Just as a bye-the-way

[Russ Abbott]

Nice gloss of Goodman.  But it also suggests a problem with philosophy: the need to make demonstrably true statements. Induction in mathematics is a proof technique. When applied to reality it doesn't work because the axiom of induction isn't available for reality.  But then notion of a true statement as applied to reality is a bit of a stretch anyway. Yet philosophers keep insisting that it's important to make statements that can be shown to be true. But that's a cause lost before one even begins because there is no real connection between words and things -- only imagined connections.

 

-- Russ

On Tue, Mar 27, 2012 at 2:53 PM, Douglas Roberts <[hidden email]> wrote:

Very clever.

--Doug

On Tue, Mar 27, 2012 at 3:37 PM, Nicholas Thompson <[hidden email]> wrote:

Doug wrote

 

In retrospect, I suppose I do have faith in one other fairly immutable quality -- the accuracy of my bullshit detector

 

Well, why not.   it’s always worked in the past …. . 

 

Nick

 

From: [hidden email] [mailto:[hidden email]] On Behalf Of Douglas Roberts
Sent: Tuesday, March 27, 2012 2:55 PM

To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Just as a bye-the-way

 

Thanks, Nick, you describe an interesting way of establishing a life-view.

 

Not quite sure how to answer, except to say that if I have faith in anything, it is in evidence.  If I have accrued a sufficient pile of evidence that supports a conclusion about some observation, then I'll probably believe it.  

 

If my collected evidence is such that the inescapable conclusion is that nothing is constant, then I suppose I'd eventually come around to believe that, so long as I had a constant framework from which to corroborate and verify the inconsistencies.  Otherwise, I'd continue to look for the missing pieces of the puzzle (a reference to the cosmological artifacts I sent you earlier).

 

As to religion:  for me it's a big "No thank you" to any cult mindthink that requires brainless acceptance of a supernatural homo-centric benevolent/malevolent boogyman. And that goes double for one particular cult whose belief system is predicated upon "hieroglyph"-inscribed disappearing golden tablets.  Oh, and I guess that goes triple for any cult that attempts to dictate what kind of skivies I must wear to become a member of the club.  I guess you could say that it would take a miracle to get me to assent to becoming a member of any of the existing flocks of theist-following sheep out there.

 

In retrospect, I suppose I do have faith in one other fairly immutable quality -- the accuracy of my bullshit detector.

 

--Doug

 

On Tue, Mar 27, 2012 at 11:47 AM, Nicholas Thompson <[hidden email]> wrote:

Dear Doug,  

 

I am afraid that the black hole example is already too technologically dense for me, so I am going to punt on the project of luring you inside my walls and slaughtering you there, and just out-right tell you what I think

. 

The argument began with my detecting in you (perhaps wrongly) the belief that you, unlike the religious, can get along without some sort of faith in your life.  Most people I have known in the past who have reached this conclusion have done so through their confidence in induction. “What do I need with faith if I can just collect the evidence and act on it?’  And the answer is that without faith of some sort, there is no foundation for induction.

 

The argument for this position is famously from Hume.  A version of it is colorfully laid out by Nelson Goodman in his  The New Riddle of Induction.  So let’s say, I want to learn if grass is green.  My religious buddy says, “Look in the Bible.  I am sure it’s in there somewhere.’  My atheist buddy says, “nonsense, go out and look at the grass.”  I’m an atheist, so I go out and start collecting samples of grass.  I collect a hundred samples and I bring them back in announce that I am satisfied that all grass is green.  At which point my religious buddy says, No, No, you have no evidence there that Grass is green.  “All you have is evidence that grass is grue.” “Grue!?” I say.  “What’s Grue?”

 

Charitably forgoing  the opportunity to ask, “I dunno.  What’s Grue with you?” my religious buddy simply says, “It’s the property of being Green until your last measurement, and Blue thereafter. “

 

“Nonsense,”  I reply.  “What kind of a property is THAT?  Nature doesn’t HAVE properties like that. 

 

“Perhaps that’s been true”, he replies, but only up till now!”

 

In other words, our belief in induction is based on our plausible but unfounded belief in induction, i.e., faith. 

 

Nick

 

 

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of glen e. p. ropella
Sent: Monday, March 26, 2012 11:40 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Just as a bye-the-way

 

 

This is a red herring.  The argument for dark matter/energy need not be inductive.  The inductive form is:

 

o we've defined the set based on the laws of physics we've observed o everything is in this set o gravity seems stronger/weaker than predicted in some contexts

.: there are unobserved members of the set: dark matter and energy.

 

A non-inductive argument for dark matter/energy is just as valid:

 

o the model we've induced is not completely consistent with the data o the laws characterize everything we've encountered so far

.: there must be something we haven't encountered that will refine the laws.

 

No induction is necessary to motivate a hypothesis for some form of matter that's imprecisely or inaccurately described by the laws we've, so far, induced.  But parsimony suggests that a theory that assumes it's complete is more testable than a theory with metaphysical holes in it.

So, the argument for dark matter _seems_ inductive, even though it's not.  Only someone who assumes our laws are complete (fully refined) would think the argument is inductive.  My sample is small.  But I don't know of any physicists or cosmologists who think our laws cannot be modified.

 

I.e. it's naive to assume identity between a scientific theory and the reasoning surrounding the pursuit of a scientific theory.

 

 

Douglas Roberts wrote at 03/24/2012 03:08 PM:

> There's also an interesting "dark matter" inference that has found its

> way into grudging cosmological acceptance.  This time the role of the

> inferred substance is to keep galaxies from flying apart, as it has

> recently been observed that based on the amount of their measurable,

> observable mass and rotational velocities, they should flung their

> stars off ages ago.

>

> --Doug

>

>

> On Sat, Mar 24, 2012 at 3:16 PM, Douglas Roberts <[hidden email]

> <[hidden email]>> wrote:

>

>     I feel that I am being drawn in to an enemy encampment, but:

>

>     Developing a proof would be far better than choosing to rely

>     on inference, if the goal is to develop a larger-scale understanding

>     of a system.

>

>     Take "dark energy" as an example.  Its presence is inferred from

>     having observed that the rate of expansion of the observable

>     universe began to accelerate relatively recently, on a cosmological

>     time scale.  In response to this, the cosmologists have inferred the

>     existence of a mysterious energy with magical gravitational

>     repulsive properties as a means to explain away an otherwise

>     inexplicable observation.  A much more satisfying approach will be

>     to develop a sufficient understanding of the underlying physics of

>     our universe from which a rigorous proof of the phenomenon could be

>     derived.

>

>     But, without that understanding, we are left with cosmological

>     "magic dust", instead of a real understanding of the observed dynamics.

>

>     --Doug

 

 

--

glen e. p. ropella, <a href="tel:[phone]" target="_blank">971-222-9095, http://tempusdictum.com

 

 

============================================================

FRIAM Applied Complexity Group listserv

Meets Fridays 9a-11:30 at cafe at St. John's College

lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

 

--
Doug Roberts
[hidden email]
[hidden email]

http://parrot-farm.net/Second-Cousins

<a href="tel:[phone]" value="[phone]" target="_blank">505-455-7333 - Office
<a href="tel:[phone]" value="[phone]" target="_blank">505-670-8195 - Cell

 

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

--
Doug Roberts
[hidden email]
[hidden email]

http://parrot-farm.net/Second-Cousins

<a href="tel:[phone]" value="[phone]" target="_blank">505-455-7333 - Office
<a href="tel:[phone]" value="[phone]" target="_blank">505-670-8195 - Cell

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[Nick Thompson]

Dear Doug and Russ,

 

Russ,

 

I have been reading a lot of CS Peirce who defines truth as what will in the long run be agreed upon if we keep doing science about the world, and “real’ as all that is true, as that upon which rational inquiry converges.  It’s a strange view, but it seems to have had a profound effect on the people who taught the people who taught us in graduate school.  Even though Peirce and rorty have both been called “pragmatists”, he is about as far from Rorty as you can get.  Peirce’s father was America;s first and foremost mathematical star, and Peirce took much of his inspiration from statistical mathematics of the time.  He would say things like, what is true about humans is what an insurance company can make money betting on, in the long run. 

 

Doug,

 

I didn’t MEAN to be clever.(Accused of being flippant AND clever in the same correspondence, and I don’t want to be either)  It was just such a wonderful example of how faith plays a role in drawing any conclusion from experience, that I wanted to underline it.   There is a great philosophical joke which philosophers use to make fun of psychologists:  there once was a drunk who fell off a ten story building.  And as it happened, there were psychologists with pencils and clipboards standing on each of the balconies to hear what he said as he went by.  It was, “So far, so good.”  Taleb’s Black Swan is another great example. 

 

The problem is how do we continue doing science given the problem of induction.  What I am liking about Peirce is that he charts a reasonable course between sophomoric skepticism (eg Rorty, Fish, etc.) and naïve empiricism.  He so values rational inquiry that he makes it the measure of all things, even meaning.

 

Thanks to  you both,

 

Nick

 

From: [hidden email] [mailto:[hidden email]] On Behalf Of Russ Abbott
Sent: Tuesday, March 27, 2012 4:27 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Just as a bye-the-way

 

Nice gloss of Goodman.  But it also suggests a problem with philosophy: the need to make demonstrably true statements. Induction in mathematics is a proof technique. When applied to reality it doesn't work because the axiom of induction isn't available for reality.  But then notion of a true statement as applied to reality is a bit of a stretch anyway. Yet philosophers keep insisting that it's important to make statements that can be shown to be true. But that's a cause lost before one even begins because there is no real connection between words and things -- only imagined connections.

