Philosophy Reading Group / Kant & Math

[nikman]

But cells are an example of "interpolated" order - evolved boundaries - and our universe is different in being what I might call an example of "extrapolated" order. Developing boundaries.

The universe "imported" all its energy in one bite at the beginning with the big bang (dark energy of course is a complication to this simple statement). And it is "exporting" all this energy by the creation of a vast heat sink - the expanding void.

So there are two (dichotomously) ways to be a stable dissipative structure. Stay still and transact, or expand and dilute.

Can the Universe really be categorized as a dissipative structure, though? Do we know enough about it to make that judgment? Did Prigogine go that far? (Of course I think he balked for a while at classifying life as a dissipative structure.)

And aren't multicellular organisms partly extrapolative, at least in their developmental stages when the same fundamental (epi)genetic complex is involved in the expanding creation of such an enormous variety of cells?

(I may well not be getting something here.)

 

[apeiron]

Can the Universe really be categorized as a dissipative structure, though? Do we know enough about it to make that judgment? Did Prigogine go that far? (Of course I think he balked for a while at classifying life as a dissipative structure.)

Of course, even applying dissipative structure thinking to bios, life and mind, is still a controversial exercise for many as you say. But not among the theoretical biologists I work with at least.

And extending the idea to the universe itself would be the new rather bold step. There are actually a fair number of journals, conferences and seminars trying to take this tack. But even I say they are 99% flaky.

Yet the universe is clearly dissipating and clearly structured. It is just that we then have to answer the question, well, what is the larger world in which it arose and what exactly is it dissipating to pay for its structuring?

We could answer heat (the big bang Planckscale temperature and energy density). Or entropy (the big bang density of microstates - but we have seen how hard it is to make that model comprehensible).

I think there is a more general answer in the idea of vagueness. But that is another story finding little favour (and I would note that Prigogine has a kind of vagueness model for QM if you read End of Certainty, for example).

And aren't multicellular organisms partly extrapolative, at least in their developmental stages when the same fundamental (epi)genetic complex is involved in the expanding creation of such an enormous variety of cells?

Yes, life (and mind) depend on the harnessing of developmental processes. This is a huge issue in biology these days as people try to get past the simplicities of darwinian selection as the primary cause of complexity. It is what Kauffman, Oyama, Salthe and hundreds of others are on about.

Neurogenisis of the infant cortex is a good example of what you say. The free production of neurons and dendrites (simple development) followed by the selection - the constraints - imposed by experience and learning that winnow the pathways.

The term "interpolation" is a bit of jargon from hiearchy theory, stressing the fact that the more complex is nested within the simpler. So it is really a "cross-sectional" view. Life is interpolated as a level of complexity within the physico-chemical realm. And life itself is then an interaction between developmental potentials and evolutionary constraints (the metabolism and repair, or M/R systems, of Rosen).

So I was making the point that cells do have evolved boundaries that create a static context within which new hierarchical levels of development (and evolution) can take place.

The radical idea is then that the universe itself could be read in dissipative structure terms. But you would have to find a different route than the familiar biotic one of interpolation. Playing on words, I suggested extrapolation. Which has the correct sense of free and untrammeled growth or expansion. Whatever was just keeps diverging, keeps happening.

But interpolation is an accepted term and extrapolation would be a non-standard neologism here - yet a nicely dichotomous one I am hoping.

 

[nikman]

Of course, even applying dissipative structure thinking to bios, life and mind, is still a controversial exercise for many as you say. But not among the theoretical biologists I work with at least.

Are you familiar with the work of Howard Pattee (and more currently Luis Rocha)?

And extending the idea to the universe itself would be the new rather bold step. There are actually a fair number of journals, conferences and seminars trying to take this tack. But even I say they are 99% flaky.

Yet the universe is clearly dissipating and clearly structured. It is just that we then have to answer the question, well, what is the larger world in which it arose and what exactly is it dissipating to pay for its structuring?

I have a problem with the reference in your previous post to the expanding void as a vast heat sink. In order to have a heat sink you need matter (per the Second Law ... heat transfer is from hotter to colder molecules). Are you casting dark matter in that role? Unless matter is continually created along with the expansion (per Fred Hoyle's theory) why would you need expansion in order to have a heat sink?

I think there is a more general answer in the idea of vagueness. But that is another story finding little favour (and I would note that Prigogine has a kind of vagueness model for QM if you read End of Certainty, for example).

I haven't read it but I think I should. I didn't know he'd discussed QM.

Yes, life (and mind) depend on the harnessing of developmental processes. This is a huge issue in biology these days as people try to get past the simplicities of darwinian selection as the primary cause of complexity. It is what Kauffman, Oyama, Salthe and hundreds of others are on about.

