where are the "patriot hackers"?

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Re: where are the "patriot hackers"?

thompnickson2
Hi,Glen,

No, I think you've straw-manned it.  EricS assumes only that, ==> IFF <== if there are any stable rules of experience, that scientific practice are those that will get you to them.  Not to hang this on EricS, but in my rendering of the idea, it is a tautology.  Scientific practices are just those that bring us to the most stable formulations of experience.  Peirce is quite content fundamentally with the notion that all experience is random.  However, from his perspective, it seems not always to be the case, and those cases, he thinks, should be a great interest to organisms trying  to make their way in the flow of experience.  Like you and me, for instance.  Note that in my formulation above, if drug use, or meditation, or standing in large crowds cheering for Trump, can result in conceptualizations that endure and hold their shape despite the heavy grinding of scientific practice, then, I have to admit conceptualizations so derived to the company of scientific conceptualizations.  

Nick

Nicholas Thompson
Emeritus Professor of Ethology and Psychology
Clark University
[hidden email]
https://wordpress.clarku.edu/nthompson/
 


-----Original Message-----
From: Friam <[hidden email]> On Behalf Of u?l? ???
Sent: Wednesday, December 30, 2020 12:18 PM
To: [hidden email]
Subject: Re: [FRIAM] where are the "patriot hackers"?

That seems a bit strange. EricS seems to *assume* there is a truth (consistent network of things that hang together) to be converged upon. But I thought Peirce was not metaphysically committed to the idea that a final opinion was inevitably possible, only that *if* it's there, it can be converged upon.

And given Peirce's work in alternative logics, it seems completely reasonable that he would allow for different types of consistency and, perhaps even, multiple sets of different networks, each of which may be self-consistent, but perhaps not connected to other networks. And if *that's* right, then there could be >2 final opinions converged upon by >2 collections of seekers, yet who disagree about what is real/true.

And even further, because the real and the extant might be somewhat decoupled, the >2 truths might be able to interact (exist) without requiring them to merge into 1 truth.

So it seems odd that you'd say EricS' description is Peircian. Maybe it's only part of it (weaker)? Maybe it's stronger? But is it really the same?

Thanks in advance for any corrections.


On 12/30/20 8:53 AM, [hidden email] wrote:
> What you wrote here is one of the most succinct, persuasive, and all around nifty explications of Peircean Pragmati[ci]sm I have ever read.  Complete with the ricochet  shot to the heart of  Rorty.  Thanks.