 

-- Russ

 

On Tue, Mar 27, 2012 at 2:53 PM, Douglas Roberts <[hidden email]> wrote:

Very clever.

 

--Doug

 

On Tue, Mar 27, 2012 at 3:37 PM, Nicholas Thompson <[hidden email]> wrote:

Doug wrote

 

In retrospect, I suppose I do have faith in one other fairly immutable quality -- the accuracy of my bullshit detector

 

Well, why not.   it’s always worked in the past …. . 

 

Nick

 

From: [hidden email] [mailto:[hidden email]] On Behalf Of Douglas Roberts
Sent: Tuesday, March 27, 2012 2:55 PM

To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Just as a bye-the-way

 

Thanks, Nick, you describe an interesting way of establishing a life-view.

 

Not quite sure how to answer, except to say that if I have faith in anything, it is in evidence.  If I have accrued a sufficient pile of evidence that supports a conclusion about some observation, then I'll probably believe it.  

 

If my collected evidence is such that the inescapable conclusion is that nothing is constant, then I suppose I'd eventually come around to believe that, so long as I had a constant framework from which to corroborate and verify the inconsistencies.  Otherwise, I'd continue to look for the missing pieces of the puzzle (a reference to the cosmological artifacts I sent you earlier).

 

As to religion:  for me it's a big "No thank you" to any cult mindthink that requires brainless acceptance of a supernatural homo-centric benevolent/malevolent boogyman. And that goes double for one particular cult whose belief system is predicated upon "hieroglyph"-inscribed disappearing golden tablets.  Oh, and I guess that goes triple for any cult that attempts to dictate what kind of skivies I must wear to become a member of the club.  I guess you could say that it would take a miracle to get me to assent to becoming a member of any of the existing flocks of theist-following sheep out there.

 

In retrospect, I suppose I do have faith in one other fairly immutable quality -- the accuracy of my bullshit detector.

 

--Doug

 

On Tue, Mar 27, 2012 at 11:47 AM, Nicholas Thompson <[hidden email]> wrote:

Dear Doug,  

 

I am afraid that the black hole example is already too technologically dense for me, so I am going to punt on the project of luring you inside my walls and slaughtering you there, and just out-right tell you what I think

. 

The argument began with my detecting in you (perhaps wrongly) the belief that you, unlike the religious, can get along without some sort of faith in your life.  Most people I have known in the past who have reached this conclusion have done so through their confidence in induction. “What do I need with faith if I can just collect the evidence and act on it?’  And the answer is that without faith of some sort, there is no foundation for induction.

 

The argument for this position is famously from Hume.  A version of it is colorfully laid out by Nelson Goodman in his  The New Riddle of Induction.  So let’s say, I want to learn if grass is green.  My religious buddy says, “Look in the Bible.  I am sure it’s in there somewhere.’  My atheist buddy says, “nonsense, go out and look at the grass.”  I’m an atheist, so I go out and start collecting samples of grass.  I collect a hundred samples and I bring them back in announce that I am satisfied that all grass is green.  At which point my religious buddy says, No, No, you have no evidence there that Grass is green.  “All you have is evidence that grass is grue.” “Grue!?” I say.  “What’s Grue?”

 

Charitably forgoing  the opportunity to ask, “I dunno.  What’s Grue with you?” my religious buddy simply says, “It’s the property of being Green until your last measurement, and Blue thereafter. “

 

“Nonsense,”  I reply.  “What kind of a property is THAT?  Nature doesn’t HAVE properties like that. 

 

“Perhaps that’s been true”, he replies, but only up till now!”

 

In other words, our belief in induction is based on our plausible but unfounded belief in induction, i.e., faith. 

 

Nick

 

 

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of glen e. p. ropella
Sent: Monday, March 26, 2012 11:40 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Just as a bye-the-way

 

 

This is a red herring.  The argument for dark matter/energy need not be inductive.  The inductive form is:

 

o we've defined the set based on the laws of physics we've observed o everything is in this set o gravity seems stronger/weaker than predicted in some contexts

.: there are unobserved members of the set: dark matter and energy.

 

A non-inductive argument for dark matter/energy is just as valid:

 

o the model we've induced is not completely consistent with the data o the laws characterize everything we've encountered so far

.: there must be something we haven't encountered that will refine the laws.

 

No induction is necessary to motivate a hypothesis for some form of matter that's imprecisely or inaccurately described by the laws we've, so far, induced.  But parsimony suggests that a theory that assumes it's complete is more testable than a theory with metaphysical holes in it.

So, the argument for dark matter _seems_ inductive, even though it's not.  Only someone who assumes our laws are complete (fully refined) would think the argument is inductive.  My sample is small.  But I don't know of any physicists or cosmologists who think our laws cannot be modified.

 

I.e. it's naive to assume identity between a scientific theory and the reasoning surrounding the pursuit of a scientific theory.

 

 

Douglas Roberts wrote at 03/24/2012 03:08 PM:

> There's also an interesting "dark matter" inference that has found its

> way into grudging cosmological acceptance.  This time the role of the

> inferred substance is to keep galaxies from flying apart, as it has

> recently been observed that based on the amount of their measurable,

> observable mass and rotational velocities, they should flung their

> stars off ages ago.

>

> --Doug

>

>

> On Sat, Mar 24, 2012 at 3:16 PM, Douglas Roberts <[hidden email]

> <[hidden email]>> wrote:

>

>     I feel that I am being drawn in to an enemy encampment, but:

>

>     Developing a proof would be far better than choosing to rely

>     on inference, if the goal is to develop a larger-scale understanding

>     of a system.

>

>     Take "dark energy" as an example.  Its presence is inferred from

>     having observed that the rate of expansion of the observable

>     universe began to accelerate relatively recently, on a cosmological

>     time scale.  In response to this, the cosmologists have inferred the

>     existence of a mysterious energy with magical gravitational

>     repulsive properties as a means to explain away an otherwise

>     inexplicable observation.  A much more satisfying approach will be

>     to develop a sufficient understanding of the underlying physics of

>     our universe from which a rigorous proof of the phenomenon could be

>     derived.

>

>     But, without that understanding, we are left with cosmological

>     "magic dust", instead of a real understanding of the observed dynamics.

>

>     --Doug

 

 

--

glen e. p. ropella, <a href="tel:[phone]" target="_blank">971-222-9095, http://tempusdictum.com

 

 

============================================================

FRIAM Applied Complexity Group listserv

Meets Fridays 9a-11:30 at cafe at St. John's College

lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

 

--
Doug Roberts
[hidden email]
[hidden email]

http://parrot-farm.net/Second-Cousins

<a href="tel:[phone]" target="_blank">505-455-7333 - Office
<a href="tel:[phone]" target="_blank">505-670-8195 - Cell

 

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

 

--
Doug Roberts
[hidden email]
[hidden email]

http://parrot-farm.net/Second-Cousins

<a href="tel:[phone]" target="_blank">505-455-7333 - Office
<a href="tel:[phone]" target="_blank">505-670-8195 - Cell

 

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

 

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[Owen Densmore]

Could anyone summarize the recent several thread that originated with this one?

I'm sorry to have to ask, but we seem to have exploded upon an interesting stunt, but with the multiple threads (I Am The Thread Fascist) and the various twists and turns, I'd sorta like to know what's up!

   -- Owen

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[Robert J. Cordingley]

Nick
But what about all the work that uses truth values... for example and Probabilistic Logic Networks and Inference. When was truth ever black or white?  This article talks about strong and weak induction how does this fit?
Robert C
PS There's only one thing I know with 100.0'% certainty anyway. R



On 3/27/12 6:31 PM, Nicholas Thompson wrote:

Dear Doug and Russ,

 

Russ,

 

I have been reading a lot of CS Peirce who defines truth as what will in the long run be agreed upon if we keep doing science about the world, and “real’ as all that is true, as that upon which rational inquiry converges.  It’s a strange view, but it seems to have had a profound effect on the people who taught the people who taught us in graduate school.  Even though Peirce and rorty have both been called “pragmatists”, he is about as far from Rorty as you can get.  Peirce’s father was America;s first and foremost mathematical star, and Peirce took much of his inspiration from statistical mathematics of the time.  He would say things like, what is true about humans is what an insurance company can make money betting on, in the long run. 

 

Doug,

 

I didn’t MEAN to be clever.(Accused of being flippant AND clever in the same correspondence, and I don’t want to be either)  It was just such a wonderful example of how faith plays a role in drawing any conclusion from experience, that I wanted to underline it.   There is a great philosophical joke which philosophers use to make fun of psychologists:  there once was a drunk who fell off a ten story building.  And as it happened, there were psychologists with pencils and clipboards standing on each of the balconies to hear what he said as he went by.  It was, “So far, so good.”  Taleb’s Black Swan is another great example. 

 

The problem is how do we continue doing science given the problem of induction.  What I am liking about Peirce is that he charts a reasonable course between sophomoric skepticism (eg Rorty, Fish, etc.) and naïve empiricism.  He so values rational inquiry that he makes it the measure of all things, even meaning.

 

Thanks to  you both,

 

Nick

 

From: [hidden email] [[hidden email]] On Behalf Of Russ Abbott
Sent: Tuesday, March 27, 2012 4:27 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Just as a bye-the-way

 

Nice gloss of Goodman.  But it also suggests a problem with philosophy: the need to make demonstrably true statements. Induction in mathematics is a proof technique. When applied to reality it doesn't work because the axiom of induction isn't available for reality.  But then notion of a true statement as applied to reality is a bit of a stretch anyway. Yet philosophers keep insisting that it's important to make statements that can be shown to be true. But that's a cause lost before one even begins because there is no real connection between words and things -- only imagined connections.

