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Old 18th February 2014, 11:32 AM   #2401
BurntSynapse
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Originally Posted by Perpetual Student View Post
The point is that the platonic solids are the only regular, convex polyhedrons with congruent faces of regular polygons that can exist within the context of three dimensional Euclidean geometry. Change the context and some other mathematical realities and relationships will result.
Thanks!

I'd welcome your suggestions communicating the idea that contexts are always subject to change in unpredictable ways, thereby changing what we consider true.
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Old 18th February 2014, 01:18 PM   #2402
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Originally Posted by Dancing David View Post
Hi BurntSynapse

Please explain exactly how the many pet theories you have would have helped Edwin Hubble and his research assistant in their paradigm shift.
Even if you'd clarified what you mean by "pet theory", and "show", adding the new requirement of exactness takes the request outside of what seems productive.

The more precision we attempt with guesses about real world implementations of theory, the less accurate such guesses tend to be. Thus, such efforts for exactness generally seem a waste, and fairly certain to be grossly inaccurate - leaving us wondering whether our approach is wrong or we strove for too much detail.

Originally Posted by Dancing David View Post
Then explain how your pet theories would have helped Alan Guth (which is unfair), so I will say Ernest Rutherford instead who was involved in a huge paradigm shift.
Absent what you mean by "my pet theories", the "involvement" you have in mind, and what you regard as Rutherford's involvement, any description given would probably be far off the mark.

Originally Posted by Dancing David View Post
I am asking how all the different things you claim would help research and in particular paradigm shift would have any practical application.
My main practical recommendation is that improving standards like NSB 07-032 with information from experts in HPS specializing in scientific revolutions is, all things being equal, a good idea. Technically, the recommendations apply to administration of research, not the research.

It is for experts in application of policy standards to research standards (which I almost never do) to use their judgment in how to influence improvement of researchers.

Originally Posted by Dancing David View Post
Guth was unfair because it is a theoretical paradigm shift,
If you tell me the shift you have in mind, I'd be interested to look at it. I've never modeled a cognitive frame cold.

Last edited by BurntSynapse; 18th February 2014 at 01:23 PM.
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Old 18th February 2014, 01:20 PM   #2403
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Originally Posted by BurntSynapse View Post
Correct. Kassler quotes some author as finding 26 different meanings of "paradigm" in Kuhn's work - perhaps even with just SSR.
Excellent.

Originally Posted by BurntSynapse View Post
That the usage I describe seems very common in HPS material I've read...like "problem". I've heard different reasons for moving away from "paradigm shift" that have convinced me that more technical concepts and jargon enable better analysis, more detailed understanding, and more precise reasoning we are getting into. Since my field is application, my interest in definitions leans more toward lexicographers, and whether that sort of definition meets acceptable scoping criteria.
Uhm, the phrase you were questioning the usage of was “common & ordinary”. So what did you mean by that phrase? You may find our usages were not dissimilar.

Originally Posted by BurntSynapse View Post
My current preference for distinguishing potentially revolutionary cognitive frames by whether and how they tend to recategorize exemplars in ways impossible in previous frames. I suspect HPS people will continue improving and expanding on that, if they haven't already. Perhaps its already frowned on by some, but the last critique I read seemed weak.
Ok so you ain’t quite got one you really want to use yet but take an approach similar to Justice Potter Stewart on hard-core pornography in that ‘I know it when I see it’?

Originally Posted by BurntSynapse View Post
The meanings and use have changed, and current uses seem different (and better) than uses from decades ago.
Exactly how have those “meanings and use” changed? What do you think tends to make those changes seem better to you? “seem different” you say? So you’re just not sure if those “current uses” are in fact different?


Originally Posted by BurntSynapse View Post
Confusion over whether some meanings of 'paradigms" & "shifts" support or should support various claims is exactly the kind of confusion that lead to clarifications like development of the recategorization criterion in the late 90's & early 2000's.
Great, so what exactly is the criteria of that “criterion” and how exactly does it “lead to clarifications” or adress the confusion you mentioned.


Originally Posted by BurntSynapse View Post
To dive into that, we should probably use more modern, precise terms and concepts. Human cognitive processes are regarded as utilizing the same basic mental machinery, and as Nersessian points out, external cultural resources and other factors change.
Well more “precise terms and concepts” would certainly be a step in the right direction. As you note that “Human cognitive processes are regarded as utilizing the same basic mental machinery” so that ain’t changed from previous paradigm shifts and if “external cultural resources and other factors” are basically always changing that condition is no different than before as well.

Originally Posted by BurntSynapse View Post
That conclusion hits the nail quite squarely, I'd say.
Which nail is that? The one where things just “seem different” but what you cite doesn't “seem different” or explicitly isn’t different. The one where things are in fact different but you just don’t seem able to cite that difference or the changes that have resulted effectively. Perhaps the one where you would just like things to be different and “better” (heck, who wouldn’t) but seem either unable or just unwilling to cite just what you would change, how you would change it, why and how you would determine those changes get the results you intend.

Though I expect that when trying to nail Jell-O to a wall hitting a Jell-O nail “quite squarely” is as efficacious as any other.
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Old 18th February 2014, 01:21 PM   #2404
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Originally Posted by Dancing David View Post
Hi BurntSynapse

Please explain exactly how the many pet theories you have would have helped Edwin Hubble and his research assistant in their paradigm shift.
Even if you'd clarified what you mean by "pet theory", and "show", adding the new requirement of exactness takes the request outside of what seems productive.

The more precision we attempt with guesses about real world implementations of theory, the less accurate such guesses tend to be. Thus, such efforts for exactness generally seem a waste, and fairly certain to be grossly inaccurate - leaving us wondering whether our approach is wrong or we strove for too much detail.

Originally Posted by Dancing David View Post
Then explain how your pet theories would have helped Alan Guth (which is unfair), so I will say Ernest Rutherford instead who was involved in a huge paradigm shift.
Absent what you mean by "my pet theories", the "involvement" you have in mind, and what you regard as Rutherford's involvement, any description given would probably be far off the mark.

Originally Posted by Dancing David View Post
I am asking how all the different things you claim would help research and in particular paradigm shift would have any practical application.
My main practical recommendation is that improving standards like NSB 07-032 with information from experts in HPS specializing in scientific revolutions is, all things being equal, a good idea. Technically, the recommendations apply to administration of research, not the research.

It is for experts in application of policy standards to research standards (which I almost never do) to use their judgment in how to influence improvement of researchers.

Originally Posted by Dancing David View Post
Guth was unfair because it is a theoretical paradigm shift,
If you tell me the shift you have in mind, I'd be interested to look at it. I've never modeled a cognitive frame cold.
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Old 18th February 2014, 01:49 PM   #2405
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Originally Posted by BurntSynapse View Post
My main practical recommendation is that improving standards like NSB 07-032 with information from experts in HPS specializing in scientific revolutions is, all things being equal, a good idea. Technically, the recommendations apply to administration of research, not the research.
For your own edification “improving standards like NSB 07-032 with information from experts in HPS specializing in scientific revolutions is, all things being equal, a good idea.” is an opinion not a practical recommendation.

Yes we all still know that some experts in HPS aren’t being relied upon as much as you or perhaps even they would like.

The main thing I get for NSB 07-032 is just this…

http://www.nsf.gov/nsb/news/news_sum...cntn_id=108494
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Old 18th February 2014, 02:12 PM   #2406
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Originally Posted by The Man View Post
Excellent.
Originally Posted by BurntSynapse View Post
Originally Posted by The Man View Post
Originally Posted by BurntSynapse View Post
Paradigm shifts are processes over time, and it would seem very strange not to allow consideration of what is going on during that process. Discussing the state "after a process is complete" seems common & ordinary.

We may use process verbs as nouns, referring to things such as "a birth" in the past, but there's nothing inherent in most definitions that prohibit us from saying a birth will be like this in the future, is proceeding like that right now, or took place some other way a century ago.
While attempting to discuss paradigm shifts where the paradigm hasn’t shifted makes them so “common & ordinary” as to be meaningless.
AFAIK, the term "incomplete paradigm shift" is most often used [now] to refer to a situation where some, but not all members of the community adopt a new cognitive frame.
Uhm, the phrase you were questioning the usage of was “common & ordinary”. So what did you mean by that phrase? You may find our usages were not dissimilar.
As indicated in use of "birth" as a noun for a process, I was questioning how a word with dual use becomes meaningless if invoking more modern variations of the original, confusing "paradigm shift".

