Why is there so much crackpot physics?

[BurntSynapse]

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.

 

[BurntSynapse]

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.

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.

 

[ben m]

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.

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.)

 

[W.D.Clinger]

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:

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.

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:

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:

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:

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.

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.

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.

[size=+1]The technical meaning of "completeness" and "incompleteness" in Gödel's theorems[/size]

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.

[size=+1]What this has to do with BurntSynapse[/size]

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.

 

[BurntSynapse]

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.

 

[dasmiller]

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?

 

[Hellbound]

To borrow (and possibly mangle) a quote:

Where correct, he is unoriginal. Where original, incorrect.

 

[BurntSynapse]

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.

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.

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.

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.

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.

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.

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.

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.

You do indeed appear to be completely ignorant of what Gödel's theorems say.

As I’ve agreed many, many, many times.

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.

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!!!

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.

 

[BurntSynapse]

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.

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.

"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.

 

[ben m]

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.

 

[dasmiller]

<sigh> deleted

 

[Dancing David]

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?

 

[steenkh]

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!

 

[W.D.Clinger]

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."

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.

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):

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.

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.

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.)

 

[BurntSynapse]

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.

 

[BurntSynapse]

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."

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.

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?

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.

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.

 

[Dancing David]

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.

 

[Dinwar]

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-Scientific-Revolutions-Edition/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.

 

[W.D.Clinger]

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."

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:

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.

 

[BurntSynapse]

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.