 

-- Russ

 

On Tue, Mar 27, 2012 at 2:53 PM, Douglas Roberts <[hidden email]> wrote:

Very clever.

 

--Doug

 

On Tue, Mar 27, 2012 at 3:37 PM, Nicholas Thompson <[hidden email]> wrote:

Doug wrote

 

In retrospect, I suppose I do have faith in one other fairly immutable quality -- the accuracy of my bullshit detector

 

Well, why not.   it’s always worked in the past …. . 

 

Nick

 

From: [hidden email] [mailto:[hidden email]] On Behalf Of Douglas Roberts
Sent: Tuesday, March 27, 2012 2:55 PM

To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Just as a bye-the-way

 

Thanks, Nick, you describe an interesting way of establishing a life-view.

 

Not quite sure how to answer, except to say that if I have faith in anything, it is in evidence.  If I have accrued a sufficient pile of evidence that supports a conclusion about some observation, then I'll probably believe it.  

 

If my collected evidence is such that the inescapable conclusion is that nothing is constant, then I suppose I'd eventually come around to believe that, so long as I had a constant framework from which to corroborate and verify the inconsistencies.  Otherwise, I'd continue to look for the missing pieces of the puzzle (a reference to the cosmological artifacts I sent you earlier).

 

As to religion:  for me it's a big "No thank you" to any cult mindthink that requires brainless acceptance of a supernatural homo-centric benevolent/malevolent boogyman. And that goes double for one particular cult whose belief system is predicated upon "hieroglyph"-inscribed disappearing golden tablets.  Oh, and I guess that goes triple for any cult that attempts to dictate what kind of skivies I must wear to become a member of the club.  I guess you could say that it would take a miracle to get me to assent to becoming a member of any of the existing flocks of theist-following sheep out there.

 

In retrospect, I suppose I do have faith in one other fairly immutable quality -- the accuracy of my bullshit detector.

 

--Doug

 

On Tue, Mar 27, 2012 at 11:47 AM, Nicholas Thompson <[hidden email]> wrote:

Dear Doug,  

 

I am afraid that the black hole example is already too technologically dense for me, so I am going to punt on the project of luring you inside my walls and slaughtering you there, and just out-right tell you what I think

. 

The argument began with my detecting in you (perhaps wrongly) the belief that you, unlike the religious, can get along without some sort of faith in your life.  Most people I have known in the past who have reached this conclusion have done so through their confidence in induction. “What do I need with faith if I can just collect the evidence and act on it?’  And the answer is that without faith of some sort, there is no foundation for induction.

 

The argument for this position is famously from Hume.  A version of it is colorfully laid out by Nelson Goodman in his  The New Riddle of Induction.  So let’s say, I want to learn if grass is green.  My religious buddy says, “Look in the Bible.  I am sure it’s in there somewhere.’  My atheist buddy says, “nonsense, go out and look at the grass.”  I’m an atheist, so I go out and start collecting samples of grass.  I collect a hundred samples and I bring them back in announce that I am satisfied that all grass is green.  At which point my religious buddy says, No, No, you have no evidence there that Grass is green.  “All you have is evidence that grass is grue.” “Grue!?” I say.  “What’s Grue?”

 

Charitably forgoing  the opportunity to ask, “I dunno.  What’s Grue with you?” my religious buddy simply says, “It’s the property of being Green until your last measurement, and Blue thereafter. “

 

“Nonsense,”  I reply.  “What kind of a property is THAT?  Nature doesn’t HAVE properties like that. 

 

“Perhaps that’s been true”, he replies, but only up till now!”

 

In other words, our belief in induction is based on our plausible but unfounded belief in induction, i.e., faith. 

 

Nick

 

 

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of glen e. p. ropella
Sent: Monday, March 26, 2012 11:40 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Just as a bye-the-way

 

 

This is a red herring.  The argument for dark matter/energy need not be inductive.  The inductive form is:

 

o we've defined the set based on the laws of physics we've observed o everything is in this set o gravity seems stronger/weaker than predicted in some contexts

.: there are unobserved members of the set: dark matter and energy.

 

A non-inductive argument for dark matter/energy is just as valid:

 

o the model we've induced is not completely consistent with the data o the laws characterize everything we've encountered so far

.: there must be something we haven't encountered that will refine the laws.

 

No induction is necessary to motivate a hypothesis for some form of matter that's imprecisely or inaccurately described by the laws we've, so far, induced.  But parsimony suggests that a theory that assumes it's complete is more testable than a theory with metaphysical holes in it.

So, the argument for dark matter _seems_ inductive, even though it's not.  Only someone who assumes our laws are complete (fully refined) would think the argument is inductive.  My sample is small.  But I don't know of any physicists or cosmologists who think our laws cannot be modified.

 

I.e. it's naive to assume identity between a scientific theory and the reasoning surrounding the pursuit of a scientific theory.

 

 

Douglas Roberts wrote at 03/24/2012 03:08 PM:

> There's also an interesting "dark matter" inference that has found its

> way into grudging cosmological acceptance.  This time the role of the

> inferred substance is to keep galaxies from flying apart, as it has

> recently been observed that based on the amount of their measurable,

> observable mass and rotational velocities, they should flung their

> stars off ages ago.

>

> --Doug

>

>

> On Sat, Mar 24, 2012 at 3:16 PM, Douglas Roberts <[hidden email]

> <[hidden email]>> wrote:

>

>     I feel that I am being drawn in to an enemy encampment, but:

>

>     Developing a proof would be far better than choosing to rely

>     on inference, if the goal is to develop a larger-scale understanding

>     of a system.

>

>     Take "dark energy" as an example.  Its presence is inferred from

>     having observed that the rate of expansion of the observable

>     universe began to accelerate relatively recently, on a cosmological

>     time scale.  In response to this, the cosmologists have inferred the

>     existence of a mysterious energy with magical gravitational

>     repulsive properties as a means to explain away an otherwise

>     inexplicable observation.  A much more satisfying approach will be

>     to develop a sufficient understanding of the underlying physics of

>     our universe from which a rigorous proof of the phenomenon could be

>     derived.

>

>     But, without that understanding, we are left with cosmological

>     "magic dust", instead of a real understanding of the observed dynamics.

>

>     --Doug

 

 

--

glen e. p. ropella, <a moz-do-not-send="true" href="tel:[phone]" target="_blank">971-222-9095, http://tempusdictum.com

 

 

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--
Doug Roberts
[hidden email]
[hidden email]

http://parrot-farm.net/Second-Cousins

<a moz-do-not-send="true" href="tel:[phone]" target="_blank">505-455-7333 - Office
<a moz-do-not-send="true" href="tel:[phone]" target="_blank">505-670-8195 - Cell

 

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--
Doug Roberts
[hidden email]
[hidden email]

http://parrot-farm.net/Second-Cousins

<a moz-do-not-send="true" href="tel:[phone]" target="_blank">505-455-7333 - Office
<a moz-do-not-send="true" href="tel:[phone]" target="_blank">505-670-8195 - Cell

 

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[Robert Holmes]

I like C D Broad's take on this: "Induction is the glory of science and the scandal of philosophy." (1926, The Philosophy of Francis Bacon).

I think there's a lot of truth in this... induction is simply not a problem for science and scientists. Scientists have used induction to give the most amazing, useful awe-inspiring descriptions of the universe and its contents. Sure, philosophers can hop around shouting "You can't do that! It's not possible!" but you know what? We just did.

—R

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[Eric Charles]

Owen,
As I understand it:
Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience.... but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction.

The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century.

These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form "Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth?"

Hope that helps,

Eric

 

On Tue, Mar 27, 2012 10:05 PM, Owen Densmore <[hidden email]> wrote:

Could anyone summarize the recent several thread that originated with this one?

I'm sorry to have to ask, but we seem to have exploded upon an interesting stunt, but with the multiple threads (I Am The Thread Fascist) and the various twists and turns, I'd sorta like to know what's up!

   -- Owen

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Eric Charles

Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601

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[Russ Abbott]

The inductive argument for induction [paraphrased from Eric]: The fact that induction has been so successful in the past should convince of its usefulness in the future. 

 

-- Russ Abbott
_____________________________________________

  Professor, Computer Science
  California State University, Los Angeles

  Google voice: 747-999-5105

  Google+: https://plus.google.com/114865618166480775623/

  vita:  http://sites.google.com/site/russabbott/
_____________________________________________ 

On Tue, Mar 27, 2012 at 9:49 PM, ERIC P. CHARLES <[hidden email]> wrote:

Owen,
As I understand it:
Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience.... but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction.

The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century.

These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form "Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth?"

Hope that helps,

Eric

 

On Tue, Mar 27, 2012 10:05 PM, Owen Densmore <[hidden email]> wrote:

Could anyone summarize the recent several thread that originated with this one?

I'm sorry to have to ask, but we seem to have exploded upon an interesting stunt, but with the multiple threads (I Am The Thread Fascist) and the various twists and turns, I'd sorta like to know what's up!

   -- Owen

============================================================
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Eric Charles

Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601

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[Nick Thompson]

Owen,

 

Eric is basically correct, although I think he may have misread the order of things (which is easy to do given that one HAS to read threads backwards.  My caving in and just stating my position came very late in the game and was a response in part to all the confusion created by my laconic (and perhaps devious) attempts to draw Doug out.  So far as I have read,all  the responses to my statement have been thoughtful and sensible and not confused at all.

 

… Oh OWEN IS there a software that will turn a thread into a manageable text for editing. I need that so bad.    If I had such, I would have made you all my collaborators by now and we should have published hundreds of articles.  Generated thousands of offspring from what has become, for want of a way of collecting it, spilled seed.   We would be rich and famous. 