What I was talking about is probably better as: "We are attempting to discuss paradigm shifts (of a particular individual) where the paradigm (of the community) hasn’t completely shifted to the new model..." this seems to make the subject I've got in mind more clear...but replacing the chimeric "paradigm" for more precise terms seems like a good idea.


Originally Posted by The Man View Post
Ok so you ain’t quite got one you really want to use yet but take an approach similar to Justice Potter Stewart on hard-core pornography in that ‘I know it when I see it’?
If you mean definition of paradigm, and it has 26 meanings in SSR alone, I prefer using entirely different terms. Many people know the word though, enabling quick, if inaccurate communication of the general topic we are addressing.

Originally Posted by The Man View Post
Exactly how have those “meanings and use” changed?
I'd guess by research of people in the "Kuhnian tradition" (or whatever they call it), teasing out the consequences of logical inquiry and historical evidence they've gathered, but I've never watched.

Originally Posted by The Man View Post
What do you think tends to make those changes seem better to you?
Eliminating confusion by distinguishing among those 26 potential ambiguities seems like reasonable evidence. Integration with other disciplines is a flag for hot research areas James Burke cited at dConstruct a couple of years ago.

That's a good question...I should probably have a more rigorous answer.
(makes note)

Originally Posted by The Man View Post
So you’re just not sure if those “current uses” are in fact different?
I'm sure that the answer depends on one's perspective, but I want to be sure I can avoid any appearance of implying I can or would want to try to convince anyone either way.

There's been enough grief of context already, IMO.

Originally Posted by The Man View Post
Great, so what exactly is the criteria of that “criterion” and how exactly does it “lead to clarifications” or adress the confusion you mentioned.
The criterion I place some importance on is whether the new cognitive frame recategorizes exemplars in ways impossible in previous frames. IMO, this implies that revolutionary frame replacement is impossible if we don't already have a frame that enables such impossibility.

It also explains why we don't experience the humor of a joke when the underlying violation of expectation is sufficiently unfamiliar. AFAIK, that's an original interpretation of my own, and I can't cite anyone who shares it.

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Old 18th February 2014, 02:41 PM   #2407
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Originally Posted by Perpetual Student View Post
The point is that the platonic solids are the only regular, convex polyhedrons with congruent faces of regular polygons that can exist within the context of three dimensional Euclidean geometry. Change the context and some other mathematical realities and relationships will result.

The same would be true of polychorons, in that any civilization interested in polychorons would discover the same characteristics we have.
This brings up an interesting point, if perhaps there are only a finite number of paradigm shifts to be discovered or that human cognition can handle. Having cleared a lot of the 'low hanging' fruit already the really big shifts or (like we've had over the past century or so) may be far and few between. Certainly experimental requirements are far more demanding, instrumentality far more expensive and resource time more limited. Conversely data, theories and research papers are far more generally available then they have been throughout our entire history. Additionally more powerful computers and molding software are also more readily available. Lump that all together and we find ourselves at a choke point with enough rope to wrap ourselves up like a mummy.
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Old 18th February 2014, 02:51 PM   #2408
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Originally Posted by BurntSynapse View Post
Even if you'd clarified what you mean by "pet theory", and "show", adding the new requirement of exactness takes the request outside of what seems productive.

The more precision we attempt with guesses about real world implementations of theory, the less accurate such guesses tend to be. Thus, such efforts for exactness generally seem a waste, and fairly certain to be grossly inaccurate - leaving us wondering whether our approach is wrong or we strove for too much detail.


Absent what you mean by "my pet theories", the "involvement" you have in mind, and what you regard as Rutherford's involvement, any description given would probably be far off the mark.


My main practical recommendation is that improving standards like NSB 07-032 with information from experts in HPS specializing in scientific revolutions is, all things being equal, a good idea. Technically, the recommendations apply to administration of research, not the research.

It is for experts in application of policy standards to research standards (which I almost never do) to use their judgment in how to influence improvement of researchers.


If you tell me the shift you have in mind, I'd be interested to look at it. I've never modeled a cognitive frame cold.
Excuse em BS, I have read this thread throughout although I refrained from comments for a long time.

-you either feel you have ideas that could benefit the 'scientific revolutions' or not, so if you don't then justa dmit it.

- you claim that something out there could benefit shift in paradigms and 'scientific revolutions', but I think it is obvious you don't know what those are.

Edwin Hubble led one of the biggest paradigm shifts and 'scientific revolutions' in astronomy.
Earnest Rutherford the same as the discovery of modern atomic theory and particle physics.

So either your ideas have merit, and if they do then how exactly would your ideas have benefited them.

I think you just have magical thinking and loose association, I could point out the apparent dodges and waffling in your response.

I am saying, you seem to be mistaken about what leads to 'scientific revolutions', I chose two and I am asking how you would have made them better.


So this is where you have a chance to stop just using fancy words and phrases, I chose two big 'scientific revolutions', now you say how you pet theories and ideas could have benefited them.
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Old 18th February 2014, 03:18 PM   #2409
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Welcome, Max Tegmark.

If BurntSynapse's questions seem odd, it's because they are. Let me explain where he's coming from.

Originally Posted by BurntSynapse View Post
It seems odd to claim such broad reach for ideas that apply to such restricted domains. Stipulating "Platonic solids" seems artificially narrow. We would have to rule out infinities of other conditions, like pi dimensions, wouldn't we?
BurntSynapse thinks physicists have been paying too little attention to non-Euclidean geometries, and appears to have been taken in by some of the fractal woo. He didn't realize general relativity is based upon non-Euclidean geometry, and he still seems not to realize that Mandelbrot's fractal dimensions apply to curves (and hyperspaces in general) whose topological dimension is integral even when their so-called fractal dimension is not.

Originally Posted by BurntSynapse View Post
What about polychorons - could they count? http://en.wikipedia.org/wiki/Polychoron
Polychorons are 4-dimensional polytopes, so they don't count as Platonic solids. There's nothing wrong with either concept, but they're different concepts. What Max Tegmark was saying is that any sufficiently advanced alien civilization would discover exactly the same five Platonic solids we know, just as they would discover exactly the same 47 non-prismatic convex uniform polychora we know.

BurntSynapse appears to be unaware that mathematicians routinely work with arbitrary simplicial complexes in arbitrary (topological) dimensions.

Originally Posted by BurntSynapse View Post
As I understand science, such frameworks should (at least in in principle), always be subject to revision.
Mathematics is unusual in that respect. Any alien mathematics that discovers more than five Platonic solids is either wrong or is using a different definition of Platonic solid (which means it may have discovered more than five of something, but it hasn't discovered more than five of what we mean by the Platonic solids). This extreme objectivity of mathematics may explain Perpetual Student's annoyance when people say math is "just" a language.

Responding now to remarks BurntSynapse addressed directly to me:

Originally Posted by BurntSynapse View Post
Originally Posted by W.D.Clinger View Post
Consider, for example, the rules that specify the context-free syntax of a programming language.
We are asked to consider things that fall within the category of what we might call "rules".

The rules category seems here further qualified by stipulating we are only considering rules that "specify".

The domain is then further narrowed to only those specifying rules which apply to "syntax".

The kind of syntax under consideration is further refined to those in "context-free" categories...and so on.

This seems like providing alot of (IMO necessary) contextual support for whatever claims are going to be made, and it seems like this is needed for the claim to be interpreted and meaningful. "Meaning" certainly seems like it has to be relative to something, and Quine's "web of belief" seems like a good model for that.

It may well be wrong, but it it intelligible?
Well, "it it intelligible" if we regard it as an example of your remarkable determination to demonstrate your own personal failure to comprehend critical thinking 101.

As a coherent refutation of the principle that counterexamples to unqualified general claims can be drawn from any domain, it is not intelligible.

It would be even less intelligible to those who remember my first counterexample (Gödel's completeness theorem) and realize I gave you this second class of counterexamples only because you were completely unfamiliar ("Even if true") with Gödel's theorem.

For the seventh time, BurntSynapse has mentioned this Kassler person:

Originally Posted by BurntSynapse View Post
Correct. Kassler quotes some author as finding 26 different meanings of "paradigm" in Kuhn's work - perhaps even with just SSR.
Which Kassler is that, BurntSynapse? Are you talking about Dr Jeanne Kassler, who died in 2002? Are you talking about Michael Kassler, the musician?

I ask because you have earned an impressive reputation for misrepresenting the views of philosophers whose names you drop here (Gödel, Quine, and others) so I'd like to see for myself what this Kassler person actually says.

