no inside or outside) similar to our nervous systems.

The point I am making is that mathematical system need not have any resemblance whatsoever to objects experienced in the real physical world.

Mathematics, done abstractly and formally, need not have any empirical content whatsoever.

All that is required is internal consistency, not resemblance to anything real.

Ba'al Chatzaf

[Brant Gaede]

How is an uncountably infinite, linearly ordered, locally compact set similar to our nervous system?

Bob,

From common sense:

Uncountably infinite. The infinite does not exist in the sense of establishing a limit on it. For human use, it only exists as a possibility on which to locate limited things. With sight, to use one example, there is no limit to how many new things it is capable of seeing (from the thing end and restricted to things that fall within the size, etc., that can be seen). So long as the conditions for seeing are met, the range of objects and backgrounds that can be seen are uncountably infinite.

Linearly ordered. In a more general way, there are the nerves. We are basically processing tubes and tubes are linear. You progress from the beginning, go through the middle and get to the end. That's the linear way tubes work.

Locally compact. There are pretty clear laws of nature operating on the nervous system that do not apply to other things. There are not many and they are local to nervous systems.

Big-picture-wise, there are similarities.

Michael

Big Picture wise how are Klein Bottles (a kind of four dimensional manifold with no inside or outside) similar to our nervous systems.

The point I am making is that mathematical system need not have any resemblance whatsoever to objects experienced in the real physical world.

Mathematics, done abstractly and formally, need not have any empirical content whatsoever.

All that is required is internal consistency, not resemblance to anything real.

Ba'al Chatzaf

Where do we start and where do we end? Are those places "real?"

--Brant

Edited September 12, 2007 by Brant Gaede

[Michael Stuart Kelly]

All that is required is internal consistency, not resemblance to anything real.

Bob,

There can be no internal consistency without the law of identity and hierarchy. These are the governing principles of everything "out there." In this respect, math certainly does.

Big Picture wise how are Klein Bottles (a kind of four dimensional manifold with no inside or outside) similar to our nervous systems.

Hell. That's easy. From common sense:

No start or end. With sight, to use one example, there is no start or end point as to what new things are capable of being seen (from the thing end and restricted to things that fall within the size, etc., that can be seen). And we can keep seeing the same things over and over.

I could go on, but you get the picture. Besides, as cool as Klein Bottles are, they are not the total of existence, so in any analogy, it would be a double standard for them to be used for the total of the nervous system.

For as much as we may not like it, we are part of the big picture. We are not above it or outside it. That hurts, but there it is.

Michael

[Ellen Stuttle]

Korzybski theorized that not only was mathematics similar in structure to nature but it was also similar in structure to our nervous system. It's a rather radical idea but one can imagine an example by thinking about how our eyes integrate static pictures into a continuously changing image similar to what is done in integral calculus. This may explain why mathematics does have such success in discovering relations because, after all, our consciousness is a joint phenomenon of what is around us and how we interact with it.

It sounds as if he had the (mistaken) idea that the eye works like a motion picture camera. When did he form this theory?

Ellen

___

[tjohnson]

It sounds as if he had the (mistaken) idea that the eye works like a motion picture camera. When did he form this theory?

Ellen

___

Not sure I understand, doesn't a motion picture do the opposite, ie. take a bunch of static pictures of a continuously changing image? What I am talking about is what happens when we watch a motion picture. His major work, Science & Sanity, was published in 1933.

Incidently, dividing up a continuously changing process into static "snapshots", like the camera, is what we do in differential calculus. Our brains cannot process change directly, we need to break it into static steps and words are just that - static abstractions from changing processes (mental images, feelings, etc.).

[Guyau]

Here is a page that tells of the wonderful works of Ruth Millikan:

http://www.philosophy.uconn.edu/department...likan/index.htm

Here is a little piece I wrote concerning Millikan's biological approach to truth theory (up to 1993):

http://www.bomis.com/objectivity/millikan.html

Millikan’s Contribution to Materialist Philosophy of Mind

Nicholas Shea (2006)

This paper is a nice introduction to Millikan’s account of intentionality as from evolutionary biological nature. There are interesting parallels with Binswanger’s setting of Rand’s theory of norms as from evolutionary biological nature.$

[tjohnson]

Millikan's Contribution to Materialist Philosophy of Mind

Nicholas Shea (2006)

This paper is a nice introduction to Millikan's account of intentionality as from evolutionary biological nature. There are interesting parallels with Binswanger's setting of Rand's theory of norms as from evolutionary biological nature.$

...distributed across such as such cortical areas in Pierre’s brain (or whatever). This time, it

has some different complex relational property which is its content, one that we specify by

mentioning cats, amongst other things. However, there is another crucial difference

between the two cases: in one Pierre is thinking something true, in the other something

false. And the truth or falsity of Pierre’s belief seems to be fixed by its content, together

with some facts about the world (in particular, facts about the nature of canine and feline

vocalisations). Belief contents must be some complex relational property that is suited to

forming the basis of this distinction between truth and falsity. Arguably, not any old

descriptive distinction will do here, since it is a difference that can have normative import.