 

Nick

 

From: [hidden email] [mailto:[hidden email]] On Behalf Of ERIC P. CHARLES
Sent: Tuesday, March 27, 2012 10:50 PM
To: Owen Densmore
Cc: The Friday Morning Applied Complexity Coffee Group
Subject: [FRIAM] Clarifying Induction Threads

 

Owen,
As I understand it:
Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience.... but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction.

The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century.

These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form "Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth?"

Hope that helps,

Eric

 

On Tue, Mar 27, 2012 10:05 PM, Owen Densmore <[hidden email]> wrote:

Could anyone summarize the recent several thread that originated with this one?

 

I'm sorry to have to ask, but we seem to have exploded upon an interesting stunt, but with the multiple threads (I Am The Thread Fascist) and the various twists and turns, I'd sorta like to know what's up!

 

   -- Owen

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Eric Charles

Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601

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[Nick Thompson]

Ok.  So now it’s probably time for me to admit that as Faith goes, belief in induction is pretty weak tea. 

 

Certainly doesn’t compare with the belief that ritual can change wine in to blood.

 

Now, I think it’s easy to show that even catholics don’t believe it, using the pragmatic  maxim that any thought is not a belief unless it can be shown to guide behavior.   

 

Let us say that christ’s body is exhumed and that its perfectly preserved.  The priest comes to you with a cup  and a plate and says “thisis the blood and body.  Etc.”  I think your response, catholic or not, would be OH YUCH!

 

The logic goes

 

Catholics will consume what they think is the blood and body of Christ

This is the blood and body of Christ

This catholic did not consume it. 

 

TILT!

 

My apologies to any catholics on the list .  this is one of the examples in Peirce’s work and it is much on my mind at the moment.  I hope I have represented the facts of the ritiual more or less correctly and not been …. Um …too flippant or clever.  I am pretty tired and it is pretty late.

 

Nick

 

From: [hidden email] [mailto:[hidden email]] On Behalf Of Russ Abbott
Sent: Tuesday, March 27, 2012 11:03 PM
To: The Friday Morning Applied Complexity Coffee Group
Cc: Owen Densmore
Subject: Re: [FRIAM] Clarifying Induction Threads

 

The inductive argument for induction [paraphrased from Eric]: The fact that induction has been so successful in the past should convince of its usefulness in the future. 

 

-- Russ Abbott
_____________________________________________

  Professor, Computer Science
  California State University, Los Angeles

  Google voice: 747-999-5105

  Google+: https://plus.google.com/114865618166480775623/

  vita:  http://sites.google.com/site/russabbott/
_____________________________________________ 

On Tue, Mar 27, 2012 at 9:49 PM, ERIC P. CHARLES <[hidden email]> wrote:

Owen,
As I understand it:
Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience.... but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction.

The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century.

These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form "Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth?"

Hope that helps,

Eric

 

On Tue, Mar 27, 2012 10:05 PM, Owen Densmore <[hidden email]> wrote:

Could anyone summarize the recent several thread that originated with this one?

 

I'm sorry to have to ask, but we seem to have exploded upon an interesting stunt, but with the multiple threads (I Am The Thread Fascist) and the various twists and turns, I'd sorta like to know what's up!

 

   -- Owen

============================================================

FRIAM Applied Complexity Group listserv

Meets Fridays 9a-11:30 at cafe at St. John's College

lectures, archives, unsubscribe, maps at http://www.friam.org

Eric Charles

Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601

============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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[Owen Densmore]

Sorry for the late response, Russ, but thank you for your sanity.  In these days of despising The Other, good manners are much appreciated.

A Jesuit wrote a book about interviews he had with silicon valley engineers/scientists about religion and their attitudes towards it. (Talk about the lion's den!)  In it he talks about The Litany.  Not one used in a mass, but the flood of "I can't believe you believe/did XX".  

He learned to stay quiet for the several minutes it took for the flood to abate. (As the Vatican Astronomer, he's used to it, 1/2 the year in Flagstaff, the other just south of Rome where pretty good small body astronomy is done)

Then at the end, very gently, he had to explain: I really don't care about these things, I only care about what I can control/be and do that the best I can.

It was the most liberating realization of its kind for me because it was true for me as well.

So thanks again!

   -- Owen

On Thu, Mar 22, 2012 at 11:31 PM, Russ Abbott <[hidden email]> wrote:

Doug, I don't want to pick on you, but your certificate strikes me as indirect bullying.  

I'm as atheistic as they come, but I know a number of people who (for reasons that I don't understand) take religion quite seriously.  They are intelligent, pleasant people, not the sort to rub their beliefs in anyone's face. Most are politically left of center. One has a bumper sticker that reads "A proud member of the religious left".

Why pick on them? I'm sure you don't intend to. I'm sure you are making fun of the Rick Santorums of the world. It's just that by casting as wide a net as the Flying Spaghetti Monster does, it also makes fun of everyone with religious feelings. 

The answer someone like Sam Harris would give is that what they say is either false or without any shred of objective support. But the people I'm thinking of don't go around proclaiming their beliefs as The Truth. They go about their business simply wanting to experience the world through a different lens. The fact that I don't understand it -- and I don't; I'm completely mystified by their way of thinking about certain things -- doesn't give me the right to ridicule it.

Sorry for the rant.

 

-- Russ

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[Owen Densmore]

Wow, Eric, thanks!  Lovely gift this beautiful morning.

And Nick, AFAIK, there is no such ThreadMagic software.  But lets have a coffee over it.  And in terms of the body and blood of Christ, that takes a bit and too can be done over coffee.  But it basically has to do with The Wisdom of Metaphor and its place in both evolution of theology and religious belief.

All: Did no one discuss the mathematics of induction .. the inductive proof?  Certainly that is accepted by us all, even tho anyone can make a sequence of a set of N numbers, who's generator can provide any number for its N+1th number.  It is in the fact that the induction works by proving the N=1 case, assuming the Nth and proving the N+1th from that.

   -- Owen

On Wed, Mar 28, 2012 at 12:51 AM, Nicholas Thompson <[hidden email]> wrote:

Ok.  So now it’s probably time for me to admit that as Faith goes, belief in induction is pretty weak tea. 

 

Certainly doesn’t compare with the belief that ritual can change wine in to blood.

 

Now, I think it’s easy to show that even catholics don’t believe it, using the pragmatic  maxim that any thought is not a belief unless it can be shown to guide behavior.   

 

Let us say that christ’s body is exhumed and that its perfectly preserved.  The priest comes to you with a cup  and a plate and says “thisis the blood and body.  Etc.”  I think your response, catholic or not, would be OH YUCH!

 

The logic goes

 

Catholics will consume what they think is the blood and body of Christ

This is the blood and body of Christ

This catholic did not consume it. 

 

TILT!

 

My apologies to any catholics on the list .  this is one of the examples in Peirce’s work and it is much on my mind at the moment.  I hope I have represented the facts of the ritiual more or less correctly and not been …. Um …too flippant or clever.  I am pretty tired and it is pretty late.

 

Nick

 

From: [hidden email] [mailto:[hidden email]] On Behalf Of Russ Abbott
Sent: Tuesday, March 27, 2012 11:03 PM
To: The Friday Morning Applied Complexity Coffee Group
Cc: Owen Densmore
Subject: Re: [FRIAM] Clarifying Induction Threads

 

The inductive argument for induction [paraphrased from Eric]: The fact that induction has been so successful in the past should convince of its usefulness in the future. 

 

-- Russ Abbott
_____________________________________________

  Professor, Computer Science
  California State University, Los Angeles

  Google voice: <a href="tel:[phone]" value="[phone]" target="_blank">747-999-5105

  Google+: https://plus.google.com/114865618166480775623/

  vita:  http://sites.google.com/site/russabbott/
_____________________________________________ 

On Tue, Mar 27, 2012 at 9:49 PM, ERIC P. CHARLES <[hidden email]> wrote:

Owen,
As I understand it:
Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience.... but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction.

The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century.

These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form "Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth?"

Hope that helps,

Eric

 

On Tue, Mar 27, 2012 10:05 PM, Owen Densmore <[hidden email]> wrote:

Could anyone summarize the recent several thread that originated with this one?

 

I'm sorry to have to ask, but we seem to have exploded upon an interesting stunt, but with the multiple threads (I Am The Thread Fascist) and the various twists and turns, I'd sorta like to know what's up!

 

   -- Owen

============================================================

FRIAM Applied Complexity Group listserv

Meets Fridays 9a-11:30 at cafe at St. John's College

lectures, archives, unsubscribe, maps at http://www.friam.org

Eric Charles

Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

 

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FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

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[glen ep ropella]

Owen Densmore wrote at 03/28/2012 08:20 AM:
> All: Did no one discuss the mathematics of induction .. the inductive
> proof?  Certainly that is accepted by us all, even tho anyone can make a
> sequence of a set of N numbers, who's generator can provide any number
> for its N+1th number.  It is in the fact that the induction works by
> proving the N=1 case, assuming the Nth and proving the N+1th from that.

Yep.  Doug listed it as one of the types.  Personally, I don't regard it
as categorically exceptional.  It's defining a a predicate and then
establishing whether or not new instances belong to the set or not.  I
suppose I think there are 3 categories: 1) predicative (well-founded),
2) impredicative (non-well-founded), and 3) psychological induction
(what most of this conversation is about).

--
glen e. p. ropella, 971-222-9095, http://tempusdictum.com


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[Nick Thompson]

Glen,

I am out of my depth here, but ...