Could it be you don't know how to spell this person's name? Might you mean Professor Jeffrey Kasser of Colorado State University, who "specializes in epistemology and the history of American pragmatism"?
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Old 18th February 2014, 03:51 PM   #2410
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Originally Posted by BurntSynapse View Post
As indicated in use of "birth" as a noun for a process, I was questioning how a word with dual use becomes meaningless if invoking more modern variations of the original, confusing "paradigm shift".

What I was talking about is probably better as: "We are attempting to discuss paradigm shifts (of a particular individual) where the paradigm (of the community) hasn’t completely shifted to the new model..." this seems to make the subject I've got in mind more clear...but replacing the chimeric "paradigm" for more precise terms seems like a good idea.
Oh, so in your reconstruction you’re just going to leave out the relevant quote…

Originally Posted by BurntSynapse View Post
I'm not entirely sure what is meant here by common & ordinary, but the lack of clarity on the term seems to be cited as leading to replacement of the term "paradigm" itself by more technical terms.
…has that ever worked for you?

I knew exactly what you were talking about which is why I said it “makes them so “common & ordinary” as to be meaningless”.

Originally Posted by BurntSynapse View Post
If you mean definition of paradigm, and it has 26 meanings in SSR alone, I prefer using entirely different terms. Many people know the word though, enabling quick, if inaccurate communication of the general topic we are addressing.
No I meant paradigm shift which was the definition you gave. OK, you don’t want to use the one you gave. What one do you want to use now?


Originally Posted by BurntSynapse View Post
I'd guess by research of people in the "Kuhnian tradition" (or whatever they call it), teasing out the consequences of logical inquiry and historical evidence they've gathered, but I've never watched.
So you just don’t know how or even if they've changed. Keep on guessing.

Originally Posted by BurntSynapse View Post
Eliminating confusion by distinguishing among those 26 potential ambiguities seems like reasonable evidence. Integration with other disciplines is a flag for hot research areas James Burke cited at dConstruct a couple of years ago.
Not bad, but weren't they distinguished already in having “26 meanings”, hence the “potential ambiguities”? Settling on perhaps one meaning and perhaps some modifiers would seem a better approach at reducing “potential ambiguities”.

Originally Posted by BurntSynapse View Post
That's a good question...I should probably have a more rigorous answer.
(makes note)
No problem and it wouldn't be a bad idea to see if you can actually formulate one.

Originally Posted by BurntSynapse View Post
I'm sure that the answer depends on one's perspective, but I want to be sure I can avoid any appearance of implying I can or would want to try to convince anyone either way.
Makes it rater subjective doesn’t it? Isn’t that the basis of your “practical recommendation” that things have changed and new information needs to be considered? So whether or not you “can or would want to try to convince anyone either way” it seem to be the task you’ve asked to have criticized.

Originally Posted by BurntSynapse View Post
There's been enough grief of context already, IMO.
Grief and context, the corner stones of criticism.


Originally Posted by BurntSynapse View Post
The criterion I place some importance on is whether the new cognitive frame recategorizes exemplars in ways impossible in previous frames. IMO, this implies that revolutionary frame replacement is impossible if we don't already have a frame that enables such impossibility.
Yes in order to have something impossible in a previous frame you have to have a previous frame where that is impossible. A rather tautological criterion to say the least. Before you remarked to “how they tend to recategorize exemplars” have you abandoned that aspect or do you actually have a criteria for that?

Say since with no previous frame “revolutionary frame replacement is impossible” and with just any frame it now becomes possible. Thus the exemplar of “revolutionary frame replacement” has been recotagorized from impossible to possible. Looks like your “impossible” “revolutionary frame replacement” satisfies your stated “criterion” for “revolutionary frame replacement”. Talk about a paradigm shift in paradigm shifts. It is always a bad sign when your criteria makes what you assert as impossible, well, possible.

Originally Posted by BurntSynapse View Post
It also explains why we don't experience the humor of a joke when the underlying violation of expectation is sufficiently unfamiliar. AFAIK, that's an original interpretation of my own, and I can't cite anyone who shares it.
Not much of a joke if you expect just a familiar punch line.
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Old 18th February 2014, 04:50 PM   #2411
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Originally Posted by Dancing David View Post
-you either feel you have ideas that could benefit the 'scientific revolutions' or not, so if you don't then justa dmit it.
I propose a third option: that the answer depends on perspective. Carl Sagan said: "To make an apply pie, first create the universe."

From one perspective yes, that claim seems technically true...but it seems very odd. On the other hand: no would be our everyday answer, and doesn't seem entirely correct either.

Originally Posted by Dancing David View Post
you claim that something out there could benefit shift in paradigms and 'scientific revolutions', but I think it is obvious you don't know what those are.
Working closely with HPS experts in revolutionary scientific during the next revision of TR support guidelines may not be specific enough for some.

Originally Posted by Dancing David View Post
So either your ideas have merit, and if they do then how exactly would your ideas have benefited them.
If we believe one only has...
Originally Posted by Dancing David View Post
...magical thinking and loose association...
...then even if we receive serious, cautious answers, it is hard for us to avoid interpreting them as ...
Originally Posted by Dancing David View Post
apparent dodges and waffling
.

Originally Posted by Dancing David View Post
I am saying, you seem to be mistaken about what leads to 'scientific revolutions'
My memory is pretty dodgy, so I don't recall this ever being mentioned as a specific topic previously in this thread, which forces me to ask: What / where have claimed what leads to scientific revolutions?

If you refer to something like "problem solving" in the Nersessian model, I would respond that for Edwin Hubble, the most obvious anomalous data problem was the redshift, which he solved by development of an explanatory model. For Rutherford, the anomalous deflection of alpha particles described at: http://en.wikipedia.org/wiki/Ernest_...oil_Experiment
are what I think a reasonable example of the problem which he worked to solve for about 2 years, succeeding with the nuclear model.

Originally Posted by Dancing David View Post
So this is where you have a chance to stop just using fancy words and phrases, I chose two big 'scientific revolutions', now you say how you pet theories and ideas could have benefited them.
I take it as progress to simply have more precise & accurate models, so to me, understanding the structure of scientific creativity as starting with anomalies that become regarded as anomalies needing explaining, and how problem solving leads to beneficial ideas, etc., to me this understanding is likely to be a benefit to scientists even if they can't state exactly how.

BTW - Good questions.

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Old 18th February 2014, 05:14 PM   #2412
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Originally Posted by BurntSynapse View Post
Thanks!

I'd welcome your suggestions communicating the idea that contexts are always subject to change in unpredictable ways, thereby changing what we consider true.
I'm not sure what you mean by this. I suppose an example might be Einstein's introduction of spacetime, which created a context that changed "in unpredictable ways," thus "changing what we consider true." The same might be said of Guth's inflation hypothesis, Gell-Mann's theory of quarks, etc. Is that what you have in mind?
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Old 18th February 2014, 06:42 PM   #2413
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Originally Posted by W.D.Clinger View Post
Responding now to remarks BurntSynapse addressed directly to me:

Well, "it it intelligible" if we regard it as an example of your remarkable determination to demonstrate your own personal failure to comprehend critical thinking 101.

As a coherent refutation of the principle that counterexamples to unqualified general claims can be drawn from any domain, it is not intelligible.
I don't think I've provided any reason to think my question is anything other that an effort to understand your objections.

The idea that stipulating restrictions by the meaning of terms doesn't seem like it should be controversial, nor do we need to specify the exact number of hairs on a chin to be able to call something a beard, IMO.

Originally Posted by W.D.Clinger View Post
It would be even less intelligible to those who remember my first counterexample (Gödel's completeness theorem) and realize I gave you this second class of counterexamples only because you were completely unfamiliar ("Even if true") with Gödel's theorem.
My prior confessions of abject ignorance of advanced (and no doubt some basic) math bear repeating it seems. To all: I'm completely unqualified to understand, much less assess the validity of proofs for just about anything more complex than 5 or 6. I'm no mathematician - at all.

Originally Posted by W.D.Clinger View Post
For the seventh time, BurntSynapse has mentioned this Kassler person:
Seven? That's dogged focus. I misspelled "Kasser" as you diligently corrected. Thank you.

My references to him and his examples come from The Teaching Company course I enjoyed very much, and highly recommend. http://www.thegreatcourses.com/tgc/c....aspx?cid=4100

Last edited by BurntSynapse; 18th February 2014 at 06:54 PM.
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Old 18th February 2014, 06:49 PM   #2414
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Originally Posted by Perpetual Student View Post
I'm not sure what you mean by this.
The poor wording is obvious now that it's cooled off and I reread it. The reply was in a blazing hot sun, no ice, and vicious mosquito clouds.