There is a sense in which a representation that is misrepresenting is doing something

wrong. What kind of complex relational property can be like that?

In Korzybski's language, if a representation correctly represents then we have similarity of structure, if not, the structures are dissimilar and can mislead us the same way that following an incorrect map can.

[Christopher]

GS,

In Objectivism, all symbolic systems like words, logic and math have their basis in reality. Math is abstract, but it does follow the law of identity. As reality does also, it works. That's the initial connection. It is not just a set of arbitrary rules in the mind completely disconnected from the rest of reality.

I connected one set of dots and came up with the following. We are part of reality, therefore we fall under the same laws of organization that govern reality, therefore, our mental system of organization (even when using symbols) works according to the laws of organization that govern reality.

So in a metaphysical sense (law of identity), all math is applied math. A math unit is a "thing." It is just a mental thing and not a perceptual thing.

Michael

Joseph Campbell would disagree. I believe he would argue that man uses symbols from external reality to describe internal states and processes that are actually independent of the reality we perceive.

[jeffrey smith]

Big Picture wise how are Klein Bottles (a kind of four dimensional manifold with no inside or outside) similar to our nervous systems.

The point I am making is that mathematical system need not have any resemblance whatsoever to objects experienced in the real physical world.

Mathematics, done abstractly and formally, need not have any empirical content whatsoever.

All that is required is internal consistency, not resemblance to anything real.

Ba'al Chatzaf

I would suggest that, from a philosophical viewpoint, the more interesting question is the reverse of what Ba'al is dealing with:

Why does reality--the actually existing universe--resemble mathematics?

Why is it that physical reality can be, by and large, described successfully by mathematics? Why is it that physics can be explored by mathematical methods, and why is that the laws of physics are mathematical functions (Kepler's and Newton's laws, the relationship of energy, mass and the speed of light in relativity, etc.) Is it just happenstance that the universe as it exists can be so described, or is there something fundamental to the universe that makes it so? Or is it something fundamental to mathematics that explains the matter? Is it possible to have a universe in which those laws could not be mathematically expressed? And if not, why not?

(And I'm not going to pretend to have the chops--philosophical, scientific, or mathematical--to even suggest what the answers could be.)

Jeffrey S.

Edited November 29, 2009 by jeffrey smith

[tjohnson]

Do you really think those questions could be answered? It doesn't matter why physics and mathematics are similar in structure to the world in which we live, it just is.

[9thdoctor]

Joseph Campbell would disagree. I believe he would argue that man uses symbols from external reality to describe internal states and processes that are actually independent of the reality we perceive.

Do you have a reference on this? There’s still plenty of Joseph Campbell I haven’t read, but I haven’t seen him enunciate a wide theory of perception and concept formation. I do remember him referring to Kant’s Critique of Pure Reason in Transformations of Myth through Time, and I think the same material appears in The Hero’s Journey. He talks about modes of perception and categories of thought, culminating in the characterization of religious symbols as metaphors which make reference to the “transcendent”. I think he meant that to apply only to religious concepts.

[Guyau]

. . .

Mathematical system need not have any resemblance whatsoever to objects experienced in the real physical world.

Mathematics, done abstractly and formally, need not have any empirical content whatsoever.

All that is required is internal consistency, not resemblance to anything real.

I would suggest that, from a philosophical viewpoint, the more interesting question is the reverse of what Ba'al is dealing with:

Why does reality--the actually existing universe--resemble mathematics?

Why is it that physical reality can be, by and large, described successfully by mathematics? Why is it that physics can be explored by mathematical methods, and why is that the laws of physics are mathematical functions (Kepler's and Newton's laws, the relationship of energy, mass and the speed of light in relativity, etc.) Is it just happenstance that the universe as it exists can be so described, or is there something fundamental to the universe that makes it so? Or is it something fundamental to mathematics that explains the matter? Is it possible to have a universe in which those laws could not be mathematically expressed? And if not, why not?

(And I'm not going to pretend to have the chops--philosophical, scientific, or mathematical--to even suggest what the answers could be.)

Do you really think those questions could be answered? It doesn't matter why physics and mathematics are similar in structure to the world in which we live, it just is.

Thomas,

Jeffrey’s questions are reasonable and of lively interest to some thinkers. Those questions have been pondered by physicists Hertz, Einstein, Feynman, and most famously, by Wigner. Philosophers of science and mathematics today continue to work on competent answers.

I wouldn’t be too quick to say for questions: things just are the way they are in the respect the question seeks explanation. I remember when I was first learning a little about gauge theory and supersymmetry in the 70’s, it really struck me that to that point I really had never wondered, and would have supposed it unreasonable to expect any explanation of, why the most elementary massive particles have the masses they have. I would have said: they just do.

Some questions are not sensible, of course, such as: Why is there something rather than nothing? “Something is” is where sensible regress ends.