> On 12/30/20 3:12 AM, David Eric Smith wrote:
>> All points here good to know, Stephen, and many premises I agree with.
>>
>> It seems to me that, if this conversation is ever to do more than have people talk past each other, all discussants need to find it valuable to use restricted scopes for words, to remain within each other’s scopes along the track of a discussion to figure out what premises are common and what follows from them, and to operate on however many tracks in parallel are needed to include the things people want to talk about.  
>>
>> Here is a concrete example.  In the Rights of Nature article, I find:
>>
>> “Christianity and science, the legitimising powers of the western society, have been in agreement on this fundamental tenet."
>>
>> Well, that’s one thing the word “science” can stand for in a conversation: one of the two legitimizing powers of ’the western society’, together with Christianity (what lovely bedfellows).  
>>
>>
>> When Nick uses the word science in the sense his original objection, I am willing to recast it in my language as a label for what many of us believe is a new domain of linguistic, behavioral, and social cognitive practice distinguished by the following premises (or tenets):
>>
>> — there is some truth-notion characterized above and before all else
>> by internal consistency, allowing it to be converged toward by a
>> suitable body of practice which we aspire to build.  One could even
>> say that this premise of a stable truth-notion is put forth as the
>> replacement for Descartes’s Cogito, as a starting point on which to
>> build commitments, even if all subsequent steps are fluid and subject
>> to update and overhaul
>>
>> — the state of knowledge (so, recipes, propositions, lexicons, etc.)
>> is something like a very elaborate sample estimator for the values
>> that make up “what is true”.  It’s very fluid, if every instance of
>> the adoption of a term, the commitment to rules of language or logic,
>> interpretations of experiments, and every other habit is considered
>> potentially in error and subject to overhaul; so it is essential to
>> what one means here by “science” that this premise of a stable
>> truth-notion is its starting tenet
>>
>> — all the methods traditionally invoked as constituting “scientific
>> method” could be seen as some first finite components in an
>> open-ended toolbox for trying to recursively find and identify errors
>> by classes of family resemblances they have, in the expectation that
>> correcting the error makes the state of knowledge a better reflection
>> of whatever is true.  So, intersubjectivity or rigorous rules of
>> argument to overcome sample omissions, observation bias, deluded
>> thinking, etc.; empiricism as a corrective to delusions that can
>> persist in group levels of any size, etc.  But unlike the
>> Encyclopedists, the body of method for error discovery is just as
>> open-ended as the state of knowledge it has produced at any given
>> time.  Since errors tend to propagate recursively, we probably have
>> to assume that the tools to detect them can be expended indefinitely,
>> else the premise that one can converge on true assertions would be
>> implausible
>>
>> (Apologies that these first three reiterate something I wrote here a
>> couple of months ago.  I don’t like repeating oneself either.)
>>
>> — that the above criteria separate out some propositions at any given
>> time from everything we might be capable of thinking or feeling at that time, making it not all equivalent.  Thus the unhappiness of Tolstoy’s unhappy families, each according to its own fashion, is not really a pattern for what a “true assertion” looks like.  Or more neurologically, synaesthesics may see the letters of the alphabet in colors.  However, each synaesthesic may see a each of the letters in a different color than the other synaesthesics do.  Do I deny that they experience the letters with colors?  No, of course I don’t.  However, do I expect science to arrive at a conclusion that it is in the nature of a printed letter to _have_ a particular color, or to have any color at all?  Also No.  And so on.  If no state of belief a person can sincerely hold can ever be batshit crazy, then there can’t be category distinctions, and the true assertions don’t actually exist in the sense the scientific tenet supposes.
>>
>>
>> I would argue that any good-faith person has to recognize that these two operationalizations of the word “science” simply are not referring to the same thing.  Having recognized it, what can one then do?
>>
>> 1. You can argue, like Richard Rorty, that it is the nature of people that they cannot possess the truth-version of “science” without having it coopted into the “legitimizing power” version, and therefore we should try to exterminate the truth-version in a kind of totalitarianistic PC, William James’s pragmatism-as-social-utilitarianism taken to its limit, which is the annihilation of Peirce’s pragmatism.  To me this is only a stone’s throw from the Unabomber argument.  One can make and then debate the quality of such arguments.  They can be insightful about how the various aspects that are simultaneously present in human life and thought affect each other, and thus can contribute to solving problems and righting wrongs even if one doesn’t think the original arguments hang together as wholes.
>>
>> 2. One could, instead (also like Rorty), insist on changing the subject, but not acknowledge that that is what is being done.  Whenever a discussant tries argues for keeping the truth-version, one can act as if the legitimizing-power version was intended, and then give the counterargument for dismantling the latter.  That could be done, I guess, innocently, or obstinately, or maliciously.  But it doesn’t seem like it resolves to anything.
>>
>> Anyway,
>>
>> Eric




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Re: where are the "patriot hackers"?

thompnickson2
In reply to this post by gepr
Ach!  Glen, EricS, I am sorry.  I mis read this, contribution.  I should stay out of this conversation.  You-guys are doing just fine without me.

n

Nicholas Thompson
Emeritus Professor of Ethology and Psychology
Clark University
[hidden email]
https://wordpress.clarku.edu/nthompson/
 


-----Original Message-----
From: Friam <[hidden email]> On Behalf Of u?l? ???
Sent: Wednesday, December 30, 2020 12:18 PM
To: [hidden email]
Subject: Re: [FRIAM] where are the "patriot hackers"?