I don't think we've been talking about psychological induction, here but
logical induction.  And I think mathematical induction is actually a species
of Deduction.  I am in a  rush now, but I am putting in this marker in the
hope that others will help out.

Nick

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf
Of glen e. p. ropella
Sent: Wednesday, March 28, 2012 9:53 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Clarifying Induction Threads

Owen Densmore wrote at 03/28/2012 08:20 AM:
> All: Did no one discuss the mathematics of induction .. the inductive
> proof?  Certainly that is accepted by us all, even tho anyone can make
> a sequence of a set of N numbers, who's generator can provide any
> number for its N+1th number.  It is in the fact that the induction
> works by proving the N=1 case, assuming the Nth and proving the N+1th from
that.

Yep.  Doug listed it as one of the types.  Personally, I don't regard it as
categorically exceptional.  It's defining a a predicate and then
establishing whether or not new instances belong to the set or not.  I
suppose I think there are 3 categories: 1) predicative (well-founded),
2) impredicative (non-well-founded), and 3) psychological induction (what
most of this conversation is about).

--
glen e. p. ropella, 971-222-9095, http://tempusdictum.com


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Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org


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[glen ep ropella]

Nicholas Thompson wrote at 03/28/2012 09:38 AM:
> I don't think we've been talking about psychological induction, here but
> logical induction.  And I think mathematical induction is actually a species
> of Deduction.  I am in a  rush now, but I am putting in this marker in the
> hope that others will help out.

I disagree.  I think we've ranged over all sorts of meanings for the
word "induction" ... because we're speaking English. ;-)  I tried to
make my perspective clear when I challenged the law of the excluded
middle ... or by extension this false assumption of _crisp_ sets that
underlies your example of grass being green.  (RussA gives the same
criticism from a different angle.)  It's just a plainly flawed argument
because the set we refer to as "grass" is not crisp.  There are plants
that are a little bit like grass and a little bit not like grass.  And
just because grass is dead doesn't mean it's no longer grass.  And I
know a few people whose _hair_ looks like grass!  Etc.  The same is true
of the set we refer to as "green things".  Ideological arguments like
that fail miserably when we disambiguate and wander into math and logic.

Anyway, compare and contrast that sort of rhetoric with a predicative
definition of a set (like that of the Natural Numbers).  That set is crisp.

We are still talking about sets and set membership.  And we're still
talking about the ability to define a set based on "previous"
(predecessor) observations and then establish the membership of a newly
constructed object.  That's why mathematical induction is a form of
induction.  Reasoning methods are not entirely disjoint.  Any
non-trivial act of reasoning requires all 3 forms.  Hence, it's
reasonable and pragmatic to think that induction and deduction aren't
crisp sets either.

--
glen e. p. ropella, 971-222-9095, http://tempusdictum.com


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[David Eric Smith]

I agree, Wow, to Eric Charles's summary.

Can I ask, is there any role for finiteness in this discussion?  There seem to me to be two places the constraints of being finite enter, and the specific point at which they seem forced by one of the questions that has been asked (Why would you accept the inductive hypothesis, except on faith?)  is to offer the alternative answer (Because I am incapable of doing otherwise).  The latter answer seems more operational than invoking the word "faith", which for all I know may not mean anything more than "I am incapable of doing otherwise because I am finite", or the circularity that the inductive hypothesis is the only premise from which to defend its own use.  

Here is one argument for finiteness, which I have pestered Nick with in conversations long ago.

Suppose I am an input-output machine with a finite number of outputs (and for that matter, of internal states).  (I intend here to be in the general domain of Ross Ashby's notions of "requisite variation", but let me not get off on that.)  If a philosopher objects that I have no _right_ to be finite, and that, like Paris Hilton, I must "from now on, promise to pay complete attention to everything", then don't consider me, consider a single type of cell-surface receptor on any of my cells.  Surely, for practical purposes, we want to model it as having a finite repertoire of behaviors, whether it has a right to or not.  It's only a protein.

But a finite thing, in an indefinitely variable world, must then produce at least one of its outputs as the response to an indefinite set of distinct circumstances.  (Here, I would be happy to say "infinite", but I mean "indefinite" as that which "might grow toward infinity if we could keep accumulating cases".)  In practice, of course, for most cases I could think of, _each_ of the output states occurs as a response to indefinitely many distinct circumstances.  Thus, my input-output box partitions an indefinite environment into equivalence classes, at least one, and probably many of them, of indefinitely large size.  It cannot do otherwise, being finite.

But my cell-surface receptor has been (naturally-)selected from a finite history of events.  Again, a practical man, being honest about noise and the erasure of memory, about costs, etc., would say that it has probably been selected by a rather short recent history from a rather narrow set of cases.  Thus, the response it will generate, for an indefinite range of circumstances, has been chosen from a finite set of selection criteria.  It appears that survival-under-selection of finite objects, then, is perforce a commitment to one form of induction.   The generation, by the device for however long it survives, of a potentially-indefinitely-large set of input-output pairs is being conditioned on a finite set of input-output pairs.

Of course, natural selection is just Bayes's theorem for model selection, with the fitness being the log-likelihood, and selection on spaces with a finite number of types is then Bayesian induction on probability distributions over a finite number of tokens.  I think (?) we believe in statistics that Bayesian updating is the best general-purpose method we can formalize (Cosma Shalizi, sometimes solo and sometimes with Andrew Gelman, has written on this).  So either in thinking or in science, can we claim to be capable of any better actual, implementable mechanism than an algorithm that (if I am not wrong in the last par) instantiates the inductive hypothesis?  If we can't be capable of anything better, than what is the nature of an objection against such algorithms, besides reminders that they are finite in an infinite world (which, being unable to fathom an infinite world, we may tend to forget)?  

The second argument for caring about finiteness is related.  I am still a finite input-output machine.

I have a choice.  I can either suppose that a future event will be the same as -- or structurally close to, in some way I can operationalize -- one of my past-experienced events under suitably-identified conditions, or I can suppose it will "not be".  My past is finite.  The number of its histories that I can actually distinguish may be (for me, _is_) even smaller.  Let's suppose that the set of all non-comparable futures to anything I have experienced and can distinguish and remember is, again, indefinitely large.

If I suppose the future will repeat the past, and I am in a circumstance where that is true, since the past has finitely-many tokens, then I have non-zero probability to guess the right future.  If I am not in that circumstance, then I am sure to be wrong.  If I suppose the future will _not_ resemble the past -- and, CRUCIAL POINT HERE , if I am at all honest -- then I must make my bets over an indefinite set of futures with non-singular measure, meaning I have measure zero on everything.  Whether or not my environment will repeat its past, my chances of being right are zero either way.  Again, among my options, where do I find an argument against choosing induction from the past?  That is, fine, we recognize the logical limits of induction, but do we have any argument that any specific alternative could be supported in any better way, or by any better premises?

Of course, this sounds like Pascal's wager, and the structure of the argument is similar, but its topic is not similar, because the premises for which one is arguing in the two cases are not comparable.  A punishing God, whom one doesn't want to cross -- whether one believes He is a an emotional imprint of punishing parents, punishing spouses, punishing colleagues, any of whom may hold grudges forever in response to any act of disobedience, or one believes that the universe and existence are a subset of human social-psychology (rather than the other way around) -- is still a particular and arbitrary premise.  The previous paragraph was about search and methodology.  Search in finite spaces, which may be feasible, versus search infinite spaces, which is almost-surely infeasible, addresses a specific problem with which we are already specifically stuck, and which it is not ours to arbitrarily choose to escape from.

So the rhetorical argument about the religious person who claims that the grass-is-green induction is an expression of the same flavor of faith as his support of a cultural dogma, seems to me methodologically unclear in a way that usually gets used disingenuously.  If we admit that we are all finite, then the only remaining question is which templates we are inductively generalizing _from_, in a particular situation.  If you want to generalize from human-social emotion in discussions about plate tectonics, dark matter, dark energy, or whatever (I have relatives who do), then that is your option out of finitely many.  If instead you want to narrow the arbitrariness and try to bundle the constraints that give the polynomial expansion for gravitational action functionals (and then just try to identify parameters), or to do the more complicated version of that for planet formation, then at least we can say by Occam's razor that you have made a smaller search space that overlaps with a larger set of more-apparently similar evidence.  


I realize that my email here seems (and presumably is) stupid, since every child knows there can be no discussion of induction that is not predicated on the availability of infinities.  But, since I am finite, I have tended to think that the point of these abstractions is to extract salient features of a class of (actual, realizable) problems which may not fulfill the abstraction, but for which the abstraction can serve as the appropriate index of a class of problems that can be extended in a particular direction.  So, in looking at these "grass-is-grue" arguments, or at almost anything Rorty writes when he wants to be a gadfly against someone who is getting something useful done (notably, I do not extend this criticism to his constructive comments about desirable societies), and in trying to figure out where there is a productive discussion about scientific methods or claims, it is hard for me to feel other than confused unless I look at the specific role that finiteness has played in creating the structure of any of the specific propositions being discussed.


There are, of course, other classes of propositions where one could well argue against induction, but again, it would be for reasons that can be made operational and thus comprehensible.  Economists would dislike David Wolpert's no-free-lunch theorems if they felt them worth reading, since David samples over complete sets of combinatorial search and optimization problems, and shows that any expectation that can be satisfied by some cases in such spaces, must be violated on an equal measure of cases.  The economists (the particular ones I know) don't want to pursue this, because the discipline wants preferred solution concepts, preferred equilibria, etc.  But of course, if we were talking about the design of regulatory systems, in which any set of published rules becomes a target for gaming, by those who wish to set up an expectation and violate it, then the need to guard against anti-induction solutions becomes large.  All this, though, I can do on finite spaces, and compare the severity of simplified inferences to the size of the violation set, and then look at limits under scaling of the number of cases.


