The analytic/synthetic dichotomy is sustainable in some particular circumstances where "analytic" can be identified with an objectively definable notion such as "provable", "valid", or some such.
As your references pointed out convincingly, objective definition appears beyond reach, but where we seem to disagree here is whether subjective, relative definition is permissible which justifies the distinction. If tons of people agree, but objective criteria prove difficult, shall we assert no such distinction exists? Kassler claims philosophers definitions are not the same as lexicographers.
Kassler’s explanation: “Mere agreement about the cases, like "this counts as science while this as pseudo-science," even if almost all of us agree and agree confidently, won't tell us what our criteria are, much less how good they are. So a definition would be lovely, yet good definitions are hard to come by. We don't always need a definition in order to draw a confident distinction.”
In those common cases, however, the analytic/synthetic distinction just adds misleading synonyms to existing technical nomenclature.
When we say the distinction "just adds misleading synonyms", it seems to conflict with Kassler’s claims: “If we have necessary conditions, we can confidently rule certain things out from counting as bourbon or as science. We can say, here are the necessary conditions, this thing doesn't meet a necessary condition, hence it's not science. Similarly, if we have sufficient conditions, we can definitively rule certain things in.”
For transdisciplinary linking, this seems significant.
When no objectively definable notion of analytic is available, then Quine's objections hold with full force and the analytic/synthetic dichotomy just adds muddle.
I think you're repeating for emphasis, and I acknowledge your objection is both substantial and defensible. I suspect we further agree the importance of the objectively definable criteria you present (as one of the math & physics experts here) is less important within utilitarian perspectives, where we are concerned with doing something different than formally proving.
We may be unable to define pornography or childhood with any objective precision, but we do want some legal restrictions, especially when those attributes intersect.
Cite your sources instead of plagiarizing them.
Good advice & I'll work on doing better with that.
As I said VERY early: the only idea I can claim (AFAIK) is treating physics as an information system for providing decision-relevant information...or something pretty close to that.
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. Reminder: this is exactly what your critic of the mis-use of Gödel, Escher, Bach stated. His argument, IMO, reflect the utilitarian view that functionality trumps objective definition...even going so far as to claim it can make absolutely certain claims, which seems to contravening the “always subject to revision or incorporation in a larger theory” condition required in science.
When using math, there is the obvious and mundane risk that someone (e.g. a physicist) might make a mistake. Had you been talking about that risk, everyone would have agreed with you at the outset and we would not be having this conversation.
Perhaps, but I'm concerned with underdetermination regarding which math or model to use. My reading is that historically there’s nothing within geo-centric math, the model itself, or its related theories that will tell us it should be excluded, or included. From
http://en.wikipedia.org/wiki/Tarski's_indefinability_theorem : “…truth in the standard model of the system cannot be defined within the system”.
Quine’s web of belief explained how theories are protected from disconfirming evidence, and this protection seems to lie outside the model or math.
I find the argument that quaternions were less risky compelling because advocates provided arguments which seem compelling even if I don't understand them, while critics' denials seem to lack the same depth. This criterion lies outside the math, even outside the mathematicians. I also tend to judge based on how many top experts go from one side to the other, and I even advocate this as a good heuristic. I tell people: “Want to know if climate change/religion/autism links to vaccines are real? Top experts usually only go one way at a time – and we should not blindly follow, but we should follow.”
I've never spoken to a quaternion expert who didn't have a solid grounding in vectors, and then eschewed Q's for reasons that the techniques were more capable. I can't prove they’re better for anything, but if I have to provide some sort of example for a new approach that has does not seem to have been done yet, Q’s are the first pain-reliever I reach for. Better criteria & examples are invited.
There is a smaller risk that someone (typically a mathematician) might make a mistake that gets past peer review and enters a paper that describes faulty mathematics upon which physicists might eventually rely.
Yeah...but we agree this is very small, and I hope we agree different than a mistake in which mathematics to use.
Mathematicians make a fair number of such mistakes, but the risk here is small because most (though not all) of the math physicists rely upon has been in widepread use for a long time and is pretty thoroughly debugged. I thought at first that this was the kind of risk you were talking about in vector math, but whenever I say anything about this kind of risk you say it has nothing to do with the risk you're talking about.
Yup...and I said it again above. The technique or tool and its selection are related, but different, IMO.
Gödel's incompleteness theorems have nothing to do with risk in math or physics.
I think given sufficiently strict definitions, I’d agree, but the Tarski stuff does seem awfully close to what I’m saying. I’d be interested to know what Quine wrote in the last chapter of Mathematical Logic described at:
http://en.wikipedia.org/wiki/Willard_Van_Orman_Quine
When you dragged Gödel into the conversation, it was a clear signal you didn't know what you were talking about.
You think?
Hopefully repeated agreement with my limitless inadequacies will enable critics to take yes for an answer, and help compensate for them.
I remember a conversation from Gödel, Escher, Bach where there was an infinite regress of "Suppose I agree with all those, and still don't accept X" (note: trying to remember from approx. 35 years ago.)
I'm no mathematician, physicist, or HPS expert. I am an expert in designing standards for successful delivery of a defined goal, with lots of experience in making it happen.
There is a small risk of inconsistency in ZF, and I suppose there may be some theoretical risk that even Peano arithmetic is inconsistent.
If you were saying those risks are undocumented, you'd be as wrong as it's possible to be.
OK! That's delightfully different than a previous "you're wrong as it's possible to be".
I'm not arguing that sort of risk. I refer to the undocumented risk inherent in using cognitive frames without any awareness of how they are reconfigured during paradigm change.
(Pro tip: Refusing to explain your position with any real clarity makes it easier for you to say critics are attacking a position you don't hold, but it is possible to protest so often as to rule out all reasonable positions you could have held.)
This sounds like a generalization of the all the particulars for which we cannot and (IMO) should not be trying to establish clarity, such as specific impacts far in the future.
That's a fairly bizarre misreading of Gödel's incompleteness theorems. If you tell us which section(s) of Hofstadter's book led you to that impression, perhaps we can help you to debug your thinking.
Described above.
“My claim” actually comes from Kassler’s explanation of why Quine advocates “simplicity and conservatism” as criteria for preferring different webs of belief. This seems related to underdetermation and incompleteness, but I don’t think any segments of the PMBOK on risk management are going to be rewritten if that perception proves illusory.
(Pro tip: When complaining about attacks on opinions you don't hold, your habit of mangling or deleting links in the attacks you quote could lead readers to suspect you are trying to make it harder for them to view the evidence. In your quotation of my words above, I took the liberty of restoring the link you deleted.)
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My apologies for invoking Hanlon's Razor again, and I'd really appreciate more focus on substance than form, unless agreement on even the smallest point is prohibited by some rule I don't share.
If there is a way to easily include sub-quotes that otherwise get deleted, I’d appreciate any help with that.
!
) cracked open my paperback copy this afternoon and found nothing that could have led to your misreading Gödel's incompleteness theorems as "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 misreading also seems to be a long way from any conversation Hofstadter might have invented about an infinite regress of contrariness.