Originally Posted by Perpetual Student View Post
I suppose an example might be Einstein's introduction of spacetime, which created a context that changed "in unpredictable ways," thus "changing what we consider true." The same might be said of Guth's inflation hypothesis, Gell-Mann's theory of quarks, etc. Is that what you have in mind?
Somewhat, but when speaking with policy-makers, I try to use examples that everyone "should" know, like redefinition of sunrise from sun movement to an observational consequence of human observation. That source hadn't previously been considered a possible source of uncertainty for basic definitions for a number of reasons, and some of those reasons are no longer true.

In Copernicus' day, there was no notion that anyone should be mindful such possibilities. It seems some think no one should be focusing on these now.

One of my concerns is effectively communicating that we hope to produce revolutions which alter our understanding of terms as radically as we have with other terms in the past like "sunrise", "species", or "planet".

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Old 18th February 2014, 08:34 PM   #2415
W.D.Clinger
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Originally Posted by BurntSynapse View Post
I don't think I've provided any reason to think my question is anything other that an effort to understand your objections.
Fair enough. I will answer in that spirit.

Originally Posted by BurntSynapse View Post
The idea that stipulating restrictions by the meaning of terms doesn't seem like it should be controversial, nor do we need to specify the exact number of hairs on a chin to be able to call something a beard, IMO.
The language you are using is not language you would be using if you understood the counterexamples to your claim, and the questions you have asked are not questions that would help you to understand the counterexamples or why the counterexamples are counterexamples. If your goal here is to understand the counterexamples to your claim, then it would be unhelpful of me to answer the questions you asked; answering your questions as asked would not improve your understanding, and might well encourage the false sense of understanding that has bedevilled you with respect to a number of other subjects.

It's possible you believe your questions had some purpose other than helping you to understand the counterexamples. If so, please state your purpose in asking those questions so we can help you to formulate better questions.
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Old 18th February 2014, 08:42 PM   #2416
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Originally Posted by BurntSynapse View Post
In Copernicus' day, there was no notion that anyone should be mindful such possibilities. It seems some think no one should be focusing on these now.
My bold. Not even close. Where are you getting this idea? Where? Your critics have been saying, over and over:

a) Physicists are already very mindful of the possibility of revolutionary paradigm change and are actively engaged in seeking such changes. How is that "no one should be focusing"?

b) Several physics experts here think that you do not know of any new or useful method for "focusing" on paradigm changes, and moreover that you have a poor appreciation for the methods currently in use.

c) More specifically, several physics experts here think that your actual method, insofar as you have one, has produced zero good suggestions but numerous really bad ones, as though your "method" was a bafflegab-encrusted update of the generic crackpot instinct to latch on to simple, old, known-incorrect ideas.

I don't see how that translates into "It seems some think no one should be focusing on these now."
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Old 19th February 2014, 07:58 AM   #2417
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Originally Posted by BurntSynapse View Post
I propose a third option: that the answer depends on perspective. Carl Sagan said: "To make an apply pie, first create the universe."

From one perspective yes, that claim seems technically true...but it seems very odd. On the other hand: no would be our everyday answer, and doesn't seem entirely correct either.


Working closely with HPS experts in revolutionary scientific during the next revision of TR support guidelines may not be specific enough for some.


If we believe one only has...

...then even if we receive serious, cautious answers, it is hard for us to avoid interpreting them as ...
.


My memory is pretty dodgy, so I don't recall this ever being mentioned as a specific topic previously in this thread, which forces me to ask: What / where have claimed what leads to scientific revolutions?

If you refer to something like "problem solving" in the Nersessian model, I would respond that for Edwin Hubble, the most obvious anomalous data problem was the redshift, which he solved by development of an explanatory model. For Rutherford, the anomalous deflection of alpha particles described at: http://en.wikipedia.org/wiki/Ernest_...oil_Experiment
are what I think a reasonable example of the problem which he worked to solve for about 2 years, succeeding with the nuclear model.


I take it as progress to simply have more precise & accurate models, so to me, understanding the structure of scientific creativity as starting with anomalies that become regarded as anomalies needing explaining, and how problem solving leads to beneficial ideas, etc., to me this understanding is likely to be a benefit to scientists even if they can't state exactly how.

BTW - Good questions.
So in the two examples, no benefit from any of yuor ideas, would you like to go through more or do you admit that you can't provide any practical application of your ideas to scientific revolution.

Remember that Fermi, Pauli , Heisenberg and about twenty others still wait.

I again contend that you don't have a basis for any suggestion on how to improve scientific revolutions or paradigm shifts.
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Old 19th February 2014, 08:16 AM   #2418
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Originally Posted by Perpetual Student View Post
Let me know if I can be of any assistance.
It's painfully obvious that you can't. Again, if you don't understand something and ask questions about it, it's really rather bizarre to insult and argue with the people who do understand it and answer your questions. Sadly, this appears to be fairly common behaviour for you. However, I must thank you for providing a perfect example of exactly the point I made in my previous post.

Originally Posted by Max Tegmark View Post
Thanks Cuddles for raising this important question about whether mathematics is invented or discovered
I did not raise any such question. Perhaps you have me confused with someone else?
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Old 19th February 2014, 08:54 AM   #2419
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Originally Posted by Cuddles View Post
It's painfully obvious that you can't. Again, if you don't understand something and ask questions about it, it's really rather bizarre to insult and argue with the people who do understand it and answer your questions. Sadly, this appears to be fairly common behaviour for you. However, I must thank you for providing a perfect example of exactly the point I made in my previous post.
Why don't you review the Wikipedia link I provided and make some meaningful comment instead of carping?
As that Wikipedia article begins,
Quote:
"Mathematics is the abstract study of topics such as quantity (numbers), structure, space, and change."
Yes, we use a unique language to pursue those topics, but that language is a tool, not the subject. Your comment that mathematics is "essentially just a language" is like saying the human brain is essentially just amino acids.
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Old 19th February 2014, 01:15 PM   #2420
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Originally Posted by BurntSynapse View Post
Working closely with HPS experts in revolutionary scientific during the next revision of TR support guidelines may not be specific enough for some.
Originally Posted by BurntSynapse View Post
My main practical recommendation is that improving standards like NSB 07-032 with information from experts in HPS specializing in scientific revolutions is, all things being equal, a good idea. Technically, the recommendations apply to administration of research, not the research.
BurntSynapse, when I say "your recommendations are not specific", I am not asking for specificity regarding what part of the org chart you want to add HPS experts to.

Rather, and this should have been more than clear, I would have been pointing out that HPS experts do not have any specific suggestions about what scientists (or agencies) should do differently. It doesn't matter where they go on the org chart if they don't have any specific, actually-implementable insights.

Is that so hard to understand?

ETA: in the ongoing effort to ask a blunt-enough, no-misinterpretation-possible question: Please show evidence that HPS experts have insights about transformative-research which are specific and concrete enough to lead actual researchers to alter their conduct.

Last edited by ben m; 19th February 2014 at 02:19 PM.
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Old 19th February 2014, 05:49 PM   #2421
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Originally Posted by W.D.Clinger View Post
If your goal here is to understand the counterexamples to your claim...It's possible you believe your questions had some purpose other than helping you to understand the counterexamples. If so, please state your purpose in asking those questions so we can help you to formulate better questions.
The goal of my last question was understand how the words in your explanation (or any sentence) can provide meaning without establishing some context.
Quine and Duhem used the term "auxilliary hypotheses" for the contextual resources that provide meaning, without them meaning cannot exist.

When we say "rules of syntax", we know what it refers to - the words establish meaning by virtue of conceptual webs of belief about those words & concepts. Each of them has the same property.

It's fine to refer to a "context free something", but as soon as we say a "context free syntax" we've established it as not a "context free panda bear". As soon as we say "syntax", or "panda", we are establishing limits that are subject to definition, changes in definitions, (including radical changes) and any weakness we inherited from the evolution of the term, etc. This is stipulating some context, and necessary.

Your counter example is represented by meaningful statements. Meaningfullness is an entirely different attribute of statements than whether they are right, wrong, accurate, supported, fallacious, or whether anyone understands any of their meaning, especially me.

This is why I don't think the content of those statements matter to my claim about their reliance on auxiliary hypotheses.

I'm not the Sochi skier, I'm the coach.