Also, if I had read Pierce, I expect I would have found that he shows in the first few pages that arguments of this type are trivial and don't address anything.  In another life...

Eric

> Owen,
> As I understand it:
> Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience.... but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction.
>
> The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century.
>
> These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form "Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth?"
>
> Hope that helps,
>
> Eric
>
>

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[glen ep ropella]

That's an awesome essay!  Thanks.

Of course, I never say anything unless I have something to disagree
with... So, I have 2 points to argue about:

1) Your finiteness is illusory because you assume crisp sets, and
2) The problem of induction is about the origins of a conjecture, not
merely about the evaluation of candidate set members.

I've beaten (1) quite to death.  So, I'll just try to lay out (2).
Alternatives for the origins of conjecture abound.  Not all conjecture
is based on previous experience.  Or, at least, we can conjecture that
not all conjecture is based on previous experience, if we believe in
illusion, hallucination, and that ideas are more plastic than things.  I
don't intend to dicker about the meanings of words like "based".  But
there is a difference between, say, a griffin and a unicorn.  The
griffin is more fantastic than the unicorn.  It's pretty easy for me to
imagine all horses are unicorns who have lost their horns.  But it would
be difficult to think that lions are griffins with mutated heads and no
wings.

Conjecture can come from _anywhere_ ... from dreams, fevers, and sci-fi
novels.  They need not be based on previous experiences in the
(rigorous?) way we tend to think of them being based on previous
experiences.

In that sense, the finite nature of our past experiences is fuzzified
... not so finite after all.  I can read Heinlein or Vern and form a
conjecture based on a fuzzy mix of those "experiences".  From this
"alphabet" of ideas, I can generate an infinite (or at least indefinite)
number of words and sentences.

This seems to provide plenty of origins for alternative conjecture
beyond induction.


Eric Smith wrote at 03/28/2012 12:02 PM:

> I agree, Wow, to Eric Charles's summary.
>
> Can I ask, is there any role for finiteness in this discussion?
> There seem to me to be two places the constraints of being finite
> enter, and the specific point at which they seem forced by one of the
> questions that has been asked (Why would you accept the inductive
> hypothesis, except on faith?)  is to offer the alternative answer
> (Because I am incapable of doing otherwise).  The latter answer seems
> more operational than invoking the word "faith", which for all I know
> may not mean anything more than "I am incapable of doing otherwise
> because I am finite", or the circularity that the inductive
> hypothesis is the only premise from which to defend its own use.
>
> Here is one argument for finiteness, which I have pestered Nick with
> in conversations long ago.
>
> Suppose I am an input-output machine with a finite number of outputs
> (and for that matter, of internal states).  (I intend here to be in
> the general domain of Ross Ashby's notions of "requisite variation",
> but let me not get off on that.)  If a philosopher objects that I
> have no _right_ to be finite, and that, like Paris Hilton, I must
> "from now on, promise to pay complete attention to everything", then
> don't consider me, consider a single type of cell-surface receptor on
> any of my cells.  Surely, for practical purposes, we want to model it
> as having a finite repertoire of behaviors, whether it has a right to
> or not.  It's only a protein.
>
> But a finite thing, in an indefinitely variable world, must then
> produce at least one of its outputs as the response to an indefinite
> set of distinct circumstances.  (Here, I would be happy to say
> "infinite", but I mean "indefinite" as that which "might grow toward
> infinity if we could keep accumulating cases".)  In practice, of
> course, for most cases I could think of, _each_ of the output states
> occurs as a response to indefinitely many distinct circumstances.
> Thus, my input-output box partitions an indefinite environment into
> equivalence classes, at least one, and probably many of them, of
> indefinitely large size.  It cannot do otherwise, being finite.
>
> But my cell-surface receptor has been (naturally-)selected from a
> finite history of events.  Again, a practical man, being honest about
> noise and the erasure of memory, about costs, etc., would say that it
> has probably been selected by a rather short recent history from a
> rather narrow set of cases.  Thus, the response it will generate, for
> an indefinite range of circumstances, has been chosen from a finite
> set of selection criteria.  It appears that survival-under-selection
> of finite objects, then, is perforce a commitment to one form of
> induction.   The generation, by the device for however long it
> survives, of a potentially-indefinitely-large set of input-output
> pairs is being conditioned on a finite set of input-output pairs.
>
> Of course, natural selection is just Bayes's theorem for model
> selection, with the fitness being the log-likelihood, and selection
> on spaces with a finite number of types is then Bayesian induction on
> probability distributions over a finite number of tokens.  I think
> (?) we believe in statistics that Bayesian updating is the best
> general-purpose method we can formalize (Cosma Shalizi, sometimes
> solo and sometimes with Andrew Gelman, has written on this).  So
> either in thinking or in science, can we claim to be capable of any
> better actual, implementable mechanism than an algorithm that (if I
> am not wrong in the last par) instantiates the inductive hypothesis?
> If we can't be capable of anything better, than what is the nature of
> an objection against such algorithms, besides reminders that they are
> finite in an infinite world (which, being unable to fathom an
> infinite world, we may tend to forget)?
>
> The second argument for caring about finiteness is related.  I am
> still a finite input-output machine.
>
> I have a choice.  I can either suppose that a future event will be
> the same as -- or structurally close to, in some way I can
> operationalize -- one of my past-experienced events under
> suitably-identified conditions, or I can suppose it will "not be".
> My past is finite.  The number of its histories that I can actually
> distinguish may be (for me, _is_) even smaller.  Let's suppose that
> the set of all non-comparable futures to anything I have experienced
> and can distinguish and remember is, again, indefinitely large.
>
> If I suppose the future will repeat the past, and I am in a
> circumstance where that is true, since the past has finitely-many
> tokens, then I have non-zero probability to guess the right future.
> If I am not in that circumstance, then I am sure to be wrong.  If I
> suppose the future will _not_ resemble the past -- and, CRUCIAL POINT
> HERE , if I am at all honest -- then I must make my bets over an
> indefinite set of futures with non-singular measure, meaning I have
> measure zero on everything.  Whether or not my environment will
> repeat its past, my chances of being right are zero either way.
> Again, among my options, where do I find an argument against choosing
> induction from the past?  That is, fine, we recognize the logical
> limits of induction, but do we have any argument that any specific
> alternative could be supported in any better way, or by any better
> premises?
>
> Of course, this sounds like Pascal's wager, and the structure of the
> argument is similar, but its topic is not similar, because the
> premises for which one is arguing in the two cases are not
> comparable.  A punishing God, whom one doesn't want to cross --
> whether one believes He is a an emotional imprint of punishing
> parents, punishing spouses, punishing colleagues, any of whom may
> hold grudges forever in response to any act of disobedience, or one
> believes that the universe and existence are a subset of human
> social-psychology (rather than the other way around) -- is still a
> particular and arbitrary premise.  The previous paragraph was about
> search and methodology.  Search in finite spaces, which may be
> feasible, versus search infinite spaces, which is almost-surely
> infeasible, addresses a specific problem with which we are already
> specifically stuck, and which it is not ours to arbitrarily choose to
> escape from.
>
> So the rhetorical argument about the religious person who claims that
> the grass-is-green induction is an expression of the same flavor of
> faith as his support of a cultural dogma, seems to me
> methodologically unclear in a way that usually gets used
> disingenuously.  If we admit that we are all finite, then the only
> remaining question is which templates we are inductively generalizing
> _from_, in a particular situation.  If you want to generalize from
> human-social emotion in discussions about plate tectonics, dark
> matter, dark energy, or whatever (I have relatives who do), then that
> is your option out of finitely many.  If instead you want to narrow
> the arbitrariness and try to bundle the constraints that give the
> polynomial expansion for gravitational action functionals (and then
> just try to identify parameters), or to do the more complicated
> version of that for planet formation, then at least we can say by
> Occam's razor that you have made a smaller search space that overlaps
> with a larger set of more-apparently similar evidence.
>
>
> I realize that my email here seems (and presumably is) stupid, since
> every child knows there can be no discussion of induction that is not
> predicated on the availability of infinities.  But, since I am
> finite, I have tended to think that the point of these abstractions
> is to extract salient features of a class of (actual, realizable)
> problems which may not fulfill the abstraction, but for which the
> abstraction can serve as the appropriate index of a class of problems
> that can be extended in a particular direction.  So, in looking at
> these "grass-is-grue" arguments, or at almost anything Rorty writes
> when he wants to be a gadfly against someone who is getting something
> useful done (notably, I do not extend this criticism to his
> constructive comments about desirable societies), and in trying to
> figure out where there is a productive discussion about scientific
> methods or claims, it is hard for me to feel other than confused
> unless I look at the specific role that finiteness has played in
> creating the structure of any of the specific propositions being
> discussed.
>
>
> There are, of course, other classes of propositions where one could
> well argue against induction, but again, it would be for reasons that
> can be made operational and thus comprehensible.  Economists would
> dislike David Wolpert's no-free-lunch theorems if they felt them
> worth reading, since David samples over complete sets of
> combinatorial search and optimization problems, and shows that any
> expectation that can be satisfied by some cases in such spaces, must
> be violated on an equal measure of cases.  The economists (the
> particular ones I know) don't want to pursue this, because the
> discipline wants preferred solution concepts, preferred equilibria,
> etc.  But of course, if we were talking about the design of
> regulatory systems, in which any set of published rules becomes a
> target for gaming, by those who wish to set up an expectation and
> violate it, then the need to guard against anti-induction solutions
> becomes large.  All this, though, I can do on finite spaces, and
> compare the severity of simplified inferences to the size of the
> violation set, and then look at limits under scaling of the number of
> cases.
>
>
> Also, if I had read Pierce, I expect I would have found that he shows
> in the first few pages that arguments of this type are trivial and
> don't address anything.  In another life...