That seems a bit strange. EricS seems to *assume* there is a truth (consistent network of things that hang together) to be converged upon. But I thought Peirce was not metaphysically committed to the idea that a final opinion was inevitably possible, only that *if* it's there, it can be converged upon.

And given Peirce's work in alternative logics, it seems completely reasonable that he would allow for different types of consistency and, perhaps even, multiple sets of different networks, each of which may be self-consistent, but perhaps not connected to other networks. And if *that's* right, then there could be >2 final opinions converged upon by >2 collections of seekers, yet who disagree about what is real/true.

And even further, because the real and the extant might be somewhat decoupled, the >2 truths might be able to interact (exist) without requiring them to merge into 1 truth.

So it seems odd that you'd say EricS' description is Peircian. Maybe it's only part of it (weaker)? Maybe it's stronger? But is it really the same?

Thanks in advance for any corrections.


On 12/30/20 8:53 AM, [hidden email] wrote:
> What you wrote here is one of the most succinct, persuasive, and all around nifty explications of Peircean Pragmati[ci]sm I have ever read.  Complete with the ricochet  shot to the heart of  Rorty.  Thanks.

> On 12/30/20 3:12 AM, David Eric Smith wrote:
>> All points here good to know, Stephen, and many premises I agree with.
>>
>> It seems to me that, if this conversation is ever to do more than have people talk past each other, all discussants need to find it valuable to use restricted scopes for words, to remain within each other’s scopes along the track of a discussion to figure out what premises are common and what follows from them, and to operate on however many tracks in parallel are needed to include the things people want to talk about.  
>>
>> Here is a concrete example.  In the Rights of Nature article, I find:
>>
>> “Christianity and science, the legitimising powers of the western society, have been in agreement on this fundamental tenet."
>>
>> Well, that’s one thing the word “science” can stand for in a conversation: one of the two legitimizing powers of ’the western society’, together with Christianity (what lovely bedfellows).  
>>
>>
>> When Nick uses the word science in the sense his original objection, I am willing to recast it in my language as a label for what many of us believe is a new domain of linguistic, behavioral, and social cognitive practice distinguished by the following premises (or tenets):
>>
>> — there is some truth-notion characterized above and before all else
>> by internal consistency, allowing it to be converged toward by a
>> suitable body of practice which we aspire to build.  One could even
>> say that this premise of a stable truth-notion is put forth as the
>> replacement for Descartes’s Cogito, as a starting point on which to
>> build commitments, even if all subsequent steps are fluid and subject
>> to update and overhaul
>>
>> — the state of knowledge (so, recipes, propositions, lexicons, etc.)
>> is something like a very elaborate sample estimator for the values
>> that make up “what is true”.  It’s very fluid, if every instance of
>> the adoption of a term, the commitment to rules of language or logic,
>> interpretations of experiments, and every other habit is considered
>> potentially in error and subject to overhaul; so it is essential to
>> what one means here by “science” that this premise of a stable
>> truth-notion is its starting tenet
>>