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Old 19th February 2014, 07:15 PM   #2422
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Originally Posted by ben m View Post
BurntSynapse, when I say "your recommendations are not specific", I am not asking for specificity regarding what part of the org chart you want to add HPS experts to.
Implying I made a statement about org charts, which I would disagree with.

Originally Posted by ben m View Post
Rather, and this should have been more than clear, I would have been pointing out that HPS experts do not have any specific suggestions about what scientists (or agencies) should do differently.
In my book, incorporating knowledge of specialized experts on the cutting edge while improving organizational standards is pretty specific, and something every big agency / organization I've ever worked with does.

I don't know of any organizational standards development efforts moving toward processes like what you envision, but some agile framework for this is probably around somewhere.

Last edited by BurntSynapse; 19th February 2014 at 07:18 PM.
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Old 19th February 2014, 10:02 PM   #2423
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Originally Posted by BurntSynapse View Post
Implying I made a statement about org charts, which I would disagree with.
Your "specific" recommendation was that the HPS experts be put on the committee to reword the statement about transformative research in instructions-to-grant-reviewers.

While that is a specific statement---clarifying that, for example, HPS experts are not put on the grant-review panels, nor do they shadow grant monitors, nor do they conduct a one-time portfolio audit and report back to the GAO---it's indeed a statement about the org chart, not about science or content.

Quote:
In my book, incorporating knowledge of specialized experts on the cutting edge while improving organizational standards is pretty specific, and something every big agency / organization I've ever worked with does.
<sigh>

I bet you would have no trouble identifying concrete, specific ways that your other experts' knowledge trickles down and becomes action items. My collaboration actually hired an expert on grounds sort of like this---we realized that certain manufacturing contracts were slowing down the experiment, we weren't writing or monitoring these contracts effectively, and the expert flew in from CERN. It was not a mysterious process. For example, he looked at our engineering team and pointed out that our Quality Assurance responsibilities looked too diffuse and we would be better to centralize them.

That was in general category of on-the-ground actions we knew we needed, which is exactly the category of expertise that was on his CV when we brought him in, which is the thing that generated concrete changes in our engineers' conduct. There was no magical thinking involved, no coy refusal-to-speculate, no weird kowtowing to unspecified "expertise".

By contrast, you can't offer a guess at what categories of on-the-ground advice physics might need; what aspects of your experts' knowledge might lead to that advice. Indeed, you appear to have an extremely shallow grasp of what your experts are actually experts on, and you appear to have picked up virtually none of that expertise in the course of what ought to have been repeated and close reading of their work. (An undergraduate history-of-science seminar at my institution would get a book like Nersessian's as a two-week reading assignment, and they'd be expected to explain it and dissect it and attempt to apply its insights to new situations to a greater extent than you are.)
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Old 19th February 2014, 10:20 PM   #2424
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I think I have figured out why BurntSynapse has been saying such bizarre things about Gödel's theorems. Explaining and documenting my diagnosis will make this a long post, and my attempt to explain Gödel's theorems to him will make it even longer.

Until today, I did not understand why BurntSynapse writes things like this:

Originally Posted by BurntSynapse View Post
The goal of my last question was understand how the words in your explanation (or any sentence) can provide meaning without establishing some context.
Quine and Duhem used the term "auxilliary hypotheses" for the contextual resources that provide meaning, without them meaning cannot exist.

When we say "rules of syntax", we know what it refers to - the words establish meaning by virtue of conceptual webs of belief about those words & concepts. Each of them has the same property.

It's fine to refer to a "context free something", but as soon as we say a "context free syntax" we've established it as not a "context free panda bear". As soon as we say "syntax", or "panda", we are establishing limits that are subject to definition, changes in definitions, (including radical changes) and any weakness we inherited from the evolution of the term, etc. This is stipulating some context, and necessary.

Your counter example is represented by meaningful statements. Meaningfullness is an entirely different attribute of statements than whether they are right, wrong, accurate, supported, fallacious, or whether anyone understands any of their meaning, especially me.

This is why I don't think the content of those statements matter to my claim about their reliance on auxiliary hypotheses.

I'm not the Sochi skier, I'm the coach.

What's going on here, I think, is that BurntSynapse doesn't have the slightest idea of what the words "incompleteness" and "completeness" mean when we're talking about Gödel's incompleteness and completeness theorems. Those are technical terms, with precise mathematical meanings. When someone like BurntSynapse tries to understand Gödel's theorems or their implications without realizing the words "completeness" and "incompleteness" mean something rather different from what English dictionaries say they mean, we're liable to hear the sort of thing BurntSynapse said above.

Originally Posted by BurntSynapse View Post
My prior confessions of abject ignorance of advanced (and no doubt some basic) math bear repeating it seems. To all: I'm completely unqualified to understand, much less assess the validity of proofs for just about anything more complex than 5 or 6. I'm no mathematician - at all.

I'm glad you realize that, but I don't think you've thought it through. Because you are not a mathematician, you should listen when mathematicians warn you about your mistakes, and you should not continue to assert your own uninformed opinions after mathematicians have told you you're wrong.

Three days ago, I told you your reading of Gödel's incompleteness theorems is wrong:

Originally Posted by W.D.Clinger View Post
Originally Posted by BurntSynapse View Post
My read of Gödel's incompleteness theorems, (first learned from Gödel, Escher, Bach and as described therein) is that the incompleteness he describes in dialog form is analogous to the project management principles of inherently incomplete documentation, and the issue that PM standards are limited in their ability to define when to apply any particular guideline.
That's a fairly bizarre misreading of Gödel's incompleteness theorems.
Apparently I didn't say that strongly enough. Let me try again: Your reading of Gödel's incompleteness theorems is spectacularly wrong, hopelessly incorrect. Your reading of Gödel's incompleteness theorems is so stupendously wrong that it's fair to say you know less about their implications for mathematics or physics than someone who's never even heard of those theorems.

For example:

Originally Posted by BurntSynapse View Post
Yes, that seems accurate as an illustration of where completeness for rules governing the application of rules can never be totally documented, it must be assumed.
No, no, a thousand times no. That is spectacularly wrong, hopelessly incorrect.

I corrected you by citing Gödel's completeness theorem as a counterexample. You didn't understand that counterexample, so I cited an entire class of mundane counterexamples I thought would be familiar to anyone who's ever heard of software project management. You then went off on a tangent that made no sense to me.

You, however, thought it made sense. That means you didn't pay attention when I told you your understanding of Gödel's incompleteness theorems is "fairly bizarre". Instead of listening to correction by domain experts, you continued to rely on your own incorrect understanding of the theorems.

If we assume you continued to believe the notion of incompleteness that Gödel proved in his incompleteness theorems "is analogous to the project management principles of inherently incomplete documentation, and the issue that PM standards are limited in their ability to define when to apply any particular guideline", then it becomes much easier to understand why you have been writing stuff like this:

Originally Posted by BurntSynapse View Post
Underdetermination regarding which math or model to use does seem related by some thinkers to incompleteness, rejected by others & some here.

Math studies found inherent incompleteness, PM studies found inherent incompleteness, HPS studies found incompleteness.
Although the incompleteness Gödel proved in his incompleteness theorems is related to the fact that first order axiomatizations of arithmetic fail to rule out non-standard models, I now realize you have no idea what that means.

You seem to think you can understand Gödel's theorems in terms of English dictionary definitions of words like "underdetermination", "completeness", and "incompleteness". As you have demonstrated, understanding Gödel's theorems on that level is worse than not understanding Gödel's theorems at all.

Originally Posted by BurntSynapse View Post
This comment suggests no distinction between the content of the theorems (about which I've consistently declared my complete ignorance) and their value to illustrate an important epistemological truth in scientific development efforts.
You do indeed appear to be completely ignorant of what Gödel's theorems say. That you regard your complete ignorance of those theorems as an adequate foundation for using them "to illustrate an important epistemological truth in scientific development efforts" is mind-boggling.

Originally Posted by BurntSynapse View Post
Arguments against math claims I don't make, cannot make, have not made, and repeatedly declared that I've not made them - these arguments seem emotionally motivated and quite misguided. If one wishes to show that the principle of incompleteness appearing in multiple fields by multiple means absolutely cannot be considered a plausible clue for directing research, then it seems one should try to make that case.
You're free to regard "the principle of incompleteness appearing in multiple fields by multiple means" as "a plausible clue for directing research", but claiming Gödel's theorems as support for that approach is clueless.