--
glen e. p. ropella, 971-222-9095, http://tempusdictum.com


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[lrudolph]

Eric Smith:  

> every child knows there can be no discussion of induction that is not
> predicated on the availability of infinities.

Not so (independent of what every child knows)!  I have to rush off
but will try to get back to this later.

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[David Eric Smith]

Thank you Lee and Glen both,

Yes, I could not disagree.  

There is an interesting question, Glen, on which I don't have a dog in the fight either way.  Is the worry about induction only (or even mostly) about the origin of conjectures, or is it (equally much, or even mostly) about the source of confidence in conjectures?  The issue of what we would like to regard as truth values seems to me to suggest at least large weight on the latter.  I think, "truth" descending from a common root of "trust" and so forth.  

I look forward to Lee's particular refutation, because I was wondering whether I would argue against the same point myself, say for flipping coins where there are only two possibilities, and trying to decide whether it is better to expect that the next one will be the same as previous ones, or not.  But even there, I might niggle with something on algorithm complexity and description length, and argue that it is "harder" to expect a violation of a long string of repeats, than it is for a short string.

But, I look forward to listening to Lee's refutation.

All best,

Eric


On Mar 28, 2012, at 4:06 PM, [hidden email] wrote:

> Eric Smith:  
>
>> every child knows there can be no discussion of induction that is not
>> predicated on the availability of infinities.
>
> Not so (independent of what every child knows)!  I have to rush off
> but will try to get back to this later.
>
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> Meets Fridays 9a-11:30 at cafe at St. John's College
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[Tom Carter]

All -

  Probably too much to respond to, but for no particularly good reason, a few comments . . .

  1.)  Whenever I teach about logic / scientific-method, one thing I make sure to do is remind students that "deduction" is not a "truth *producing*" system, but is at best a "truth *preserving*" system.  In order to claim that your particular deductive system deals with "true statements," you have to inject the "truth" from outside the system . . .

  One typical approach is to play the "axiomatics" game -- but one should be careful to remember that in (good :-) formal mathematics, an "axiom" is a "statement accepted without proof" (i.e., the "proof" of an "axiom" within the system is one line -- the statement of the "axiom").  In particular, it is important to very clearly distinguish between "I will (for the time being) be using this axiom" and "I believe this axiom to be *true*" . . .

  A related approach is to play the "induction" game:  I have observed these regularities in the world, so I will inject into my deductive system a new "axiom" which, to whatever extent makes sense and is feasible, encapsulates the regularity I have observed.  I can then wander around in a "hypothetical-deductive cycle" arena, and see, for example, what other regularities I might expect to see, etc.

  My habit is to leave the concept "truth" out of the picture.  My experience has been that introducing Platonic Ideals like "Truth" into the process (almost) inevitably leads to any number of frustrating blind alleys . . . more generally, I'm not a fan of "Platonic Ideal"-ism.  My first direct experience with "Platonic Ideals" was through the Baltimore Catechism (if you're not familiar, go ahead and Google it . . . :-), and specifically the Ideal "God" . . .  And, perhaps hence, the idea that "belief" consists of the "acceptance of" (or "commitment to"?) some particular Platonic Ideal.

  2.)  Which leads (back) to the question "Do you believe in (the validity of) induction?" . . . when I read that question, I went to the word "believe," rather than "induction" . . .     Asked whether he "believed in full immersion baptism," the apocryphal farmer apparently responded, "Believe in it?  Hell, I've *seen* it!!!"      So, do I "believe that induction is useful"?  Hell yes, I use it all the time.  Do I "believe that induction leads to 'truth' (or 'Truth')?" -- see above about "truth" !!! . . . for me, an at best irrelevant question, but, more likely, more or less meaningless . . .

  3.)  And then a hint at a digression on some things like "law of the excluded middle" and "finiteness" . . . a little personal history . . . long ago (1975) I took my first graduate math course in Logic.  The professor was David Nelson (at GWU, who was Kleene's first Ph.D. student).  Dr. Nelson identified himself as a "negationless intuitionist" (or sometimes, a "negationless constructivist").  He only "believed in" positive constructive proofs.  The logical system he worked in didn't have a "negation operator."  He didn't "believe in" the "law of excluded middle," or "proof by contradiction," or anything like that.  He didn't "believe in" (completed) infinities.  But, on the other hand, he "taught" us traditional mathematical logic, because he knew that we were going to be expected to know all the standard stuff.  I'll leave it as an exercise to link this up with some of the discussion -- perhaps most specifically with respect to "finiteness," and assumptions one might make about where and when the chimera (  :-) ???) of "infinity" might enter the discussion . . .  But I'll also claim that the effects on me of this (early . . .) exposure to significantly alternative "logics" weren't *all* harmful . . . :-)    . . .  David used to say -- mathematics is all tautological, or all subjunctive (or both) . . .

  Possibly related note:  it turns out that characterizing finiteness, or countability, is not possible in first-order logic -- one needs to enter the somewhat counter-intuitive realm of second-order logic . . .  wherein things can get very sticky . . .

  4.)  "When you believe in things that you don't understand, then you suffer . . ." (S. Wonder)

  Thanks . . .

tom

 
On Mar 28, 2012, at 12:02 PM, Eric Smith wrote:

> I agree, Wow, to Eric Charles's summary.
>
> Can I ask, is there any role for finiteness in this discussion?  There seem to me to be two places the constraints of being finite enter, and the specific point at which they seem forced by one of the questions that has been asked (Why would you accept the inductive hypothesis, except on faith?)  is to offer the alternative answer (Because I am incapable of doing otherwise).  The latter answer seems more operational than invoking the word "faith", which for all I know may not mean anything more than "I am incapable of doing otherwise because I am finite", or the circularity that the inductive hypothesis is the only premise from which to defend its own use.  
>
> Here is one argument for finiteness, which I have pestered Nick with in conversations long ago.
>
> Suppose I am an input-output machine with a finite number of outputs (and for that matter, of internal states).  (I intend here to be in the general domain of Ross Ashby's notions of "requisite variation", but let me not get off on that.)  If a philosopher objects that I have no _right_ to be finite, and that, like Paris Hilton, I must "from now on, promise to pay complete attention to everything", then don't consider me, consider a single type of cell-surface receptor on any of my cells.  Surely, for practical purposes, we want to model it as having a finite repertoire of behaviors, whether it has a right to or not.  It's only a protein.
>
> But a finite thing, in an indefinitely variable world, must then produce at least one of its outputs as the response to an indefinite set of distinct circumstances.  (Here, I would be happy to say "infinite", but I mean "indefinite" as that which "might grow toward infinity if we could keep accumulating cases".)  In practice, of course, for most cases I could think of, _each_ of the output states occurs as a response to indefinitely many distinct circumstances.  Thus, my input-output box partitions an indefinite environment into equivalence classes, at least one, and probably many of them, of indefinitely large size.  It cannot do otherwise, being finite.
>
> But my cell-surface receptor has been (naturally-)selected from a finite history of events.  Again, a practical man, being honest about noise and the erasure of memory, about costs, etc., would say that it has probably been selected by a rather short recent history from a rather narrow set of cases.  Thus, the response it will generate, for an indefinite range of circumstances, has been chosen from a finite set of selection criteria.  It appears that survival-under-selection of finite objects, then, is perforce a commitment to one form of induction.   The generation, by the device for however long it survives, of a potentially-indefinitely-large set of input-output pairs is being conditioned on a finite set of input-output pairs.
>
> Of course, natural selection is just Bayes's theorem for model selection, with the fitness being the log-likelihood, and selection on spaces with a finite number of types is then Bayesian induction on probability distributions over a finite number of tokens.  I think (?) we believe in statistics that Bayesian updating is the best general-purpose method we can formalize (Cosma Shalizi, sometimes solo and sometimes with Andrew Gelman, has written on this).  So either in thinking or in science, can we claim to be capable of any better actual, implementable mechanism than an algorithm that (if I am not wrong in the last par) instantiates the inductive hypothesis?  If we can't be capable of anything better, than what is the nature of an objection against such algorithms, besides reminders that they are finite in an infinite world (which, being unable to fathom an infinite world, we may tend to forget)?  
>
> The second argument for caring about finiteness is related.  I am still a finite input-output machine.
>
> I have a choice.  I can either suppose that a future event will be the same as -- or structurally close to, in some way I can operationalize -- one of my past-experienced events under suitably-identified conditions, or I can suppose it will "not be".  My past is finite.  The number of its histories that I can actually distinguish may be (for me, _is_) even smaller.  Let's suppose that the set of all non-comparable futures to anything I have experienced and can distinguish and remember is, again, indefinitely large.
>
> If I suppose the future will repeat the past, and I am in a circumstance where that is true, since the past has finitely-many tokens, then I have non-zero probability to guess the right future.  If I am not in that circumstance, then I am sure to be wrong.  If I suppose the future will _not_ resemble the past -- and, CRUCIAL POINT HERE , if I am at all honest -- then I must make my bets over an indefinite set of futures with non-singular measure, meaning I have measure zero on everything.  Whether or not my environment will repeat its past, my chances of being right are zero either way.  Again, among my options, where do I find an argument against choosing induction from the past?  That is, fine, we recognize the logical limits of induction, but do we have any argument that any specific alternative could be supported in any better way, or by any better premises?
>
> Of course, this sounds like Pascal's wager, and the structure of the argument is similar, but its topic is not similar, because the premises for which one is arguing in the two cases are not comparable.  A punishing God, whom one doesn't want to cross -- whether one believes He is a an emotional imprint of punishing parents, punishing spouses, punishing colleagues, any of whom may hold grudges forever in response to any act of disobedience, or one believes that the universe and existence are a subset of human social-psychology (rather than the other way around) -- is still a particular and arbitrary premise.  The previous paragraph was about search and methodology.  Search in finite spaces, which may be feasible, versus search infinite spaces, which is almost-surely infeasible, addresses a specific problem with which we are already specifically stuck, and which it is not ours to arbitrarily choose to escape from.
>
> So the rhetorical argument about the religious person who claims that the grass-is-green induction is an expression of the same flavor of faith as his support of a cultural dogma, seems to me methodologically unclear in a way that usually gets used disingenuously.  If we admit that we are all finite, then the only remaining question is which templates we are inductively generalizing _from_, in a particular situation.  If you want to generalize from human-social emotion in discussions about plate tectonics, dark matter, dark energy, or whatever (I have relatives who do), then that is your option out of finitely many.  If instead you want to narrow the arbitrariness and try to bundle the constraints that give the polynomial expansion for gravitational action functionals (and then just try to identify parameters), or to do the more complicated version of that for planet formation, then at least we can say by Occam's razor that you have made a smaller search space that overlaps w
> ith a larger set of more-apparently similar evidence.  
>
>
> I realize that my email here seems (and presumably is) stupid, since every child knows there can be no discussion of induction that is not predicated on the availability of infinities.  But, since I am finite, I have tended to think that the point of these abstractions is to extract salient features of a class of (actual, realizable) problems which may not fulfill the abstraction, but for which the abstraction can serve as the appropriate index of a class of problems that can be extended in a particular direction.  So, in looking at these "grass-is-grue" arguments, or at almost anything Rorty writes when he wants to be a gadfly against someone who is getting something useful done (notably, I do not extend this criticism to his constructive comments about desirable societies), and in trying to figure out where there is a productive discussion about scientific methods or claims, it is hard for me to feel other than confused unless I look at the specific role that finiteness has
>  played in creating the structure of any of the specific propositions being discussed.
>
>
> There are, of course, other classes of propositions where one could well argue against induction, but again, it would be for reasons that can be made operational and thus comprehensible.  Economists would dislike David Wolpert's no-free-lunch theorems if they felt them worth reading, since David samples over complete sets of combinatorial search and optimization problems, and shows that any expectation that can be satisfied by some cases in such spaces, must be violated on an equal measure of cases.  The economists (the particular ones I know) don't want to pursue this, because the discipline wants preferred solution concepts, preferred equilibria, etc.  But of course, if we were talking about the design of regulatory systems, in which any set of published rules becomes a target for gaming, by those who wish to set up an expectation and violate it, then the need to guard against anti-induction solutions becomes large.  All this, though, I can do on finite spaces, and compare
> the severity of simplified inferences to the size of the violation set, and then look at limits under scaling of the number of cases.
>
>
> Also, if I had read Pierce, I expect I would have found that he shows in the first few pages that arguments of this type are trivial and don't address anything.  In another life...
>
> Eric
>
>
>
>
>
>
>
>
>
>> Owen,
>> As I understand it:
>> Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience.... but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction.
>>
>> The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century.
>>
>> These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form "Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth?"
>>
>> Hope that helps,
>>
>> Eric
>>
>>
>
>
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[Nick Thompson]