[Christopher]

Joseph Campbell would disagree. I believe he would argue that man uses symbols from external reality to describe internal states and processes that are actually independent of the reality we perceive.

Do you have a reference on this? There’s still plenty of Joseph Campbell I haven’t read, but I haven’t seen him enunciate a wide theory of perception and concept formation. I do remember him referring to Kant’s Critique of Pure Reason in Transformations of Myth through Time, and I think the same material appears in The Hero’s Journey. He talks about modes of perception and categories of thought, culminating in the characterization of religious symbols as metaphors which make reference to the “transcendent”. I think he meant that to apply only to religious concepts.

He discusses this in the video "Joseph Campbell: The Hero's Journey." He is basically discussing how there are pan-cultural pan-historical themes in human literature and mythology that use different symbols but demonstrate the same basic psychological architecture. He specifically talks about symbols and how there are no problems with religious symbolism so long as the symbols are taken to represent inner psychological states rather than objective concretes.

Edited November 30, 2009 by Christopher

[Steve Gagne]

Joseph Campbell would disagree. I believe he would argue that man uses symbols from external reality to describe internal states and processes that are actually independent of the reality we perceive.

Do you have a reference on this? There’s still plenty of Joseph Campbell I haven’t read, but I haven’t seen him enunciate a wide theory of perception and concept formation. I do remember him referring to Kant’s Critique of Pure Reason in Transformations of Myth through Time, and I think the same material appears in The Hero’s Journey. He talks about modes of perception and categories of thought, culminating in the characterization of religious symbols as metaphors which make reference to the “transcendent”. I think he meant that to apply only to religious concepts.

A few years back, Bill Moyers interviewed Campbell on PBS. (Wouldn't recommend it if it was your last chance in your life to watch TV.) He talked about the Serpent in the Garden of Eden, and how the Ouruborous (sp?), the serpent that eats its own tail, was the symbol of life -- live birth -- in ancient Hindu culture. So he added these two together and came up with the conclusion that Judeo-Christian culture was automatically anti-woman & anti-life -- not because of any patriarchal heritage, but because the symbol of the Ouruborous was supposedly hated by the ancient Hebrews. He derived this from these symbols that he divorced from reality, then turned into scrambled eggs in his head, then tried to claim that the scrambled eggs in his head resembled anything in reality.

His writing is equally obtuse. Jung and Eliade had far more to say that is relevant. Campbell was a narcissistic fool.

Edited November 30, 2009 by Steve Gagne

[9thdoctor]

A few years back, Bill Moyers interviewed Campbell on PBS. (Wouldn't recommend it if it was your last chance in your life to watch TV.) He talked about the Serpent in the Garden of Eden, and how the Ouruborous (sp?), the serpent that eats its own tail, was the symbol of life -- live birth -- in ancient Hindu culture. So he added these two together and came up with the conclusion that Judeo-Christian culture was automatically anti-woman & anti-life -- not because of any patriarchal heritage, but because the symbol of the Ouruborous was supposedly hated by the ancient Hebrews. He derived this from these symbols that he divorced from reality, then turned into scrambled eggs in his head, then tried to claim that the scrambled eggs in his head resembled anything in reality.

His writing is equally obtuse. Jung and Eliade had far more to say that is relevant. Campbell was a narcissistic fool.

Hate to be harsh, but this reads like something by Lindsay Perigo. Add the epithet “pomowanker” and you’d be spot on. Power of Myth is 6 hours long, and you didn’t give enough info to help me quickly look up the material you’re attributing to Campbell, so I’ll restrict myself to saying that that doesn’t sound like him.

Here’s Wikipedia on Ouroboros, its not specifically Hindu. http://en.wikipedia.org/wiki/Ouroboros

[Brant Gaede]

A few years back, Bill Moyers interviewed Campbell on PBS. (Wouldn't recommend it if it was your last chance in your life to watch TV.) He talked about the Serpent in the Garden of Eden, and how the Ouruborous (sp?), the serpent that eats its own tail, was the symbol of life -- live birth -- in ancient Hindu culture. So he added these two together and came up with the conclusion that Judeo-Christian culture was automatically anti-woman & anti-life -- not because of any patriarchal heritage, but because the symbol of the Ouruborous was supposedly hated by the ancient Hebrews. He derived this from these symbols that he divorced from reality, then turned into scrambled eggs in his head, then tried to claim that the scrambled eggs in his head resembled anything in reality.

His writing is equally obtuse. Jung and Eliade had far more to say that is relevant. Campbell was a narcissistic fool.

Hate to be harsh, but this reads like something by Lindsay Perigo. Add the epithet "pomowanker" and you'd be spot on. Power of Myth is 6 hours long, and you didn't give enough info to help me quickly look up the material you're attributing to Campbell, so I'll restrict myself to saying that that doesn't sound like him.

Here's Wikipedia on Ouroboros, its not specifically Hindu. http://en.wikipedia.org/wiki/Ouroboros

And it was a lot more than "a few years back."

--Brant