By "simplicities of Darwinian selection" are you referring to the "radical adaptationists" (like Dawkins and his large Mini-Me, Dennett)? That issue's also being addressed by Allen Orr, among others. Also, on a more purely philosophical level, Jerry Fodor.

The radical idea is then that the universe itself could be read in dissipative structure terms. But you would have to find a different route than the familiar biotic one of interpolation. Playing on words, I suggested extrapolation. Which has the correct sense of free and untrammeled growth or expansion. Whatever was just keeps diverging, keeps happening.

But interpolation is an accepted term and extrapolation would be a non-standard neologism here - yet a nicely dichotomous one I am hoping.

I believe I need to know more than I do about hierarchy theory to follow this line of thought ...

 

[apeiron]

Hi Nikman

Are you familiar with the work of Howard Pattee (and more currently Luis Rocha)?

Yes, Pattee is one of the key thinkers I have worked with. My position is not identical with his by any means, but it certainly grew out of debates we had about the epistemic cut and the dichotomy involved. He is of course a hierarchy theorist and close colleague of Robert Rosen and Stan Salthe. And these three would be the best I have come across.

I've read Rocha's work and I think he was on some of the old chat forums like VCU Complexity, but felt like many of these guys' grad students, the original deeper ideas have become rather diluted in repetition - homogenised to fit with the mainstream to some extent.

Is there some particular aspect of Rocha you are thinking of here?

I have a problem with the reference in your previous post to the expanding void as a vast heat sink. In order to have a heat sink you need matter (per the Second Law ... heat transfer is from hotter to colder molecules). Are you casting dark matter in that role? Unless matter is continually created along with the expansion (per Fred Hoyle's theory) why would you need expansion in order to have a heat sink?

Here I would cite Lineweaver's MEP papers as a useful source.

The basic story of the universe is about the cooling of radiation via expansion - redshifting. Lineweaver runs the figures. The dissipation of matter becomes almost an afterthought. A secondary "interpolated" level of dissipative structure in fact.

So radiant matter does get "sunk" by simple expansion. And if protons, and whatever dark matter is, are subject to decay (recycled through black holes eventually if need be), then they will join this story.

By "simplicities of Darwinian selection" are you referring to the "radical adaptationists" (like Dawkins and his large Mini-Me, Dennett)? That issue's also being addressed by Allen Orr, among others. Also, on a more purely philosophical level, Jerry Fodor.

Dennett Nice guy but shallow as...

And as for the current Darwin backlash, I'm not really following it closely as it is not a critical issue for me at the moment. Also it is a rather sociological movement, the science at risk of being co-opted by the intelligent design crew.

I've worked closely with Stan Salthe for many years and so I've heard much of it before...

http://cache.zoominfo.com/CachedPag...+2:17:52+PM&firstName=Stanley&lastName=Salthe

I believe I need to know more than I do about hierarchy theory to follow this line of thought ...

If you are really interested, then PM me and I can send you links. The fundamentals of hierarchy theory are what I am researching.

 

[nikman]

Is there some particular aspect of Rocha you are thinking of here?

He worries a lot about the epistemic cut, and (maybe you consider this compromising with the mainstream) building bridges between dynamicists and computationalists. But I don't know of anyone else who's been doing more to carry on the Pattee tradition. (I'm not especially familiar with HP's work as a hierarchy theorist, which I know he was back in the 1970s. He caught my attention in his broader role as a theoretical biologist.)

Here's some Rocha stuff I know about and like, some or all of which you may very well know too:"Material Representations: From the Genetic Code to the Evolution of Cellular Automata" (with Wim Hordijk)

http://informatics.indiana.edu/rocha/ps/caalife04.pdf"Artificial Semantically Closed Objects"

http://informatics.indiana.edu/rocha/ps/tilsccai.pdf"Eigenbehavior and Symbols"

http://www.informatics.indiana.edu/rocha/ps/sr.pdfYou may very well also know this paper by Evan Thompson, but anyway I like to toss it into the mix whenever I see an opening. He worked with Dennett back in the early 90s, it's true, but he's come a long way since then:

"Symbol Grounding: A Bridge from Artificial Life to Artificial Intelligence"

http://individual.utoronto.ca/evant/SymbolGrounding.pdf I'm very much opposed to functionalism and the whole substrate neutrality/multiple realizability ethos, but I also believe there has to be a natural limit to reductionism. I see a possible solution emerging from the QM informatics work by Zeilinger, Brukner et al and abetted by onlookers like Hans C von Baeyer. I feel an affinity toward the basic ideas behind biosemiotics (including the work of Claus Emmeche and Jesper Hoffmeyer) but at the moment it's somewhat, well, hand-wavy.