>> — all the methods traditionally invoked as constituting “scientific
>> method” could be seen as some first finite components in an
>> open-ended toolbox for trying to recursively find and identify errors
>> by classes of family resemblances they have, in the expectation that
>> correcting the error makes the state of knowledge a better reflection
>> of whatever is true.  So, intersubjectivity or rigorous rules of
>> argument to overcome sample omissions, observation bias, deluded
>> thinking, etc.; empiricism as a corrective to delusions that can
>> persist in group levels of any size, etc.  But unlike the
>> Encyclopedists, the body of method for error discovery is just as
>> open-ended as the state of knowledge it has produced at any given
>> time.  Since errors tend to propagate recursively, we probably have
>> to assume that the tools to detect them can be expended indefinitely,
>> else the premise that one can converge on true assertions would be
>> implausible
>>
>> (Apologies that these first three reiterate something I wrote here a
>> couple of months ago.  I don’t like repeating oneself either.)
>>
>> — that the above criteria separate out some propositions at any given
>> time from everything we might be capable of thinking or feeling at that time, making it not all equivalent.  Thus the unhappiness of Tolstoy’s unhappy families, each according to its own fashion, is not really a pattern for what a “true assertion” looks like.  Or more neurologically, synaesthesics may see the letters of the alphabet in colors.  However, each synaesthesic may see a each of the letters in a different color than the other synaesthesics do.  Do I deny that they experience the letters with colors?  No, of course I don’t.  However, do I expect science to arrive at a conclusion that it is in the nature of a printed letter to _have_ a particular color, or to have any color at all?  Also No.  And so on.  If no state of belief a person can sincerely hold can ever be batshit crazy, then there can’t be category distinctions, and the true assertions don’t actually exist in the sense the scientific tenet supposes.
>>
>>
>> I would argue that any good-faith person has to recognize that these two operationalizations of the word “science” simply are not referring to the same thing.  Having recognized it, what can one then do?
>>
>> 1. You can argue, like Richard Rorty, that it is the nature of people that they cannot possess the truth-version of “science” without having it coopted into the “legitimizing power” version, and therefore we should try to exterminate the truth-version in a kind of totalitarianistic PC, William James’s pragmatism-as-social-utilitarianism taken to its limit, which is the annihilation of Peirce’s pragmatism.  To me this is only a stone’s throw from the Unabomber argument.  One can make and then debate the quality of such arguments.  They can be insightful about how the various aspects that are simultaneously present in human life and thought affect each other, and thus can contribute to solving problems and righting wrongs even if one doesn’t think the original arguments hang together as wholes.
>>
>> 2. One could, instead (also like Rorty), insist on changing the subject, but not acknowledge that that is what is being done.  Whenever a discussant tries argues for keeping the truth-version, one can act as if the legitimizing-power version was intended, and then give the counterargument for dismantling the latter.  That could be done, I guess, innocently, or obstinately, or maliciously.  But it doesn’t seem like it resolves to anything.
>>
>> Anyway,
>>
>> Eric