Dear Eric Smith (and other patient people),

 

I have been trying to get the chance to lay this out for three days, and have just not had the time.  I am enthralled at the moment by the scientific philosophy of Charles Saunders Peirce because, weird as it is, it seems to capture a lot of what I think about a lot of things.  It also, it stands at the root of many of our institutions.  You can access this connection through Menand's, The Metaphysical Club.   Many of the foundational beliefs we hold about education and science and even jurisprudence are partly due to Peirce.

 

I am not sure Peirce thought he needed (1) below,  but I need it to get him started, so I will attribute it to him.

 

(1) Humans are a knowledge-gathering species by nature. Darwinism tells us that humans have survived both as communities and as a species because their cognitive processes have brought their beliefs into concert with the world.  (Peirce is a bit of a group Selectionist.) A belief is that on which I act.  There are no latent beliefs in Peirce.  Doubt is an incapacity to act. 

 

(2) True propositions and the best methods for discovering them are those on which the human species, as a community of inquiry, will converge ULTIMATELY.  By ultimately, I mean the infinite future.   Note that this is a definition of "true."  There is no other truth in Peirce, no correspondence theory, except possibly that inferred by me in (1 ) . The current views of contemporary communities of inquiry may be our best shot at the truth, but they are NOT true, by definition, unless they happen to be that on which the human community of inquiry will ultimately converge. Peirce was a chemist, a mathematician and an expert in measurement.  There was no doubt in his mind that the best methods for producing enduring convergence of opinion were what we think of as Scientific methods -- experiments and mathematical analysis .

 

(3) The real world consists of all that is true. 

 

(4) Our knowledge of the world is through a stream of logical inferences. All human beings are informal scientists by nature.  All human belief is arrived at, whether consciously or unconsciously, whether by scientist or by layman, whether by infant or mature adult, by the application of forms of inference and by experiments and observations whether formal or informal. 

 

(5) Contrary to what many of us were taught in graduate school, there are three forms of valid inference.  Communities of inquiry (principally “Sciences” to Peirce) use all three forms of inference, to produce networks of inference.  

 

 

(6) Deductive inferences such as "A. All Swans are White; B. this bird is a swan; C. This bird is white." are categorically true.  However, those who taught us in Graduate School that only deductive inferences are valid, failed to tell us how we come by either the Major (A) or the Minor (B) premise of such inferences.   Popper, who influenced many of the scientists in my generation, used to tell us that they were "bold conjectures."  Big lot of help THAT is!  One of the great strengths of Peirce’s work is that he gives an account of the origin of “bold conjectures”.  

 

(7)  Peirce honors two additional forms of valid logical inference, which he calls forms of "probable" inference. .  A probable inference is one whose strength improves with the multiplication of concordant cases.  Probably inference can supply the major (A) and minor (B) premises of deductive inferences from empirical observations. Much of scientists’ daily work consists in improving the strength of our probable inferences. 

 

(8) The first of these types is induction.  “C. This bird is white; B. This bird is a swan; A.  All Swans are White.”  It generates the major premise of the deductive inference above (A), but needs other inferences to supply C. and B.  With a single case, an inductive inference is valid, but extremely weak.  With the discovery of larger and larger numbers of swans that are white, the strength (probability) of the inference approaches 1.00. 

 

(9) The second of these types of probable inference is “abduction”.  “C. This bird is white; A. All Swans are White; B. This bird is a swan.”   Abductions can generate the minor premise of the deductive inference above (B) but need other inferences to supply A and C.  An abductive inference based on the discovery of a single concordant property between swans and the bird at hand is valid but extremely weak. As more concordant properties are discovered, our certainty that the bird is a swan approaches 1.00. 

 

(10) The beliefs in the self and in an inner private world are all arrived at in this manner.  They are the result of inferences (“signs, Peirce would say”) arising from our experience with the world.   The self’s view of the self is no more privileged an inference than the other’s view of the self. In fact, on Peirce’s account, the former is probably based upon the latter by abductive inference.

 

(11)  On the account of Many Wise Persons, all the above is based upon Peirce’s theory of signs.  I confess I don’t really understand that theory, and tried very hard to get to this point without invoking it.  Your skepticism should be heightened by this admission.  

 

I will send this off to some people who know Peirce better than I in the hope that they will correct me.  I will send along any corrections I receive.

 

Nick

 

FN#1. Yes, I know that all swans are not white.  I know my ornithology, my childhood literature and my chaotic economics as well as the next guy. 

 

FN#2.  Some readers may struggle with the idea that calling a bird “white” is itself an inference.  But, think about how you would go about deciding the color of something.  You would observe it over time, you would observe it in various lights, etc., and then DECIDE that it was white.  Whether that process is conscious or unconscious, systematic or unsystematic, is irrelevant to Peirce.  It is still an inference. 

 

 

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of Eric Smith
Sent: Wednesday, March 28, 2012 5:10 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Clarifying Induction Threads

 

Thank you Lee and Glen both,

 

Yes, I could not disagree. 

 

There is an interesting question, Glen, on which I don't have a dog in the fight either way.  Is the worry about induction only (or even mostly) about the origin of conjectures, or is it (equally much, or even mostly) about the source of confidence in conjectures?  The issue of what we would like to regard as truth values seems to me to suggest at least large weight on the latter.  I think, "truth" descending from a common root of "trust" and so forth. 

 

I look forward to Lee's particular refutation, because I was wondering whether I would argue against the same point myself, say for flipping coins where there are only two possibilities, and trying to decide whether it is better to expect that the next one will be the same as previous ones, or not.  But even there, I might niggle with something on algorithm complexity and description length, and argue that it is "harder" to expect a violation of a long string of repeats, than it is for a short string.

 

But, I look forward to listening to Lee's refutation.

 

All best,

 

Eric

 

 

On Mar 28, 2012, at 4:06 PM, [hidden email] wrote:

 

> Eric Smith: 

>

>> every child knows there can be no discussion of induction that is not

>> predicated on the availability of infinities.

>

> Not so (independent of what every child knows)!  I have to rush off

> but will try to get back to this later.

>

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> at St. John's College lectures, archives, unsubscribe, maps at

> http://www.friam.org

 

 

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FRIAM Applied Complexity Group listserv

Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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