The technical meaning of "completeness" and "incompleteness" in Gödel's theorems

Gödel's theorems are a bit confusing because the technical notion of completeness used in his completeness theorem is not the same as the technical notion of completeness used in his incompleteness theorems. In Gödel's completeness theorem, the intuitive meaning of "completeness" is that it's possible to write down an algorithm for proving all valid theorems; in modern terms, Gödel's completeness theorem says it's possible to write a certain computer program (which is only moderately difficult to write). In Gödel's incompleteness theorems, the "incompleteness" means there's a formula such that neither it nor its negation is provable.

To simplify my explanation of Gödel's theorems and to make them more accessible to computer-literate readers, I'm going to rely upon the modern theory of formal languages and automata.

A formal language is a particular set of strings formed from the characters in some finite alphabet. The set of all sentences (well-formed, closed formulas) of first order logic is a formal language. The set of all sentences of first order Peano arithmetic is another formal language.

An automaton is the mathematical idealization of a computing device. Turing machines are the kind of automata that's most relevant to Gödel's theorems, but there are many other interesting kinds of automata, including finite state machines and pushdown automata.

Automata are related to formal languages in the following way: When given a string s that might or might not belong to some formal language L, an automaton M can do one of three things:
  • It can accept the string s.
  • It can reject the string s.
  • It can do something else (go into an infinite loop, get stuck, blow a fuse, ...)
An automaton M is said to recognize a formal language L if and only if M accepts every string in L and does not accept any strings that are not in L. (Note well that M does not have to reject strings not in L; it just has to avoid accepting them.)

An automaton M is said to decide a formal language L if and only if M accepts every string in L and rejects every string not in L. If M decides L, then M also recognizes L, but the converse is not necessarily true.

Using those modern definitions, we can state modern versions of Gödel's theorems and related results. To state those theorems, we'll need the highly technical definition of what it means for a formula to be true in an interpretation. I'm going to omit those definitions, but I will mention that Alfred Tarski defined this notion of "true" using essentially the same techniques that are used today to define the denotational semantics of some programming languages.
ETA: A sentence is valid if and only if it's true in all interpretations.
Gödel's completeness theorem. There exists an automaton M that recognizes the language consisting of all valid first order sentences.

Church's theorem. No automaton decides the language consisting of all valid first order sentences.

Undecidability of arithmetic. No automaton decides the language consisting of all first order sentences of arithmetic that are true in the standard interpretation.

On 21 November 2013, I defined two formal languages that are proper subsets of the set of all first order sentences of arithmetic that are true in the standard interpretation. One of those formal languages is Q, which consists of the ten axioms of Q together with their logical consequences. The other formal language is P (for first order Peano arithmetic), which consists of the ten axioms of Q together with the infinitely many instances of the first order induction schema, plus all logical consequences of those axioms.

Gödel's first incompleteness theorem. If
  • A is any set of axioms for which some automaton decides A, and
  • T is the set of logical consequences of A, and
  • T contains Q as a subset, and
  • T is consistent,
then there exists a true sentence of first order arithmetic that is not an element of T and whose negation is also not an element of T.
ETA:

Corollary. No automaton recognizes the language consisting of all first order sentences of arithmetic that are true in the standard interpretation.
For the following version of Gödel's second incompleteness theorem, we need a highly technical definition of Consis(M), which is a sentence of first order arithmetic that says a certain theory is consistent (contains no self-contradictions). That highly technical definition amounts to a computer program that, given the description of an automaton M that decides the set A of axioms for the theory T in question, produces a particular consistency sentence for T as its output. In my statement of the theorem, the consistency sentence produced from M is written as Consis(M).

Gödel's second incompleteness theorem. If
  • A is any set of axioms for which some automaton M decides A, and
  • T is the set of logical consequences of A, and
  • T contains P as a subset, and
  • T is consistent,
then Consis(M) is not an element of T.

What this has to do with BurntSynapse

With those definitions and theorems in mind, I invite BurntSynapse to take another look at my counterexamples to his claim that "completeness for rules governing the application of rules can never be totally documented, it must be assumed."

If history is any guide, and it has been heretofore, I'm sure BurntSynapse will find this entire post irrelevant to his claim. And this post of mine may very well be irrelevant to BurntSynapse's claim. If so, then BurntSynapse was using the word "completeness" to mean something very different from what that word means in Gödel's theorems, and my mistake lay in assuming BurntSynapse possessed any understanding of what that word means in the context of Gödel's theorems.

Last edited by W.D.Clinger; 19th February 2014 at 10:56 PM. Reason: added corollary
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Old 20th February 2014, 05:08 AM   #2425
BurntSynapse
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Originally Posted by ben m View Post
I bet you would have no trouble identifying concrete, specific ways that your other experts' knowledge trickles down and becomes action items.
If I said "Advances in variable speed motors look promising. Let's bring together people who can help us design a variable speed hand drill for carpenters."

If someone were to request "Please explain exactly how you this changes how and what master carpenters actually do," I have to answer that I can't say.

Maybe they'd do nothing different, maybe they'd never use it, but generally giving them more options and finer distinctions with tools they're already using seems like a good idea.

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Old 20th February 2014, 08:38 AM   #2426
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Originally Posted by BurntSynapse View Post
If I said "Advances in variable speed motors look promising. Let's bring together people who can help us design a variable speed hand drill for carpenters."

If someone were to request "Please explain exactly how you this changes how and what master carpenters actually do," I have to answer that I can't say.

Maybe they'd do nothing different, maybe they'd never use it, but generally giving them more options and finer distinctions with tools they're already using seems like a good idea.
First, you know that your "concrete example" is a device that's been in common use for decades, right?

Second, your example of improved project management is to spend money on a project without being able to articulate a single potential benefit? "Seems like a good idea" is sufficient justification?
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Old 20th February 2014, 08:43 AM   #2427
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To borrow (and possibly mangle) a quote:

Where correct, he is unoriginal. Where original, incorrect.
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Old 20th February 2014, 10:13 AM   #2428
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Clearly you are putting in significant effort on this, which I respect. I hope no one will object to me referring to you as an expert in mathematics. In management, you are called a subject matter expert, or SME. True, my opinion is a guess, based on non-math evidence. This is what people working within my field of expertise have (and often should) rely on.
Originally Posted by W.D.Clinger View Post
BurntSynapse doesn't have the slightest idea of what the words "incompleteness" and "completeness" mean when we're talking about Gödel's incompleteness and completeness theorems.
I take “we”, to mean the math community members with something like command of the field of math and Gödel's theorems roughly at a level similar to yours, which I take to be very high.

Originally Posted by W.D.Clinger View Post
Those are technical terms, with precise mathematical meanings. When someone like BurntSynapse tries to understand Gödel's theorems or their implications without realizing the words "completeness" and "incompleteness" mean something rather different from what English dictionaries say they mean, we're liable to hear the sort of thing BurntSynapse said above.
That’s a fair and reasonable objection. Lack of understanding could invalidate some, most, or all existing claims of the type you describe. It could apply to claims anyone might make, including mine. That is possible, even probable if the claim is of that type.

I assert a different sort of claim exists, however: these are claims about some arbitrary theory (T), that are not dependent on the theory’s content T(C). If we say a theory tends to be better if it is falsifiable, it does not seem like we need to understand the steps and implications of proofs offered in order to recognize whether the advocates of that theory are willing to provide a falsifiable prediction.

While falsifiability is widely rejected now in HPS compared to Popper’s era, it still is a generally good rule of thumb. Such claims like “falsifiability is a good rule of thumb” don’t say anything about heliocentrism, darwinism, or GR, but they seem good and useful for the real world, like showing why other theories should not be given the same respect as heliocentrism, darwinism, or GR.

Originally Posted by W.D.Clinger View Post
I'm glad you realize that, but I don't think you've thought it through. Because you are not a mathematician, you should listen when mathematicians warn you about your mistakes, and you should not continue to assert your own uninformed opinions after mathematicians have told you you're wrong.
I agree 100% if math SME’s are telling me about math mistakes.

In their disciplines, we should defer to both the creationist expert and the biology expert on their particular fields. Is it better for us to trust one of them regarding application of the falsifiability criteria? They each will advise what best reinforces the supremacy of their preferred model, naturally. Should we not seek the HPS expert who studies and knows the advantages and disadvantages of applying such criteria better than anyone?

If we don't know such a field exists, it is natural for us to assume it doesn't, and the obvious place to look is the technical SME to settle such questions.