I'm in a rush much of the time right now, but will get back.

 

[apeiron]

(maybe you consider this compromising with the mainstream) building bridges between dynamicists and computationalists.

Yes. Simply put, I was finding that many wanted to "find the truth" of a dynamic view by reframing it in computational terms. But then I came away from debates with Pattee, Salthe and others wanting to do the opposite - to find a dynamic way to frame the truths of computationalism. Define an organic logic to complement the more familiar mechanical logic, so to speak.

Other grad students of Pattee, like Peter Cariani, also had more radical ambitions and consequently, I would say, struggled to make it in academia.

 

[nikman]

Frankly, I see no important difference between Rocha and Cariani ...

 

[nikman]

Just re-read Cariani's "Symbols and Dynamics in the Brain" (linked from Rocha's website) and Rocha's papers linked above ...

Are you perhaps factoring in some personal dimension here?

 

[SixNein]

We might, indeed at first suppose that the proposition 7 + 5 = 12 is a merely analytical proposition, following (according to the principle of contradiction) from the conception of a sum of seven and five. But if we regard it more narrowly, we find that our conception of the sum of seven and five contains nothing more than the uniting of both sums into one, whereby it cannot at all be cogitated what this single number is which embraces both. The conception of twelve is by no means obtained by merely cogitating the union of seven and five; and we may analyse our conception of such a possible sum as long as we will, still we shall never discover in it the notion of twelve. We must go beyond these conceptions, and have recourse to an intuition which corresponds to one of the two− our five fingers, for example...​

Do you agree with Kant here? Do you agree that our conception of the number 12 depends to some degree on experience and isn't something we can derive rationally?
/QUOTE]

I disagree with Kant.

All you need is rules.

 

[JoeDawg]

All you need is rules.

But where does one get the rules?

Without some foundation, the selection process is random.

 

[SixNein]

But where does one get the rules?

Without some foundation, the selection process is random.

The foundation is the rules. We could invent our own rules and create our own numbers.

The letter @ is a number.
Every number has a subsequent number.
No numbers share the same former number.
@ does not come after any number.
Any property that belongs to the number @, and any property that belongs to subsequent numbers, belongs to all numbers.

Using the above rules, I have created the following list:
@, A, B, C, D, E, F, G, ... N

But you need more rules to do anything with it.

In a basic nutshell, the rules of the number serve as the foundation.

 

[Sorry!]

The foundation is the rules. We could invent our own rules and create our own numbers.

The letter @ is a number.
Every number has a subsequent number.
No numbers share the same former number.
@ does not come after any number.
Any property that belongs to the number @, and any property that belongs to subsequent numbers, belongs to all numbers.

Using the above rules, I have created the following list:
@, A, B, C, D, E, F, G, ... N

But you need more rules to do anything with it.

In a basic nutshell, the rules of the number serve as the foundation.

The question was WHERE do you get the rules, not how can we formulate them. So explain why you have chosen those rules above... and what parameters we should use to select further rules?

 

[SixNein]

The question was WHERE do you get the rules, not how can we formulate them. So explain why you have chosen those rules above... and what parameters we should use to select further rules?

You obtain the rules from thinking and asking questions. You could create different rules that are weaker or stronger, and the nature of your numbers would change depending upon the rules. In this example, I just spit out a rehash of Peano's axioms.

 

[SixNein]

Most?

Most is correct.

The continuum hypothesis is independent of our current system, so we cannot solve it without creating new axioms. Quite a few different problems are independent.

 

[JoeDawg]

You obtain the rules from thinking and asking questions. You could create different rules that are weaker or stronger, and the nature of your numbers would change depending upon the rules. In this example, I just spit out a rehash of Peano's axioms.

How do you measure strength of a rule?

 

[SixNein]

How do you measure strength of a rule?

Through the means of consistency.

I personally think Kant is off base. Counting is one human field that can be found in nature. A wolf can count, and it doesn't use its fingers. The concept of numbers is extremely primitive even though the definition of numbers is quite complex. Although our counting abilities are developed through external means, life could find the means to count through thought.

 

[JoeDawg]

Through the means of consistency.

Consistency demands that you have at least 2 axioms, how do you select the first one?
This is where experience comes in. Even the very idea of 'consistency' comes from experience. We value consistency because of its value in predicting outcomes which are beneficial to us. We evolved this ability, because its benefitial to survival.

Although our counting abilities are developed through external means, life could find the means to count through thought.

And a millions monkeys typing on keyboards for an infinite amount of time could write the complete works of shakespeare. But 99.9999...% of what they churn out would be nonesense, and some would be 'consistent' but not resemble reality.