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Re: where are the "patriot hackers"?

gepr
In reply to this post by David Eric Smith
I really like the construction. Thanks for engaging! The 2 remaining questions I have are:

1) do you imagine the underlying generator(s) evolving over time (i.e. open-ended spaces), and
2) do you commit (even if kindasorta) to the idea that the *structure* of the states of knowledge map well to the structure of the generator(s) (i.e. something like R. Rosen's "natural law")?

It seems like we must say yes to (2), even if we hedge a bit. (1) is relevant to the *rates* of any convergence. If the answer is "yes, but the rate of convergence is faster than the evolution of the generator", then we can safely answer "no, for practical purposes". If the answer is "no", then it amounts to some metaphysical commitment to convexity. And (2) is relevant to my problem with using any singular logic to model reasoning (inferential vs. physical entailment). Together, an answer of "no" to (1) and "yes" to (2) seems to imply a commitment to a GUT. But that's really a tangent.


On 12/30/20 11:24 AM, David Eric Smith wrote:

>
>> On Dec 30, 2020, at 1:18 PM, uǝlƃ ↙↙↙ <[hidden email]> wrote:
>>
>> And given Peirce's work in alternative logics, it seems completely reasonable that he would allow for different types of consistency and, perhaps even, multiple sets of different networks, each of which may be self-consistent, but perhaps not connected to other networks. And if *that's* right, then there could be >2 final opinions converged upon by >2 collections of seekers, yet who disagree about what is real/true.
>
> Yes.  I would hope that these mutually-incompatible positions are features of a state of knowledge, and not the refutation that there is any possible referent-notion for the term “truth”.
>
> Again, I have mental images that to me make this comfortable, but they aren’t good models in any literal sense.  I think of stochastic processes with multiple basins of attraction, which on the short term can lead to distributions of fluctuations entirely within one basin or another, with the basin determined by initial conditions.  On the longer term, however, the process has an ergodic distribution, within which either of the former distributions can be contextualized as a conditional distribution, relative to the ergodic which is unconditioned.
>
> The generator for the underlying process would stand in analogy to what I am looking for as the truth to be represented, and the various conditioned or unconditioned distributions would be outputs from sample estimators in any state of investigation or characterization.  As we build up more and more ways to situate the conditioned distributions within the unconditional, our state of knowledge reflects more of the properties of the underlying generator, and leaves fewer opportunities for incommensurate distributions or unexplained differences in moments.  But all these states of knowledge (the various distributions) remain different kinds of things from the underlying generator (the true generator of the process), and the states of knowledge are of the same type as each other even as the knowledge is refined.

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uǝʃƃ ⊥ glen
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Re: where are the "patriot hackers"?

David Eric Smith
Glen, thank you, 

1) do you imagine the underlying generator(s) evolving over time (i.e. open-ended spaces), and

I wouldn’t want to rule out anything one could get to work.  The obvious common application would be to evolutionary systems.  I tend not to like overdoing the “evolution is special because its state at any time changes the rules for its dynamics”, as if somehow a science of evolution would float above those plebeian physical sciences and the people who practice them.  Having different kinds of transitions available from different states is generic; to me the cases that are “evolutionary” in an interesting sense tend to be set apart by their dimensionality, complexity, and statefulness — what Yoshi Oono calls “fundamental conditions” as distinct from “boundary conditions”.  
Where possible I find it preferable to look for a set of stable laws governing the space of all possible histories, and to locate state-dependence as a property of solutions within a history, much as one embeds an open dynamic thermal system as a transient within a larger in-principle closed system.  But the evolutionists do have a good point: for systems where one can’t practically compute (and doesn’t care about) all possible trajectories, it would be nice to have a science that is more local to the trajectory, and to have ways to handle time-dependent “laws” or “aspects of truth”.

The modern community that goes by the name of “rule-based modeling” does this in a way that I like, using category-theoretic constructs of pushouts and pullbacks to be explicit about how much context is needed.  I have pointed on this list before to 
and there is some really great work on more general rule-based systems by Nicolas Behr, finally installed in the CNRS:
They are interested in such questions as: what can you compute from the algebra of rule dependencies, without having to solve for a whole state?  Or: when can you obtain information about correlation functions for limited sets of properties (effectively, governed by some marginal distribution) without having infinite regress of dependencies on the whole system?  Walter Fontana et al. have a particular structure for such dependencies, which he calls “stories”, and has developed within the context of Kappa.  
I don’t understand exactly what these are, and need to learn.

2) do you commit (even if kindasorta) to the idea that the *structure* of the states of knowledge map well to the structure of the generator(s) (i.e. something like R. Rosen's "natural law”)?

Yes, I think this is necessary in order to be saying anything at all.  The question of how two very different formal systems can have “the same structure” or “the same information” seems hard and interesting.  With what further assumptions can I say that a small collection of unconditioned and conditional stationary distributions, and perhaps a few dynamical correlations functions, contain all the same information as is contained in an underlying generating process, and are effectively just one of the available representations of it.  This would seem to be at the foundation of what reductionism in science can be.  It is also about the theory of representations, of which I don’t know very much.  I seem to remember JonZ's having some comments on this subject in the last go-round.  Category theory appears to be the universal language these days for rule-based modeling.

The ML implication here is of course obvious (I know, to all): can we learn useful things about the difference between an abstract structure and its representations by studying cases?  Implicit representations, self-presentation by a learner, and things we have discussed here before.

It seems like we must say yes to (2), even if we hedge a bit. (1) is relevant to the *rates* of any convergence. If the answer is "yes, but the rate of convergence is faster than the evolution of the generator", then we can safely answer "no, for practical purposes”.