Originally Posted by W.D.Clinger View Post
Three days ago, I told you your reading of Gödel's incompleteness theorems is wrong…I didn't say that strongly enough… spectacularly wrong, hopelessly incorrect… so stupendously wrong…you know less about their implications for mathematics or physics…No, no, a thousand times no...spectacularly wrong, hopelessly incorrect.
It almost sounds like you think something’s amiss?

Seriously though: I’m quite sure that from a math perspective, what I’m saying appears as incorrect as one can be. When I Googled something like “Duhem Gödel”, I got hundreds of thousands of pages and papers I scanned were all from HPS. I don’t recall any math papers where that analogy is drawn.

This one: http://cogprints.org/4356/1/UC586bf.pdf seems to make much stranger analogies than I claim, and constructs what seems a plausible case, and there seems no shortage.

“…just as the discovery of mathematical incompleteness did not make the mathematician’s cause hopeless, but rather opened up whole new worlds of fruitful research (e.g., meta-mathematics), so will the discovery of scientific incompleteness.”

I don’t think math is the right tool to evaluate that claim.

Originally Posted by W.D.Clinger View Post
I corrected you by citing Gödel's completeness theorem as a counterexample. You didn't understand that counterexample, so I cited an entire class of mundane counterexamples I thought would be familiar to anyone who's ever heard of software project management. You then went off on a tangent that made no sense to me.
Claims and replies do not make sense when taken to be mathematical in nature when they're not written or intended in that way. My claims are more akin to your claims that the counter-examples are “mundane & familiar in software project management”. That claim of yours should not be criticized on the basis of anything WITHIN the counter-example, since your making an assertion regarding the theory's status within the software community. “Mundane & familiary” has to do with real world use of the examples, not their theoretical content, whether they are true, or whether you understand them.

Originally Posted by W.D.Clinger View Post
You, however, thought it made sense. That means you didn't pay attention when I told you your understanding of Gödel's incompleteness theorems is "fairly bizarre".
If I thought you were supporting the claim “this example is mundane & familiar” based on an interpretation of the content of the example, I’d think your interpretation of the example fairly bizarre as well.

Originally Posted by W.D.Clinger View Post
You seem to think you can understand Gödel's theorems in terms of English dictionary definitions of words like "underdetermination", "completeness", and "incompleteness". As you have demonstrated, understanding Gödel's theorems on that level is worse than not understanding Gödel's theorems at all.
Until your post, I never knew Gödel's used “underdetermination” – so it would be impossible for me to have such an opinion. I’m using the word in what is undoubtedly a poor understanding of Duhem’s sense - but that analogy doesn't seem especially controversial in HPS.

Originally Posted by W.D.Clinger View Post
You do indeed appear to be completely ignorant of what Gödel's theorems say.
As I’ve agreed many, many, many times.

Originally Posted by W.D.Clinger View Post
That you regard your complete ignorance of those theorems as an adequate foundation for using them "to illustrate an important epistemological truth in scientific development efforts" is mind-boggling.
Again: within math, that's probably understandable.

Originally Posted by W.D.Clinger View Post
You're free to regard "the principle of incompleteness appearing in multiple fields by multiple means" as "a plausible clue for directing research",
An accurate quote of one of my claims, and is very much appreciated!!!

Originally Posted by W.D.Clinger View Post
but claiming Gödel's theorems as support for that approach is clueless.
Mathematically clueless, yes. From HPS and PM considerations though, that seems less certain.

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Old 20th February 2014, 11:24 AM   #2429
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Originally Posted by dasmiller View Post
First, you know that your "concrete example" is a device that's been in common use for decades, right?
Yes. Familiar cases are typically better for communicating in many situations.

Originally Posted by dasmiller View Post
Second, your example of improved project management is to spend money on a project without being able to articulate a single potential benefit?
Generally, having more flexible tools offering better control is regarded as a benefit, whether assessing theories or drilling holes.

Originally Posted by dasmiller View Post
"Seems like a good idea" is sufficient justification?
Very frequently - especially when you have to make a dozen decisions a day to complete the project on schedule. Other times, such a heuristic would be disastrous.
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Old 20th February 2014, 12:40 PM   #2430
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Originally Posted by BurntSynapse View Post
If I said "Advances in variable speed motors look promising. Let's bring together people who can help us design a variable speed hand drill for carpenters."

If someone were to request "Please explain exactly how you this changes how and what master carpenters actually do," I have to answer that I can't say.
Great analogy, let's run with it.

The above failure---your lack of expertise on motor-use-cases---is not quite what is currently happening in this discussion. You have not permitted yourself to say anything as specific as "advances in variable speed motors look promising". You are saying "I have a method for developing new tools but I can't tell you any examples of tools it could develop---specificity would be inappropriate."

Nobody is asking you to explain how we would use a variable-speed motor. We (the carpenters in this example) are asking you to say "I suggest variable-speed motors", and we, the domain experts, could say whether that's useful or not, and whether it's original or not. (In this case: useful yes, original no.)

Moreover, you are daydreaming that some future tool-suggestions will turn out to be useful ones. For example, you'd like to imagine yourself saying "how about variable speed motors". I would imagine you saying things like:
  • "how about a hammer with a cupholder built in" (dumb idea)
  • "how about there's a motorized shaft running through the shop from which multiple tools could be powered by belts" (an old idea we already replaced with something much better)
  • "how about some sort of new fastener that holds things better" (too vague to count as an idea)

This is, in fact, a common outcome in a world already full of tool inventors. It is hard to invent useful new tools because the experts themselves are very good at inventing new tools. Those experts/inventors have more interdisciplinary scope than you give them credit for (there already ARE master carpenters who also keep track of advances in motor technology.)

In fact, if you wanted to convince people that you actually had tool-inventing skills, wouldn't it be nice to prove that by stepping up and inventing a tool? If I have the choice between "a guy who actually invented a new tool" versus "a guy who explains the philosophical reasons he believes he has the ability to invent tools", I'll bet on the former.

ETA: and, to clarify, the analogy is between "BurntSynapse tells a roomful of carpenters about his idea for a drill" and statements like "BurntSynapse tells the physics community about the the idea to look into 2D spacetimes". BurntSynapse might want to claim that the analogy is to "BurntSynapse tells the NSF about his idea to put an HPS expert on committee X". As I've said, I don't care about the org chart. There's an HPS expert on committee X, and committee X influences the behavior of Y, and eventually there's a physicist somewhere whose behavior has to be influenced by something. What we care about is whether or not whatever-happened-in-the-org-chart has a positive influence when it gets to the bottom.

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Old 20th February 2014, 01:20 PM   #2431
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Old 20th February 2014, 02:15 PM   #2432
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Originally Posted by BurntSynapse View Post

Generally, having more flexible tools offering better control is regarded as a benefit, whether assessing theories or drilling holes.
.
So what flexible tool would you have offered E. Hubble?
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Old 20th February 2014, 02:19 PM   #2433
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Originally Posted by BurntSynapse View Post
Mathematically clueless, yes. From HPS and PM considerations though, that seems less certain.
So … you will still use Gödel as support, but only in a non-mathematical way? Excuse me, but the mind boggles at this!
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Old 20th February 2014, 08:12 PM   #2434
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Originally Posted by BurntSynapse View Post
In their disciplines, we should defer to both the creationist expert and the biology expert on their particular fields.
Why not? You've already said it's "very difficult to formally demonstrate one theory (Zeus) is better or worse at explaining falling than a theory of gravity."

Originally Posted by BurntSynapse View Post
When I Googled something like “Duhem Gödel”, I got hundreds of thousands of pages and papers I scanned were all from HPS. I don’t recall any math papers where that analogy is drawn.
As I've said, much nonsense has been written about Gödel's theorems.

If we rely on Google to settle these things, the world will end ended in 2012, and creation science is thousands of times more solid than the connection between Pierre Duhem (1861-1916) and Gödel (1906-1978).

If absence of math papers serves as a reliable indicator of credibility, however, then I must admit that far more math papers have been written about the end of the world and about creation science than about the Duhem-Gödel connection.

Originally Posted by BurntSynapse View Post
This one: http://cogprints.org/4356/1/UC586bf.pdf seems to make much stranger analogies than I claim, and constructs what seems a plausible case, and there seems no shortage.
The World-Wide Web has made it much easier to publish.

At the top of page 3, Mathen writes (with italics as in the original):

Originally Posted by Jolly Mathen
A scientific theory on a given domain of empirical phenomena will be said to be complete if all questions constructible within the language of the theory are answerable within the theory, or, equivalently, if for all statements constructible within the language of the theory, it is decidable whether the statement is a true or false statement of the theory.
Pure logic is already incomplete in that sense. See Church's theorem. (Mathen fails to recognize the distinction between recognizers and deciders.)