Math was invented by generalizing experience.

 

[SixNein]

Consistency demands that you have at least 2 axioms, how do you select the first one?
This is where experience comes in. Even the very idea of 'consistency' comes from experience. We value consistency because of its value in predicting outcomes which are beneficial to us. We evolved this ability, because its benefitial to survival.



And a millions monkeys typing on keyboards for an infinite amount of time could write the complete works of shakespeare. But 99.9999...% of what they churn out would be nonesense, and some would be 'consistent' but not resemble reality.

Math was invented by generalizing experience.

Thought is an experience. Mathematics is a manor of symbolic thinking.


When was math invented exactly? Mathematical abilities can be found in other species.

 

[JoeDawg]

Thought is an experience. Mathematics is a manor of symbolic thinking.

Thought is qualitatively different from sense experience.

When was math invented exactly? Mathematical abilities can be found in other species.

Hard to say, but geometry goes back at least as far as the Ancient Egyptians. Before writing, I'm not sure one could even have a formal system.

Mathematical ability derives from logical ability, which comes from observing the world.
If you've ever watched a baby learn, you'll see how they start to form logical patterns.

Formalized mathematics is different from ability however. Simple counting doesn't really require a formal system. Few, some, many... is counting.

A formal system of math probably requires writing.

 

[SixNein]

Thought is qualitatively different from sense experience.

Hard to say, but geometry goes back at least as far as the Ancient Egyptians. Before writing, I'm not sure one could even have a formal system.

Mathematical ability derives from logical ability, which comes from observing the world.
If you've ever watched a baby learn, you'll see how they start to form logical patterns.

Formalized mathematics is different from ability however. Simple counting doesn't really require a formal system. Few, some, many... is counting.

A formal system of math probably requires writing.

In the particular situation we are discussing, the person probably can't do much math. In fact, a person isolated from the rest of humanity could not do much either. But I believe the person could grasp the concept of numbers without senses. Could you tell if you had more than one thought?

 

[JoeDawg]

Could you tell if you had more than one thought?

I think this is one of the problems faced by those who want to create an AI. I think our consciousness is a function of interacting experiences from multiple stimuli. Creating a brain in box, or brain in a vat, means there is really only one source of stimuli. If we want to mimic intelligence, I think we need to include a variety of input sources. A robot with eyes, ears... a sense of touch...etc..

But to answer your question, I think you would have to have a need to distinguish between thoughts, and that need would undoubtedly rely on an external influence.

 

[wofsy]

A pretty big problem from what I have read. I think you're idealizing mathematics, like the ancient greeks did with geometry. It all happens in the human brain. And different cultures have developed different mathematical systems. Ours has simply absorbed all the aspects we find most useful.

Math is in large part analytic, but its axioms and basic logic are derived from experience. All logic comes from how we see the world working. Math is just a way to represent and predict experience using highly abstract language.

Axioms are little more than assumptions, or constraints. And those constraints are based on our experiences in the world.

A couple unrelated thoughts: They are meant as talking points not as assertions of anything that I believe.

- in some sense everything happens in the human brain. Mathematics and experience are inescapably unified.

- Logic is intrinsic. If it were not we would not be able to think.

- "Derived from expeience" is a vague idea. Derived has no rigorous definition.

- Math is not "just" a way to represent and predict experience". Here is a quote from Felix Klein's introduction to his book, Riemann's Theory of Algebraic Functions and their Integrals."

"He(Riemann ) had in mind far more general methods of determination than those we employ in the following pages;methods of determination in which physical analogy ...fails us."

- Experience suggests an underlying mathematical reality but that reality supercedes direct experience

 

[apeiron]

A couple unrelated thoughts: They are meant as talking points not as assertions of anything that I believe.

- in some sense everything happens in the human brain. Mathematics and experience are inescapably unified.

- Logic is intrinsic. If it were not we would not be able to think.

- "Derived from expeience" is a vague idea. Derived has no rigorous definition.

- Math is not "just" a way to represent and predict experience". Here is a quote from Felix Klein's introduction to his book, Riemann's Theory of Algebraic Functions and their Integrals."

"He(Riemann ) had in mind far more general methods of determination than those we employ in the following pages;methods of determination in which physical analogy ...fails us."

- Experience suggests an underlying mathematical reality but that reality supercedes direct experience

If you want to demystify and make rigorous the relationship between minds and worlds, Rosen's modelling relations work serves as a good template...

http://www.panmere.com/?page_id=18

http://www.osti.gov/bridge/servlets/purl/10460-5uGkyu/webviewable/10460.pdf