Totally agree.

If the answer is "no", then it amounts to some metaphysical commitment to convexity. And (2) is relevant to my problem with using any singular logic to model reasoning (inferential vs. physical entailment). Together, an answer of "no" to (1) and "yes" to (2) seems to imply a commitment to a GUT. But that's really a tangent.

Also, yes.  It’s interesting, GUTs have a bad name, I guess for a variety of reasons, whether boasting, false claims, cutting off useful questions just because they aren’t final, etc., all of which seem to me to be about human bad behavior and not about what is needed by an idea.  It could be that associating “truth” with unification is appropriate, and need not be harmful to practice if one understands that states of knowledge don’t claim to be truth, but at best isomorphic to it in patches if we get lucky.  

Best,

Eric




On 12/30/20 11:24 AM, David Eric Smith wrote:

On Dec 30, 2020, at 1:18 PM, uǝlƃ ↙↙↙ <[hidden email]> wrote:

And given Peirce's work in alternative logics, it seems completely reasonable that he would allow for different types of consistency and, perhaps even, multiple sets of different networks, each of which may be self-consistent, but perhaps not connected to other networks. And if *that's* right, then there could be >2 final opinions converged upon by >2 collections of seekers, yet who disagree about what is real/true.

Yes.  I would hope that these mutually-incompatible positions are features of a state of knowledge, and not the refutation that there is any possible referent-notion for the term “truth”.

Again, I have mental images that to me make this comfortable, but they aren’t good models in any literal sense.  I think of stochastic processes with multiple basins of attraction, which on the short term can lead to distributions of fluctuations entirely within one basin or another, with the basin determined by initial conditions.  On the longer term, however, the process has an ergodic distribution, within which either of the former distributions can be contextualized as a conditional distribution, relative to the ergodic which is unconditioned.

The generator for the underlying process would stand in analogy to what I am looking for as the truth to be represented, and the various conditioned or unconditioned distributions would be outputs from sample estimators in any state of investigation or characterization.  As we build up more and more ways to situate the conditioned distributions within the unconditional, our state of knowledge reflects more of the properties of the underlying generator, and leaves fewer opportunities for incommensurate distributions or unexplained differences in moments.  But all these states of knowledge (the various distributions) remain different kinds of things from the underlying generator (the true generator of the process), and the states of knowledge are of the same type as each other even as the knowledge is refined.

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Re: where are the "patriot hackers"?

gepr
Very nice. I had never seen the Oono article! I'm only barely familiar with Kappa, though more aware of the rule-based systems in general. It's great that you invoked them, here, because I haven't been thinking about them in the context of multi-paradigm modeling of human reasoning. When I asked the (1) question, I was thinking of progressive freezing as presented in your (and M's) book, contextual change over time more than gen-phen evolution. But you covered the larger ground with the self-modifying languages.

And I appreciate the comment on reduction(ism) to a best representation. In particular, the problem of uniqueness is a good foil for clear thinking. I agree completely re: GUTs. I always argue against them, but only because I *want* them, preferably many of them. >8^D

I've got lots to work on, now. Thanks.


On 12/31/20 7:33 AM, David Eric Smith wrote:

> Glen, thank you, 
>
>> 1) do you imagine the underlying generator(s) evolving over time (i.e. open-ended spaces), and
>
> I wouldn’t want to rule out anything one could get to work.  The obvious common application would be to evolutionary systems.  I tend not to like overdoing the “evolution is special because its state at any time changes the rules for its dynamics”, as if somehow a science of evolution would float above those plebeian physical sciences and the people who practice them.  Having different kinds of transitions available from different states is generic; to me the cases that are “evolutionary” in an interesting sense tend to be set apart by their dimensionality, complexity, and statefulness — what Yoshi Oono calls “fundamental conditions” as distinct from “boundary conditions”.  
> https://link.springer.com/chapter/10.1007/978-4-431-54029-8_5 <https://link.springer.com/chapter/10.1007/978-4-431-54029-8_5>
> Where possible I find it preferable to look for a set of stable laws governing the space of all possible histories, and to locate state-dependence as a property of solutions within a history, much as one embeds an open dynamic thermal system as a transient within a larger in-principle closed system.  But the evolutionists do have a good point: for systems where one can’t practically compute (and doesn’t care about) all possible trajectories, it would be nice to have a science that is more local to the trajectory, and to have ways to handle time-dependent “laws” or “aspects of truth”.
>
> The modern community that goes by the name of “rule-based modeling” does this in a way that I like, using category-theoretic constructs of pushouts and pullbacks to be explicit about how much context is needed.  I have pointed on this list before to 
> https://cheminf.imada.sdu.dk/mod/ <https://cheminf.imada.sdu.dk/mod/>
> https://kappalanguage.org/ <https://kappalanguage.org/>
> and there is some really great work on more general rule-based systems by Nicolas Behr, finally installed in the CNRS:
> https://scholar.google.com/scholar?q=Nicolas+Behr+rule-based+modeling&hl=en&as_sdt=0&as_vis=1&oi=scholart <https://scholar.google.com/scholar?q=Nicolas+Behr+rule-based+modeling&hl=en&as_sdt=0&as_vis=1&oi=scholart>
> They are interested in such questions as: what can you compute from the algebra of rule dependencies, without having to solve for a whole state?  Or: when can you obtain information about correlation functions for limited sets of properties (effectively, governed by some marginal distribution) without having infinite regress of dependencies on the whole system?  Walter Fontana et al. have a particular structure for such dependencies, which he calls “stories”, and has developed within the context of Kappa.  
> https://academic.oup.com/bioinformatics/article/34/13/i583/5045802 <https://academic.oup.com/bioinformatics/article/34/13/i583/5045802>
> I don’t understand exactly what these are, and need to learn.
>
>> 2) do you commit (even if kindasorta) to the idea that the *structure* of the states of knowledge map well to the structure of the generator(s) (i.e. something like R. Rosen's "natural law”)?
>
> Yes, I think this is necessary in order to be saying anything at all.  The question of how two very different formal systems can have “the same structure” or “the same information” seems hard and interesting.  With what further assumptions can I say that a small collection of unconditioned and conditional stationary distributions, and perhaps a few dynamical correlations functions, contain all the same information as is contained in an underlying generating process, and are effectively just one of the available representations of it.  This would seem to be at the foundation of what reductionism in science can be.  It is also about the theory of representations, of which I don’t know very much.  I seem to remember JonZ's having some comments on this subject in the last go-round.  Category theory appears to be the universal language these days for rule-based modeling.
>
> The ML implication here is of course obvious (I know, to all): can we learn useful things about the difference between an abstract structure and its representations by studying cases?  Implicit representations, self-presentation by a learner, and things we have discussed here before.
>
>> It seems like we must say yes to (2), even if we hedge a bit. (1) is relevant to the *rates* of any convergence. If the answer is "yes, but the rate of convergence is faster than the evolution of the generator", then we can safely answer "no, for practical purposes”.
>
> Totally agree.
>
>> If the answer is "no", then it amounts to some metaphysical commitment to convexity. And (2) is relevant to my problem with using any singular logic to model reasoning (inferential vs. physical entailment). Together, an answer of "no" to (1) and "yes" to (2) seems to imply a commitment to a GUT. But that's really a tangent.
>
> Also, yes.  It’s interesting, GUTs have a bad name, I guess for a variety of reasons, whether boasting, false claims, cutting off useful questions just because they aren’t final, etc., all of which seem to me to be about human bad behavior and not about what is needed by an idea.  It could be that associating “truth” with unification is appropriate, and need not be harmful to practice if one understands that states of knowledge don’t claim to be truth, but at best isomorphic to it in patches if we get lucky.  

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