I stopped reading shortly after Mathen (1) said he isn't actually going to use Gödel's theorems or give a Gödel-like proof of incompleteness for physics or other sciences, (2) admits scientists already know science doesn't settle all questions that can be phrased within the language of science, and (3) began to discuss "the undecidability of God", taking care to make "no claim concerning the existence or non-existence of God."

Although Mathen's paper reads like a term paper, he's just an unaffiliated amateur philosopher who became interested in Gödel's theorems and decided to see whether he could dream up some connection to undecidability in science.

Even so, Mathen's paper turns up near the top of a Google search on "Duhem"+"Gödel". You may take that to mean Mathen's paper is authoritative. I take it to mean any connection between Duhem and Gödel is so tenuous that few professional philosophers have written about it.

Originally Posted by BurntSynapse View Post
Until your post, I never knew Gödel's used “underdetermination”
So far as I know, he didn't. You used that word, so I admitted there's a vital connection between Gödel's incompleteness theorems and the fact that first order Peano arithmetic has nonstandard models. I also predicted you wouldn't know what that means.

Originally Posted by BurntSynapse View Post
Originally Posted by W.D.Clinger View Post
but claiming Gödel's theorems as support for that approach is clueless.
Mathematically clueless, yes. From HPS and PM considerations though, that seems less certain.
Jerry Fodor and Ernest Lepore wrote an entire book arguing against the views you have expressed over the last few days. They say the Duhem-Quine thesis would be untenable if any remnant of the traditional analytic/synthetic dichotomy can be preserved.

Although Quine rejected that dichotomy within the same paper that led some philosophers to attach Quine's name to Duhem's, you said retaining that dichotomy on Carnap's "utilitarian grounds" would "seem more in line with my work".

Fodor has been notably wrong about some things, as has Quine, but it's fun to imagine what Fodor would do with your argument here.


Fodor is a famously formidable opponent, in face-to-face conversation as well as in writing, even when he's wrong. (Some would say: especially when he's wrong.)
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Old 21st February 2014, 06:46 AM   #2435
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Originally Posted by ben m View Post
Great analogy, let's run with it.

The above failure---your lack of expertise on motor-use-cases---is not quite what is currently happening in this discussion. You have not permitted yourself to say anything as specific as "advances in variable speed motors look promising".
I'd intended the analog to be "advances in cognitive science of scientific revolutions look promising" which seems of at least equal detail to "advances in variable speed motors look promising".

My actual claim is more specific than the analog when citing the Nersessian model, the recategorization of exemplar criterion, and methods of integrating these advances into current operations, none of which possess a hypothetical counterpart in the analogy.
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Old 21st February 2014, 07:02 AM   #2436
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Originally Posted by W.D.Clinger View Post
Actually, Quine seems to have said "...at explaining lightening" which I appear to have mis-quoted, but the underdetermination point he argued and is a point in every introductory course in HPS seems well established. The objection raised to "my" claim appears to avoid dealing with the merit of the claim in favor of a red herring.

Originally Posted by W.D.Clinger View Post
As I've said, much nonsense has been written about Gödel's theorems.
Since there's no disagreement on that, its continued emphasis might seem to deliberately look away from the issue at hand: Is the widely-accepted analogy in HPS circles is reliable, or not?

Originally Posted by W.D.Clinger View Post
If we rely on Google to settle these things, the world will end ended in 2012, and creation science is thousands of times more solid than the connection between Pierre Duhem (1861-1916) and Gödel (1906-1978).
Settle? No. Able to provide links to reasonable evidence? Certainly.

Also see: http://en.wikipedia.org/wiki/Fallibilism, if interested.

Originally Posted by W.D.Clinger View Post
If absence of math papers serves as a reliable indicator of credibility,
It does not serve as such without obvious, common restrictions everyone able to reach the forum certainly possesses. The Google results support credibility of the notion that the topic is of interest to people in philosophy rather than mathematics, not whether any particular claims within that category have merit.

It is striking that hundreds, perhaps thousands of potentially reliable HPS citations seem all but invisible to a math SME, when dealing with the claim that HPS studies this topic. The lack of math papers is perceived as paramount importance for undermining a claim predicting this is what we should expect.

An aside: This seems similar to the apparent inability to deal with statements about categories of ideas in math, seeming to assume on mathematical statements exist. The belief "Reality is math" seems to really take on a religious character in that it seems to admit of nothing which is not ultimately, mathematical.

The reductio ad absurdum objection to the use of google again favors objection of style over merit. I would say this is avoiding the issue, but the evidence suggests that none of the massive effort on Tarski-like proofs are perceived as meaningful.

The Google results you cite in support of its unreliability can (were they real), support credibility of the notion that the year 2012 is of particular interest to end of the world enthusiasts, and that thousands of more people in general ascribe to creation science than Duhem and Quine. If we argue (poorly) that people can draw bad conclusions from information obtained via Google to imply a position citing evidence obtained via Google cannot be trusted, our position would seem awfully weak.

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Old 21st February 2014, 07:05 AM   #2437
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And again Burnt Synapse, you seem to be ignorant of any actual scientific revolutions or paradigm shifts and what causes them to occur.

"recategorization of exemplar criterion, and methods of integrating these advances into current operations" has nothing to do with how they actually happen.

It is time you actually looked at teh history of scientific revolutions and paradigm shifts, you ideas have yet to be shown to have any applications to how events actually occur.

Choose one paradigm shift that has occurred since 1900, explain exactly how "recategorization of exemplar criterion, and methods of integrating these advances into current operations" would have helped that paradigm shift or scientific revolution. I think that you mistake things like the Manhattan project for the actual paradigm shift that proceeded it.

Do you know what Fermi's paradigm shift was? It did not involve the first atomic pile.

the technology of gas centrifuges and chemistry of the uranium refinement in the Manhattan project were not the paradigm shift nor the scientific revolution that led to the theory of atomic fission and fusion, is seriously suggest you didn't know that.

One was a paradigm shift in theory that led to the development of the atomic bomb, the shift in theory however (starting with Becquerel through many many steps), how exactly do you think that ""recategorization of exemplar criterion, and methods of integrating these advances into current operations"" would have helped that?

Do you know how Heisenberg developed the HIP theory, or the how Pauli developed the exclusion principle. This are the things that led to the fission theory.

""recategorization of exemplar criterion, and methods of integrating these advances into current operations" might help things like the production of fissile materials at Hanford and other sites, but please explain exactly how '"recategorization of exemplar criterion, and methods of integrating these advances into current operations"" would have helped the development of atomic theory.
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Old 21st February 2014, 07:19 AM   #2438
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Originally Posted by Dancing David
It is time you actually looked at teh history of scientific revolutions and paradigm shifts, you ideas have yet to be shown to have any applications to how events actually occur.
For anyone looking to get their feet wet in the academics of this, I highly recommend The Structure of Scientific Revolutions" (http://www.amazon.com/The-Structure-.../dp/0226458083). It's a fantastic introduction to how scientific revolutions take place. I don't claim to agree with everything in the book (my copy is heavily annotated), but it's a good source for the basics, and the disagreements I have with the authors have been informative.
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Old 21st February 2014, 07:42 AM   #2439
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Originally Posted by BurntSynapse View Post
Originally Posted by W.D.Clinger View Post
Actually, Quine seems to have said "...at explaining lightening" which I appear to have mis-quoted, but I think the point he argued was valid. You seem to be avoiding dealing with the merit of his claim in favor of what looks like a red herring.
Are you citing Quine the blogger, who posted (something like) that online in September 2013?

Or are you citing Willard Van Orman Quine, who died in December 2000 after a distinguished career in which he often wrote things like this:

Originally Posted by Willard Van Orman Quine
As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience....Let me interject that for my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise.

—Willard Van Orman Quine, Two Dogmas of Empiricism. The Philosophical Review 60 (1951): 20-43.

We are well aware of your belief that it shouldn't matter who wrote such things, but knowing who wrote it would make it easier for us to track down the passage in question and see for ourselves whether you are giving us an accurate summary of it.

Last edited by W.D.Clinger; 21st February 2014 at 07:59 AM. Reason: added correction in gray
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Old 21st February 2014, 08:22 AM   #2440
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Originally Posted by W.D.Clinger View Post
Jerry Fodor and Ernest Lepore wrote an entire book arguing against the views you have expressed over the last few days.
If true, I've expressed my views poorly, and apologize.
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